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TEACHER’S GUIDEPre-K-2
2
TO CONTACT
Math Monsters™
� click on:
www.mathmonsters.com
� write:
Math Monsters™P.O. Box 242Lincolnville CenterMaine 04843
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� call:
(207) 230-0399
� fax:
(207) 230-0795
Cousin Cal Q. Lator
3
Table of ContentsMath Monsters™ Friends and Advisors .................................................................................................... 4
Teacher’s Guide Overview .......................................................................................................................................... 7
Avenues of Assessment ................................................................................................................................................ 13
Data Collection ........................................................................................................................................................................ 15
Measurement .............................................................................................................................................................................. 19
Number Conservation .................................................................................................................................................... 23
The Making of Tens .......................................................................................................................................................... 29
Geometry ........................................................................................................................................................................................ 33
Doubles and Their Neighbors .............................................................................................................................. 39
Mapping ............................................................................................................................................................................................ 45
Time ........................................................................................................................................................................................................ 53
Patterns .............................................................................................................................................................................................. 59
Counting and Symbolizing ........................................................................................................................................ 65
Computers ...................................................................................................................................................................................... 71
Teacher Utilization ............................................................................................................................................................ 75
Notes ...................................................................................................................................................................................................... 77
Blackline MastersData Collection (2 masters) .................................................................................................................................... 82
Measurement (4 masters) .......................................................................................................................................... 84
Number Conservation (3 masters) .................................................................................................................. 88
The Making of Tens (3 masters) ........................................................................................................................ 91
Geometry (7 masters) ...................................................................................................................................................... 94
Doubles and Their Neighbors (4 masters) ........................................................................................ 101
Mapping (2 masters) ...................................................................................................................................................... 105
Time (3 masters) .................................................................................................................................................................. 107
Patterns (4 masters) ........................................................................................................................................................ 110
Counting and Symbolizing (3 masters) .................................................................................................. 114
Computers (2 masters) ................................................................................................................................................ 117
AppendicesTeacher Resources .......................................................................................................................................................... 119
Literature Connections .............................................................................................................................................. 123
Bibliography ............................................................................................................................................................................ 125
Aunt Two Lips
4
Teacher’s Guide Reviewers
Marti Wolfe
Marti Wolfe received the 1999 Presidential Award for
Excellence in Mathematics and Science Teaching from
the National Science Foundation. Marti also received a
Project SEEDS Award in 1998 from the state of Maine
for her innovative practices in mathematics teaching.
She has presented at state level conferences and is
active in state and local mathematics education forums.
Marti has taught mathematics in elementary school for
nineteen years. During her years in the classroom Marti
has worked in numerous school settings. Her career has
been enriched by her students and their variety of
learning styles.
Kristi Hardy-Gilson
Kristi Hardy-Gilson is an elementary educator working
with five- to eight-year olds in a multi-age classroom.
She has been working in a developmentally appropriate
setting for eight years. In 1991, she was recognized with
the Sallie Mae First Year Teacher Award and
Scholarship given to 50 beginning teachers across the
United States. Ms. Hardy-Gilson worked for her district
to create a K-8 math curriculum that incorporates the
Maine State Learning Results with the NCTM
Standards. She is a graduate of the University of Maine
with a B.S. in elementary education.
Math Monsters™ FRIENDS AND ADVISORS
Teacher’s Guide Authors
Grace M. Burton
Dr. Grace Burton is a professor of Mathematics
Education and Chair of the Department of Curricular
Studies at the University of North Carolina at
Wilmington. Dr. Burton earned a B.A. in Mathematics
from Amhurst College, a M.A. in Mathematics
Education from the University of Connecticut and a
Ph.D. in Elementary Education/Mathematics Education
from the University of Connecticut. Dr. Burton's inter-
ests include teaching about number sense, math anxiety
and mathematics curriculum and instruction at the K-6
level.
Her books and articles include over 90 publications in
professional journals; Towards a Good Beginning, an
early childhood mathematics methods book;
Mathematics Plus, Grades 1 and 2, pupil textbooks and
teacher's editions published by Harcourt Brace; and
Anytime Math, Grades K, 1 and 2, a constructivist-
based mathematics program published by Harcourt
Brace. She is also the Senior Author for Grades K-4 in
the Harcourt Series, Math Advantage. She has delivered
over 250 presentations on teaching mathematics at the
pre-school to grade 6 level. She also reviews articles for
several national journals.
Douglas H. Clements
Douglas H. Clements, Professor of Mathematics, Early
Childhood, and Computer Education at SUNY/Buffalo,
was a kindergarten teacher for five years. He received a
Ph.D. in Elementary Education from the State
University of New York at Buffalo in 1983. He has con-
ducted research and published widely in the areas of
the learning and teaching of geometry, computer appli-
cations in mathematics education, the early develop-
ment of mathematical ideas, and the effects of social
interactions on learning.
He has co-directed several NSF projects, producing
Logo Geometry, Investigations in Number, Data, and
Space, and over 70 referred research articles. Active in
the NCTM, he is editor and author of the NCTM
Addenda materials and was an author of NCTM's
Principles and Standards for School Mathematics (2000).
He was chair of the Editorial Panel of NCTM's
research journal, the Journal for Research in
Mathematics Education. In his current NSF-funded pro-
ject, Building Blocks-Foundations for Mathematical
Thinking, Pre-Kindergarten to Grade 2: Research-based
Materials Development, he and Julie Sarama are devel-
oping mathematics software and activities for young
children.
Senior Consultant for Video Series
Project Consultant for NCTM
5
Pat Hess
As a former board member at the NCTM, Pat facilitat-
ed for the NCTM/Exxon K-3 Math Specialist Project.
She is a former elementary mathematics teacher and
math specialist for the Albuquerque Public School
District in Albuquerque, New Mexico.
Math Monsters™ FRIENDS AND ADVISORS
Catherine Twomey Fosnot, Ed.D.
Catherine Twomey Fosnot is Professor of Mathematics
Education at City College of the City University of
New York where she helps elementary classroom teach-
ers improve the way they teach mathematics. She has
worked in the field of mathematics education for over
fifteen years and is currently at work as Director of
Mathematics in the City, a large scale National Science
Foundation project on mathematics reform that helps
teachers improve their practice.
She is the author of several books and articles on early
childhood education, among them Reconstructing
Mathematics Education (co-authored with D. Schifter);
Young Mathematicians at Work (co-authored with M.
Dolk); Enquiring Teachers, Enquiring Learners; and
Constructivism: Theory, Perspectives, and Practice.
She has twice received awards from the American
Educational Research Association/SIG, as well as the
Young Scholar Award from the Association for
Educational Communication and Technology.
Maarten Dolk, Ph.D.
Dr. Dolk, with the Freudenthal Institute at the Utrecht
University in Holland, works with many different inter-
national research and development projects in mathe-
matics education. He assists the institute in the areas of
research, education, in-service training and societal ser-
vice for primary and secondary education. The collabo-
rative staff consists of mathematicians, physicists, psy-
chologists, teachers, teacher trainers and educators
from outside working together in an interdisciplinary
approach with the Freudenthal Institute. Dr. Dolk has
been highly instrumental in the United States with the
development of materials for primary and secondary
education and the in-service of primary school teachers.
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Math Monsters™ Executive Producers
John Burstein
John Burstein has been producing award winning chil-
dren’s television programming for the past twenty years.
Though best known for his work in the areas of health
and fitness—he created the character of Slim
Goodbody—Mr. Burstein has worked extensively in
other subject areas including reading readiness, social
studies, environmental education and corporate training.
Six television series, produced by Mr. Burstein, are cur-
rently airing on more than 150 public television stations
nationwide. These include: The Inside Story with Slim
Goodbody; Well, Well, Well; All Fit; Goodbodies, The
Outside Story and The Story of Read-Alee-Deed-Alee, a
fifteen-part reading readiness series developed in coop-
eration with the International Reading Association.
A recognized expert in delivering educational content
for children in creative and imaginative ways, Mr.
Burstein has worked with the American Academy of
Pediatrics on a film introducing children to surgery,
with Greenpeace on an environmental special co-pro-
duced with several nations, with Public Television on an
AIDS education program for fourth- and fifth-graders
and with HBO as the special children’s interviewer for
the Peabody Award-winning How Do You Spell God.
In addition to his television work, he has written seven
books for McGraw-Hill and Coward McCann
Publishers, composed music for several major children’s
labels and regularly performs his original young peo-
ple’s concert with symphony orchestras all across the
United States and Canada. He is a two-time Parent’s
Choice Award winner. His other awards include: the
New York, Milan, Houston, Chicago and Birmingham
Film Festivals; Athens Video Festival; the Silver Cindy
Award for audio visual achievement; and awards from
the Odyssey Institute, Society for Technical
Communication, Ohio State, as well as the Corporation
for Public Broadcasting.
Tim Lawrence, Co-Executive Producer
Tim Lawrence has worked on and off in the Film and
Television Industry for over thirty years. He has worked
on various special effects projects for motion pictures
and recently helped form the Camden Film Group.
Raised in Australia, Mr. Lawrence brings a unique per-
spective to the Math Monsters™ series.
Math Monsters™ was:Created, written and directed by John Burstein
Produced by John Burstein and Tim Lawrence
Animated by Destiny Images, Inc.
www.mathmonsters.com
7
The Math Monsters™ series is an
entertaining gateway to in-depth
mathematical thinking and reason-
ing involving meaningful real-world
problems. It is an educational
opportunity for both teachers and
students. Teachers will become
familiar with the recently updated
national standards and practices
which fuel the curiosity of young
mathematicians. Young students who
are beginning to develop their own
understanding of mathematical con-
cepts can find support and comfort
in the humorous and questioning
approach the Monsters use to solve
their mathematical problems.
NCTM STANDARDSThe Math Monsters™ series was
developed in cooperation with the
National Council of Teachers of
Mathematics (NCTM) and is
designed to meet and support NCTM
Standards for Pre-K-2 mathematics
content and process instruction.
Towards that end, the following
mathematical processes are interwo-
ven into every episode:
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation
MATH MONSTERS™MATRIXWe have designed this guide carefully
in order to enhance student learning.
We begin with an outline of the
NCTM Pre-K-2 Standards for teacher
reference along with a Math
Monster™ Matrix cross-referencing
the individual episodes with the
NCTM standards that they support.
This Matrix is designed to help teach-
ers integrate the episodes into their
mathematics program.
AVENUES OFASSESSMENTThis is followed by a chapter called
Avenues for Assessment that focuses
helpful ways to observe students,
study their work samples, and
encourage them to talk about their
strategies, so that you can best plan
your next moves and give the feed-
back so necessary to students.
CORRELATINGCHAPTERSFollowing this are chapters that cor-
relate with each of the programs in
the Math Monster series. Please note
that the programs in the series are
designed to "stand alone" and that
the sequence of programs can be
modified to meet your individual
needs. These chapters feature:
• The NCTM Standards addressed
• A Program Overview
• Student Objectives
• A list of vocabulary words
• A Program Synopsis
• Previewing Activities
• Pause Points Suggestions
• Post viewing Activities
• Sideline Suggestions to enhance
instruction
• Reproducible blackline masters
™Math MonstersTEACHER’S GUIDE OVERVIEW
8
LITERATURE CONNECTIONS AND TEACHERRESOURCESFinally, we have included two appen-
dices: Literature Connections is
intended to assist you in integrating
reading and language arts into your
mathematics program; and Teacher
Resources lists many of the books
and materials that we have found
valuable to both our professional
development and program planning
for our young mathematicians.
POINTS TO REMEMBERAs you work with the Math
Monsters™ videos along with this
guide, please keep the following
in mind :
• Active Learning is at the heart of
every Math Monster™ episode.
We believe children learn mathe-
matics by doing and problem
solving; by discussing and creat-
ing their own solutions.
• It’s helpful for your students to
make inquiries and construct
meaning during the preview activi-
ties, episode and post viewing
activities.
• Pause Points are indicated visu-
ally when a question mark (?)
appears on the screen. They are
important mathematical
moments that provide opportuni-
ties for discussion with the chil-
dren as they follow the Math
Monsters' progress. If possible,
it’s best if you stop the program
in order to spend more time
exploring the question asked.
• Sideline Suggestions and com-
ments are provided to guide dis-
course and give practical infor-
mation to the teacher. Ultimately,
every teacher will use and extend
the content of each episode to
match the particular group of
students.
• Field trips connect the math in
the segment to occupations in the
real world.
TEACHER UTILIZATION TAPEAs part of the series, there is a
Teacher’s Utilization Tape that
explains the foundation upon which
the Math Monsters™ program is
built. After viewing it, the user will
better understand how to implement
the Math Monsters™ program in
the primary classroom.
Your students will have fun as they fol-
low the Math Monsters through simi-
lar developmental stages in their think-
ing. The Monsters communicate, rea-
son, problem solve, create and use rep-
resentations and make connections in
mathematics the same way as young
children. Join our characters, Addison,
Mina, Split and Multiplex, as they
explore mathematics for all learners.
9
NCTM CONTENT STANDARDS
NUMBER AND OPERATIONS• understand numbers, ways of representing numbers,
relationships among numbers and number systems
• understand the meaning of operations and how they
relate to each other
• compute fluently and make reasonable estimates
ALGEBRA• understand patterns, relations and functions
• represent and analyze mathematical situations and
structures using algebraic symbols
• use mathematical models to represent and under-
stand quantitative relationships
• analyze change in various contexts
GEOMETRY• analyze characteristics and properties of two-
and three-dimensional geometric shapes and
develop mathematical arguments about geometric
relationships
• specify locations and describe spatial relationships
using coordinate geometry and other
representational systems
• apply transformations and use symmetry to analyze
mathematical situations
• use visualization, spatial reasoning and geometric
modeling to solve problems
MEASUREMENT• understand measurable attributes of objects and the
units, systems and processes of measurement
• apply appropriate techniques, tools and formulas to
determine measurements
DATA ANALYSIS AND PROBABILITY• formulate questions that can be addressed with data
and collect, organize, and display relevant data to
answer them
• select and use appropriate statistical methods to
analyze data
• develop and evaluate inferences and predictions that
are based on data
• understand and apply basic concepts of probability
Instructional programs from pre-kindergarten through grade 12should enable all students to:
Mina
NCTM Content and Process StandardsCopyright ©2000 by The National Council of Teachers of Mathematics, Inc.1906 Association Drive, Reston, VA 20191-9988www.nctm.org
10
NCTM PROCESS STANDARDS
PROBLEM SOLVING• build new mathematical knowledge through
problem solving
• solve problems that arise in mathematics and in
other contexts
• apply and adapt a variety of appropriate strategies to
solve problems
• monitor and reflect on the process of mathematical
problem solving
REASONING AND PROOF• recognize reasoning and proof as fundamental
aspects of mathematics
• make and investigate mathematical conjectures
• develop and evaluate mathematical arguments
and proofs
• select and use various types of reasoning and
methods of proof
COMMUNICATION• organize and consolidate their mathematical thinking
through communication
• communicate their mathematical thinking coherently
and clearly to peers, teachers and others
• analyze and evaluate the mathematical thinking and
strategies of others
• use the language of mathematics to express mathe-
matical ideas precisely
CONNECTIONS• recognize and use connections among
mathematical ideas
• understand how mathematical ideas interconnect and
build on one another to produce a coherent whole
• recognize and apply mathematics in contexts outside
of mathematics
REPRESENTATION• create and use representations to organize, record
and communicate mathematical ideas
• select, apply and translate among mathematical
representations to solve problems
• use representations to model and interpret physical,
social and mathematical phenomena
Instructional programs from pre-kindergarten through grade 12should enable all students to:
NCTM Content and Process StandardsCopyright ©2000 by The National Council of Teachers of Mathematics, Inc.1906 Association Drive, Reston, VA 20191-9988www.nctm.org
Multiplex
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Math Monsters™ MATRIXThe Math Monster™ Matrix will help teachers integrate
the episodes into their mathematics program. Each
episode is cross-referenced with the NCTM standard
that it supports. The NCTM Pre-K-2 Standards are also
listed separately for teacher reference on page 3 and 4.
An asterisk after a process objective denotes particu-
lar emphasis in that episode.
EPISODE CONTENT STANDARD PROCESS OBJECTIVES
Data Collection Data Analysis and Probability Problem SolvingReasoning and ProofCommunication*ConnectionsRepresentation*
Measurement Measurement Problem Solving*Reasoning and ProofCommunication*ConnectionsRepresentation*
Number Conservation Number and Operations Problem Solving*Measurement Reasoning and Proof
Communication*ConnectionsRepresentation*
The Making of Tens Number and Operations Problem Solving*Algebra Reasoning and Proof
CommunicationConnectionsRepresentation*
Geometry Geometry Problem Solving*Reasoning and Proof*CommunicationConnections*Representation*
Doubles and Number and Operations Problem Solving*Their Neighbors Algebra Reasoning and Proof
CommunicationConnections*Representation
12
EPISODE CONTENT STANDARD PROCESS OBJECTIVES
Mapping Geometry Problem Solving*Reasoning and Proof
Measurement CommunicationConnections*Representation*
Time Measurement Problem Solving*Reasoning and ProofCommunication*Connections*Representation*
Patterns Algebra Problem SolvingReasoning and Proof*Communication*Connections*Representation
Counting and Number and Operations Problem SolvingSymbolizing Reasoning and Proof*
CommunicationConnections*Representation*
Computers Data Analysis and Probability Problem Solving*Measurement Reasoning and Proof*Algebra Communication
ConnectionsRepresentation
Math Monsters™ MATRIX
AddisonSplit
Math MonstersAVENUES OF ASSESSMENT
The Math Monsters™ program
provides teachers with rich opportu-
nities for informal assessment. We
believe that ongoing assessment
practices during the Math
Monsters™ episodes and activities
will pave the way for optimal stu-
dent growth.
The first step in the assessment
process is to become familiar with
the learning standards and student
objectives that apply to the episode.
The NCTM standards are listed at
the heading of the teacher’s guide
and the student objectives are con-
tained in the overview of each
guide. The assessment process con-
tinues as the teacher considers these
questions:
• What are the learning stan-
dards that my students will be
working towards?
• What are the instructional goals
that will need to be assessed as
the students work through the
Math Monsters activities?
• What will the students need to
experience before viewing the
episode?
• Which preview activity from
the guide is most appropriate
for meeting the developmen-
tal and academic needs of
your students?
• What modifications will need
to be in place in order to pro-
vide all of the students with
the opportunity to grow in
mathematics?
The Math Monsters™ program
lends itself well to the use of obser-
vation, conversation and analysis of
student work as assessment tools
for the teacher. As a result of using
these tools, the teacher is continual-
ly aware of the developmental and
academic levels of the students.
This awareness will aid the teacher
in making an informed decision
about the next, most appropriate
learning challenge for the student.
As you observe your students
working with Math Monster™
activities, ask yourself:
• How students are using the
materials available to solve
problems?
• How easily students are moving
from concrete representations
to the abstract?
• Are students using a variety of
problem-solving strategies?
• How well do they keep
records?
• Do the students persevere in a
problem-solving challenge?
Observation is a simple but power-
ful assessment tool.
The Math Monsters™ program
engages the students in mathemati-
cal conversations with one another
and with the teacher. By asking
probing questions the teacher gains
a sense of how well students can
explain their thinking, justify their
solutions to problems and use the
language of mathematics. This is an
ideal setting to find out how well the
students understand that a problem
may be solved in more than one way.
These conversations also allow stu-
dents to demonstrate the connec-
tions they are making between
mathematical ideas and mathematics
in the world around them.
The analysis of student products
from Math Monster™ activities
adds another dimension to measur-
ing student achievement and
growth:
• Do the students show their
thinking using concrete or
abstract symbols?
• Do students show more than
one way to explain the same
idea?
• How well can students organize
ideas on paper?
Products from the Math Monster™
activities make a nice addition to
student portfolios.
By employing these three assess-
ment tools, observation, conversa-
tion and analysis of student work,
the teacher is equipped to make
effective Math Monster™ activity
choices and monitor changes in stu-
dent thinking and reasoning over
time. Each Math Monster™ activity
will spiral into the next and build a
chain of meaningful mathematics
experiences for young children.
™
13
Annie Ant
14
www.mathmonsters.com
15
NCTM CONTENT STANDARDSData Analysis and Probability
• pose questions and collect, organize and represent data to answer those questions
• interpret data using methods of exploratory data analysis
• develop and evaluate inferences, predictions, andarguments, that are based on data
• understand and apply basic notions of chance and probability
NCTM PROCOCESS STANDARDSProblem Solving
Reasoning and Proof
Communication*
Connections
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
DATA COLLECTION
OVERVIEW
This episode allows children to inves-
tigate the mathematics of data collec-
tion and graphic representation.
As a result of viewing this episode, the
children will:
• explore methods for collecting
and organizing data
• interpret various representations
of data
• design and create graphs
VOCABULARY
data collectionorganize popularfavorite graph
PROGRAMSYNOPSIS
Addison makes the best
pancakes around.
Multiplex, Split, and
Mina enjoy them so much that
they think it may be time to open
a pancake restaurant so that all
the monsters in town can share in
the tasty treat. The problem is
that they can only serve three
kinds of pancakes, and so they
need to find out which three are
the most popular among the mon-
sters.
They decide to go door-to-door
and collect the data. They record
the information, but each monster
represents the data differently.
Multiplex draws a color-coded pic-
ture for each pancake that some-
body names. Addison also draws a
picture, but organizes his pancakes
in piles. Split writes down the
names of each pancake selected,
and Mina makes a chart using check
marks to represent the selected
pancakes.
Now the monsters must figure
out how to combine their various
representations of data to deter-
mine which pancakes are the mon-
ster favorites. They accomplish this
through the use of a bar graph.
Our field trip takes us to an animal
farm where we see how and why data
is collected.
The show is constructed so that
the viewer joins the monsters as
they figure out how to collect and
organize the information they find
in Monster Land. Let your stu-
dents investigate, and problem
solve with the monsters on their
™
16
YOU WILL NEED: pencils (col-
ored, plain), paper, any relevant
math manipulatives, graph paper
and clipboards.
• Pose a question to the class similar
to that which the monsters will
face in the story. For example, you
might present the following sce-
nario: “The cafeteria staff wants to
know the four most popular meals
that are served to students here at
school. They have asked our class to
help them figure it out.” You could
use a similar scenario applied to pop-
ular fast food restaurants, favorite piz-
zas, popular ice cream flavors, etc.
• Organize the students into small
groups and let them plan for
answering the question posed
earlier.
• Discuss with students the following
points: What will we need to do first?
What information do we need? How
will we gather this information? How
will we organize it? How will we
show and share (represent) our infor-
mation with the cafeteria staff when
we are done?
• Allow the children to discuss their
group plans or ideas for collecting
information and representing it.
