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Place Value and Addition and Subtraction to 1000 1
st Nine Weeks
Investigations Unit 1 and 3 and The T-Shirt Factory by Fosnot SOL 3.1, 3.2, 3.4, 3.20 – See VDOE SOL Curriculum Framework for Details
Note: For help with setting a math community in the classroom, see the optional First Eight
Days of School in the Appendix 2, or Investigations Unit 1.
Big Ideas
The positions of digits in numbers determine what they represent
The groupings of ones, tens, and hundreds can be taken apart in different ways.
Addition and Subtraction are connected. Addition names the whole in terms of the parts, and
subtraction names a missing part.
Models can be used to solve contextual problems for all operations.
Numbers are related to each other through a variety of number relationships( i.e comparing and
ordering)
Anchor Experience
Fosnot: The T-Shirt Factory (through day 6)
Classroom Routines and Mini-lessons
Practicing Place Value
More or Less
What’s the Temperature? – every Wed.
Number strings from “Number Talks” or from “Mini-lessons for Extending Addition and
Subtraction” by Fosnot.
Calendar – smartboard calendar available at Smart Exchange – go to http://exchange.smarttech.com
and search for daily calendar, many include money, time, counting etc.
Resources
T-shirt Factory Fosnot
Based on students’ needs, use the following: Investigations: Unit 1 Inv.1 Hundreds, Tens, and Ones Inv.2 Working With 100 Investigations: Unit 3 Inv.1 Building 1,000 Inv. 2 Addition Inv. 3 Finding the Difference Inv.4 Subtraction Stories
Math Expressions : Volume 1, Unit 1, Lessons 1, 5, 6, 10, 11, 13 Volume 1, Unit 3, Lessons 1, 2, 3
Minilessons for Extending Addition and Subtraction (Fosnot)
VDOE Enhanced Scope and Sequence http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php
Comparing Numbers
Inverse Relationships
Addition and Subtraction
My Identity Is in My Pocket
Property Commute
Assessments
Example rubrics for Investigations activities are located in Appendix 2
Pre and post-assessment: Located in Appendix 1 of this document
Strategies
Models
Landmark Numbers
Splitting
Regrouping
Skip Counting
Varying adding on and removing
Constant Difference
T-Chart
Proof Drawings
Visual Representations
Vocabulary
Celsius
degree
Fahrenheit
analog/digital
difference
digit
equation
sum
number line
equivalent
greater than/less than
inverse relationship
Place Value
Expanded Form
Standard Form
Written Form
value
Online Resources/Games
VDOE Mathematics instructional video
http://www.doe.virginia.gov/instruction/mathematics/resources/videos/index.shtml
VDOE Vocabulary Word Wall Cards
http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml
Mathwire
http://www.mathwire.com/numbersense/morepv.html
Place Value Games
http://www.free-training-tutorial.com/place-value-games.html Virtual Manipulative Kit
http://highered.mcgraw-hill.com/sites/0073519456/student_view0/virtual_manipulative_kit.html
Suffolk County Resources
http://star.spsk12.net/
Rockingham County Resource page:
http://www.rockingham.k12.va.us/resources/elementary/3math.htm#1learning
Illuminations.com
VDOE enhanced scope and sequence
ABCYA.COM (100 Number chart and many other good things)
Investigations Smartboard activities
Data Analysis
1st Nine Weeks
Investigations Unit 2 and Supplemental Materials
SOL 3.17 – See VDOE SOL Curriculum Framework for Details
Big Ideas
A collection of objects with various attributes can be classified or sorted in different ways.
The same set of data can be sorted in different ways.
Data are gathered, organized, and compared in order to answer questions.
Different types of graphs provide different information about the data.
Anchor Experience
Investigations, Unit 2: Inv.1 Representing and Describing Categorical Data
Classroom Routines and Mini-lessons
More or Less
Guess My Rule
Today’s Number
What’s the Temperature? – every Wed Number strings from “Number Talks” or from “Mini-lessons for Extending Addition and
Subtraction” by Fosnot.