They may use the tools you have
put in front of them, and they may
add to these resources as they wish.
Sideline SuggestionsBefore viewing this episode with yourclass you will want to gather materials tohelp with the exploration of data collec-tion, types of graphs (real, picture, rep-resentational), and organization ofinformation.
The episode and the preview activitypresent a real problem for to the chil-dren. You will want them to constructtheir own solutions, rather than makinga type of representation you haveexplained.
Measuring length using connecting
cubes is a prerequisite for this
activity.
YOU WILL NEED: a copy of the
blackline master, Me-o-graph-y,
some crayons, and connecting or
unifix cubes for each student.
• Ask your students how long our
feet are, our toes, our hands, and
our thumbs? Do we all have the
same size body parts? How can we
show the lengths of our feet,
hands, toes and thumbs using con-
necting cubes?
• Let a student model his/her idea
for connecting and measuring
using the cubes. Distribute the
Me-o-graph-y sheet to the class,
and allow them to share their ideas
about recording this information
on the graph sheet. Let them work
alone or in pairs to complete the
graph with their own personal
measurements.
• Bring your group back together to
compare and contrast the informa-
tion on their personal graphs.
• Did everyone have the same foot
length? How many different sizes
of thumbs did we have? Have
each student find a partner and fig-
ure out how their graphs are differ-
ent, and how they are the same.
Sideline SuggestionsBy actually problem solving and invent-ing themselves, children are involved indoing mathematics and in being youngmathematicians.
You will probably witness your studentsworking at various developmentalstages as they discuss ways to gatherinformation and represent it.
This activity will allow for the recom-mended concrete experiences thatshould precede a more pictorial orabstract one.
PREVIEWING ACTIVITY TWO
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
17
• What Works? Have your class
discuss what they saw happening
in the story. Review strategies
they saw the monsters use that
they thought worked or didn’t
work. Were any methods more
helpful to solving the monsters’
problems?
The second question mark appears
when the monsters have collected
all the data, but it’s been represent-
ed in many different ways. Their
problem now becomes one of orga-
nizing the information so they can
understand and interpret it. Do you
think the monsters have collected
helpful information? Do they
know the three most popular kinds
of pancakes yet? Can this data be
used even though it’s in many dif-
ferent forms? What can you tell
from each of the monsters’ repre-
sentations? How might you orga-
nize all of this data?
Sideline SuggestionsEncourage your students to reflect ontheir experiences in the PreviewingActivities. How could the monsters findthis information?
POST VIEWING ACTIVITY ONE
• Give your class a challenge similar
to that of the monsters opening a
restaurant: “We are going to open
a classroom snack shop where we
will sell some of the most popular
and nutritious snacks. It is our job
to find out the three most popular
beverages, fruits and snacks that
kids will buy.”
• Divide your class into data collect-
ing groups. Each team can be
responsible for gathering data
about the different items (fruits,
beverages and snacks). Students
should be prepared to present their
information to the rest of the class
in an organized format. They might
choose from the various types of
graphs they have seen or experi-
ment with a new format.
PAUSE POINTS
The first time a question mark
appears, the monsters have identified
a challenge and a problem. They
need to find out what the three most
popular pancakes are in Monster
Land. How might you go about gath-
ering this information (data)? What
strategies can you suggest for them to
find out the most popular pancakes?
PAUSE POINT ONE
?PAUSE POINT TWO
POST VIEWING ACTIVITIES
Snack Shop
Sideline SuggestionsBe aware that children often begin rep-resenting their data as pictures—arecording of the information with littleor no organization. Later they categorizeit, showing one type got six votes, whileanother got only four. Even here theymight show the picture of four as largerthan six, making counting necessary inorder to tell how many are represented.They often make tables or charts show-ing how people voted, but these repre-sentations also do not readily show howmany people voted for each type socounting once again may be necessary.
POST VIEWING ACTIVITY TWO
18
• For older students, explain how
social scientists (social studies) and
scientists often use questionnaires
to collect information and study a
question they are interested in.
Have children work in small
research teams, designing a ques-
tionnaire, collecting data, and rep-
resenting it. Have them report their
information to classmates, teachers,
parents or administrators depend-
ing on their question.
• Topics could include:
• Intermural activity or sports
offerings at school
• Amount of paper recycled at the
copy machine
• Most popular types of books
read in class (sports, bio, etc.)
• Kids that walk, ride the bus, are
dropped off, or ride bikes to
school
• Most/least popular subjects
at school
• Let your children experience the
dilemma of representing their data
and trying to read each other’s way
of representing.
POST VIEWING ACTIVITY THREE
Sideline SuggestionsThe mathematical idea of arranging thedata into a bar graph is the biggest ideafor children, because this representa-tion involves two axes. One verticallyshows how many, and one horizontallyshows the types.
Research teams
Basehound
POST VIEWING ACTIVITIES
19
NCTM CONTENT STANDARDSMeasurement
• understand measurable attributes of objects and theunits, systems and processes of measurement
• apply appropriate techniques, tools and formulas todetermine measurements
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof
Communication*
Connections
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
MEASUREMENT
OVERVIEWThis episode illustrates the impor-
tance of measurement using stan-
dard and non-standard measures.
Through trial and error, the
Monsters will come to the conclu-
sion that a standard measurement
tool is very important. As a result
of viewing this episode children
will:
• recognize the attributes of
length and area
• explore the making and use of
measurements in natural situations
• measure with the same size unit
(standard and non-standard)
• observe the use of tools such as
rulers to guide measurement
VOCABULARYsize rulerwidth lengthheight exact standardnon-standardmeasurement
PROGRAMSYNOPSIS
There’s nothing like playing
ball outside on a beautiful
day. The Monsters each
have their own way of playing, too—
kicking, rolling, throwing and bounc-
ing. They want to know which of
them moves the ball the farthest.
This leads them to wonder about
measuring distances.
Before they can explore the mea-
surement challenge it begins to rain
forcing them inside where it’s not
safe to play ball. They decide they
need a playhouse so even if it rains
they’ll still have a place to play.
They call Annie Ant at the Ant Hill
Construction Company to come and
build their new playroom. Multiplex
tries to give Annie all the informa-
tion she will need about the size of
the playhouse. Annie explains to
the Monsters that she needs num-
bers explaining how long, wide
and tall the building needs to be.
They give her the numbers she
needs using Addison’s steps as
their measurement. The Monsters’
problem arises when they return
home to find a playhouse built 50
steps long, 30 steps wide, and 15
steps tall—in ant steps!
Join us on our field trip to meet a
carpenter who relies heavily on
standard measurement tools to per-
form his work each day.
The Monsters will try to under-
stand measurement using non-stan-
dard and standard tools as they
work with Annie Ant to create a
playhouse they can use. Invite your
students to join in the adventure.
™
Annie Ant
20
YOU WILL NEED: materials to
fill a “mystery box”—pencil, chalk,
toothbrush, paper clip, comb, pop-
sicle stick, toothpick, etc. There
should be one object that is clearly
the shortest and one that is the
longest. This should be obvious to
students.
• Explain that you have a “mystery
box” with objects inside and that
there are many ways to sort these
different objects. Say that you
would like them to be thinking
about how long the objects are.
• Allow students to explore the
materials and talk about the
attribute of length in relation to
the objects. Question the students
by asking them which one is the
longest? Which is the shortest?
Can you find two objects that are
about the same length? Is it harder
to tell which is longer when they
look almost the same? Can you do
it? How?
• Copy the “Mystery Box” blackline
master to record answers.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsFor primary schoolchildren, experiencesin introducing linear measurementshould focus on the idea of an identifi-able attribute (in this case length) that isdetermined by the distance between twopoints. This attribute can be compared,ordered and measured by students.
The first question for the Monsters
arises when they would like to know
which Monster sends the ball the
farthest. Split wonders if there is a
way the distances could be mea-
sured. Do you think they could
measure to find out who sent the
ball the farthest? What kind of tools
could they use to help them?
PAUSE POINTS
• Ask students to begin thinking
about distance. You will not need
any materials for this quick ques-
tion and answer activity to get stu-
dents thinking about this attribute.
• Generate questions appropriate to
your school community such as:
➤ Which is farther from your desk,
the gym or the cafeteria?
➤ Is the library or the office closer
to our classroom?
➤ Which is farther from our
school, the grocery store or the
fast food restaurant?
➤ How can you tell which is farther?
➤ Are there ways we can measure
distance?
• Think of a place that you have
been to that is even farther away
than a neighboring town.
PREVIEWING ACTIVITY TWO
Sideline SuggestionsThis may also be a good time to talkabout the importance of estimation. Thepurpose of estimation activities are tohelp children begin to understand theattributes and process of measuring.Estimation also promotes the awarenessof the sizes of units of measure. Exactmeasurements are not always neededfor answering questions, and childrenshould begin to recognize that it is oftenappropriate to share a measurement asan estimation.
PAUSE POINT ONE
?
21
The Monsters thought they had given
Annie all of the information she
needed to build them a new play-
room. What she really needs to know
is how long, how wide and how tall
the room needs to be. How can the
monsters find this information for
Annie? Will they need any tools to
help them? Would it make sense for
the Monsters to measure the lengths
in cubes, blades of grass, miles, feet,
inches, or some other unit?
PAUSE POINT TWO
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
This activity will allow your stu-
dents to explore different units of
measurement when finding length.
Students should be encouraged to
compare their results and be ques-
tioned as to why their numbers
aren’t the same.
YOU WILL NEED: to set up two
or three work stations for students
to begin this measurement activity.
At one station give students paper
clips that can be linked together.
At the second station give them
linking cubes to create a measure-
ment tool (a third table could be
set up with even another unit for
measure). Be sure that each table
has objects for them to measure
and that these objects are the
same length. Pencils, markers, sta-
plers, popsicle sticks, textbooks,
paintbrushes, sheets of paper and
desktops are some fairly standard
size objects.
• Divide your class into groups to
work at the different tables.
• Have them measure the objects on
the table.
• Copy My Measuring Record black-
line master and allow students to
fill in the information they gather
from measuring objects.
• Students should be encouraged to
share their numbers with the
group(s) that used a different unit
of measure. Ask questions such
as: What happened when the
Math Monsters and Annie Ant
didn’t use the same unit of mea-
sure? Why aren’t our numbers the
same? Can you think of a reason
why we would need to have the
same information and numbers?
Exploring measurement
Sideline SuggestionsThese kinds of measuring activities canbe emphasized at the first and secondgrade levels. The goal would be for chil-dren to recognize that using units of thesame length is more reasonable thanusing individually created or selectedones.
We can’t assume that young mathemati-cians understand measurement fully justbecause they complete a series of activi-ties and worksheets that demonstrateskill competency. They will need manyhands-on experiences to to develop theirskills and understanding of concepts inmeasurement.
These suggestions apply to both PostViewing Activity One and Two.
PAUSE POINTS
22
POST VIEWING ACTIVITY TWO
YOU WILL NEED: to copy
the“Standard” Addison Foot black-
line master for your students and
provide scissors.
• Ask students to cut out their copies
of the “Standard” Addison Foot.
• Have them measure distances
around the classroom. Have them
measure a table top, the chalk-
board, a door opening, the teacher’s
desk or the height of a bookshelf.
They can record and share this
information. Ask them if they now
all have the same numbers when
they measure using a standard unit.
• How can we use this unit to mea-
sure how far it is to the gym, the
library or the cafeteria? Should we
use one Addison foot at a time? If
not, what can we do? Could we call
this new unit something different?
• Allow students to measure dis-
tances to another part of the
school using their newly created
tool. Encourage students to share
their knowledge about other stan-
dard units of measure.
• A follow-up for this activity in
the next couple of days would be
to allow students to measure
using other standard units they
brainstormed.
YOU WILL NEED: metric and
customary tools available such as
rulers, yardsticks, tape measures,
meter and centimeter sticks etc.
Allow the students to measure
objects and distances that they
have explored before and try
adding some new ones.
A standard Addison foot
POST VIEWING ACTIVITIES
Sideline SuggestionsSometimes it’s best not to emphasizevarious units of measurement too soonin measurement instruction. Go at apace you feel is appropriate for yourstudents.
You also might have children trace andcut out an outline of their own foot orhand to use for measuring.
NCTM CONTENT STANDARDSNumber and Operations
• understand numbers, ways of representing num-bers, relationships among numbers and number sys-tems
• compute fluently and make reasonable estimates
Measurement
• understand measurable attributes of objects and theunits, systems and processes of measurement
• apply appropriate techniques, tools and formulas todetermine measurements
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof
Communication*
Connections
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
NUMBER CONSERVATION
OVERVIEWIn this episode, the Monsters decide
to plant two gardens, each with an
identical number of monster mel-
ons. From seed to harvest, the
Monsters explore problems involv-
ing number conservation and one-
to-one correspondence. As a result
of viewing this episode, the children
will:
• apply one-to-one
correspondence
• compare and contrast length,
quantity and number of objects
• employ counting skill
VOCABULARYnumber lengthquantity arrangementequal longermore lesssame biggersmaller organize
PROGRAMSYNOPSIS
It’s spring. The Monsters are
happy and excited because they
are ready to plant their spring
garden. Monster melons from Aunt
Two Lips’ shop are the favorite fruit
for our foursome this season. They
want to make two gardens on the cas-
tle grounds. Mina suggests two teams
with two monsters each, and that
they can draw straws to make the
teams.
The monsters will need the same
amount of space and the same num-
ber of seeds, but when the seeds are
delivered it appears they have a
problem. The piles don’t look alike,
so how can they each have the same
amount? This introduces the concept
of conservation of number. They
decide that counting the seeds in
each pile will help them to be sure
they have equal amounts. Counting
becomes a challenge when the seeds
are all piled up in a big heap.
Spreading the seeds out into two
rows that can be easily counted
proves that each pile is the same,
just organized differently.
When the holes have been dug
and the seeds have been planted
and covered with dirt, it’s time for
the seeds to have a drink of water.
This brings about a conservation of
length challenge. There are two
hoses at Uncle Fraction’s home.
One hose appears to be long
enough while the other seems too
short. The monsters will try to solve
this confusion over length as they
line the hoses up side-by-side and
stretch them to the garden. Once
again, objects that are equal but
arranged differently lead to confu-
sion, problem solving and an under-
standing of how this could be.
Our field trip takes us to the
bakery where the baker explains
that when making bread the same
amount of dough can be used in
™
23
24
This activity, Lady Bugs and
Leaves, is an active way to engage
your students in thinking about
number quantity and comparing
numbers.
YOU WILL NEED: to copy the
Lady Bugs and Leaves blackline
master for this activity. Your stu-
dents may cut out the lady bugs
and use the remainder of the sheet
as a work mat. You may wish to
have students create their own
leaves and use cubes or tiles to
represent lady bugs. Or, you can
spray paint small white beans red
on both sides. Then decorate them
with a permanent black marker.
• Tell your students a story about
eight lady bugs and two leaves.
Explain that Lady bugs are helpful
beetles. They love to eat aphids,
tiny little plant lice, that can dam-
age plants. Lady bugs help to keep
plants healthy. This is good for the
plant and the creatures that con-
sume it. You might tell this story:
Once there was a lady bug
who laid eight eggs on two
different leaves. When the
eggs hatched, little lady bug larva
began to devour aphids. They grew
and grew. These lady bug larva need-
ed a rest, so they took a nap in a
quiet corner. When they awoke, they
had turned into beautiful red beetles
with black spotted wings! And now
there were four lady bugs on each of
the two leaves.”
• Ask students to suggest ways to
find our how many lady bugs there
are in all.
• Create more lady bug stories for
your students. Ask them to show
more lady bugs on one leaf than the
other. How do you know which leaf
has more and which leaf has less?
• Try a story where some of the lady
bugs are on one leaf while the others
are hiding under the other leaf. How
many lady bugs are hiding? How can
we find out without looking?
• You may wish to challenge your
students to find as many ways as
they can for eight lady bugs to sit
on two leaves. Will there always be
eight lady bugs no matter how they
are arranged on two leaves?
Create a chart to show the chil-
dren's arrangements.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsBefore viewing this episode with yourstudents, you will want to be knowl-edgeable about conservation of number,length and quantity.
A child who conserves number knowsthat the number of objects does notchange when the objects are moved,rearranged or hidden. Conservation ofnumber typically occurs between theages of five and seven.
Number conservation and one-to-onecorrespondence are explored in this pre-view activity. These concepts are essen-tial for further development of numberconcepts.
Please remember that children can notbe expected to master these types ofconservation at the same age.
Aunt Two Lips
“
25
Conservation of length is explored
in this activity, Garden Snakes.
YOU WILL NEED: six to twelve
inches of string, yarn or chenille
strips for each student
• Ask them to cut two equal pieces
and verify that they are the same
length.
• Participate in the following story so
that you may guide this activity:
Let's pretend that these
strings are garden snakes.
Are your garden snakes
the same length? Is one longer? Is
one shorter? Okay! They are the
same length.
Now I will pretend that my little
garden snakes are crawling along
... crawling along ... and this one is
crawling out ahead of the other
(make sure that snakes are coiled
differently). Try this with your
garden snakes. Do you think the
snake ahead of his buddy is the
same length?
Oh, here go the little snakes again!
I will pretend that my little garden
snakes are crawling along ... crawl-
ing along ... but the one out ahead
is getting very tired. Look, he is
curling up to take a nap (coil one
string). Try this with your garden
snakes. Do you think the curled up
sleepy snake is the same length as
his buddy? Do you think he is
shorter? Do you think he is the
same length?”
• After each story problem, one
snake out in front and one sleepy
curled up snake, ask your students
to share their responses to the
questions. Encourage them to
explain their answers. Record their
answers and explanations to fuel
further discussion.
• You may wish to provide tools for
measurement such as paper clips or
color tiles for students who have
conservation of length. Ask them
how these tools could be used to
answer the snake story problems.
PREVIEWING ACTIVITY TWO
The two piles of monster melon
seeds that Aunt Two Lips delivered
are supposed to have the same
number. They look very different
because of the way they are
arranged. Ask your students how
they would find out if the same
number of seeds are in each pile.
The Monsters’ first problem arises
when they must make equal garden-
ing teams. Have your students think
about and share strategies they have
used to create fair working and
playing teams. As they share, high-
light the strategies that involve
mathematics.
PAUSE POINTS
PAUSE POINT ONESideline Suggestions“Hands on tools” of the “math trade”such as beans or counters should behandy during these pause points.
If possible, stop the program andexplore the students ideas and solutions.
PREVIEWING ACTIVITIES
Sideline SuggestionsA child who conserves length willmaintain that an object has the samelength regardless of a change in itsposition, shape or form. Conservationof length typically occurs between theage of seven and eight.
An understanding of conservation oflength will translate to other areas ofmathematics such as: measuring dis-tances on a map, using standard unitsof measurement, and interpreting atime line.
Assess the various stages of develop-ment and understanding your studentshave as they share responses andexplain their work during the previewactivities.
PAUSE POINT TWO
“
26
PAUSE POINTS
The seed piles have been laid out
straight for counting and each line
has 35 seeds. The Monsters notice
that one line is longer than the
other. How can this be? Do both
lines truly have 35 seeds? Ask your
students to explain how both lines
could have 35 seeds regardless of
the length. How could you prove
you are correct?
PAUSE POINT FOUR
The Monsters thought they had
come up with a perfect plan to
check the number of seeds in each
pile. Counting is a bit more difficult
than they expected due to the
arrangement of the seeds. Ask you
students what ideas they have for
making this counting easier and
more accurate.
PAUSE POINT THREE
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONEDoing is believing
YOU WILL NEED: about 60
beans to reenact the portion of the
video relating to the two piles of
seeds that the Monsters had deliv-
ered.
• Divide the beans into two equal
piles. Stack one of the piles high
and spread the other out.
• Encourage your students to experi-
ence for themselves how these two
seemingly different piles can con-
tain the same number of beans.
Sideline SuggestionsChildren may not be convinced by thevideo enactment of the strategies. Thisactivity will help them see it for them-selves.
27
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
YOU WILL NEED: some dough.
Here’s a recipe.
OH! DOUGH RECIPE
This dough* is a quick mix and keeps
well when stored in an airtight con-
tainer. You may double this recipe,
however, batches larger than that can
become difficult to handle.
You will need:
2 cups of unbleached flour
1 cup salt
1 tablespoon cream of tartar
1 tablespoon vegetable oil
2 cups boiling water
food coloring (optional)
You will:
• Mix the flour, salt and cream of
tartar together.
• Add the oil, water and
food coloring.
• Knead for 5 or 6 minutes until the
consistency feels right for the job.
* “King Arthur’s Flour 200th
Anniversary Cookbook,” 1991.
• Guide your students through con-
servation of quantity activities
using a soft modeling dough. If you
need to make your own dough, see
the recipe that follows.
• Give each student two balls of
dough that are the same size.
• Ask your students if they think the
two balls are the same. Direct them
to flatten one ball into a pancake
shape and leave the other ball
unchanged. Ask your students if
the ball and the pancake are the
same amount of modeling dough?
What could you do to find out if
you are correct?
• Ask your students to roll the pan-
cake into a ball again. Now they
will have two balls of clay that are
the same size. Direct the children
to roll one ball into a snake. Do the
snake and ball have the same
amount of dough? What could you
do to find out if you are correct?
• Try other investigations. Your stu-
dents could create two smaller balls
out of one of the larger balls. Now
do you have the same amount of
clay in the two smaller balls and
one larger ball? What could you do
to find out if you are correct?
• Continue to explore conservation
of quantity. It is important that the
children have one ball that remains
constant and one that they change.
This provides a reference for them.
Oh! Dough!
Sideline SuggestionsA child who conserves quantity recog-nizes that the amount of dough does notchange when the shape is changed.
They also see that the amount of doughdoes not change when the shape is bro-ken into many pieces. It is still the sameamount of dough.
Conservation of quantity typically occursbetween the ages of seven and eight.
Your student's responses during, “Oh!Dough,” will give you insight about theirconservation of quantity.
28
This challenge will provide experi-
ence with conservation of length
and spark a lively discussion about
the size of gardens.
YOU WILL NEED: copies of
the blackline master Garden Dot
Paper, coloring tools, scissors
and paper.
• Tell the students that they will
design a garden plot that must be
exactly 10 units all the way
around, have only four sides, and
form a rectangle.
• Define a unit as the space between
two dots on the Garden Dot
Paper. Model several incorrect
garden plots using the Dot Paper.
• Ask your students to tell why
these examples do not meet the
three standards.
• Allow the students time to
explore the two possible solutions
to this puzzle. Ask them to draw
their garden plot on the Garden
Dot Paper.
• Ask the children to cut out the
five plant circles and glue them
onto the garden plot in any way
they wish. Post each child's garden
on a large board for group sharing
and comparing.