Calendar – smartboard calendar available at Smart Exchange – go to
http://exchange.smarttech.com and search for daily calendar, many include money, time,
counting etc.
Resources
Investigations Unit 2: Inv.1
Expressions Volume 1: Unit 3 Lessons 15, 16, 17
Enhanced Scope and Sequence
http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php
o Statistics Through the Year
o Data Mania (Part1)
Assessments
Enhanced scope and sequence activities and Investigations Unit 2 have assessments.
Rubric for Investigations at the end of this document.
Strategies
Models
representing information visually
organizing data
comparing data
interpreting data
picture graph
bar graph
Vocabulary
bar graph
picture graph
fewer
more
data
organize
columns
rows
title
axes
comparing
symbol
less
table
classify
survey
horizontal
vertical
label
key
representation
categories
Online Resources/Games
Create a Graph http://nces.ed.gov/nceskids/createagraph/
Data Analysis in the 3rd
grade
http://www.internet4classrooms.com/skill_builders/data_analysis_math_third_3rd_grade.html
VDOE Mathematics instructional video
http://www.doe.virginia.gov/instruction/mathematics/resources/videos/index.shtml
VDOE Vocabulary Word Wall Cards
http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml
Mathwire
http://www.mathwire.com/numbersense/morepv.html
Virtual Manipulative Kit
http://highered.mcgraw-hill.com/sites/0073519456/student_view0/virtual_manipulative_kit.html
Suffolk County Resources
http://star.spsk12.net/
Rockingham County Resource page:
http://www.rockingham.k12.va.us/resources/elementary/3math.htm#1learning
Illuminations.com
VDOE enhanced scope and sequence
ABCYA.COM (100 Number chart and many other good things)
Investigations Smartboard activities
Appendix
Part 1 Assessments
Name________________ Date_______________ Pre-Assessment Place Value and Addition and Subtraction Common Assessment
1. Which number is shown below? _______________
Draw a circle around the word form that goes with the number represented above.
forty-seven four hundred seven
seven hundred four seventy-four
2. Write the numbers, in words, that come just before and just after these numbers:
Number Before Number Number After
two
thirty-three
seven hundred seven
Name________________ Date_______________ Pre-Assessment Place Value and Addition and Subtraction Common Assessment
3. Write two numbers, in words, that are less than each of the following:
twelve____________________ ________________________
one hundred_______________ ________________________
thirty___________________ ________________________
4. What number is ten more than each of the following:
57 ____________
42 ____________
317 ____________
5. Write the number that is two more than each of the following:
78 ____________
355 ____________
99 ____________
6. Draw a circle around the greatest number in each set.
448 848 884 484
216 612 261 621
359 953 539 395
Name________________ Date_______________ Pre-Assessment Place Value and Addition and Subtraction Common Assessment
7. Write these numbers in order, from smallest to largest:
34 72 27 43
_______ _______ _______ _________
smallest largest
213 241 247 413
_______ _______ _______ _______
smallest largest
8. What number is pictured below?
_____________
Name________________ Date_______________ Pre-Assessment Place Value and Addition and Subtraction Common Assessment
9. Marie has 125 buttons in a box. If she puts ten buttons in a bag, how many bags can she
fill?
__________________
Will there be buttons left over? Yes No
How many will be left over? _____________________
10. Pat had 256 baseball cards in his collection. His brother gave him some baseball cards
and now he has 521 cards. How many cards did his brother give him?
Name________________ Date_______________
1. Nora took some books to school.
She gave four books to Tom and then put two books on her desk.
Which of the following number sentences shows how many books Nora brought
to school? Circle the correct number sentence.
4 + = 2 4 - = 2
+ 2 =4 - 4 = 2
2. Which represents 745? Circle the correct answer.
700 + 40 + 5 700 + 40
70 + 45 600 + 40 + 5
3. Which represents 2,584?
2,000+500 + 80 + 4 400 + 84
300 + 80 + 4 500+ 75 + 4
4. Which number is shown here? _________________
Name________________ Date_______________
4. Match the numbers in standard and word form. Draw a line connecting the
equivalent numbers.
724 three hundred twenty-four
324 two hundred thirty-seven
473 seven hundred twenty-four
273 four hundred seventy-three
5. The Walton Toy Company received orders from 12 stores for ten games each
during the holidays.
The Speedy Delivery Company billed them for shipping 1,200 games.
Was that correct? If not, what is the correct number? How do you know?
Show your work with pictures, words, or numbers.
Walton Toy Company sent _____ games.
For the problems below: Which is greater? How do you know? Show your work in
pictures, words, or numbers.
Name________________ Date_______________
6. 20 tens or 3 hundreds
7. 12 ones or 3 tens
8. 6 thousands or 35 hundreds
9. Jessie turned over four number cards. The numbers were:
Using 4 of the numbers, what is the largest
7 3 1 9
Name________________ Date_______________
number you can make?
___________
Using 4 of the numbers, what is the smallest
number you can make?
____________
Explain your answers with pictures, words, or numbers.
10. Jordan Candy Store has 1,421 jelly beans, Taylor Candy Store has 1,241 jelly
beans, and Fisher Candy Store has 1,142 jelly beans.
List the numbers in order from least to greatest number of jelly beans.
_______________ , ______________ , _____________
Name________________ Date_______________
11. Bobby drives from Staunton to Roanoke and then to Lynchburg. He travels a
total of 125 miles. Find the distance from Staunton to Roanoke using the map
below, explain your work using pictures, words, or numbers.
46 miles
?
The distance from Staunton to Roanoke is ___________.
12. Eight plums are needed to make a pie. If Max makes seven pies, about how
many plums will he need?
Circle the correct answer:
A. Fewer than 20 plums.
B. Between 20 and 40 plums.
C. Between 40 and 60 plums.
D. More than 60 plums.
Show your work with pictures, words, or numbers.
Staunton
Roanoke
Lynchburg
Name________________ Date_______________
13. Use the map to answer the following
questions.
About how far will Joe drive from his house
to Raleigh?
____________miles
About how far is Demonte’s house from
Raleigh?
_____________ miles
Show your work below.
14. Jacob rounded his sticker collection to the nearest thousands place. He had
about 4,000 stickers. How many stickers do you think Jacob might have actually
had? Explain your answer.
15. Compare two whole numbers between 0 and 9,999 using symbols (>, <, =).
48 ________ 78 129 ________ 129
705 _______ 792 1,653 _______ 1,655
Solve the following related fact sentences.
Name________________ Date_______________
16. 5 + 3= 8, so 8-3 = ____________
17. 8+9= 17, so 17-9 =____________
Write three related basic fact sentences when given one basic fact sentence for
addition or subtraction.
18. 9 + 7 = 16 ___________________
___________________
____________________
19. 14 - 6 = 8 ___________________
___________________
Appendix 2
The First Eight Days of School
Rubrics
Getting Started: Establishing Routines & Procedures in Grade 3 The First
Days of Math in Staunton City Schools
Overview
For students, a successful experience with math begins with the basics: how to think like an active mathematician, how to speak mathematically, and how to record and share their thinking. This guide may be extended, condensed, or modified according to students’ needs. As you prepare to implement the First Days of Math during the 60 minutes of math instruction, keep in mind that it will be necessary to be flexible. These 5-15 minute lessons are to be incorporated into the daily lesson. Grade level teams may meet periodically to monitor and adjust progress. Clear statements and clear demonstrations of roles and procedures need to be established. All points and aspects need to be repeated, charts or anchors of support are to be posted and referred to again and again.
Goals
The goals of implementing the instructional strategies included in this document are to
• help students think of themselves as mathematicians who enjoy and actively participate in
math;
• establish consistent classroom roles, routines and procedures that support teaching and
learning;
• increase rigor by having students explore, express, and better understand mathematical content through NCTM process skills (communication, connections, reasoning and proof, representations, and problem solving) that are listed on the following page.
Background
Based on the idea of The First 20 days of Independent Reading by Fountas & Pinnell,
these lessons have been developed to establish the roles, routines and procedures
needed for effective mathematics instruction.