POST VIEWING ACTIVITY FOUR
Sideline SuggestionsThe questions that follow will guideyour class discussion. Your students’responses will illustrate their ability toconserve length.
• How are these gardens the same/ dif-ferent?
• Is there a garden that is larger thananother?
• How can we find out?
Choosing sides
POST VIEWING ACTIVITY THREE
YOU WILL NEED: to copy the
How-Does-Your-Garden-Grow
blackline master. You will also
need coloring tools, glue, and scis-
sors for your creative gardeners.
• Distribute the how-does-your-
garden-grow sheets and ask the
children to tell you what they
see on the paper. They will
notice that each paper has ten
plants and one garden.
• Ask the children to cut out the
plant circles in the garden rectan-
gle. Direct them to design their
garden by attaching their plants to
the garden rectangle in any way
they wish. Post each child's garden
on a large board for group sharing
and comparing.
How does your garden grow?
Sideline SuggestionsThe questions that follow will guideyour class discussion. Your students’responses will illustrate their ability toconserve number.
How are the gardens the same/different?
Do any of the gardens have moreplants than other gardens?
Why might it look like one student'sgarden has more plants than anotherstudent's garden?
How can we check to be sure that westill have the same number of plant inevery garden?
POST VIEWING ACTIVITIES
Incorrect Correct
29
NCTM CONTENT STANDARDSNumber and Operations
• understand numbers, ways of representing numbers,relationships among numbers and number systems
• understand the meaning of operations and how theyrelate to each other
• use computational tools and strategies and estimateappropriately
Patterns Functions and Algebra
• understand various types of patterns and functionalrelationships
• use symbolic forms to represent and analyze mathe-matical situations and structures
• use mathematical models and analyze change inboth real and abstract contexts
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof
Communication
Connections
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
THE MAKING OF TENS
OVERVIEWThis episode illustrates how patterns
are used to solve problems. The
Monsters investigate all the different
ways to make ten and they begin to
notice patterns. Addition and sub-
traction are used to help the
Monsters solve their problem. As a
result of viewing this episode the
children will:
• look for patterns
• recognize the importance of
organizing information
• apply skills of addition and
subtraction
VOCABULARYadd moreless topbottom nextpattern “in all”“how many”
PROGRAMSYNOPSIS
It is holiday time in Monster
Land and the Monsters must
do their holiday shopping. They
ask Aunt Two Lips for gift ideas.
She suggests Gollywomples, the
special of the day in her shop. The
Monsters agree that blue and green
Gollywomples will make a sweet
holiday treat for their friends. Soon,
they find themselves with a sticky
problem as they prepare gift boxes
of Gollywomples.
The Math Monsters decide to
give ten Gollywomples to each
friend on their list, but no two pack-
ages will be exactly alike. Mina
packs all green Gollywomples for
Ivan Idea and Split packs nine
green and one blue for Cousin
Digit. As the Monsters continue to
pack the boxes, Split discovers a
pattern. A box of six green
Gollywomples and four blue
Gollywomples is the same when the
box is turned the other way around!
How many ways are there to
pack ten Gollywomples using com-
binations of blue and green ?
The Monsters become tangled
in their quest. How will they
know if they’ve found all the ways
to make ten?
Join us on a field trip to a bank
where many ways to make ten are
demonstrated.
Invite your students to work
along with the Monsters as they fig-
ure out how many ways there are to
pack holiday treat boxes with ten
Gollywomples.
™
30
YOU WILL NEED: a “pile” of
ten cubes or tiles in two colors.
• Ask your students to tell you how
many cubes they think are in the
pile. How many blue cubes? How
many green cubes? Ask your stu-
dents to share ideas about how
counting the cubes could be made
simpler. Their suggestions may be
to line up the cubes, snap them
together by color or make two dif-
ferent piles of cubes by color.
Model the outcomes of their solu-
tions as they organize their mathe-
matical thinking and communicate
ideas to you and their classmates.
Ask them to point out any patterns
that may occur.
PREVIEWING ACTIVITY ONE
Split comments that he “guesses”
they have found all the ways to
make ten. Addison notices that
they have probably missed some of
the ways.
What could the Monsters do to find
out if they have found all the ways
to make ten?
(Teacher’s note: There are actually
11 ways: 0-10, 1-9, 2-8, 3-7, 4-6, 5-5,
6-4, 7-3, 8-2, 9-1, 10-0)
PREVIEWING ACTIVITIES
Sideline SuggestionsOrganizing mathematical thinking, com-municating mathematical ideas and con-sidering the ideas of others are powerfultools for problem solving.
In this episode, the Monsters modelthese skills.
The first time a question mark
appears Mina is wondering if there
are any other ways to make ten.
Do you think they have found all
the ways? Can you think of any
other ways?
PAUSE POINTS
PAUSE POINT TWO
YOU WILL NEED: tiles in two
colors and paper and coloring tools
• Give students cubes or tiles in two
colors. Ask the students to find a
way to make three using one or
two colors and share their ideas
with others.
• Ask students to record their solu-
tion on paper and display it for the
group to see. It is best if the
teacher refrains from “showing”
the students how to record their
information, but allow the children
to construct their own representa-
tions.
• Ask the students which drawings
go together. Why? Group the
drawings as the children suggest.
How many different ways did we
find to make three? What did we
PREVIEWING ACTIVITY TWO
Sideline SuggestionsThe Monsters use number representa-tions and patterns to find combinationsfor the sum of ten.
Children who are familiar with combi-nations that make ten will use them todetermine larger sums.
PAUSE POINT ONE
Sideline SuggestionsEncourage the children to reflect ontheir experiences in the PreviewingActivities. How could the Monstersorganize their information?
?
31
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
This game will give your students
experience in building models to
solve a “making ten” problem.
YOU WILL NEED: to copy the
Spinner blackline master on to tag
board, counters in two colors, paper
and coloring tools, paperclips and
beaver clips.
• Your students may work in pairs for
this activity. Each student or pair
will need a spinner marked (0-10).
Attach the arrow to the face of the
spinner with a brass fastener. Place
a paper clip between the spinner
face and the arrow for a smoother
spin.
• Spin to find out the number of
counters to select. Select that num-
ber of counters in one color. The
student pairs will ask, “How many
more make ten?” Now they will use
a different color counter to find out
how many more are needed to
make ten. Ask the students to
record what happened on paper.
• Spin again until the arrow lands on
a different number and repeat the
same procedure. How many more
make ten? Record what happened.
How many more make ten?Sideline SuggestionsOpportunities to solve missing addendproblems help children develop meaningfor the operations of addition and sub-traction.
You will probably witness a variety ofcommunication styles and differing levelsof sophistication in representations. (Seestudent samples.) This is a good opportu-nity to see how children record informa-tion. Do they organize each turn theytake with the spinner and blocks onpaper? Do they choose to use two colors?Do they use numbers or number sen-tences? Do students apply the patternof “turning it around” in this activityafter viewing the episode? The stu-dents’ responses will provide theteacher with valuable information fromwhich to plan more mathematical inves-tigations.
You may wish to extend this activity fur-ther in activity two.
PAUSE POINTS
Mina and Addison notice that the
green Gollywomples decrease by
one as each box is filled (10,9,8,7).
Addison predicts that the next
box will have six green
Gollywomples. But, how many
blue Gollywomples are needed to
make ten if there are six green?
What did the Monsters notice
about green Gollywomples? What
do you notice about blue
Gollywomples?
PAUSE POINT THREE
The Monsters have built an orga-
nized model of their solution.
Multiplex states that the last box
will have one green and nine
blues. Mina suggests that they are
for-
getting something. The Monsters
need to take another look. What
have they missed? How many
ways are there to make ten?
PAUSE POINT FOUR
Sideline SuggestionsYou and your students can build a col-orful Gollywomple chart together. AGollywomple chart is available as ablackline master for use with PausePoints Three and Four.
By seeing the decreasing number ofgreen Gollywomples on a chart, the stu-dents may notice the increasing numberof blue Gollywomples.
Student sample one Student sample two
Student sample three
spin 3 7 more spin 4 6 more
spin 6I need 4 more
6 +4 = 10
32
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
How Many More Make Ten? can
be extended to explore mathemati-
cal concepts on a deeper level.
• After each student has worked
through three or four spinner prob-
lems, ask for volunteers to post
their record sheets. Collect a variety
of responses. Ask the class if they
have found all of the ways to make
ten. How could we use our record
sheets to help us? Encourage the
students to communicate their ideas
about organizing the information.
How could we use patterns to help
us?
• Discuss what worked well.
Appreciate the diversity of
How many more make ten?
Sideline SuggestionsThis problem could go in many direc-tions. Listen to your students and deter-mine what the next step should be.
Do they want to arrange the papers bythe addends 0 to 10 in order from left toright across the board?
Do some papers repeat the sameinformation?
Are there any suggestions to write 10 +0=10 and 0 + 10=10 on the bottom of eachpaper?
POST VIEWING ACTIVITY THREE
The students will create a book of
ways to make many different
numbers.
YOU WILL NEED: to copy the
Grid Paper blackline master,
color tiles or cubes, plain paper,
glue, scissors and coloring tools.
• Ask your students to find ways to
make one, two, three, four, five, six,
seven, eight, nine and ten using the
cubes or tiles. Ask the students to
design a page showing the ways to
make each number using the grid
paper to represent a cube or tile.
• On the right is a sample page for
Ways to Make Four:
• Your students could make personal
books with one page for Ways to
Make 1, one page for Ways to Make
2, one page for Ways to Make 3, and
so on. Teams could create one page
each for a class book.
• There are many ways to adapt this
activity. For example, you may
write the fact families for each
page in their booklet of Ways to
Make Different Numbers.
Explore ways to make other numbers
Sideline SuggestionsBy showing all the ways to make consec-utive numbers such as: 1, 2, 3, 4 and so on,your students can continue the study ofpatterns.
Ask your students how many ways thereare to make each of the consecutive num-bers. How many ways to make one? Howmany ways to make two? How manyways to make three? Can you find a pat-tern?
Allow the children to set up their ownpages. In this way, they will rely on theirown organization skills.
Ways to make 4
There are 5 ways
33
NCTM CONTENT STANDARDSGeometry• analyze characteristics and properties of two- and three-
dimensional geometric shapes and develop mathematicalarguments about geometric relationships
• specify locations and describe spatial relationships usingcoordinate geometry and other representational systems
• apply transformations and use symmetry to analyze mathe-matical situations
• use visualization, spatial reasoning and geometric modeling tosolve problems
NCTM PROCOCESS STANDARDS
Problem Solving*
Reasoning and Proof*
Communication
Connections*
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
GEOMETRY
OVERVIEWIn this episode, Geometry, the
Monsters decide to create a model of
Monster Land. In order to make an
accurate representation of their town
they must take a good look at the
different shapes and sizes of neigh-
borhood buildings. As a result of
viewing this episode the children will:
• recognize, describe and compare
two- and three-dimensional
shapes
• recognize and locate
geometric shapes and struc-
tures in their world
• predict the effects of transforma-
tions on shapes (rotation, flips
and turns)
VOCABULARYrectangle size shape
triangle square cube
octagon cylinder edge
model triangular prism
PROGRAMSYNOPSIS
The Math Monsters think
that Monster Town is the
greatest town around. They
decide to build a small model of
their town called Mini-Monster
Town. Addison suggests that they
study the town from the top of the
castle before they begin building.
The Math Monsters find themselves
puzzled by the appearance of an
object’s size up close and far away.
How can Aunt Two Lips’ shop be
smaller than a birdhouse?
A visit to Aunt Two Lips’ garden
shop, which seemed so small from
the top of the castle, helps the
Monsters “figure out” the idea of
perspective. Their plan takes shape
as they examine the sides, top and
bottom of a variety of buildings.
They find many two-dimensional
shapes such as, triangles, rectangles
and octagons that form three-dimen-
sional buildings.
Their quest takes an interesting
turn when they discover that a shape
remains the same when it is turned
or rotated. For example, a cube is a
cube, no matter which way one flips
it.
Join the Monsters on a field trip to
an architect who shows his process
for drawing and modeling building
ideas. He will demonstrate how tech-
nology helps an architect.
Invite your students to work
along with the Monsters as they
build a Mini-Monster Land.
™
34
YOU WILL NEED: a large sheet
of paper for one student trace the
outline of another student’s body, a
pair of scissors to cut out the form
and a second sheet of paper to
make a second cutout exactly the
same shape and size as the first.
• Ask your students if they think the
two forms are the same. When
your students agree that the forms
are the same, hang one at the end
of a long corridor. Hang the second
form close to the area where the
class is standing. How do the forms
look the same? How do they look
different? Walk down the hall to
the first form and repeat this exer-
cise. Modify this activity using the
layout of your school building as a
guide. Perhaps one form could be
hung outdoors and the second
form could be taken to the second
floor with your class. Take a look
out of a window at the form out-
side and compare it to the size of
the second form.
• How do they look the same? How
do they look different? Why do
you think so?
YOU WILL NEED: a variety of
containers such as a cereal box,
oatmeal container and a cube-like
gift box for this activity. Ask your
students to describe the containers.
• Make a chart of the descriptive
vocabulary your student use. The
expressive language on this chart
may help some students describe
what they see during their investi-
gations. Ask your students how
these containers look the same or
different when viewing from the
top, side or bottom. How does the
cylinder look when it is flipped
upside down? How does the cere-
al box look when it is turned on
its side?
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITY TWO
Mina suggests that the Monsters sur-
round the building and draw what
they see. Addison and Split drew a
triangle. Mina and Multiplex drew a
rectangle. How could that be?
PREVIEWING ACTIVITIES
PAUSE POINT TWO
Sideline SuggestionsEngaging students in making carefulobservations, describing similarities anddifferences, and creating representa-tions of two- and three-dimensionalshapes nurtures the development ofgeometric and spatial sense.
In this episode, the Monsters examinereal buildings vs. pictures. It is suggestedthat your students work with realobjects to study their attributes, theways in which they are related to oneanother, and the kinds of actions thatcan be performed on them such asslides, flips and turns.
Aunt Two Lips’ garden shop appears
very small when seen from the top of
the castle. It looks smaller than
Multiplex’s thumb.
Can you think of a reason why? If
you could talk to the Monsters, what
would you tell them right now?
PAUSE POINTS
PAUSE POINT ONESideline SuggestionsA set of geoblocks, three-dimensionalfigures, such as a triangular prism, a rec-tangular prism, cube, octagonal prismand cylinder will enrich the pause pointdiscussions in this episode. Some ofthese may be available in your class-room building block collection. Someare available as black line master pat-terns. If possible, stop the program andallow your students to examine theappropriate figure during the PausePoints.
35
PAUSE POINTS
Multiplex suggest they go and find a
house that is a cube turned on its
side. Split wonders if that could be
possible. What do you think?
PAUSE POINT FIVE
After observing and recording the
shapes on Cousin Digit’s house, the
Monsters notice that they have
drawn two triangles and three rec-
tangles. This is just like Aunt Two
Lips’ garden shop! But they look
so different! Can they really be
made of the same shapes?
PAUSE POINT THREE
Binary Bill’s computer store is made
of many squares. What shape do
you think the floor will be? Why do
you think so?
PAUSE POINT FOUR
Three Monsters counted three sides
each on the Post Office building.
Mina flew up to take a look at the
roof and found an eight-sided
shape, an octagon. How can the
Post Office have a roof with eight
sides and nine walls? Is that possi-
ble? What do you think the
Monsters should do?
PAUSE POINT SEVEN
The Post Office has the Monsters
perplexed. How can they see three
sides at once. How many sides
does this building have? What is
going on? What do you think the
Monsters should do?
PAUSE POINT SIX
Sideline SuggestionsYou may wish to turn the triangular prismwith the triangular face down and then therectangular face down. How do they lookthe same and different?
Sideline SuggestionsA hands-on experience with an octago-nal prism would allow the children totouch the edges and feel the “wallstouch the roof.”
?
Sideline SuggestionsAsk your students to examine thecube. Turn it so that it sits on differentfaces. How does it look the same ordifferent?
Did it change in the same way as thetriangular prism?
36
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
Shape Shuffle will give your stu-
dents experience in classifying and
describing shapes.
YOU WILL NEED: to copy the
Shape Shuffle blackline master on
to a set of tagboard shape cards.
• This activity works well in a circle
on the floor so that the shape cards
may be seen by all of the students.
Shuffle the shape cards and deal
one to each of your students.
• Look at your shape card. How
would you describe your shape?
• Ask a volunteer to place his or
her shape in the center of the cir-
cle and tell one thing about the
shape. Ask your students to check
their shape to see if it matches.
Place the matching shape in the
center of the circle.
• Encourage the children to examine
all the shapes that don’t match. Are
there any changes that need to be
made? Was a shape excluded that
should be included? Why?
• Repeat this activity with a second
volunteer. The discussions will lead
students to being careful observers.
Shape shuffle
Sideline SuggestionsChildren between the ages of four andseven begin to develop some concepts ingeometry that include the studies of size,shape, direction and angle.
This activity requires students to catego-rize two-dimensional shapes. They mustdecide which characteristics they aregoing to focus on and which are irrele-vant. Often the categories that youngchildren create have some overlap. Asstudents are challenged to clearly articu-late the characteristics they are using tomake their categories, they will makefiner distinctions between shapes.
Eight the Great
37
• Shape Shuffle and Sort asks stu-
dents to use a set of shape cards
to sort into two, three or four cat-
egories. Each card must be
included in one of the categories.
For younger students you may
wish to limit the number of shape
cards for sorting. Your students
may work in pairs or individually
for this activity.
• You will need a copy of the
Shape Shuffle Cards from the
blackline master for each group
or individual. Chart paper, glue
and writing utensils will be needed
for the charts.
• Ask your students to glue each
shape card group onto large
paper. Ask them to write a
description of each group. These
charts may be displayed and used
for further class discussion.
* This activity is adapted from
“Shapes, Halves and Symmetry.”
See Teacher Resources.
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
Sideline SuggestionsShape Shuffle and Sort provides a niceframework for assessing student under-standing through dialogue. Here aresome questions to help open up a mathe-matical conversation with your students:
• Which shapes seem to go together?
• If you’re sorting this way, where doesthis shape go?
• What do you call this group of shapes?
• Why is this shape in this group and notin that group?
Shape shuffle and sort
4 sides 3 sides
skinny
38
POST VIEWING ACTIVITY THREE
Here is an opportunity to identify
the two-dimensional shapes which
make up a three-dimensional
object.
YOU WILL NEED: to make sev-
eral copies of the Shapes black
line master for student pairs or
individuals; to copy and assemble
the shapes from the Cube,
Triangular Prism and Cylinder
Pattern blackline masters; an empty
cereal box; and scissors.
• Share the Shapes sheet with the
students. How are the shapes
alike? How are they different?
Many students will be able to
name these shapes.
• Ask your students to watch you
disassemble a cereal box. Take a
cereal box and tear open the bot-
tom being careful not to rip the
flaps. Now cut along one of the
folds or corners so that the box
will lay flat. Ask your students if
they can identify any of the Shapes
that make up the box.
• How many rectangles do you count?
• The teacher may build the cube,
triangular prism and cylinder using
the blackline masters.
• Ask your student which shapes
they can find. How many of each
shape do you count?
• This activity can also be extended
into a shape scavenger hunt in the
classroom or at home. Ask your
students to be shape detectives and
identify some of the shapes that
make up objects in the classroom?
The children may work in teams
and record what they find using
pictures and shapes. Your students
may circle up and share their dis-
coveries with one another.
Building blocks and cereal boxes
Sideline SuggestionsRecognizing the relationship betweentwo- and three-dimensional shapes con-nects geometry to real-world problemsand applications. For example, a blue-print for building a house, a pattern forsewing a garment, a diagram for assem-bling a jungle gym are two-dimensionalrepresentations for three-dimensionalobjects.
Please note that the constructing theshapes on Cube, Triangular Prism andCylinder Pattern blackline masterscan be challenging for children andmay require your helping hand. Alsosome shapes are repeated on theShape Shuffle blackline masters.
POST VIEWING ACTIVITIES
tabl
wndo
39
NCTM CONTENT STANDARDSNumber and Operations
• understand numbers, ways of representing numbers,relationships among numbers and number systems
• understand the meaning of operations and howthey relate to each other
• compute fluently and make reasonable estimates
Algebra
• understand patterns, relation, and functions
• use mathematical models to represent and under-stand quantitative relationships
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof
Communication
Connections
Representation
*Indicates a strong emphasis in this episode
Math Monsterspresents
DOUBLES AND THEIR NEIGHBORS
OVERVIEWThis episode illustrates how mental
math and patterns can be used to
solve real-life problems. Children
investigate the concept of using pat-
terns to make predictions. Mental
math strategies are demonstrated in
the video and encouraged in the pre-
viewing and post viewing activities.
As a result of viewing this episode,
the children will:
• make predictions based on pat-
terns of numbers
• develop an understanding of the
concept of “double”
• explore the notion of even and
odd numbers
• employ mental math strategies to
add numbers
VOCABULARYdouble pairs twiceweight change addeven take-off minuspenny dollar centsodd calculate
PROGRAMSYNOPSIS
The Math Monsters are invit-
ed to join in the fun when
the circus band and parade
arrive in Monster Land. The
Monsters are excited to share their
talents and begin to practice their
acts for the circus show.
Addison performs his doubling
juggling act and leaves the audience
wondering how many balls he will
juggle next in the pattern. Mina gets
into the juggling act too. Mina jug-
gles six pairs of colorful balls. How
many balls does that make?
Multiplex shows off his muscles
as he lifts weights on a barbell.
Addison and Mina double the
weight of the barbell by adding a
weight to each end of the bar.
Finally, they add a weight to only to
one side, and Mutiplex finds himself
out of balance when the weight of
the barbell is uneven.
Magic Mina uses her magic dou-
bling hat to lead the audience in
multi-step, real-life applications
using doubles. At the conclusion of
the program, the Monsters must fig-
ure out if an even sum always
results when two addends are the
same. What happens when one
addend is one more than the other?
Our field trip will take us to a
shopkeeper who explains how
she uses mental math to help in
her calculations.
™
40
• Tell this story or some variation to
your children. Pose the questions
which follow to spark discussion of
doubles and patterns.
Once upon a time an old
man and an old woman
found a beautiful barrel
at a neighborhood yard sale. They
decided that it would make a won-
derful container for firewood.
Little did they know that the barrel
was magic.
The next day, the old man placed
the first stick of wood into the bar-
rel. Instead of the usual “kerthunk”
he heard a “kerthunkitythunk.”
He looked inside to see what may
have caused the mysterious
“kerthunkitythunk.” To his surprise
he found two pieces of wood!