Principles of Learning are the foundation of this document. All students are told
that they are already competent learners and are able to become even better through their
persistent use of strategies and by reflecting on their efforts. Criteria for quality and
work are explicit, accessible to all students, displayed publicly, and change over time to
respond to level of rigor as learning deepens.
NCTM Process Standards
Problem Solving Instructional programs from prekindergarten through grade 12
should enable all students to—
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 Instructional programs from prekindergarten through grade 12
should enable all students to—
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 Instructional programs from prekindergarten through grade 12 should
enable all students to—
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 mathematical ideas precisely.
Connections Instructional programs from prekindergarten through grade 12 should
enable all students to—
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 Instructional programs from prekindergarten through grade 12 should
enable all students to—
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
Day 1- We are all Mathematicians
Big Ideas We’re all mathematicians. Mathematicians work in an ordered environment with established routines and procedures for independent and/or cooperative math groups.
Learning
Outcomes
Students identify criteria to create a “Good Work” chart to post. Students understand and learn that information will be posted around the classroom for them to use to make their work better, to support their learning and to help them review concepts as they are learned.
Anchor
Experience
for Students
Focusing the Lesson I have a problem . . . I had 18 Tuesday folders this morning. I left some in Ms. Smith’s room. Now I have 9 folders. What could I do to figure out how many I left in Ms. Smith’s room? Have students work with a partner to think about the teacher’s problem. 5 min. into students working . . . Everyone pause in their thinking . . . Guess what I’m noticing: we’re all mathematicians! Look around the room. What do you think it means to be a mathematician? Have students share different ideas. Work Time This year we’re all going to be mathematicians as we learn and do math together. Mathematicians work in an ordered environment so we need to decide together what that will mean. Develop “Working like a Mathematician” process chart with class to which students can refer. (A good work chart should have less than 6 criteria to be effective.) Example below and on right:
• Stay on Task
• Speak/write mathematically
• Be an active listener and participant.
• Respect and organize math materials appropriately.
Activity to support
Finish task problem.
If math were an animal, what would it be? Whole class share. Were we
working like mathematicians? Let’s look back to our chart . . .
Materials Copy of task problem displayed Chart paper Markers
Teacher
Notes
Don’t worry if the kids only come up with a few ideas at first. It’s better if the
ideas are generated slowly and meaningfully by the students. Refer to the
process standards to make sure the kids include these.
** On day 6 students will be sharing a collection of 100 items. You will need to
make this a homework assignment prior to Day 6.
Day 2-Management
Big Ideas Mathematicians use math tools to think about math and help them solve problems.
Learning
Outcomes
Students become familiar with the math tools in the classroom.
Anchor
Experience
for Students
Focusing the Lesson If you had a mathematics toolkit, what tools would you want in it to help you think about math? Have students think with a partner. Whole class share. Work Time Take a tour of mathematical tools in classroom, how they are to be used and stored. What tools might have helped us with my problem from yesterday? How and why do mathematicians use tools?
Activity to support
Investigations, Unit 1.1-Ten-Minute Math, pg. 26 (Note-Use Interactive
Whiteboard)
Add notes to the “Working like a Mathematician” process chart about
placing materials in their proper storage containers and location after use.
Materials Various classroom manipulatives students will have available for use during the year, including at least 50 Unifix cubes per pair of students
Interactive Whiteboard CD from Investigations “Working like a Mathematician” process chart developed on Day 1
Teacher
Notes
Refer to the chart frequently over the first weeks of class. Use the chart to point out positive mathematical behaviors which you’re
seeing in individual students. Use the chart to give the class specific ways which they can improve their
mathematical behaviors. Add ideas as you recognize new ways the class is working as mathematicians
or as specific issues arise in the class.
Day 3-Problem Solving
Big Ideas Mathematicians use a process to think about and solve problems.
Learning
Outcomes
Students understand the importance of problem-solving every day.
Students learn that there is a process involved when solving problem.