He removed the wood from the
barrel and was about to begin
again when Old Tom, the family
cat, jumped into the barrel. Instead
of the usual “meow” he heard a
“meow-meow;” what do you think
happened? (student responses)
Well, after retrieving the two Old
Toms from the barrel, he fetched
his wife to come and see the
strange happenings! While she was
wondering how they were going to
feed two Old Toms, the old man
got an idea. Being a very big fan of
chocolate chip cookies, he dropped
a pair of cookies into the barrel.
The old woman saw this out of the
corner of her eye. She couldn’t
understand why the old man would
discard two of her delicious cook-
ies. She peered into the barrel and
what did she see? Four chocolate
chip cookies!”
• Ask children what magic power
does the barrel have? What do
you think would happen if the
old man dropped three cookies
into the barrel? Four cookies?
ADDITIONAL PREVIEW
SUGGESTIONS
YOU WILL NEED: cubes or
counters, and to set up a magic
barrel or box in your classroom to
engage your students in thinking
about doubles (Keep a stash of
extras in the bottom of the bar-
rel.). Have your students watch as
you place two cubes or counters
into the barrel. Ask your students
how many cubes or counters will
be in the box or barrel if it is
magic, like the one in the story.
What is double two? Reach inside
the magic container and remove
four cubes or counters to show
double two. Try this with other
numbers.
• Let’s see what kind of double
adventures our math friends,
Addison, Multiplex, Split and Mina
get into on their problem solving
adventure, Doubles and Their
Neighbors.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsStudents in primary grades grades beginto develop strategies for combining andseparating numbers.
Working with doubles offers a mentalmath strategy to support fluency in com-putation.
Before watching this episode, thinkabout how numbers can be taken apartinto more convenient pieces and putback together to find sums.
You will also want to be knowledgeableabout patterns and functions.
The episode will ask the students toconstruct their own solution to a prob-lem which involves describing changequantitatively while looking for pat-terns.
Looking for patterns and searching for“what makes sense” are the basics tounderstanding mathematical concepts.
You might also use some of the excellentgames that already exist involving dou-bling. For example, play “DoubleParcheesi,” which is just like the regulargame, but you move is double what thenumber cube shows.
DOUBLE 1210 + 10 = 202 + 2 = 420 + 4 = 24
“
41
PAUSE POINTS
The monsters have set up a prob-
lem involving a pattern. They
need to find out what the next
double problem will be and its
solution. What do we already
know? How can we show what we
know? What solution makes
sense? Why?
PAUSE POINT ONE
Mina is juggling six pairs of balls.
There are striped balls, star balls,
red, green, yellow and purple
balls. How can we find out how
many balls she is juggling? Collect
ideas from your students about
how to approach this problem.
How can we use what we know to
find out how many balls Mina is
juggling?
PAUSE POINT TWO
Multiplex has successfully lifted
six and six as well as seven and
seven when the same weight was
added to both ends of the barbell.
Now he finds himself with seven
and eight. How many is that?
What do you think might happen?
PAUSE POINT THREE
After a ten-monster buck and a
five-monster buck are placed in
the magic doubling hat, students
are asked to tell what will happen.
This two-step challenge could be
re-enacted in the classroom using
play money. It is a rich opportuni-
ty for students to demonstrate
how several different strategies
may lead to the same solution.
Some may reason that $10 + $5 =
$15, and double $15 is $30. Others
may double $10 to $20 and double
$5 to $10, adding $20 +$10 is $30.
And some may recognize double
$10 by seeing them side by side,
and double $5 by seeing them side
by side, and count the money to
reach a total of $30.
PAUSE POINT FOUR
Sideline Suggestions“Hands-on tools” of the “math trade”such as counters, snap cubes, playmoney, balance scales, paper andcrayons should be available during thisepisode.
If possible, stop the program and explorethe students ideas and solutions.
Young children often need to build aconcrete model in order to gain under-standing.
Sideline SuggestionsThis activity is more appropriate forGrades 1 and 2.
?
42
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
YOU WILL NEED: to copy the
Double Game and Here’s How
blackline masters.
• Create a class book of double
games. Ask your students to think
of something that they wish to put
in the Magic Barrel. Tell them that
this will be doubling problem. Ask
them to use a double game page to
write a short story or sentence
and/or draw a picture describing
their problem.
• Challenge your students to find the
answer to their double problem.
Ask them to show how they solved
their problem and write the solution
on the Here’s How sheets.
• All of the students’ double game
problems may be put together into
a class book. You may wish to share
the doubling problems a few at a
time each day for the class to solve.
The book could also be used for
independent problem solving.
Double games
Sideline SuggestionsDouble Trouble problems illustrate forchildren alternative paths to one solu-tion.
Ask students to solve the same DoubleTrouble problem. Look for differencesin their strategies. Ask students to sharetheir thinking and celebrate the varietyof strategies used.
As you observe students at work, noticehow well they use “math tools” to solveproblem.
As they share, think about how well theyarticulate their strategies.
THE DDDDOOOOUUUUBBBBLLLLEEEE GAME
HERE’S HOW
SSSSOOOOLLLLUUUUTTTT IIIIOOOONNNN
My dog has a box of 10bones. How many boneswill there be if they gointo the magic barrel?
20 bones
POST VIEWING ACTIVITY ONE
• Ask your students to retell what
the Monsters noticed (anytime we
add the same amount of weight to
each side of the barbell, we get an
even number). Is this true for
other numbers? How could we
find out? What happens if one
side of the barbell has one more
than the other side? What tools
will we need? How will we record
the information we gather?
Balancing actSideline SuggestionsBalance Scales and counters willenhance the learning experience inBalancing Act. Try this thinking strategyfor evens and odds:
Even numbers make “partners” Odd numbers have a “leftover”
bone
10 bones
count
43
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY THREE• Let’s play the game of doubles.
Ask students which doubles they
can find in their heads? What is
double two? Double three?
Double four? Double ten? How
can we use the doubles we know to
find the double of larger numbers?
What is double eleven? Double
twelve? How can we take numbers
apart so that we can find doubles
of larger numbers in our heads?
• Pennies and dimes are great
tools for facilitating the notion
of taking apart two digit num-
bers. Use pennies and dimes to
make eleven. What is the double
for a dime? What is the double
for a penny? How can we find
the double for eleven? Try other
two-digit numbers.
Doubling larger numbers
Sideline SuggestionsStudents naturally develop the idea thatnumbers can be taken apart into piecesthat are easier to add.
This activity also makes mathematicalconnections to place value concepts.
You may wish to limit the larger numbersto those with digits less than five. It maybe appropriate to extend the activity fur-ther by using five, six, seven, eight or ninein the two-digit numbers.
POST VIEWING ACTIVITY FOUR
YOU WILL NEED: to copy the
Flip Card blackline master onto
construction paper or tag board.
• Fold the cards on the dotted line to
form a flip card. You may choose
the simple double or two digit dou-
ble practice. A blank sheet also
available for creating mental-math
flip cards.
Mental-math flip cards
44
www.mathmonsters.com
45
NCTM CONTENT STANDARDSGeometry
• specify locations and describe spatial relationshipsusing coordinate geometry and other representation-al systems
Measurement
• apply appropriate techniques, tools and formulasto determine measurements
NCTM PROCOCESS STANDARDS
Problem Solving*
Reasoning and Proof
Communication
Connections*
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
MAPPING
OVERVIEWThis episode brings the mathematics
of mapping and graphic representa-
tion up for children to investigate.
As a result of viewing this episode
the children will:
• describe, name, interpret and
apply ideas of direction and
distance in navigation using a map
• find and name locations with
simple relations (next to)
• recognize the connection between
mathematics and real-world appli-
cations; mapping and technology
VOCABULARYmap scan e-mailstreets signs rightleft north south east westforward landmarkmobile phonebackward
PROGRAMSYNOPSIS
It’s PARTY TIME in Monster
land and the Monsters have
invited their friends and rela-
tions to the castle for dancing, tasty
treats and good Monster company!
Everything was headed in the right
direction until Binary Bill called to
find out how to get to the castle for
the party.
Mina suggests that they draw a
map for Binary Bill. Multiplex
draws a map from memory showing
how to get from Binary Bill’s com-
puter shop to the castle. Split scans
the map and sends it to Binary Bill
using e-mail.
The map has just one curvy line
and Binary Bill is confused. He calls
and asks the Monsters to include
some landmarks. Mina suggests she
fly over Monster land and describe
the landmarks she sees over the
mobile phone.
The Monsters use teamwork to
try and figure out how to draw a
map that will help Binary Bill.
Finally, after a few more
attempts, the Monsters create a
map with the landmarks in correct
places, street names and clear direc-
tions. Before sending the map to
Binary Bill a fifth time, Mina flies
over Monster land with the
Monster-made map to verify that it
makes sense.
Our field trip visit is to a fire
house. The Chief explains how
fire fighters work with maps to
help them get to a fire as quickly
as possible.
Invite your children to join the
Monsters as they help Binary Bill
find his way to the big Monster bash.
™
Here is a fun way to warm your stu-
dents up to the idea of giving direc-
tions based on relative location (e.g.
next to, around, under) and estimat-
ed distance (e.g.paces, footsteps).
• Ask your students to cover their
eyes while you hide a stuffed bear
or some other novel object. Select
a volunteer to find the object by
following the directions you give.
Use relative location terms and
distance in paces or footsteps to
lead the student to the object. For
example, give these directions one
at a time:
➤ take four heel- to-toe footsteps
toward the door
➤ turn toward the bookshelf
➤ take four big paces
➤ look under the table
• A student may hide the object,
select a volunteer and give direc-
tions to the hidden item. Very
young children will need guidance
in giving simple, clear directions.
YOU WILL NEED: to collect
familiar objects such as a ball, a
book, a building block and a plant.
A box is helpful too.
• Place a variety of the items on a
table, about six in all. An object can
be placed “inside” the box.
• Tell the children that you are
thinking of one item on the table.
• Ask for a volunteer to follow your
directions to select the correct item.
Your directions will include words
which describe the position and
proximity of items in relation to
one another. For example: the item
is far away from the ball, it is next
to the building block, and in front
of the book.
• After the volunteer has identified
the object, repeat the activity.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITY TWO
PREVIEWING ACTIVITIES
Sideline SuggestionsIn this episode, the Monsters worktogether to solve a problem requiringthem to use spatial sense. They modelperseverance and make adjustments intheir thinking and planning as they workto create a map for Binary Bill. Minademonstrates how to verify a solution.Does it make sense? Does it work?
The development of spatial sense, theability to structure space and to see rela-tionships among the placement ofobjects occurs between the ages of fourand seven. Children come to see objectsin their world as having order vs. a ran-dom collection from which they are thecenter.
Children between the ages of seven andnine develop conservation of length andarea. They begin to use both horizontaland vertical references. They can repre-sent objects in space more realistically.
PREVIEWING ACTIVITY THREESideline SuggestionsPreviewing activities three and four linkmathematics to the real world. By high-lighting connections to mathematicsoutside of the classroom arena, childrencome to value mathematics as a part oftheir everyday life.
• Most schools and many homes are
equipped with computers and e-
mail access. Share this technology
with the children. If possible, send
a class-dictated e-mail to another
class or a place of interest such as a
children’s museum. Explain to
them that the message will arrive
quickly but that a reply will
depend on when the person receiv-
ing the message reads it and
decides to respond.
• If your school is equipped with a
scanner, explain its purpose.
Perhaps some of the children could
send pictures home via e-mail to
their parents.
46
47
Split sends the map to Binary Bill
through the e-mail. Within minutes,
Binary Bill has the map. But wait!
Binary Bill can’t follow the map.
What can the Monsters do to help?
PAUSE POINTS
Binary Bill has a problem. He
would LOVE to go to the party at
the castle, but he doesn’t know
how to get there. What do you
think the Monsters can do?
PAUSE POINT ONE
PAUSE POINT TWO
PREVIEWING ACTIVITY FOURYOU WILL NEED : to collect a
variety of simple maps to share
with your students.
• The collection may include a map
of the classroom, the school, your
neighborhood, county or state.
Your selection will depend on the
developmental level of your stu-
dents. The younger the child, the
closer to home you will need to
stay.
• Ask your students what they
know about maps. When they
have established the basic under-
standing that maps tell us where
things are in our world, ask them
to name the people or jobs that
require maps.
Sideline SuggestionsThe Pause Point questions will requireyour students to rely on their mind’s eyeto help them think through problemswhich involve moving, adding or delet-ing mental images from Multiplex’smap. If it is possible to stop the pro-gram, reconstruct each of Multiplex’smaps using your students’ input. Thisexercise will enhance both visualizationand spatial sense.
Binary Bill notices that the land-
marks are in the wrong places on
the revised map. Binary Bill
explains that the Post Office is not
next to the Monster Wash, it is on
the other side of town. Now what?
PAUSE POINT THREE
Binary Bill is still missing some
important information on the map.
He asks for street names and which
direction he should turn. How will
the Monsters figure this out?
PAUSE POINT FOUR
?
PREVIEWING ACTIVITIES
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONENavigating the classroom
YOU WILL NEED: to divide the
class into pairs, to draw a picture
problem on a slip of paper for each
pair (see sample below) and a bas-
ket to hold the papers.
• Give your students a challenge
such as “Mary is standing by the
sink and she needs to get to her
table. Let’s pretend she doesn’t
know the way. Which directions
will help her find her table? Are
there important landmarks that we
should use in the directions?
• Ask your students to give one
direction at a time while the stu-
dent, Mary in this case, follows
each direction to get to her table.
• Ask your students if there is anoth-
er way in which Mary can get from
the sink to her table. Which way is
best? Why?
• You may wish to group your stu-
dents in pairs. Draw picture prob-
lems for each pair of students in
your class and put them in a bas-
ket. The picture problems will be
created by using landmarks in your
classroom or, if you choose to work
outdoors, landmarks in the play-
ground.
Each student will solve the picture
problem they select from the bas-
ket. One member of each team will
give directions to the other student
who will navigate from one place
to another.
After the teams have solved their
challenge, they may tell the class
their problem and demonstrate the
solution. The picture problems can
be returned to the basket and the
teams can change roles and select
a new challenge.
Sideline SuggestionsThis activity will engage your students innavigating their way around their class-room or playground. It requires studentsto describe the position of objects and givedirections for a teammate to get from oneplace to another.
Picture problem sample
48
49
YOU WILL NEED: to duplicate
and cut out sets of four Monsters
from the Monster Hop blackline
masters, two-foot pieces of
yarn and tape.
• Using a the yarn, space the
Monster pictures out evenly.
Tape the backs of the pictures
onto the yarn.
• Ask your students to describe the
position of the Monsters.
➤ Which monsters are on the end?
➤ Which monster is next to Mina?
➤ Which monster is beside
Multiplex?
➤ Which monsters are far apart?
➤ Which are close together?
• Now give the string a loop.
• Ask your students to explain how
the position of Monsters have
changed. Is Multiplex still far away
from Aunt Two Lips? Continue to
practice using different positions of
the string and examining the order
and proximity of the Monsters.
POST VIEWING ACTIVITY TWOA string of monsters Sideline Suggestions
A String of Monsters is designed to giveyour students practice with order andproximity. This activity can be conductedin a large circle or in smaller groups of stu-dents. Many children have explored thisconcept with strings of beads.
POST VIEWING ACTIVITIES
50
POST VIEWING ACTIVITY FIVE
YOU WILL NEED: to duplicate
the Monster Hop blackline master
• Can You Find My Monster? also
uses the Monster Hop coordinate
system activity sheet. This game is
played in pairs. One student selects
a Monster from the “Monster Hop”
sheet and marks it with a counter.
The second student asks yes or no
questions, which may include direc-
tional language such as, row, col-
umn, above, below, or next to in
order to find and name the secret
Monster.
• As the student asking questions
receives a “yes” or “no” response,
he or she may mark the “Monster
Hop” sheet to eliminate Monsters
who are no longer possibilities.
Deductive reasoning is used to
“figure out” the secret Monster
marked on the teammate’s
Directions
Sideline SuggestionsYour students may not be ready to movebeyond naming Monsters in rows andcolumns. Therefore, the “Monster Hop”sheet can be used to make Monster Bingoboards. Ask your students to cut out theMonsters from the Monster Hop sheetand glue them onto the Monster BingoBoard in any order. Now they may playMonster Bingo to reinforce the ideas ofrow and column.
POST VIEWING ACTIVITY FOUR
The Monster Hop guides older stu-
dents in using a coordinate system to
identify the Math Monster in a par-
ticular position on a grid.
YOU WILL NEED: to duplicate
the Monster Hop blackline master
and get sets of skewers or chenille
strips for each student.
• Begin by modeling for your stu-
dents the meaning of “row” and
“column.” You may wish to cut
out the Math Monster pictures
that are on the “Monster Hop”
coordinate graph and use them to
show “row” and “column.”
• Ask a student to move three
Monster picture cards to form a
new row or a new column with dif-
ferent characters. Practice using
the vocabulary row and column.
Teacher: “Where is Binary Bill?”
Student: “In the row.”
Teacher: “Where is Mina?”
Student: “In a column.”
Monster hopSideline SuggestionsThis activity requires your students touse both horizontal and vertical refer-ences simultaneously. Thin skewers fromthe grocery store or chenille strips makesuperb markers for children who need tomark one direction at a time.
Simultaneously considering more thanone reference at a time should bereserved for students who demonstratereadiness. By assessing your student’sdevelopmental level and conceptualunderstanding throughout the MathMonster episode and activities, you willknow best what they are ready to expe-rience.
Example one: “This is a row.”
Example two: “This is a column.”
POST VIEWING ACTIVITIES
51
POST VIEWING ACTIVITY SIX
YOU WILL NEED: to duplicate
the Monster Hop blackline master
• Introduce the coordinate system
on the Monster Hop sheet. Ask
your students to name the
Monsters in the first row. Name
the Monsters in the second row.
Name the Monsters in the first col-
umn? And so on.
• Ask your students if they think a
Monster can be in a row and in a
column at the same time. Why or
why not? Allow your students to
talk with one another or to think
independently before responding
to the question.
• Practice finding Math Monsters on
the coordinate system using the
skewers. Ask your students to
place a skewer or pipe cleaner on
the Monster Hop sheet so that it is
on Aunt Two Lips and pointing to
the top and bottom of the paper.
Explain that this too is a column.
Now place the second skewer on
Aunt Two Lips but this time it will
point to the sides of the paper. Tell
your students that this is a row.
Where do the skewers or pipe
cleaners cross each other? Can a
Monster be in a column and a row
at the same time? Which column is
Aunt Two Lips in? Which row?
• Ask your students to identify the
Monster that is in the column and
row that you name. Which
Monster is in column A and row
3? Ask for a student volunteer to
offer a column and row for his or
her classmates to name the
Directions
POST VIEWING ACTIVITIES
52
www.mathmonsters.com
53
NCTM CONTENT STANDARDSMeasurement
• understand measurable attributes of objects and theunits, systems and processes of measurement
• apply appropriate techniques, tools and formulas todetermine measurements
NCTM PROCOCESS STANDARDSProblem Solving
Reasoning and Proof*
Communication
Connections
Representation
*Indicates a strong emphasis in this episode
Math Monsterspresents
TIME
OVERVIEWThis episode explores concepts of
time. The Monsters investigate ways
to measure the duration of time. As
a result of viewing this episode, the
children will:
• develop an understanding about
the need for standard units
• develop a sense of time through
estimation
• use non-standard tools to mea-
sure duration of time (counting,
water clocks)
• identify standard tools for
measuring time (clocks etc.)
VOCABULARYmeasure time shortlong half emptyfewer months digitalbottom middle yearshalfway hours topminutes quarteramount calendar days
PROGRAMSYNOPSIS
It is play time in Monster Land
and the Monsters are off to fly
a kite. The Monsters must take
turns flying one kite in a fair way.
How long should each of the turns
last? How can they be fair?
Multiplex takes a turn with the
kite first. Addison counts while
Multiplex takes his turn. Split
counts while Addison takes his
turn. Mina notices that Split is
counting too fast. Addison recog-
nizes that he didn’t have the same
amount of time to fly the kite.
Perplexed, the Monsters take a
break to sip water and think it over.
Addison realizes his cup is drip-
ping water. He suggests they mea-
sure time by counting the drips. The
Monsters try it out and find their
cups drip at different rates. They
standardize the cup by making the
hole in the bottom the same size
hole in the bottom of all the cups.
When the Monsters return to kite
flying, they must determine who
will have the first turn. Addison
suggest they a race around the cas-
tle, one at a time. The Monster who
makes it around the castle in the
fewest drips will be first. Addison
runs around the castle in only ten
drips (the cup takes twenty drips to
empty). Now they must learn how
to record shorter and quantifiable
amounts of time on the twenty-drip
water clock. They do this by mark-
ing the cup near the top, middle
and bottom, much like dividing an
hour into a half and quarters.
The Monsters wonder if human
beings keep track of time. Our field
trip is to a clock maker who intro-
duces the viewers to the way human
beings measure time. The clock
maker demonstrates an hourglass.
He also shows how hands and
marks on the clock face help
humans tell time.
™
Uncle Fraction
54
• Play a game of “hide and seek”
with your students. Divide them
into two groups—one hiders and
one finders. Count slowly and
loudly as the hiders scramble to
hide. Have the finders seek them
out and then gather together as a
whole group.
• Now switch the groups. Ask the
finders group to hide and the oth-
ers to seek. This time count very
quickly and loudly. You are proba-
bly going to have some complaints
from the students that didn’t have
as much time to hide. This activity
will spark some lively discussion
about how to play “hide and seek”
in a fair way.
• Ask your students if they have
ideas to help make the game fair
for seekers and hiders. How can
we give both teams have the same
amount of time to hide? Try out
some of the children’s ideas. Play
several successful rounds of “hide
and seek.”
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsExploring concepts of time and findingways to measure it using a variety ofnon-standard and standard tools willlead students to understand the natureof a unit and the mechanics of usingclocks.
Time-related ideas in this episode include;sequencing events, duration of time peri-ods, and passage of time.
• A game of “follow the leader”
using rhythms is a fun way to
inspire children to think about tim-
ing. The leader will clap a rhythm
such as clap, clap, clap, pause, clap,
clap, clap. Ask your students to
repeat what they heard.
• The leader will change the speed
of clap, clap, clap, pause, clap, clap,
clap. The children will repeat the
pattern. How was the first rhythm
different from the second? How
were they the same?
• Your students may enjoy taking
turns being the leader and invent-
ing simple rhythms for their class-
mates to repeat.
PREVIEWING ACTIVITY TWO
Sideline SuggestionsChildren should develop a sense of timebetween events such as the beginning oflunch and the end of the lunch, com-pared to the beginning of winter andthe end of winter. In this exercise, theythink about the interval of time betweenclaps.
Your daily classroom schedule and
your monthly calendar will help to
reinforce the concept of time
intervals.
YOU WILL NEED: to duplicate
the Analog Clock Faces blackline
master.
• You probably share the daily
schedule with your students each
morning. Use analog clock faces
on your daily schedule alongside
of the digital notation when you
post your schedule each day.
• Before viewing this episode, discuss
time intervals with your students.
Here are some questions to help
you “talk time” with your students:
What time do we eat lunch? How
long is math class today? When
does it begin when does it end?
How long is the month of
September? When does it begin
when does it end? How many
days? How many weeks?
PREVIEWING ACTIVITY THREE
Sideline SuggestionsDaily schedules and routines supportthe development of understanding timeintervals.
Talking about time with your studentswill reveal their understanding of timeconcepts.
55
PAUSE POINTS
The Monsters need a fair way to
measure the kite flying turns.
How can they tell if each Monster
is flying the kite for the same
amount of time? Do you have any
ideas for the Monsters?
PAUSE POINT ONESideline SuggestionsOlder students may suggest conven-tional ways for measuring time such asclocks, watches or stop watches.
It is clear to Addison that he did
not get the same amount of kite fly-
ing time as Multiplex. Why didn’t
counting solve the problem? What
can the Monsters do?
PAUSE POINT TWO
Your classroom calendar is an
excellent tool for discussion during
this Pause Point. Multiplex sug-
gests that they each take a turn for
a day. Mina said, “Wait a minute! I
don’t want to wait that long.”
Show the students what it would
look like if the four Monsters
shared the kite on four consecutive
days. Does that seem like a long
time?
How can the Monsters measure
time so that they each get to fly
the kite fairly? Are there any new
ideas for the chart? What do you
think the Monster might try next?
PAUSE POINT THREE
Sideline SuggestionsHere is a good opportunity to exploretime in larger units such as days, weeksand months.
The Monsters created water clocks
to measure a time fairly. But some-
thing went wrong. How could
Addison’s kite time be so short and
Multiplex’s kite time be so long?
They both had water clocks. What
went wrong?
PAUSE POINT FOUR
Sideline SuggestionsThe purpose of standard units of mea-surement is illustrated in this portion ofthe episode. This concept will be revis-ited when the students explore themeasurement of length, capacity,weight and area.
A race around the castle will
determine who will fly the kite.
The fastest Monster wins! But the
path isn’t wide enough for all of
the Monsters and they must run
one at a time. How will they know
which Monster gets the kite? Do
you have any suggestions?
PAUSE POINT FIVE
?
56
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
• Let’s Face It uses a clock face to
count intervals of time shorter than
one hour. A clock face blackline
master is provided for this activity.
It is marked in five minute intervals.
Tell your students that each section
represents five minutes. Ask them
to color each section so that the
same colors never touch. Use the
clock face for counting aloud by
fives. What is the last number we
hear when we get all the way
around the clock?
• You may use the clock face to
color thirty minute sections as
well. What does half an hour
mean? How is it like half a cup of
water in the water clock?
• Another application of the clock
face is to explore a quarter of an
hour. Ask your students to cut out a
clock faces, fold it in half and then
in half again. Open the clock face
and cut the face on the creases.
How many pieces do you have?
Ask your students to place the four
quarters of an hour on the whole
clock face. What do you notice?
• Manipulate the quarters to show
one quarter, two quarters or half
past and three quarters of an hour.
Let’s face it
Sideline SuggestionsIf your students are beginning to “telltime,” you can use this activity to launchfurther investigations.
Young children learn to use the fraction1/2 to describe concrete situations.
Using fractions to tell “how much “of anobject one has, is the first idea that chil-dren develop.
This activity may be more appropriate forolder students. You can best judge theacademic developmental challenges yourstudents require.
POST VIEWING ACTIVITY ONE
• How Long is A Minute? is a short
activity that requires no special
materials. Ask your students to
hide their eyes while you time a
minute. Tell them that when they
think one minute has passed to
raise their hand.
• How many students thought a
minute was shorter than it is?
How about longer? Repeat this
activity several times over the
next few days. Are your students
becoming more accurate in esti-
mating a minute?
• Your students could also guess how
many times they can do an activity
in a minute like writing their names
or the numbers from one to 20.
Time them to see how closely they
came to estimating correctly.
How long is a minute?
57
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY THREE
Water Clock Olympics gives your
students an opportunity to use
water clocks to make predictions,
measure the duration of time and
record information.
YOU WILL NEED: to collect cot-
ton balls, tape, cubes, two buckets,
a pan to catch drips, a trash can,
four scrap paper balls; to duplicate
the Water Clocks Olympics black-
line master to use as a record
sheet; and to make two water
clocks (Your students can help you
test them. Do they drip at the
same rate?)
• Tell your students that they will
participate in the Water Clock
Olympics. There will be three tasks
and each child will have a turn to
participate.
➤ TASK ONE: MOVING CUBES
Set up a bucket with twenty cubes
in it and a second empty bucket
beside it. Your students will move
the twenty cubes, one at a time,
from one bucket to another.
Remind them to pick up one cube
at a time. Ask your students to
predict how many drips they think
it will take to complete the task.
Record their predictions on the
record chart. Ask the student par-
ticipant to begin the task while
others count the drips. How many
drips did it take? Record the
information. Try this several
times.
➤ TASK TWO:
COTTON BALL ROLL
Tape a starting line and a finish
line six to eight feet apart on the
floor. Your students will blow a
cotton ball from start to finish.
Remind them that they may not
touch the cotton ball. Ask your
students to predict how many
drips they think it will take to
complete the task. Record their
predictions on the record chart.
Ask the student participant to
begin the task while others count
the drips. How many drips did it
take? Record the information. Try
this several times.
➤ TASK THREE:
MAKE THE BASKET
Make four paper balls and clear a
space for a round trash can to
serve as the basket. Mark a place
on the floor for the student to
stand when making a shot for the
basket. Your students will shoot
the paper balls into the basket,
one at a time. Ask your students
to predict how many drips they
think it will take to complete the
task. Record their predictions on
the record chart. Ask the student
participant to begin the task while
others count the drips. How many
drips did it take? Record the infor-
mation. Try this several times.
Water Clock Olympics
Sideline SuggestionsWater Clock Olympics is an active wayfor your students to engage in measuringthe duration of time.
Your management style and the needs ofyour student will determine how youwish to structure this activity.
The simplest way to make a water clockis to take a paper cup and with a pin orpencil point make a hole in the bottomsmall enough for the water to dripthrough.
Water Clock Olympics is not intended tobe a competitive experience, therefore,student names are not included on therecord sheet.
58
www.mathmonsters.com
59
NCTM CONTENT STANDARDSAlgebra
• understand patterns, relations and functions
• represent and analyze mathematical situations andstructures using algebraic symbols
• use mathematical models to represent and under-stand quantitative relationships
• analyze change in various contexts
NCTM PROCOCESS STANDARDSProblem Solving
Reasoning and Proof*
Communication*
Connections*
Representation
*Indicates a strong emphasis in this episode
MATH MONSTERSpresents
PATTERNS
OVERVIEWThis episode, Patterns, will allow
children to explore patterns with
the characters. Patterns will be
defined, and the audience will be
challenged to figure out the next
pieces of each pattern. As a
result of viewing this episode the
children will:
• identify, analyze and extend
patterns
• describe how repeating and
growing patterns are created
• recognize the same pattern in
different manifestations
VOCABULARYpattern repeatsame differentpredict
PROGRAMSYNOPSIS
In the castle we find Split deco-
rating with a pattern she has
created all on her own. When
she is interrupted the other mon-
sters need to continue the pattern.
Multiplex creates a random contin-
uation of Mina's work and the
monsters’ first challenge is to clari-
fy just what a pattern is. Next they
need to figure out Split's pattern
so that it may be extended.
This sparks an interest in pat-
terns and each of the monsters
decides to create their own type
of pattern. They explore patterns
using numbers, shapes and blocks.
Some are repeating patterns and
some are growing patterns. The
patterns become more complex as
the episode moves along. Each
time there are visual and concrete
models to assist the audience in
predicting what will come next in
the pattern.
Students can analyze, predict
and extend patterns right along
with the Monsters as they explore
the world of patterns.
Join us on a field trip to a tile
shop where students can see pat-
terns applied in the real world.
™
60
• Introducing children to the concept
of patterns through rhythms can be
a brief, entertaining and highly
effective strategy. Try leading your
students through the activities
below. Once your students become
proficient with these rhythms,
allow them to create their own
variations.
• Demonstrate a rhythmic pattern
and ask your students to join in
continuing the pattern. Eventually,
your students can lead the motions
and create the pattern.
• Here are a few suggestions
for rhythms:
-snap, snap, clap, snap, snap, clap ...
-stomp, clap, clap, stomp,
clap, clap ...
• Try these movement patterns:
(touch)
➤ head, shoulders, knees, toes,
head, shoulders, knees, toes ...
➤ eyes, ears, eyes, ears/ears, eyes,
ears, eyes ...
• Try some Math Monster move-
ment patterns. Create motions for
each of the characters with your
class. Here are some suggestions.
➤ Addison—arms straight out to
the sides
➤ Multiplex—hands overhead and
legs spread making an "X" with
the body
➤ Mina—hands flat against sides
➤ Split—arms overhead making
a circle
• Now add some patterns:
➤ Addison, Multiplex, Mina, Split,
Addison, Multiplex, Mina, Split ...
➤ Mina, Mina, Split, Split, Split,
Mina, Mina, Split, Split, Split ...
After trying various rhythmic pat-
terns encourage your students to
interpret and represent the pattern
using math materials.
YOU WILL NEED: linking cubes
•Lead a familiar rhythmic pattern.
After repeating the pattern a few
times, stop and ask students to
represent the pattern using linking
the cubes.
• Draw attention to the linking pat-
terns that replicate the rhythm,
and ask children to point to the
colors and repeat their names for
the group. Compare the patterns
represented by different students.
For example, the rhythm— clap,
snap, snap, clap, snap, snap—could
be represented by color cubes: red,
green, green, red, green, green.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITY TWO
PREVIEWING ACTIVITIES
Sideline SuggestionsChildren organize their world throughpatterns. Their school day follows aschedule and their home lives resemblea pattern of daily routines such as: din-ner, bath time, brush teeth, story, bed-time.
An understanding of patterns leads tothe mathematical idea of functions forchildren. Recording information ontables and charts helps children seenumber patterns. By coloring the multi-ples of five on a hundreds chart, chil-dren recognize a predictable function orrule for fives.
Please remember that children may take awhile to see the commonality among allthe types of patterns named.
Sideline SuggestionsWait time is very important for this activ-ity since all of the children will notunderstand exactly what it is they are todo. As they observe their peers and aregiven several opportunities to practicebuilding the pattern, they will findgreater success and expand their prob-lem-solving abilities.
61
PAUSE POINTS
Multiplex and Mina are trying to
help Split paint a pattern border in
her room using shapes. They are
using four shapes, but it just doesn't
look like Split's pattern. What do
you think is wrong?
PAUSE POINT ONE
Your students may be ready to
work with increasing or growing
patterns.
YOU WILL NEED: dried beans
to serve as counters
• Build this pattern:
What do you think comes next?
PREVIEWING ACTIVITY TWOSideline SuggestionsLearning to communicate strategies andideas by talking and listening to others isessential for young children in mathemat-ics. Ask your students to describe the pat-tern. How did we know what to buildnext? Where did we look? What did wefind out?
Ask your students to build the next set inthe pattern using the manipulatives.After building four and four, ask for thenext set in the pattern.
PREVIEWING ACTIVITIES
Split thinks that Addison has made
a mistake in his pattern. Addison is
certain that his pattern works and
Split needs to figure it out.What do
you think comes next in Addison's
pattern?
PAUSE POINT TWO
Mina is so pleased with her table-
cloth pattern. By flipping her sten-
cil over she has created a pretty
design. How can she use the same
stencil but create a different pat-
tern for her napkins?
PAUSE POINT THREESideline SuggestionsIf you are able to stop the program, youmay wish to show your students a realstencil and demonstrate the different lookthat can be created by flipping or rotatingthe shape.
Split adds a little number pattern to
her room. What is her pattern?
What comes next? Why do you
think so?
PAUSE POINT FOURSideline SuggestionsFor Pause Points four and five, a hun-dreds chart or number line will help yourstudents identify the next numbers in thepattern.
Multiplex is using blocks to build
his pattern. He is building pyra-
mid patterns. The first pyramid
has one block, the second has
three blocks and the third has six
blocks. Mina has gone to get more
blocks for Multiplex. How many
blocks will he need for the next
pyramid?
PAUSE POINT FIVESideline SuggestionsIf you are able to stop the program, askyour students to build the same patternas Multiplex using blocks. Ask them todescribe how the pyramids change inthe pattern. How can we find out howmany blocks the next pyramid willneed?
?
1 and 1 2 and 2 3 and 3
62
Extending patterns with color tiles
will give your students practice in
predicting the next step in a linear
sequence.
YOU WILL NEED: color tiles
and coloring tools; to duplicate the
Extend-a-Pattern black line mas-
ter for your students to make rep-
resentations of their patterns.
• If you have access to an overhead
projector, you can make overhead
tiles by photocopying the Extend-
a-Pattern black line master on
overhead film. Color the squares
as needed and cut them out.
Another option is to model the
activity with the children while
they are sitting in a large circle.
• Model a pattern for your students
using color tiles or cubes. For
example, line up: red cube, green
cube, green cube, red cube. Ask
the students to predict which cube
they believe will be next in the
sequence. Continue to build the
sequence under the direction of
your students. Ask them if the pat-
tern makes sense. What makes the
pattern work?
• Make a representation of your
pattern on chart paper. Color the
first square red, the next green,
the next green, the next red. You
can extend the activity by labeling
the color squares with a letter rep-
resentation. Write an "R" under
the red square, a "G" under the
green square and so on.
• Give your students a small bag of
eight to ten color tiles. You may
wish to limit the number of colors
depending on the ability of your
group to work with patterns. Ask
your students to create a pattern
using the tiles. Your students may
share their pattern with a buddy
and explain why they believe they
have a pattern. After "talking out
the pattern" ask your students to
record their pattern on the
Extend-a-Pattern black line master
sheet. Try using letters to repre-
sent the color tiles below the
boxes on the Extend-a-Pattern
sheet.
Example:
• Post your students’ patterns and
share a few each day. Encourage
your students to talk about their
patterns by asking them to
describe their pattern to the class.
Each student may ask the class to
predict the next color for their
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWOSideline SuggestionsThe ability to see patterns will help stu-dents transfer knowledge and under-stand relationships between one situa-tion and another.These post viewingactivities focus on extending linear pat-terns, growing patterns and number pat-terns. In each activity, the children areencouraged to make representations ofthe patterns they build.
Extending patterns
Understanding of mathematical con-cepts and procedures is nurtured whenchildren see the same idea manifested indifferent ways. In this activity, colorsquares represent tiles, and letters repre-sent both squares and tiles.
R G G R G G R G
• Make a pattern with color tiles and
ask students to copy it by coloring
in squares on the copy-a-pattern
section of the first blackline master.
POST VIEWING ACTIVITY ONECopying patterns
63
POST VIEWING ACTIVITY THREE
Growing Patterns shows students
that patterns can grow in a logical
sequence in addition to repeating
themselves.
YOU WILL NEED: to make an
overhead film of the Growing-
patterns Squares blackline mas-
ter and cut out the squares to
use on the overhead. (An alter-
native is to use small tiles or to
cut large squares out of con-
struction paper to model this
pattern for your students.); scis-
sors and glue so that your stu-
dents may build models of this
growing pattern.
• To engage your students in think-
ing about growing patterns, model
the sequence below by building
each model in this order and leav-
ing them all on display for your
children to examine. By number-
ing each column, your students
will see a more abstract represen-
tation of the same pattern.
• Tell your students that these are
the first three steps in a pattern.
Ask them to cut out a model of
each step using the Growing
Pattern Squares black line master
and glue them onto a large piece
of paper in the correct order and
orientation. Encourage them to
record the number of squares for
each of the columns on each step.
• After they have made a representa-
tion of the first three steps, ask
your students to predict the next
step. Encourage them to talk to
each other about their predic-
tions. What do you think? Why
do you think so?
• Ask your students to cut out the
next steps to the pattern. Some
students may cut out step four
and five, while others may go on
to build the pattern further. As
students are working, ask them
to explain to you the pattern
they are building.
• This activity can be repeated
using different growing patterns.
You may wish to use color tiles
to build the pattern instead of
cutting out the models. Here are
some ideas for other growing
patterns:
Growing patterns
Sideline SuggestionsSkills in mathematical language andcommunication are sharpened as stu-dents have opportunities to explain andsupport their thinking. By listening toyour students’ "talk math" you will gaininsight into their level of understanding.
POST VIEWING ACTIVITIES
or1 2 1 3 2 1
64
POST VIEWING ACTIVITIES
Number Chart Patterns gives your
students an opportunity to experi-
ence a few of the many number
patterns embedded in a 0-99 chart.
YOU WILL NEED: copies of the
0-99 chart blackline master, an
overhead of the blank 0-99 chart
black line master and coloring
tools for this activity.
• Using the blank chart on an over-
head projector (an enlarged chart
will do if you do not have access to
an overhead) write in a few num-
bers at random in the correct posi-
tion on the chart. (Your intended
pattern is to write the numbers 0-99 in
the correct sequence.) Use the 0-99
black line master chart to guide
you. You may fill in the 2, 3, 10, 14,
21, and 30 to start. Ask your stu-
dents if they can tell you some other
numbers to write in other squares.
Your student should not have access
to a 0-99 chart at this time.
• Continue to solicit responses to
the request for other numbers to
write in other squares. Record cor-
rect responses and help to clarify
incorrect responses by asking the
student to describe the pattern
that he/she has identified. There
are many different patterns on the
chart. Remind your students that
their job is to figure out your num-
ber pattern.
• Complete the 0-99 chart. Once your
students see that the chart simply
counts from 0-99, their responses
will fill the chart in quickly.
• Tell the children that they used
patterns to fill in the boxes. You
used the numbers you could see to
figure out the missing numbers.
What are some strategies you used
to figure out a number for the
chart? How did you figure out that
a 10 belongs here?
• Depending on the level of student
understanding, the 0-99 chart can
be used to find patterns in many
ways. You may wish to ask your
students to find a pattern and out-
line the number boxes in their pat-
tern with a coloring tool. Sharing
discoveries with others is a price-
less opportunity to practice mathe-
matical communication. Here are
a few samples of the patterns that
your students may discover. These
samples are listed from simple to
more complex.
➤ If I count by twos, I will color
every other square
➤ If I count by fives, I color
two columns
➤ If I count by ten, all of numbers
I color are in one column
➤ The number at the top of the col-
umn is the same as the number
in the ones or units place value
all the way down the column
➤ The tens place value increases
by one for each number going
down the column
*The activity is adapted from
Mathematics a Way of Thinking
listed under teacher resources.
POST VIEWING ACTIVITY FOURNumber chart patterns
Sideline SuggestionsHere is an excellent opportunity toguide your students in developingclear and careful mathematical com-munication. If a student says, put a 15by the 14, it is not clear if this meansto the right or left. Guide your stu-dents in using clear directional phras-es and correct terminology by makingany mistake in placement that yourstudents’ language dictates. You maywish to label the blank chart with thewords over, under right and left.
Young children are easily engaged insearching for patterns in the worldaround them. Take your children on apattern hunt in your school buildingand/or around the neighborhood. Pointout some examples of patterns such asthe sidewalk, a tile wall, or a gardenarrangement. Ask your students to findpatterns and report them to a class-mate. You may wish to group all thestudents together periodically so thatthey may share what they have foundwith the whole group. Your studentswill be amazed at what they find!
Some of your students will point outthat they counted up or counted back-ward to find numbers. Others may havenoticed the tens column or a row ofnumbers that increased by one in thetens place while the one’s place numeralremained the same. This dialogue is arich opportunity to assess your students’level of understanding.
65
NCTM CONTENT STANDARDSNumber and Operations
• understand numbers, ways of representing numbers, relationships among numbers and number systems
• compute fluently and make reasonable estimates
NCTM PROCOCESS STANDARDSProblem Solving
Reasoning and Proof*
Communication
Connections*
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
COUNTING AND SYMBOLIZING
OVERVIEWIn this episode, Counting and
Symbolizing, the Monsters help
Cousin Cal take an inventory of the
fish in his fish store. A variety of
counting strategies are explored. As a
result of viewing this episode the chil-
dren will:
• connect numbers to the quanti-
ties they represent
• combine sets to find the sum
• count by twos, fives and tens
• use symbols to represent objects
in a set
• check to find the reasonableness
of an answer
VOCABULARYcount inventorycircle numbersmark
“all together”“how many”
PROGRAMSYNOPSIS
Cousin Cal Q. Lator gives his
monster relatives a call to
find out if they will help him
take inventory of the fish in his store.
He knows he can count on the
Monsters to do a good job. The
Monsters, just like young children,
love to count everything!
The Monsters persevere to figure
out how many fish are in each tank.
The first tank contains fast swimmers
and Split notices that the count seems
too high. Addison suggests that some
of the fish may have been counted
twice. They decide to keep track of
the fish by drawing each fish and
counting them by color. The second
tank contains so many fish that draw-
ing them will take too much time.
The monsters scale back their strate-
gy and use color-coded tally marks
instead. The third tank holds the
jumping fish. These fish jump when
they hear a whistle blow! The
Monsters count these fish by ones,
twos and fives using whistles to com-
mand a jump from one tank to the
next. They successfully count to find
the total.
The field trip is to a supermarket
where we learn how electronic scan-
ners and other tools help the store
manager know how much food is
bought and how much food is on
the store’s shelves.
™
66
• The idea of taking an “inventory”
is the focus of this episode. One
way to introduce this vocabulary is
through role playing. Demonstrate
for your children the meaning of
“inventory.”
• Tell them that you are going to
take an inventory of the chairs in
the classroom. Count the chairs
while keeping track of which chairs
have been counted. Announce that
the “inventory” is complete and
there are (blank) number of chairs
in the room.
• Ask your children to generate a def-
inition of “inventory” in their own
words. Now, a student volunteer
may role play, “taking an inventory”
of another item in the room. Revisit
the class definition of “inventory”
before viewing this episode.
• Try this activity with other class-
room objects and have the children
perform the inventory.
In this activity, the students will
count a collection of colored
cubes from a fishbowl.
YOU WILL NEED: colored
cubes and a fishbowl to parallel
the theme of counting fish in the
episode. However, another type
of clear, see-through container
will also work.
• Place some number of colored
cubes into the fishbowl. The num-
ber you use will depend on the
level of your students. For exam-
ple, you may use six cubes of two
colors for very young children or
twenty cubes of four colors for
older students and so on. Ask your
students to take inventory of the
cubes. How would you find out
how many cubes there are in the
bowl?