Anchor
Experience
for Students
Focusing the Lesson Did you know mathematicians use a process to think about math? Why do you think they use a process? Whole class conversation. Develop a problem solving model with your class which you’ll use throughout the year. (One example is Polya’s 4-Step Problem Solving Model.) Add your class’s process to your “Working like a Mathematician” process chart or create a separate chart you can refer to throughout the year. Work Time
We’re going to use our process to think about a problem today. Remember
we’re working like mathematicians, so keep in mind what we’ve written on
our chart.
Students complete Problem A from Appendix.
Math Congress
Have students share how they worked like a mathematician to solve the
problem. After a student shares, have the class look back at the chart and cite
specific ways the student was working like a mathematician and/or using the
problem solving process.
Materials Problem A displayed or copied “Working like a Mathematician” process chart developed on Days 1 and 2 Problem solving model
Teacher
Notes
Post the chart on the wall in student-friendly language.
Day 4-Writing/Representations in Math
Big Ideas Mathematicians use and record mathematical representations to interpret and model everyday life activities.
Learning
Outcomes
Students understand that they are expected to write about their mathematical thinking on a daily basis.
Students understand that writing about their thinking is a way to represent mathematical concepts.
Students understand that the journal is a mathematical tool.
Anchor
Experience
for Students
Focusing the Lesson Today we’re going to use a mathematical tool we haven’t talked about yet: a journal. Does everyone know what a journal is? How could a math journal be a mathematical tool? Turn and talk to your partner. Whole class conversation. Develop a rubric with the class for expectations for thinking in their math journal. Work Time Let’s use your journal right now as a thinking tool.
Remind students of rubric as they respond to the following prompt: (choose
one)
Which do you like better, adding or subtracting? Why?
OR
Solve 14 – 9. Write down every step as if you were explaining how you
solved it to someone younger.
Ask a few students to share.
Activity to support
Have students work in pairs to solve Problem B from Appendix.
Select a few students to share their strategy for solving the problem.
How did thinking in your journal first help you to solve the problem? Class
debriefs. Try to highlight some of the big ideas in student responses.
Materials Problem B copied or displayed Chart paper for class rubric Student journals
Teacher
Notes
See the rubric in the Appendix.
Day 5-Vocabulary
Big Ideas Mathematicians use specialized terms to discuss mathematical ideas and build their knowledge.
Learning
Outcomes
Students understand that they will use specialized terms to discuss mathematical concepts.
Anchor
Experience
for Students
Focusing the Lesson I wonder if anyone has noticed the words which are on our word (strategy) wall. Let’s look at them for a few minutes. Does anyone recognize any of the words? Does anyone see a new word? Have a class conversation. Have you ever noticed how we use special words to talk about ideas in math? Why do you think we do that? Model how students will add new words in their journals and/or how words will be added to the classroom word wall. Work Time
Have students work in pairs to complete Problem C in Appendix. Remind
students to work as mathematicians and use a problem-solving process.
You’ll also be listening for mathematical terms from the Word Wall as they
talk together about how to solve the problem.
Select a few student groups to share how they worked through the problem-
solving process to solve the problem. After each student group shares, ask
the class if they heard any mathematical language from their classmates.
Activity to support
Materials Selected mathematical terms from vocabulary section of Unit 1 Curriculum Map posted on word wall
Problem C from Appendix, copied or displayed Student journals (to add mathematical terms in the back, if desired)
Teacher
Notes
As you introduce new vocabulary, students can record the word(s) in their journal. Have students write their definition of vocabulary word(s), make a real life connection, and draw a representation of the idea in the journal.
Introduce mathematical vocabulary, such as equation, by using terms yourself as they arise in mathematical work. If the introduction of such terms is accompanied by activities that make their meaning clear, students will begin using these terms naturally as they hear them used repeatedly in meaningful contexts.
Add terms or refresh word wall over the course of the year.
Day 6-Sharing
Big Ideas Mathematicians share their thinking strategies, listen to other mathematicians, ask questions, and make conjectures about their findings.
Learning
Outcomes
Students understand that sharing and learning from other mathematicians is an important part of working as a mathematician.