• Try and solicit a variety of ideas
for counting the cubes from your
students. Some may suggest that
the cubes be poured out and sim-
ply counted. By probing for more
strategies, your students will see
and hear that there can be more
than one way to solve a problem.
Ask your students to explain why
they believe their counting plan is
a good one.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITY TWO
PREVIEWING ACTIVITIES
Sideline SuggestionsCounting is the foundation for under-standing our number system.Young chil-dren count everything they can withgreat enthusiasm. They count while theypoint, touch and reposition objects intheir world.
In time, children learn that one numberrepresents one object being counted andthat the final number in the sequencerepresents the total quantity. They learnto keep track of what has been counted.They develop skills in grouping objectsand counting by twos, fives and tens tofind quantities.
As children grow and develop, they gainConservation of Number. They recog-nize that four cubes are still four cubeswhether they are spread out or lined upside by side. This is a cognitive processand while it cannot be taught, it will sur-face during challenges involving count-ing with young children.
Sideline SuggestionsYoung children should be given oppor-tunities to develop the ability to reasonsystematically and to explain theirthinking. By asking students to findmore than one way to solve a problem,they are encouraged to persevere, animportant disposition for approachingmathematics.
67
Multiplex counts the fish in the
tank but another Monster notices
that his count does not make
sense. There are certainly fewer
fish in the tank than the fourteen.
What went wrong? How can the
Monsters figure out how many
fish are in the tank?
PAUSE POINTS
The Monsters are helping Cousin Cal
take inventory of the fish in his fish
store. Multiplex is wondering how he
will count the fish in one tank. Do
you have any suggestions for him?
PAUSE POINT ONE
PAUSE POINT TWO
Sideline SuggestionsIf possible, stop the program andengage your students in pursuing solu-tions for the Monsters. It is importantto remind your students that often,there is more than one way to solve aproblem or use representations tokeep track while counting. A differentway is not necessarily a wrong way.
Mina drew a pictures to represent
the fish in the tank. She drew red
fish, green fish and blue fish. How
many fish are in the tank? How
can Multiplex find out?
PAUSE POINT THREE
Split notices that there are a lot
more fish in this tank than the first
tank. Split recognizes that it will
take too long to draw all the fish.
Is there another way that SPLIT
can keep track?
PAUSE POINT FOUR
?
The Monsters learn that they can
count groups of two fish and
groups of five fish and keep track
using tally marks. Now there are so
many marks on the paper. How can
they find out how many marks
there are all together?
PAUSE POINT SIX
There are jumping fish in this tank
and they look exactly alike! These
fish jump at the blow of a whistle!
How can the Monsters figure out
how many there are in this tank?
Do you have any ideas?
PAUSE POINT FIVE
68
Building Towers provides experi-
ence using one-to-one correspon-
dence and subatizing, that is, rec-
ognizing an amount without
counting. The students will also
explore the notion of adding cubes
and taking away cubes.
YOU WILL NEED: connecting
cubes and a large number cube. A
blackline master for building a
large number cube is included and
may be reproduced on tag board.
• You may wish to demonstrate this
game to the whole group in a large
circle, work with small groups, or
pair students to support each other.
• Ask your students to roll the num-
ber cube and build a tower using
the number of cubes shown. Now,
roll again. Add cubes to your
tower or take cubes off your tower
so that you have the same number
of cubes as the die indicates. This
may be repeated many times for
practice.
• Watch to see if the children
remove all the cubes each time or
add and take off cubes to make
the new number on the die.
• You may want to have the chil-
dren record the results of their
investigations.
*This activity is adapted fromDeveloping Number ConceptsUsing Unifis Cubes. See TeacherResources.
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
Sideline SuggestionsYoung children of similar age willdemonstrate a wide range of countingand number skills. These Post ViewingActivities are arranged from more basicto complex in terms of developmentallevel and skill acquisition. By observingyour students counting, keeping track oftheir counting and writing numbers torepresent quantities, you will gain anunderstanding of their experiential andinstructional needs.
Avoid the temptation to show childrenan easier or more efficient way to oper-ate in these activities. They will develop adeeper understanding of the mathemati-cal concepts and connect new concepts toold ideas through opportunities to seenumber relationships as they are devel-opmentally ready.
Building towers
POST VIEWING ACTIVITY TWO
Counting fish is an activity for
organizing a count and represent-
ing a quantity using a numeral.
YOU WILL NEED: to duplicate
the Counting Fish and Empty
Bowl blackline masters for each
student; coloring tools will also be
needed.
• Distribute the Counting Fish
sheet to each student. Ask the
children to color each fish one
color using up to three different
colors in all. The next step is to
have the students cut out the fish.
Ask them to exchange the entire
set of fish with a partner and
place them in the empty bowl on
the Empty Bowl sheet.
• Tell them that they are going to
count the fish in the tank. Ask
them to think about the ways that
the monsters counted fish. How
will you count your fish? How
many fish do you have?
• Ask your students to glue their
fish onto the bowl and record
the results by writing the number
which represents the total num-
ber of fish.
Counting fish
Sideline SuggestionsWatch and listen to your students’ count-ing strategies. Do students count one byone and keep track accurately? Is there astudent who groups the fish by color,counts by color and finds the total num-ber of fish?
Older students may use the “EmptyTank” black line master to draw andcolor ten to twenty fish in pairs. Forexample, two blue, two green, etc. Howwill you count your fish? How many fishdo you have?
Repeat this activity by asking students todraw and color 15 or 20 fish in the“Empty Tank.” Now how will you countyour fish?
Do your students choose to count by two,fives or tens? Can they count fluentlywhen counting groups of fish?
69
POST VIEWING ACTIVITY THREE
How Many Do You Think ...? is an
activity which provides a broader
classroom investigation created by
the teacher. An example might be:
suppose we wanted to take an
inventory of how many ears we
have in our whole class. How could
we find out? An important compo-
nent of the problem is to explain to
your students that they will show
how they found the solution on
paper. Create a problem that fits
the developmental and instruction-
al needs of your student group.
YOU WILL NEED: a variety of
materials such as: a class list of
first names, interlocking cubes,
counters, paper and coloring tools.
• Introduce the “How Many” chal-
lenge to your students. Show them
a variety of materials they may use
to find a solution.
• Remind them that they must show
how they solved the problem on
paper.
• Ask your students to talk to a
neighbor or think alone about
ways to solve the problem. What
tools would you use and how
would you use them? How can
you show the way you solved the
problem on paper?
How many do you think?
Sideline SuggestionsAs students share responses and sugges-tions, write them on a chart. This willreinforce the idea that there are manyways to approach a problem. Some stu-dents may refer the chart for new ideasduring the problem solving process. Doyour students include any of the strate-gies modeled by the monsters in theepisode?
Showing and/or explaining how one findsa solution may seem like a daunting taskfor some of your students. Ask them tothink about the ways that the Monstersrecorded information.
By asking students to explain how theyfound a solution, they employ skills incommunication, share representationsand demonstrate reasoning and proof.
These examples show the variety of student responses which may arise
during this problem solving adventure.Your own management style and
group needs will dictate the procedures that you use in your classroom.
Pat 10 Joy 10 Cal 10Mary Jon Aue10 10 10J0 Ann Sally10 10 10Bob Cam Betty10 10 10
100 20 fingers
Example one: How many ears? Example two: How many legs?
POST VIEWING ACTIVITIES
24 ears
24 legs
Example three: How many fingers?
70
POST VIEWING ACTIVITY FOUR
• If possible, take a field trip to a
local store where inventories are
conducted would further reinforce
counting as a real-life event. Many
stores inventory electronically and
use an inventory sheet to organize
the count. If the field trip is not
practical, invite a local retailer to
come to your class to talk about
keeping track of inventory.
• You may wish to follow up the field
trip experience by asking students
to use the play corner to reenact
what they learned on the field trip.
Listen to their language as a tell-
tale of their understanding.
A field trip
Sideline SuggestionsIt is important to emphasize the ways inwhich mathematics is embedded ourworld. Your students will come to recog-nize mathematics in contexts outside ofthe classroom.
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY THREE (CON’T)How many do you think?• After the students have finished,
ask for volunteers to share their
written work showing how they
found their solution. Then, verify
“How many ...” are in the whole
class by counting together. Count
in many different ways. Counting
ears, for example, allows a class
count by twos, counting fingers
allows a class count by fives and
tens.
• Your students may enjoy creating
their own “How many do you
think...” challenges to solve.
• Or, to continue practice, you may
make a collection of “How many do
you think ...” challenges and place
them in the fishbowl. Your students
may draw a problem to solve out of
the bowl.
71
NCTM CONTENT STANDARDSData Analysis and Probability
• formulate questions that can be addressed with dataand collect, organize and display relevant data toanswer them
• select and use appropriate statistical methods to analyze data
Measurement
• understand measurable attributes of objects and theunits, systems and processes of measurement
• apply appropriate techniques,tools and formulas todetermine measurements
Algebra
• understand patterns, relations and functions
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof*
Communication
Connections
Representation
*Indicates a strong emphasis in this episode
Math Monsterspresents
COMPUTERS
OVERVIEWThis episode illustrates the use of aweb site. The children observe themechanics of using a computer andthink about the most reasonablesolutions to a variety of problems.As a result of viewing this episode,the children will:
• name basic parts of computer• review concepts and skills in
collecting data, finding mea-surements and completing pat-terns from previous MathMonster episodes
• observe the Math Monstersusing a web site on a computer
• select the most reasonableresponse to a Math Monsterproblem
VOCABULARYmouse monitorkeyboard cursoricon web site“surfing the net”
PROGRAMSYNOPSIS
Binary Bill delivers a mysteri-
ous box to the Math
Monsters. Knowing how
much the Monsters like to solve
problems, he asks them to figure out
what is in the box before they open it.
After examining the box careful-
ly, the Math Monsters decide that it
contains a computer. They follow
the directions to set up the new
computer, and successfully turn it
on using the “power on” icon.
Binary Bill appears on the com-
puter screen to congratulate the
Monsters on setting up their com-
puter successfully. He also instructs
them on how to move items on the
screen using the mouse.
The Math Monsters visit the
mathmonster.com web site where
they get a chance to figure more
things out. On the web site, Binary
Bill gives the Monsters a problem,
time to think about a reasonable
solution and three icon-choices of
possible solutions. The Monsters
click on the icon that represents the
most reasonable solution. The click
starts a video showing the Math
Monsters solving the problem using
the solution they chose.
The Monsters solve problems
involving data collection, patterns
and measurement using familiar
scenes from previous episodes. The
Math Monsters wonder if human
beings ever use computers.
Our field trip will take us to a
school computer lab where the the
use of e-mail and web sites is
demonstrated.
™
72
• Gather your students together and
ask them to tell where they have
seen a computer or electronic tool
being used in their world. This
should open up a lively discussion
which may include describing the
difference between an electronic
tool and a mechanical tool.
• Your students may have seen com-
puters at home, at an office, in an
automobile repair shop, at the
doctor’s office and in the library.
They will probably conclude that
computers are all around us.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsChildren come to school with a broadrange of experiences in using techno-logical tools. By providing opportuni-ties for all children to use technologyin mathematics, the gap between theexperienced and inexperience beginsto close. All children can grow com-fortable in the use of calculators, com-puters and electronic learning devicesin both independent and directive set-tings.
• Before this activity, find out where
computers are used in your school
building and for what purpose.
• Arrange to visit a variety of sites
in your school building with the
students.
• Your students may interview a
variety of school personnel to find
out how computers help them do
their job.
PREVIEWING ACTIVITY TWO
Split is reading the directions for set-
ting up their new computer. The first
direction tells them to plug the
mouse into the back of the computer.
Mina calls out, “Here mousy, mousy,
mousy,” and no mouse appears. She
asks is Spit and Multiplex if they are
sure there is a mouse. What are they
looking for? Is it a small furry animal?
PAUSE POINT ONE
Split suggests that they press the
power button on the keyboard.
Mina doesn’t know what a keyboard
is and Multiplex begins looking for
keys. What is a keyboard?
PAUSE POINT TWO
Your students will have an opportu-
nity to explore shapes. Which shape
is an oval, a diamond, an octagon?
PAUSE POINT THREE
PAUSE POINTS
Sideline SuggestionsYoung children understand and use lan-guage literally. The first two pause pointswill help your students understand the fig-urative language “mouse” and “keys”used to name computer equipment. Ifpossible, have a computer close by so thatthe children may see the mouse and key-board during the pause points.
73
PAUSE POINTS
Binary Bill has another puzzle for
the Math Monsters to figure out.
This time it is about the pancake
restaurant. They need to know
what kind of pancakes the monsters
like best. What would be the most
helpful way to figure it out?
Binary Bill gives the Math
Monsters three icons. Each icon
represents a different problem solv-
ing strategy. Which strategy would
you select: Guess? Collect informa-
tion and data from Monsters in the
neighborhood? Call up another
restaurant and ask?
PAUSE POINT FOURSideline SuggestionsIf possible, stop the episode and discussthe problems posed by Binary Bill inthe following Pause Points. The mathe-matical conversations that develop willprovide valuable information aboutwhat your students know and are ableto do in the content areas of geometry,measurement and patterns.
The Monsters collect information
about the monster’s favorite pan-
cakes. Now they need to organize
the information on graph paper.
How can the Monsters figure out
which pancakes are the favorite by
using graph paper and without
counting?
PAUSE POINT FIVE
Since the Math Monsters are eager
to figure out more problems,
Binary Bill explains that Split had
just begun to paint a pattern on a
border when she received an unex-
pected phone call and had to leave.
She is not able to complete the bor-
der, however, Split pitches in to
continue the painting, but, she
doesn’t follow the pattern. What
did Split do wrong? What should
the pattern look like?
PAUSE POINT SIX
Now that the Monsters understand
that it takes ten Annie steps to
equal one Addison step, Binary Bill
asks the Monsters to figure out how
many Annie feet are seven
Addison feet long.
PAUSE POINT EIGHT
Binary Bill continues to challenge
the Math Monsters’ mathematical
minds. This time the problem
involves Annie Ant the carpenter.
Annie built a playhouse for the
Monsters using the “number of
steps” the monsters counted for the
size of the playhouse. The play-
house turns out to be very very tiny.
What went wrong, can you figure it
out? Which icon should the mon-
sters click?
She wrote down a couple of num-
bers wrong; Monster steps aren’t
the same size as ant steps. The
building shrank in the rain.
PAUSE POINT SEVEN?
74
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
• Integrate Math Monsters into your
language arts program by writing a
class e-mail letter to the Math
Monsters. The address is math-
monster.com.
Monster E-mail
POST VIEWING ACTIVITY TWO
• Your students have probably
viewed many of the Math
Monsters episodes. Ask your stu-
dents to name their favorite
episodes. Read the synopsis of
some of the programs aloud to
help your students remember the
problems that the monsters
needed to solve.
• Ask your students to design a
computer icon to represent their
favorite episode. Use the
Monster Episode Icon blackline
master. One of your classroom
bulletin boards may be set up as
a giant computer screen with
your students’ Math Monster
episode icons displayed.
Designing icons
POST VIEWING ACTIVITY THREE
• Ask your students to find their
way through the maze to connect
the Math Monsters to the Math
Monster web site. Use the
Monster Maze blackline master
for this activity.
Monster Math maze
www.mathmonster.com
Sideline SuggestionsThere are many fine programs designedfor children to use on the computer.Speak with your librarian or computerspecialist to see what is appropriate andavailable for your use.
POST VIEWING ACTIVITY FOUR
• Using calculators, have the stu-
dents do some simple activities
such as counting, counting on and
skip counting. You might explain
the value of using the + and - keys
to repeat operations.
Calculators
75
This Math Monsters™ Utilization
Video is designed to support the
teacher in planning rich and mean-
ingful learning experiences tailored to
each Math Monsters™ episode.
The video travels to a classroom to
watch a master teacher demonstrate
some of the ways to incorporate mate-
rials presented in the teacher’s guide.
The guide provides a framework that
clarifies learning standards and
objectives, broadens opportunities for
assessment, describes activities to
enhance your studentsπ viewing expe-
rience and maximize student achieve-
ment in mathematics. The following
components are contained in each of
the Math Monster teacherπs guides:
NCTM STANDARDSThe NCTM content and process stan-
dards supported in the episode
appear first in the teacherπs guide.
The Principles and Standards for
School Mathematics document is
available through the National
Council of Teachers of Mathematics
and describes the content and process
standards in detail. A matrix of the
episodes and the corresponding stan-
dards is also a helpful planning tool.
OVERVIEW
A general description of the mathe-
matical ideas for each of the Math
Monsters episodes is given. The
Overview also provides a list of spe-
cific learning objectives for the
young viewers.
VOCABULARYEach Math Monster™ episode is rich
in mathematical vocabulary. The
vocabulary list may be used to assess
your students mathematical language
before, during and after the program.
The words may be posted in the
classroom to revisit throughout your
students experiences with the Math
Monsters™ episode.
PROGRAMSYNOPSIS
It is always best to preview the
episode before viewing, however, this
may not always be possible. In the
synopsis. the story line is described
and the embedded mathematical
challenges are outlined for the
teacher.
SIDELINESUGGESTIONSThe shaded sideline suggestions give
the teacher practical information
about the episode and activities. The
suggestions are intended to assist the
teacher in preparing materials, guid-
ing discourse, applying assessment
practices, and understanding develop-
mental milestones of young learners
in mathematics.
PREVIEWINGACTIVITIESThe preview activities are designed to
prepare young viewers for the Math
Monsters episode. The preview activ-
ities tap the studentsπ prior knowl-
edge and experiences and to lay a
foundation for new learning. By
observing and listening to your stu-
dents during the previewing activities,
you will have a good idea of what
they know and are able to do prior to
viewing the episode.
Math Monsterspresents
UTILIZATION™
76
PAUSE POINTSPause points occur in every episode
and are highlighted with a question
mark. Each pause point is described
in the teacherπs guide. It is important
to be aware of the problems the stu-
dents will face with the Monsters. If
possible, stop the program at the
pause points and explore the chil-
drenπs ideas and solutions.
POST VIEWINGACTIVITIESA variety of post viewing activities
are included in the teacherπs guide.
These activities serve to sustain and
cultivate student growth in the con-
tent and process areas represented
in the episode. The teacher may
select the activity which best match-
es the developmental and academic
level of the children. The post view-
ing activities serve as an opportunity
to assess the growth that young
viewers have made as a result of
viewing the episode.
REPRODUCIBLEBLACKLINE MASTERSMany of the previewing and post
viewing activities have a corre-
sponding black line master to sup-
port the activity. The blackline mas-
ters can be found in the teacherπs
guide of each episode.
LITERATURECONNECTIONSA list of suggested childrenπs litera-
ture is intended to assist the teacher
in integrating reading and language
arts into your mathematics program.
Many of these titles may be available
in your school or local public library.
TEACHERRESOURCESThe teacher resource guide lists
many of the books and materials
that we have found valuable to both
our professional development and
program planning for our young
mathematicians.
These guides offer a teacher toolbox
of information, ideas, and suggestions
to assist the teacher in thoughtful
planning and meaningful assessment
of student growth. We hope your stu-
dents enjoy their Math Monsters™
adventures.
77
Math MonstersNOTES
™
78
Math MonstersNOTES
™
79
Math MonstersNOTES
™
80
Math MonstersNOTES
™
BLACKLINE MASTERS
Me-o-graph-y
foot toe hand thumb
Name:
DATA #1
DATA COLLECTOR DATA #2
Longest object:
How could you tell?
Shortest object:
How could you tell?
Objects that were about the same length:
How could you tell?
MYSTERY BOXMEASUREMENT #1
MY MEASURING RECORD
My units of measurement are:
Objects I am measuring How many units in length?
MEASUREMENT #2
A “STANDARD” ADDISON FOOTMEASUREMENT #3
MONSTER RULER
Instructions:1. Cut out the pattern.
2. Tape the gray area under the
second half of the ruler.
3. Secure the top face with
another piece of tape.
4. Have fun measuring!
MEASUREMENT #4
LADY BUGS AND LEAVESCONSERVATION #1
HOW DOES YOUR GARDEN GROW? CONSERVATION #2
GARDEN DOT PAPERCONSERVATION #3
01
2
3
4
56
7
8
9
10
SPINNERTENS #1
Instructions:1. Cut out the spinner circle and
the spinner arrow.
2. Make holes in the center points
of both pieces big enough to
accommodate a beaver clip.
3. Tape a paper clip to the back
of the arrow so it will spin well.
4. Fasten arrow to face with
beaver clip.
5. Have fun spinning!
GRID PAPER FOR REPRESENTATIONSTENS #2
GOLLYWOMPLES CHARTTENS #3
SHAPESGEOMETRY #1
SHAPE SHUFFLE SHEET ONEGEOMETRY #2
SHAPE SHUFFLE SHEET TWOGEOMETRY #3
SHAPE SHUFFLE SHEET THREEGEOMETRY #4
CUBE PATTERN
Instructions:1. Cut out the pattern.
2. Fold away from you along
each solid line.
3. Tape the tabs in order by
matching letters.
GEOMETRY #5
TRIANGULAR PRISM PATTERNInstructions:1. Cut out the pattern.
2. Fold away from you along
each solid line.
3. Tape the tabs in order by
matching letters.
GEOMETRY #6
CYLINDER PATTERN
Instructions:1. Cut out the pattern.
2. Fold away from you along
each solid line.
3. Tape the tabs in order by
matching letters.
GEOMETRY #7
THE DDDDOOOOUUUUBBBBLLLLEEEE GAME
DOUBLES #1
HERE’S HOW
SSSSOOOOLLLLUUUUTTTTIIIIOOOONNNN
DOUBLES #2
✁
✁
✁
✁
✁
BLANK FLIP CARDS
fold
fold
DOUBLES #3
6 7 8 9 10
1 2 3 4 5
2018161412
108642
FLIP CARD INSTRUCTIONS
Copy blank flip card on bothsides of a sheet of construc-tion paper. Print single or dou-ble digit numbers as addendson the grayed-in blocks.
On the back side of the sheet,print the doubled numbers,the sums, on the plain blocks.Make sure that the numbersface the opposite directionfrom those on the front. Cuton the solid lines and fold onthe dotted lines as indicated.
FRONT
BACK
20 A double digit flip card
DOUBLES #4
MONSTER HOP
A B C
1
2
3
MAPPING #1
MONSTER BINGO BOARDMAPPING #2
121
2
3
4
56
7
8
9
10
11
121
2
3
4
56
7
8
9
10
11
121
2
3
4
56
7
8
9
10
11
121
2
3
4
56
7
8
9
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11
121
2
3
4
56
7
8
9
10
11
121
2
3
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56
7
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9
10
11
ANALOG CLOCK FACES FOR DAILY SCHEDULETIME #1
121
2
3
4
56
7
8
9
10
11
121
2
3
4
56
7
8
9
10
11
LET’S FACE ITTIME #2
TASK
ON
E: M
OV
ING
CU
BES
TASK
TW
O:
CO
TTO
N B
ALL
RO
LL
TASK
TH
REE
: M
AK
E TH
E BA
SKET
How
man
y dr
ips
do y
ou t
hink
it w
ill t
ake?
How
man
y dr
ips
did
it t
ake?
How
man
y dr
ips
do y
ou t
hink
it w
ill t
ake?
How
man
y dr
ips
did
it t
ake?
How
man
y dr
ips
do y
ou t
hink
it w
ill t
ake?
How
man
y dr
ips
did
it t
ake?
WATER CLOCK OLYMPICSTIME #3
COPY A PATTERN
EXTEND A PATTERN
PATTERNS #1
GROWING PATTERN SQUARESPATTERNS #2
0-99 BLANK CHARTPATTERNS #3
0-99 CHART
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
PATTERNS #4
EMPTY FISH BOWLCOUNTING #1
COUNTING FISHCOUNTING #2
NUMBER CUBE PATTERNCOUNTING #3
MATH MONSTER EPISODE ICONCOMPUTERS #1
MATH MONSTER MAZE
www.mathmonsters.com
COMPUTERS #2
Math MonstersTEACHER RESOURCES
™
Data Collection • Does it Walk, Crawl, or Swim?
Investigations. Sorting and
Classifying Data, Scott Foresman,
2000. Susan Jo Russell, Karen
Economopoulos and Rebecca
B. Corwin.
• Mathematical Thinking in
Kindergarten Investigations,
Scott Foresman, 2000. Karen
Economopoulos and Megan
Murray.
• Developing Number Concepts Using
Unifix Cubes, Addison-Wesley
Educational Publishers, Inc. Kathy
Richardson.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, by Marilyn Burns,
Math Solutions Publication, 1992.
Measurement • Third Edition Mathematics: A Good
Beginning Strategies for Teaching
Children, Brooks/Cole Publishing
Company. Andria P. Troutman and
Betty K. Lichtenberg.
• Collecting, Counting, and Measuring
Investigations, Scott Foresman,
2000. Megan Murray, Karen
Economopoulos and Marlene
Kliman.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, by Marilyn Burns,
Math Solutions Publication, 1992.
Number Conservation • Building Number Sense Grade 1
(The Number System) Investigations,
Scott Foresman, 2000. Karen
Economopoulos, Joan Akers, Doug
Clements, Anne Goodrow, Jerrie
Moffet and Julie Sarama. 1998.
• Developing Number Concepts,
Addison Wesley Educational
Publishers, Inc. Kathy Richardson.
1984.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, by Marilyn Burns,
Math Solutions Publication, 1992.
The Making of Tens • Putting Together and Taking Apart
Investigations: Addition and
Subtraction, Scott Foresman, 2000.
Karen Economopoulos and
Susan Jo Russell.
• Building Number Sense Grade 1
(The Number System) Investigations,
Scott Foresman, 2000. Karen
Economopoulos, Joan Akers, Doug
Clements, Anne Goodrow, Jerrie
Moffet and Julie Sarama.
• Mathematical Thinking at Grade 2
Investigations, Scott Foresman,
2000. Karen Economopoulos, Joan
Akers, Doug Clements, Anne
Goodrow, Jerrie Moffet and Julie
Sarama.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Geometry • Shapes, Halves, and Symmetry
Geometry and Fractions,
Investigations Curriculum Unit,
Scott Foresman, 2000. Joan Akers,
Michael T Bassita, Douglas
Clements, Anne Goodrow and
Julie Sarama.
• Math By All Means: Geometry,
Math Solutions Publications.
Chris Confer.
• Fun with Architecture, The
Metropolitan Museum of Art.
David Eisen.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, by Marilyn Burns,
Math Solutions Publication, 1992.
Doubles and Their Neighbors
• Putting Together and Taking Apart
Investigations: Addition and
Subtraction, Scott Foresman, 2000.
Karen Economopoulos and
Susan Jo Russell.
• Building Number Sense Grade 1
(The Number System) Investigations,
Scott Foresman, 2000. Karen
Economopoulos, Joan Akers, Doug
Clements, Anne Goodrow, Jerrie
Moffet and Julie Sarama.
• Mathematical Thinking at Grade 2
Investigations, Scott Foresman,
2000. Karen Economopoulos, Joan
Akers, Doug Clements, Anne
Goodrow, Jerrie Moffet and Julie
Sarama.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Mapping • Primary Problem Solving in Math
101 Activities, Good Year Books.
Jack Coffland and Gilbert Cuevas.
• Usborne Young Puzzle Books,
Puzzle School, Usborne
Publishing. Susannah Leigh.
• Usborne Math Skills, Charts and
Graphs, Usborne Publishing.
• Principles and Standards for School
Mathematics, National Council of
Teachers of Mathematics, Inc.,
2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Time • Timelines and Rhythm Patterns:
Representing Time Grade Two
Investigations, Scott Foresman,
2000. Ricardo Nemirovsky, Cornelia
Tierney and Tracey Wright.
• One Hand at a Time: Using a One
Handed Clock to Teach Time-Telling
Skills, Dale Seymour Publications.
Patricia E. Smith.
• First Learning Time, Usborne
Books. J. Tyler.
• Principles and Standards for
School Mathematics, National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Counting and Symbolizing • Developing Number Concepts
Using Unifix Cubes,” Addison-
Wesley Publishing Company, 1984.
Kathy Richardson.
• Mathematical Thinking in
Kindergarten Investigations,” Scott
Foresman, 2000. Karen
Economopoulos and Megan
Murray.
• Coins, Coupons and Combinations:
The Number System,” Scott
Foresman, 2000. Karen
Economopoulos and Susan
Russell.
• Curriculum and Evaluation
Standards,” Adenda Series,
National Council of Teachers of
Mathematics.
• Principles and Standards for
School Mathematics,” National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Patterns • Developing Number Concepts
Using Unifix Cubes,” Addison
Wesley Educational Publishers,
Inc. Kathy Richardson.
• Patterns.” Creative Teaching
Press. Gwen Botka and Heather
D. Phillips.
• Pattern Trains and Hopscotch
Paths Investigations.” Scott
Foresman, 2000. Rebeka Eston
and Karen Economopoulos.
• Mathematics Their Way.” Addison
Wesley. Mary Baratta-Lorton.
• Principles and Standards for
School Mathematics,” National
Council of Teachers of
Mathematics, Inc., 2000.
• About Teaching Mathematics:
A K-8 Resource, Math Solutions
Publication. Marilyn Burns.
Computers • Making Shapes and Building
Blocks, Kindergarten Investigations,
Scott Foresman, 1998. Karen
Economopoulos, Megan Murray,
Kim O’Neil, Doug Clements, Julie
Samarama and Susan Russel.
• Investigations—Grade One Quilt
Squares and Block Towns, Scott
Foresman, 1998. Susan Russel,
Doug Clements and Julie
Samarama.
• Investigations—Grade Two Shapes,
Halves and Symmetry, Scott
Foresman, 1998. Joan Akers,
Michael Battista, Doug Clements,
Julie Samarama and Anne
Goodrow.
(All of the above offer a computer
software component.)
www.mathmonsters.com
Math MonstersLITERATURE CONNECTIONS
™
Data Collection • Charts and Graphs Usborne Math
Skills. Karen Bryant-Mole.
• Spiders, Spiders, Everywhere!
Creative Teaching Press. Rozanne
Lanczak Williams.
Standard and Non-standard Measurement
• Math Counts Length, Math Counts
Weight, Math Counts Size,
Children’s Press. Henry Pluckrose
and Ramona G. Choos.
• The Biggest Fish, Scholastic
Paperbacks. Shelia Keenan (Math
activities by Marilyn Burns).
• Let’s Measure It! Creative Teaching
Press. Luela Connelly.
Number Conservation • Spaghetti and Meatballs for All,
Scholastic Trade. Marylin Burns.
• Five Silly Fisherman, Econo-Clad
Books. Roberta Edwards.
• Inch by Inch, Mulberry Books.
Leo Lionni.
• Lunch with Cat and Dog, Creative
Teaching Press. Rozanne Lanczak
Williams.
The Making of Tens • 12 Ways to Get 11, Simon and
Schuster. Eve Merrriam.
• Mouse Count, Red Wagon. Ellen
Stoll Walsh.
Geometry • The Greedy Triangle, Scholastic
Trade. Marilyn Burns.
• Shapes, Shapes, Shapes, Mulberry
Books. Tana Hoban
• The Shapes Game, Henry Holt and
Company. Paul Rogers.
• Grandfather Tang’s Story,
A Tale Told with Tangrams, Crown.
Ann Tompert.
Doubles and Their Neighbors
• Two of Everything, Albert Whitman
& Co. Lily Toy Hong.
• Each Orange Had Eight Slices,
Econo-Clad Books. Paul Giganti, Jr.
• The Magic Money Box, Creative
Teaching Press. Rozanne Lanczak
Williams.
Mapping • Jumanji, Houghton Mifflin Co.
Chris Van Allsburg.
• Miss Rumphius, Viking Press.
Barbara Cooney.
• How Big is a Foot, Dell Publishing.
Rolf Myller.
Time • Clocks and More Clocks, Aladdin
Paperbacks. Pat Hutchins.
• P. Bear’s New Year’s Party, Tricycle
Press. Paul Owens Lewis.
• Knots on a Counting Rope, Owlet.
Bill Martin Jr. and John
Archambault.
Counting and Symbolizing • What Comes in 2s, 3s, and 4s?
Simon and Schuster. Suzanne Aker.
• Two Ways to Count to Ten Retold,
Henry Holt and Company. Ruby
Dee.
• Five Silly Fishermen, Econo-Clad
Books. Roberta Edwards.
• How Many Snails, Greenwillow.
Paul Giganti, Jr.
• Emeka’s Gift: An African Counting
Story, Puffin Books. Ifeoma
Onyefulu.
• Mouse Count, Red Wagon. Ellen
Stoll Walsh
Computers • “Arthur’s Computer Disaster,” Little
Brown Inc. Marc Tolon Brown
• Personal Computers, Children’s
Press. Charnan Kazunas
• Safety on the Internet, Gridgstone
Books. Lucia Raatma.
Patterns • The Crayola Counting Book,
Creative Teaching Press. Rozanne
Lannczak Williams.
• Times Tables Usborne Math Skills,
Usborne Books. Rebecca Treays.
• The Bugs Go Marching, Creative
Teraching Press. Rozanne Lanczak
Williams.
• What Comes in 2s, 3s, and & 4s?
Simon and Schuster. Suzanne Aker.
BOOKS FOR CHILDREN
Ahlberg, Janet and Allan Ahlberg. The Jolly Postman or
Other People’s Letters. Boston: Little, Brown and
Company, 1986.
Aker, Suzanne. What Comes in 2s, 3s and 4s. New York:
Simon and Schuster, 1990.
Anno, Mitsumasa. Anno’s Counting House. New York:
Crowell, 1977.
Anno, Mitsumasa, et al. All in One Day. New York:
Philomel, 1986.
Asbjornsen, P.C. and J. E. Moe. The Three Billy Goats
Gruff. New York: Trumpet, 1957.
Baker, Alan. Brown Rabbit’s Shape Book. New York:
Scholastic, 1994.
Bang, Molly. Ten, Nine Eight. New York: Greenwillow,
1983.
Bate, Lucy. Little Rabbit’s Loose Tooth. New York:
Crown, 1975.
Beck, Ian. Five Little Ducks. New York: Trumpet, 1992.
Berenstain, Jan and Stan Berenstain. The Berenstain
Bear’s Trouble with Money. New York: Random, 1983.
Briggs, Raymond. Jim and the Beanstalk. New York:
Scholastic, 1993.
Brown, Marcia. Stone Soup. New York: Macmillan
Children’s Group, 1986.
Calmenson, Stephanie. Dinner at the Panda Palace. New
York: Scholastic, 1991.
Carle, Eric. The Grouchy Ladybug. New York: Thomas
Y. Crowell, 1977.
Carle, Eric. Rooster’s Off to See the World. New York:
Scholastic, 1972.
Carle, Eric. The Secret Birthday Message. New York:
Harper Collins, 1972.
Carle, Eric. The Very Hungry Caterpillar. New York:
Putnam, 1969.
Clement, Rod. Counting on Fred. Milwaukee: Gareth
Stevens, 1991.
Clements, Andrew. Mother Earth’s Counting Book.
Natick, Ma: Picture Book Studio, 1992.
Cowley, Joy. Mrs. Wishy-Washy. Melbourne, Australia:
Rigby, 1980.
Crew, Donald. Ten Black Dots. New York:
Greenwillow, 1986.
Dee, Ruby. Two Ways to Count to Ten: A Liberian
Folktale. New York: Henry Holt, 1988.
Demi. The Empty Pot. New York: Henry Holt and
Company, 1990.
Dennis, Richard. Fractions Are Parts of Things. New
York: Thomas Crowell, 1973.
de Regniers, Beatrice Schenk. Little Sister and the Month
Brothers. New York: Seabury Press, 1976.
Emberly, Barbara. One Wide River to Cross. New York:
Scholastic, 1966.
Falwell, Catheryn. Feast for Ten. New York: Scholastic,
1993.
Feelings, Muriel. Moja Means One: A Swahili Counting
Book. New York, Dial, 1971.
Fisher, Leonard. Number Art: Thirteen 1, 2, 3s from
Around the World. New York: Four Winds Press, 1982.
Garne, S. T. One White Sail. New York: Green Tiger
Press, 1992.
Giganti, Paul, Jr. Each Orange Had 8 Slices. New York:
Greenwillow, 1992.
Giganti, Paul, Jr. How Many Snails? A Counting Book.
New York: Greenwillow, 1988.
Goble, Paul. The Giant Race of the Birds and Animals.
New York: Bradbury Press, 1985.
Grifalconi, Ann. The Village of Round and Square
Houses. Boston: Little, Brown and Company, 1986.
Hague, Kathleen. Numbears. New York: Scholastic, 1986.
Hoban, Russell. A Bargain for Frances. New York:
Harper and Company, 1970.
Hoban, Tana. 26 Letters and 99 Cents. New York:
Greenwillow, 1987.
Hoban, Tana. Is It Larger? Is It Smaller? New York:
™Math MonstersBIBLIOGRAPHY
Prepared for Grade 1-2 Teachers by Dr. Grace M. Burton
Greenwillow, 1985.
Hutchins, Pat. The Doorbell Rang. New York:
Greenwillow, 1982.
Jonas, Ann. Reflections. New York: Greenwillow, 1987.
Jonas, Ann. Round Trip. New York: Scholastic, 1984.
Kasza, Keiko. The Wolf’s Chicken Stew. New York,
Putnam, 1987.
Keats, Ezra Jack. Over in the Meadow. New York:
Scholastic, 1971.
Kitamura, Satoshi. When Sheep Cannot Sleep. New York:
Farrar, Straus and Giroux, 1986.
Linden, Anne Marie. One Smiling Grandma: A
Caribbean Counting Book. New York: Viking Penguin,
1992.
Lionnni, Leo. Inch by Inch. New York: Astor-Honor,
1962.
Mahy, Margret. 17 Kings and 42 Elephants. New York:
Dial, 1987.
Mathis, Sharon Bell. The Hundred Penny Box. New
York: Puffin, 1975.
McGrath, Barbara. The M and M’s Counting Book.
Cambridge: Charlesbridge, 1994.
McMillan, Bruce. Eating Fractions. New York:
Scholastic, 1991.
Medearis, Angela. Picking Peas for a Penny. Austin, TX:
State House, 1990.
Merrill, Jean. The Toothpaste Millionaire. Boston:
Houghton Mifflin, 1972.
Mistral, Gabriela. Crickets and Frogs. New York:
Atheneum, 1792.
McMillan, Bruce. Time To... New York: Scholastic, 1989.
Myllar, Rolf. How Big Is A Foot? Bloomfield, CT:
Atheneum, 1962.
Paul, Ann W. Eight Hands Round. New York: Harper
Collins, 1991.
Peek, Merle. Roll Over. New York: Clarion, 1981.
Pomerantz, Charlotte. The Half-Birthday Party. Boston:
Houghton Mifflin, 1984.
Rathman, Peggy. Ruby the Copycat. New York:
Scholastic, 1991.
Rees, Mary. Ten in a Bed. Boston: Little, Brown and
Company, 1988.
Rehm, Karl and Kay Koike. Left or Right? New York:
Scholastic, 1991.
Reid, Margarette. The Button Box. New York: Dutton
Chilren’s, 1990.
Reiss, John J. Numbers. New York: Bradbury Press, 1971.
Reiss, John J. Shapes. New York: Bradbury Press, 1974.
Ringfold, Faith. Tar Beach. New York: Scholastic, 1991.
Say, Allen. The Bicycle Man. Boston: Houghton Mifflin,
1982.
Scieszka, Jon and Lane Smith. Math Curse. New York:
Viking, 1995.
Sharman, Lydia. The Amazing Book of Shapes. New
York: Dorling Kindersley, 1994.
Sharmat, Marjorie. A Hot Thirsty Day. New York:
Macmillan, 1971.
Shaw, Charles G. It Looked Like Spilt Milk. New York:
Scholastic, 1947.
Singer, Marilyn. Nine O’Clock Lullaby. New York:
HarperCollins, 1991.
Soto, Gary. Too Many Tamales. New York: Putnam, 1993.
Titherington, Jeanne. Pumpkin, Pumpkin. New York:
Scholastic, 1986.
Tompert, Ann. Grandfather Tang’s Story. New York:
Crown, 1990.
Trapani, Iza. The Itsy Bitsy Spider. Boston: Houghton
Mifflin, 1996.
Viorst, Judith. Alexander, Who Used to Be Rich Last
Sunday. New York: Atheneum, 1978.
Walter, Marion. Another Magic Mirror Book. New York:
Scholastic, 1971.
Walter, Marion. The Magic Mirror Book. New York:
Scholastic, 1971.
Walsh, Ellen Stoll. Mouse Count. New York: Trumpet,
1991.
Williams, Vera. A Chair for My Mother. New York:
Greenwillow, 1982.
BOOKS FOR CHILDREN
Wise, William. Ten Sly Piranhas. New York: Dial, 1993.
Wylie,Joanne and David Wylie. ®Cuantos Monstruos?
Un Cuento de Numero.Chicago: Children’s Press, 1985.
Yarborough, Camille. Cornrows. New York: Coward,
McCann and Goeghegan, 1979.
Arithmetic Teacher, (February 1993), 40(6).
Braddon,Katherine L., Nancy J. Hall, and Dale Taylor.
Math Through Children’s Literature. Englewood, CO:
Teacher Ideas Press, 1993.
Burns, Marilyn. Math and Literature (K-3). White Plains,
NY: Math Solutions, 1992.
Burns, Marilyn. Math and Literature (4-6). White Plains,
NY: Math Solutions, 1995.
Griffiths, Rachel and Margaret Clyne. Books You Can
Count On: Linking Mathematics and Literature.
Portsmouth, NH: Heinemann, 1991.
Kolakowski, Jane S. Linking Math with Literature.
Greensboro, NC: Carson-Dellosa, 1992.
Madison, John and Roslyn Seidenstein. Beyond
Numbers: The Mathematics Literature Connection.
Reston, VA: NCTM, 1987.
Roberts, Patricia. Counting Books Are More Than
Numbers. Hamden, CT: Library Professional Resources,
1990.
Thiessen, Diane and Margaret Matthias. The
Wonderful World of Mathematics: A Critically
Annotated List of Children’s Books in Mathematics.
Reston, VA: NCTM, 1992.
Welchman-Tischler, Rosamond. How to Use Children’s
Literature to Teach Mathematics. Reston, VA: NCTM,
1992.
Whitin, David and Sandra Wilde. It’s the Story That
Counts. Portsmouth, NH: Heinemann, 1995.
Whitin, David and Sandra Wilde. Read Any Good Math
Lately? Portsmouth, NH: Heinemann, 1992.
Young, Sharon. Mathematics in Children’s Books: An
Annotated Bibliography, Preschool Through Grade 3.
Palo Alto: Creative Publications, 1979.
BOOKS FOR TEACHERS
www.mathmonsters.com
1
Math Monsterspresents
ESTIMATION
OVERVIEW
This episode encourages children to develop flexibility when thinkingabout numbers. The monsters willdemonstrate the importance ofusing estimation and approxima-tions when dealing with larger numbers of objects.
As a result of viewing this episode, the
children will:
• explore the purposes for making
estimates
• consider the reasonableness of
estimations
• use and view estimation as
another method for computing
large numbers
VOCABULARY
estimationclump
PROGRAMSYNOPSIS
Aunt Two Lips has contact-
ed the monsters—she
needs their help. Her
gollywomple trees are ready to be
picked and boxed. She would like
them to pick and pack the fresh gol-
lywomples. The monsters are happy
to help. In order to do this, they will
need boxes; but how many?
The monsters’ first challenge will
be to find out how many gollywom-
ples there are in the whole orchard
so that they will know how many
boxes they need. They decide to
count the gollywomples. Because it
is taking much too long to count,
they decide to try estimating
instead. They notice that by group-
ing or “clumping” the gollywomples
and then the trees, they can make
short work of finding out about how
many gollywomples will need to be
picked and packed.
The monsters will make several
estimates during this episode and
challenge children to try estimating.
They will also explore counting by
five, ten and twenty-five. Join the
monsters as they estimate their way
through Aunt Two Lips’ gollywom-
ple orchard.
Our field trip takes students to
meet an officer with the US Wildlife
Service. He discusses the impor-
tance of estimation in his work.
™
Addison
NCTM CONTENT STANDARDSNumbers and Operations
• count with understanding and recognize “how many”in sets of objects
• compute fluently and make reasonable estimates
• use a variety of methods and tools to compute,including objects, mental computation, estimation,paper and pencils, and calculators
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof*
Communication
Connections*
Representation
*Indicates a strong emphasis in this episode
2
The monsters first question will fol-
low them throughout this entire
episode. They need to know how
many boxes they will use for pack-
ing gollywomples. Here they need
to consider the possible ways they
can figure this out. Ask students to
consider the obvious solution,
counting, and then try to stretch
their thinking and encourage them
to come up with any other creative
ideas for finding out how many
boxes the monsters need.
YOU WILL NEED:
an estimating jar and copies of black-
line master #1 My Estimation Log
If you don’t already have one in
your classroom, now would be a
great time to introduce and esti-
mating jar. This activity can slide
right into your morning meeting
or circle time.