Anchor
Experience
for Students
Focusing the Lesson Yesterday after you solved the problem, some students shared how they worked through the problem-solving process. Why do you think mathematicians share? Sometimes it’s hard to know how to explain our thinking. What can we say when we’re not sure? When mathematicians are sharing, do the rest of us mathematicians have a job? What if we don’t completely understand the strategy that someone is sharing? What should we do then? I want to show you an aide to help us talk as mathematicians . . . (Appendix-bubble sheet)http://central.spps.org/information/staff/files/AccTalkV3.pdf One more thing . . . all mathematicians won’t share their thinking every day (why teacher won’t call on everyone). We’ve talked about a lot of different ideas related to sharing as mathematicians. What should we add to our chart? Work Time
Make a collection of 100. Your collection can be anything—pictures,
toothpicks, pebbles, and so on. How will you know you have exactly 100?
Scaffolding question to ask students who might be counting objects
individually- Is there a way you can group them to help you know?
Math Congress
Now it’s time to share. Look again at the bubble sheet and expectations
from “Working as a mathematician” chart.
Ask 3 or 4 students to share how they thought about counting their
collection of 100 items. Try to select students who might have used
different groupings, looking especially for a student who grouped by 10.
Point out skip counting as a strategy if a student demonstrates.
Debrief at the end of math congress what you noticed during the math
congress:
I noticed the way ___________________ was specific about explaining her
thinking. As mathematical listeners, could we have done anything
differently?
Materials Copy of task problem displayed “Working as a mathematician” chart Bubble sheet from appendix Items for students to collect and group
Teacher
Notes
Students must develop the habit of communicating their thinking in complete
sentences using mathematical terms correctly—it doesn’t happen automatically.
As teachers we must ask for and acknowledge when they successfully
communicate their thinking.
Day 7- Working Together
Big Ideas Mathematicians work collaboratively developing good work ethics and being responsible to other mathematicians
Learning
Outcomes
Students learn that they can work with others to share information and to learn new information.
Anchor
Experience
for Students
Focusing the Lesson Mathematicians work together a lot. We’ll work together as a whole class but we’ll also work with partners and small groups. Why do you think mathematicians work together? Can we learn more when we’re working with someone else? Why or why not? If I’m a mathematician working with another mathematician, what responsibilities do I have to my partner? Turn and talk to your partner about 3 ways you’re going to be responsible to each other. Students share ideas. Establish rules for group work and add to chart. Work Time
Now you’ll have the chance to put those expectations into practice.
Introduce and engage students in the game Capture 5 (Investigations, Unit
1.5)
Journal
Have students reflect in their math journals about Capture 5 using the
following prompt:
Reflect on your participation in class today and complete the following
statements:
-I learned that I . . .
-I was surprised that I . . .
-I noticed that . . .
Materials Journal prompt displayed “Working as a mathematician” chart Student math journals
Teacher
Notes
Students must develop the habit of communicating their thinking in complete
sentences using mathematical terms correctly—it doesn’t happen automatically.
As teachers we must ask for and acknowledge when they successfully
communicate their thinking.
Day 8- Proof for your thinking
Big Ideas Mathematicians give proof for their thinking.
Mathematicians push each other for accurate proof, including references to ideas shared in previous classes, to deepen their understanding of a mathematical idea.
Learning
Outcomes
Students understand that they must prove their thinking.
Anchor
Experience
for Students
Focusing the Lesson If I have 2 pencils and John has 2 pencils, how many pencils would we have together? Let’s figure it out. Turn and talk to your partner. Teacher “works” the problem on the board by writing 2 + 2 = 5. When a student says it’s wrong, be adamant that it’s correct. Why? “Because I just know 2 + 2 = 5 . . . I just know it!” If you’re so sure I’m wrong, is there a way to prove it to me? Record a way to prove this to me in your math journal. Have 3 or 4 groups share. Point out different ways groups are providing proof, like a proof drawing or other kind of representation or actual manipulatives. Have a class conversation: Does it matter whether mathematicians have proof? Why or why not? How does proving your thinking help mathematicians to understand their work? What’s the different between proving your thinking and writing a number sentence? Do we need to add any ideas to our chart about how mathematicians prove their thinking? Work Time
Now you’ll have the chance to put those expectations into practice.