• Each morning put a certain num-
ber of objects into the jar, use
larger objects one day and smaller
objects the next. Let children con-
tribute objects from home ( a rock
or marble collection) as they
become familiar with the function
and object of the daily exercise.
• When children enter the class-
room they should write their
estimate on their estimation log
located next to the jar. As part of
your group meeting you can dis-
cuss the estimates and what led
students to their guess. Students
can take turns verifying the num-
ber of objects in the jar each day
by counting in a variety of ways.
Sideline SuggestionsWhen students are given the opportuni-ty to practice their estimation skills,they can learn how to make decisionsand take appropriate risks in mathemat-ics.
PAUSE POINT ONE
PREVIEWING ACTIVITY ONE
Counting each and every gollywom-
ple is taking too long, so Aunt Two
Lips suggests the monsters try esti-
mating. Talk with your students
about what they think it means to
estimate. How do they think this will
help the monsters find out how
many gollywomples there are in all.
PREVIEWING ACTIVITIES
PAUSE POINT TWO
PAUSE POINTS
PAUSE POINT THREEThe monsters will need to measure
to find out how many gollywomples
will fit into a box. Ask your students
to consider things they have tried to
pack like backpacks, suitcases, or
cubbies and desks at school. How
do they know what will fit and what
won’t?
?
3
Allow students to use various tools
around the classroom, calculators,
counters, pencil and paper for com-
puting the solution to help the
monsters. Students should work
with partners or in small groups so
that they can discuss possible
strategies for using all of the infor-
mation they need.
PAUSE POINTS
Now the monsters know that there
are about fifty gollywomples on
each tree because they have esti-
mated. They also know that each
box will hold about 25 gollywom-
ples.But still they don’t know how
many boxes are needed. Lead your
students on a discussion about all of
the estimates that have worked so
far, five gollywomples in a clump,
ten clumps in a tree, fifty gollywom-
ples in each tree, and twenty-five
gollywomples in a box. Let students
suggest what the monsters need to
estimate next and how they might
go about estimating trees in the
orchard.
Ask your students to think about
the reasonableness of estimating
that each box will hold about 25
gollywomples. Can the monsters
apply their estimating strategy to
this measurement challenge?
PAUSE POINT FOUR
PAUSE POINT FIVE
PAUSE POINT SIX
4
The school cafeteria can be a busy
place during the lunch breaks at
most elementary schools. That
makes it a perfect setting to try an
estimating activity.
• Ask your students to try counting
the number of kids in the lunch-
room the next time they eat there.
Discuss with them the challenges
they faced in doing this. (kids
were moving around a lot, some
changed seats, counting the same
table twice, too many distractions,
etc.) Later, walk with your class to
the cafeteria when it is not full of
students, but the tables are set up
for lunch. Have the students
check to find out approximately
how many students will fit at one
table comfortably.
• Question your students to find out
if they think the table might hold
more or less fifth graders than
first graders. Is the number they
originally came up with still a
good estimate?
• Next, check to see how many
tables are in a section or row of
the cafeteria. Send teams or part-
ners to the cafeteria to gather any
final estimating information, like
how many of the tables are full
during each lunch sitting for the
different grades.
• Set aside classroom time to try
out their estimates. Make sure
they have calculators and manipu-
latives readily available to help
them with their solutions. You
should be able to find out from
the school secretary how many
students are in each grade level
lunch group. You can share this
information when students are
finished. They might enjoy seeing
how close they can come when
they estimate.
POST VIEWING ACTIVITY TWOCafeteria count
POST VIEWING ACTIVITIES
Challenge students to create a list of
things that would take a very long
time to count. Find out from them if
any of their objects would require
an accurate count (number of lot-
tery tickets sold, number of students
in school today)and which ones lend
themselves more to estimating
(number of apples in a bushel, num-
ber of fans at a ball game).Talk
about strategies for estimating num-
bers with some of their objects.
Too many to count
Sideline SuggestionsAs students are given opportunities topractice their estimating skills they cangradually become more flexible withtheir thinking about numbers.Estimating activities can support theirdeveloping number sense.Numbersense develops as students begin tounderstand the size of numbers andthe many ways that numbers can berepresented.
POST VIEWING ACTIVITY TWO
5
My estimate logName:
ESTIMATION #1
DAY ESTIMATE
Monday I estimate that there are in the jar.
Tuesday I estimate that there are in the jar.
Wednesday I estimate that there are in the jar.
Thursday I estimate that there are in the jar.
Friday I estimate that there are in the jar.
1
NCTM CONTENT STANDARDSGeometry
• relate ideas in geometry to ideas in number andmeasurement
Measurement
• measure with multiple copies of units of the same size
• develop common referents for measure to makecomparisons and estimates
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof*
Communication
Connections
Representation*
*Indicates a strong emphasis in this episode
Math Monsterspresents
AREA
OVERVIEWThis episode digs deep into the
NCTM process standards as chil-
dren are encouraged to test and
prove the strengths and weaknesses
of the monster’s blueprints. They
need to consider the most reason-
able and practical plan for design-
ing a launch for their new rocket
ship. As a result of viewing this
episode children will:
• develop an understanding of
how to find the area by using
the length and width of the a
square
• relate ideas in geometry to num-
ber and measurement concepts
• practice using a hundreds chart
and recognize patterns within the
chart to predict the order and
sequence of missing numbers
VOCABULARYarea lengthwidth squarerectangle sides
PROGRAMSYNOPSIS
Cousin Digit has given the
monsters a brand new rock-
et ship. They can explore
places all over Monster Town and
beyond. They have just one prob-
lem. Before they can launch their
ship they need to finish the con-
struction of a launch pad started by
Cousin Digit. The launch pad is
square and needs to be covered
with fireproof square tiles
The monsters will need to think
about the shape of the launch pad
and its area. To find this they will
explore the length and width using
tiles, and ultimately will need to
know how many tiles must be
ordered to cover the entire launch
pad. The monsters will also have a
chance to explore number patterns
on a hundreds chart when their
numbered tiles from Annie Ant get
a bit jumbled.
Our field trip finds us at a floor-
ing and tile center for a closer look
at the concept of area with a real
life application. Students will be
asked to consider the importance of
finding area for different-sized
rooms and spaces.
™
Split
2
• Take students to a local beach or
seashore for a class outing. You
can also use the school play-
ground. Ask them to draw shapes
in the sand with rocks or sticks.
On the playground they can use
sidewalk chalk. Have students fill
in the shapes with rocks or shells
they find. In laying these out the
students will cover the surface
area of their drawings. They may
wish to count the number of rocks
or shells it takes to cover their
shapes as they explore the concept
of area.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsAs children make or draw arrays theylearn to organize space and shape. Thiswill support later development in theirunderstanding of grids and coordinates.
The monsters need some ideas for
how they can find out how many
tiles are needed to cover the entire
launch pad. Allow students to brain-
storm their problem solving ideas
that may help the monsters. Help
students to recognize the impor-
tance of knowing both the length
and the width of the launch pad.
PAUSE POINTS
YOU WILL NEED: copies of the
blackline master Area #1 Square
Tiles, and color tiles or squares
• Use color tiles or squares to cover
each of the monsters shapes. Have
students compare the number of
tiles they used with each monster’s
shape. How does this help them to
know which shape is bigger or
smaller? Ask students to think of
some problems in which they
might need to know how much flat
space there is to be covered.
PREVIEWING ACTIVITY TWO
Sideline SuggestionsFor young children spatial visualizationcan be developed by building andmanipulating concrete objects.
PAUSE POINT ONE
?
Seashell coverup
Compare the squares
Why do the monsters find only nine-
teen tiles if both sides of the square
are the same size? This would be a
great activity to actually stop the
program and let students test for
themselves. The squares they mea-
sure can be smaller and classroom
color tiles or squares can be used to
simulate the monsters’ dilemma.
PAUSE POINT TWO
3
Again, this would be a great oppor-
tunity to stop the program and let
students draw their own “blueprint”
or plan for the launch pad. Let stu-
dents compare their designs and
answers for the number of tiles
needed.
PAUSE POINT THREE
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONE
Students can play this game in
groups of two or more.The object
of the game is to connect dots,
one line at a time, and make
squares.
YOU WILL NEED: copies of the
blackline master #2 Dot Grid
• Make copies of the blackline mas-
ter Area #2 that has the grid of
dots. The first player will draw a
line to connect two dots. The next
player will do the same thing.
• As the grid gets filled in with lines,
the students will be able to com-
plete a square and put their initial
inside. Each time a square is com-
pleted, the player may draw
another line connecting two dots.
Students may even be able to
complete several squares in only
one turn.
• When all the squares are complet-
ed, players count up the number
of squares that have their initial
inside. The student with the most
squares completed wins.
Squares
Sideline SuggestionsWhen students are given opportunitiesto visualize numbers in a geometricsense, as they model arrangements of thesame number with square tiles, they mayalso begin to make connections to area.
PAUSE POINTS
The monsters have jumbled their
tiles and are not sure where the
next tile will go. If your students are
familiar with using a hundreds
chart, they may find solving this
problem easy. If not, support stu-
dents as they try to continue the
pattern of numbers on the launch
pad by providing them with a com-
pleted hundreds chart or board in
the classroom.
PAUSE POINTS FOUR AND FIVE
4
POST VIEWING ACTIVITY TWO
The objective of this activity is for
students to create squares and rec-
tangles that represent arrays. This
introduces them to multiplication
through repeated addition. Students
can pair up for this activity.
YOU WILL NEED: one number
cube for each child (dice), copies
of blackline master #3 Grid Paper
or graph paper, colored pencils or
crayons, a highest/lowest spinner
(optional)
• The first child rolls the number
cube. Using a crayon or colored
pencil he/she will need to trace a
line (vertical) on the graph paper
that is as many squares long as the
number they rolled on the cube.
The next student takes a turn and
does the same on their own piece
of graph paper.
• The first student now rolls the
number cube again, this time mak-
ing a line (horizontal) as many
squares long as the number on the
cube. The first player has now
determined length and width and
should be able to add in the miss-
ing lines to close the square or rec-
tangle. The second player will do
the same , rolling the number
cube, drawing the horizontal line,
closing in the square or rectangle.
• When both players have complet-
ed their shapes, they need to find
out how many squares they have
enclosed inside their larger shape.
They can represent their work
under their shape writing the num-
ber of squares or using develop-
mentally appropriate number sen-
tences. Some students will be able
to write addition equations with
several addends and some may
represent their work in a multipli-
cation equation.
For example:
12 3+3+3+3=12 4x3=12
4+4+4=12 3x4=12• The winner can be the student
with the highest or lowest number
of squares in the round. The stu-
dents can decide whether higher of
lower wins the round at the begin-
ning. They should do this after
each round and play until they
have filled their graph paper with
squares and rectangles.
Finding area is as easy as length X width
POST VIEWING ACTIVITIES
Sideline SuggestionsSometimes it’s best not to emphasizevarious units of measurement too soonin measurement instruction. Go at apace you feel is appropriate for yourstudents.
You also might have children trace andcut out an outline of their own foot orhand to use for measuring.
3x4=12
5
POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY THREE
YOU WILL NEED: copies of
|the blackline master Area #4
hundreds chart
• Using the hundreds chart (or one
you have students create them-
selves) challenge students to
explore and make predictions
about the various patterns made
by numbers on the chart. You
could have children shade in num-
bers on the chart to reveal even
numbers, odd numbers, numbers
ending with “0” or “5,” etc. Ask
students to try these and look for
more patterns.
• Give students a chart with missing
numbers and see what their
predictions are for the empty
squares. Do the patterns they’ve
discovered help them to make
new predictions?
Hundreds chart patterns
SQUARE TILESAREA #1
How many square tiles do you need to cover Multiplex’ shape?
Multiplex’ shape
Split’s shape
How many square tiles do you need to cover Split’s’ shape?
6
DOT GRIDAREA #2
7
GRID PAPERAREA #3
8
9
HUNDREDS CHARTAREA #4
1
NCTM CONTENT STANDARDSNumber and Number Sense
• develop understanding of the relative position and magnitude of whole numbers
Geometry
• describe, name and interpret direction and distancein navigating space and apply ideas about directionand distance
• find and name locations with simple relationshipssuch as “near to”
NCTM PROCOCESS STANDARDSProblem Solving*
Reasoning and Proof
Communication*
Connections
Representation
*Indicates a strong emphasis in this episode
Math Monsterspresents
LANDMARK NUMBERS
OVERVIEWIn this episode, the Monsters figure
out how to help Multiplex, the tow
truck driver, find the breakdowns on
the road. They explore the concepts
of Landmark numbers, number
lines and the notion of integers. As a
result of viewing this episode, the
children will:
• recognize multiples of ten as
important Landmarks on a
number line
• identify locations on a number
line between and including
Landmarks
• discover the importance of
knowing “which way” and “how
far” when using a number line
VOCABULARYlandmark numbers“Positivity City”“Negativityville”zero
PROGRAMSYNOPSIS
Multiplex’ new job as a
tow truck driver has him
puzzled, because when
someone calls for help, he can’t
seem to find them. The Math
Monsters try to figure out a way to
help Multiplex find the break-
downs.
Addison suggests that they put a
numbered sign up at each Monster
meter from the castle. The drivers
can tell Multiplex the number writ-
ten on the sign nearest to them.
Mina reminds the Monsters that the
road goes in two directions from the
castle, one way to Positivity City
and the other to Negativityville, and
both directions should be marked.
The Monsters begin placing a
sign at every Monster meter but the
work is exhausting. They decide
that it is more efficient to place
signs at 100, 500 and 1,000 meters.
But the signs are so far apart they
don’t help Multiplex.
They figure out that if they mark
every ten Monster meters using the
landmark numbers 10, 20, 30, 40,
50, 60, 70, 80, 90 and 100, Multiplex
will find the breakdowns more easi-
ly.
But he is unable to find a break-
down at marker 20 because the
driver at marker 20 is on the road
to Negativityville and not the road
to Positivity City. So the Monsters
agree to paint the landmark signs
heading toward Positivity City
green and the signs heading toward
Negativityville blue. But what about
the the castle? How should it be
marked? The monsters will figure
that out, too.
The field trip takes us to a televi-
sion station to visit a meteorologist.
The weatherman uses positive and
negative numbers to report the
temperatures. This field trip con-
nects the number line concept to a
real life application familiar to
™
2
Where Is It? is a game of commu-
nication.
YOU WILL NEED: twenty paper
cups placed upside down in a line
with a number 1 on the first cup
and a number 20 on the last cup; a
small object such as a ball of clay,
toy or coin
• The students should cover their
eyes while you place the small
item under one of the cups. Tell
the students that the item is hid-
den under one of the cups
between 1 and 20. The object of
the game is to ask as few questions
as possible to find out which cup is
covering the object.
• Because the students have so few
clues they will begin to guess with-
out reasoning. Ask them what
could be done to give them the
information they need to ask good
questions. How can we make this a
thinking game instead of a guess-
ing game without numbering all of
the cups?
• Try some of the students ideas.
Guide them in discovering that
numbering every other cup or
every fifth cup will help them ask
the questions that will help them
find the hidden item quickly.
PREVIEWING ACTIVITY ONE
PREVIEWING ACTIVITIES
Sideline SuggestionsTeachers can extend young mathemati-cian’s knowledge of relative position inspace through conversations anddemonstrations. Use this activity to helpthem understand that by numberingmore of the cups, but not all of them,they can provide clues using languagesuch as, “beside,” “between,” “far” and“near” to express location.
• Take a field trip to the front of
your school. Ask your students to
pretend they are in a car or on a
bus. If the vehicle turned right,
name some of the places you
would see. If the vehicle turned
left, name some of the places you
would see. Help your students
understand that the road goes in
two directions from the school.
• Now ask them to think about one
of the far away places they named.
Ask your students to name some
of the landmarks between the
school and the far away place.
PREVIEWING ACTIVITY TWO
Sideline SuggestionsNavigation is a mathematical conceptinvolving direction, distance, locationand representations. This activity isdesigned to help young children under-stand the problems faced by theMonsters in this episode and to sparktheir thinking about landmarks as key“places along the way.”
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After deciding that it was too
exhausting to place a sign at every
Monster meter, Basehound suggests
they place a sign every hundred
meters. When a call comes in for
Multiplex, the monsters use the
clues to figure out that the break-
down is between 10 and 100. That is
a long, long way and they decide the
numbers are not helping very much.
Ask the students to help the
Monsters figure out what they can
do.
PAUSE POINT TWO
The monsters place a sign every 10
Monster meters. The next call that
Multiplex receives is from a driver
between sign 50 and 60. Ask the
students where the driver with the
break down can be found?
Multiplex receives a call from a dri-
ver with a flat tire. He tells
Multiplex that he is beside a green
tree. Monster town has many green
trees and Multiplex drives up and
down the road looking but he never
found the driver. Mina thinks he
drove in the wrong direction.
Addison thinks he didn’t drive far
enough. Allow students to develop
problem solving ideas that may help
Multiplex find out how far to drive.
PAUSE POINTS
PAUSE POINT ONESideline SuggestionsThis is a good opportunity to talk withyour students about the need to haveenough information when solving aproblem. Role play with your studentsto demonstrate how a lack of informa-tion leads to misunderstandings. Tryplacing a familiar object in the class-room where it can be found with a fewclear directions. Give a very generalclue telling your students where to findthe object. For example, “over there”or “up high” and then offer them morespecific directions to help them findthe object easily. Talk about the differ-ences in the information you offered.
PAUSE POINT THREE
It is getting dark. Mina calls
Multiplex and asks for a ride back to
the castle. She reports her position
as two Monster meters away from
30. Multiplex is puzzled when he
cannot find Mina 32 Monster meters
from the castle. Ask the students
why Multiplex could not see Mina.
PAUSE POINT FOUR
Sideline SuggestionsYour students will benefit from havinga number line to refer to during thesepause points.
Before viewing this episode, ask yourstudents to construct the number linesfrom the blackline masters in thisguide. Or your students may usemeter sticks.
When a call comes from sign number
20, it sounds like an easy breakdown
to find. But the car is not there. Ask
the students why.
PAUSE POINT FIVE
The numbers on the signs from the
castle to Positivity City are the same
as the numbers going from the cas-
tle to Negativityville. Ask the stu-
dents how can the drivers who need
help tell Multiplex where they are.
PAUSE POINT SIX
Sideline SuggestionsThe notion of integers is embedded inthis episode. Some everyday uses thatmay be familiar to young students aretemperatures on a thermometer, ele-vations above and below sea level andscore keeping procedures in gamesthat allow you to go “in the hole.”
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POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY ONEBuilding a Monster Town Road model
A model of Monster Town Road
will give your students a concrete
representation of the number line
in the episode.
YOU WILL NEED: Landmark
blackline masters #1–6, student
scissors, glue sticks and coloring
tools for this activity.
• Guide your students in building a
model of the Monster Town Road.
Cut out the number line and glue
the tabs together to create a road
to Positivity City from 1 to 100 and
Negativityville from 1 to 100. The
picture of the castle on Landmark
blackline master #3 belongs in the
middle. (Save the figure of
Multiplex for Post Viewing Activity
Two.) Glue the tab to the back of
the castle so that the two number
lines extend out opposite of one
another.
• Ask your children to draw a line
under the numbers or color the
direction going to Positivity City
in green and the road to
Negativityville in blue. Use the
same landmarks as the monsters
to count to 100 by tens. Explore
the different sets of landmark
numbers that the monsters could
have used such as 5s or 25s. Ask
your students why they think these
numbers were not used by the
Monsters to mark the road.
• Now put a red box around each of
the landmark numbers used by
the monsters. What number did
the monsters use to mark the cas-
tle? Use the model of Monster
Town Road to discuss how many
roads go in two directions from
one point.
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POST VIEWING ACTIVITIES
POST VIEWING ACTIVITY TWO
Multiplex to the Rescue is a num-
ber line game for the whole class.
YOU WILL NEED: Your students
will need the Monster Town Road
number line from Activity One. In
addition, your students will cut out
the Multiplex marker from the
blackline Landmark master #3.
• Give your students directions and
send Multiplex to the Rescue from
his castle headquarters. For exam-
ple, “Hello, is this Multiplex Tow?
I have a flat tire and I am between
the green sign 20 and the green
sign 30.” Your students then move
the Multiplex marker to the num-
ber 25. The teacher may keep this
activity simple by having Multiplex
always begin his rescue mission
from the castle. Or, the emergency
call created by the teacher can eas-
ily lead the students to thinking
about “which way?” as well as
“how far?” by moving from one
emergency call to another.
Multiplex to the rescue!
Sideline SuggestionsThis activity offers a wide range of flex-ibility to meet your students develop-mental learning needs. Create theemergency calls for Multiplex to matchthe challenge level of your students.Have fun giving them the opportunityto ask you questions when your direc-tions are purposely vague. What wouldyou ask the caller before you headedout on the road to find them?
POST VIEWING ACTIVITY THREE
Can You Find Multiplex on the
Road? is an activity in communi-
cation and reasoning.
YOU WILL NEED: each student
needs a Monster Road Number
Lines from Activity One, one
Multiplex marker from Activity
Two and a set of beans or small
chips as markers.
• Working in teams, the students
will sit back to back with their
number line in front of them. One
student will place the Multiplex
marker on their number line and
keep the location a secret.
The second student will ask yes or
no questions to try and find the
secret location of the Multiplex
marker on their partners number
line. The student asking questions
will use the beans or chips to mark
the places on the number line that
their questions have eliminated as
possible locations.
For example, a student begins the
game by placing the Multiplex
marker on the green number 30.
The second student asks, “Is
Multiplex on the green road?”
Because the answer is yes, all num-
bers on the blue road are eliminat-
ed. In this case the student will not
need to mark all of the numbers on
the blue road. But, remember that
Multiplex is not on a blue number.
The the student may ask,”Is
Multiplex on a number higher than
50?” A yes or no answer will elimi-
nate another 50 possibilities.
Through the process of elimina-
tion, the student asking questions
will find the secret location of the
Multiplex marker. Ask your stu-
dents to play the game several
times. Discuss the strategies they
used to help them find the
Multiplex marker more quickly.
Can you find Multiplex on the road?
Sideline SuggestionsThe challenge level of all post viewingactivities is flexible. You may limit thenumber line that your students workby simply folding or cutting in short-er. For example, it may only span asfar as 10 or 20 or perhaps 50 in eachdirection.
POSITIVITY CITY NUMBER LINELANDMARK #1
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POSITIVITY CITY NUMBER LINELANDMARK #2
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POSITIVITY CITY NUMBER LINELANDMARK #3
MA
RK
ER
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NEGATIVITYVILLE NUMBER LINELANDMARK #4
9
NEGATIVITYVILLE NUMBER LINELANDMARK #5
10
NEGATIVITYVILLE NUMBER LINELANDMARK #6
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