What might the missing numbers be?
_____ _____ + _____ = 32
Complete task problem independently in math journal. Remind students to
give proof in their journal entry.
Have 3 or 4 students share proof for their thinking, using the document
camera.
In summary
Let’s evaluate how we’re doing as mathematicians. Teacher reads over
“Working as a mathematician” chart.
What do we do really well as a class of mathematicians?
What are some areas that are hard for us/things we can focus on to get
better at during the next few weeks of math class?
Materials Task problem displayed “Working as a mathematician” chart Student math journals
Rubric Grades K-3
As a Mathematician, I can…..
Level
Understand the Math
Use a Strategy
and Reasoning
Communicate My
Thinking
4 (S+)
Superior
Work.
WOW
☺
I understand the problem very
well and have a complete plan to
solve it.
I complete all of the math in the
problem very well.
I get a complete and correct
answer.
I can use quite a few
strategies to get an answer.
I use good reasoning.
I can tell if my answer
makes sense.
I can think of how this
problem is like another
problem.
I can clearly explain my
answer and all of the steps.
I can record my thinking
very well on paper with
words, drawings and math
symbols.
I use the right words,
drawings and math symbols
all of the time.
3 (S)
Good work.
Got it
I understand the problem and
have a plan to solve it.
I complete all of the math in the
problem.
I get a complete and correct
answer
I can use one strategy to
get an answer.
I use some reasoning.
Sometimes I can tell if my
answer makes sense.
Sometimes I can think of
how this problem is like
another problem.
I can explain my answer
and most of the steps.
I can record my thinking on
paper most of the time.
I use the right words,
drawings and math symbols
most of the time.
Level
Understand the Math
Use a Strategy
and Reasoning
Communicate My
Thinking
2 (S-)
Incomplete
work.
I need some
help.
Not Quite
I understand only some of the
problem and I may not have a
plan to solve it.
I complete only some of the
math in the problem.
I get a wrong answer.
I might not have a strategy
or it is the wrong one.
My reasoning is not always
complete or helpful.
I try, but I do not know
how this is like another
problem.
I explain a little bit of my
answer but not the steps.
I record my thinking on
paper very little.
I use very few simple
words, drawings and math
symbols.
1 (N)
Beginner work.
I need a lot of
help.
I need help.
I am confused by the problem
and need help to solve it.
I do not complete all of the math
in the problem.
I get a wrong answer.
I don’t use any strategies to
get an answer.
I do not use reasoning.
I can’t tell if my answer
makes sense.
I can’t think of a similar
problem.
I do not explain my answer
at all.
I do not record my answer
or it is very confusing.
I get confused about which
math symbols to use.
Rubric for Assessing Student Understanding of Mathematical Concepts Grades K-2
Level Understanding Strategies and Reasoning Communication
4 (S+)
Superior
performance,
independence
Shows a superior understanding of the problem
including the ability to identify the appropriate
mathematical concepts and the information necessary
for its solution
Completely addresses all mathematical components
presented in the task
Puts to use the underlying mathematical concepts
upon which the task is designed
Solution must be complete and correct.
Uses a very efficient and sophisticated
strategy leading directly to a solution
Employs refined and complex reasoning
Evaluates the reasonableness of the solution
Makes mathematically relevant
observations and/or connections
Clear, effective explanation detailing how
the problem is solved; all of the steps are
included so that the reader does not need to
infer how and why decisions were made
Mathematical representation effectively used
Precise and effective use of mathematical
terminology and notation
3 (S)
Adequate
performance and
mastery
Shows an adequate understanding of the problem and
the major concepts necessary for its solution
Addresses all of the components presented in the
task
Solution must be complete and correct.
Uses a strategy that leads to a solution of
the problem
Uses effective mathematical reasoning
All parts are correct and a correct answer is
achieved
Clear explanation given
Appropriate use of accurate mathematical
representation
Appropriate use of mathematical
terminology and notation
2 (S-)
Meets competency
with assistance,
needs support and
practice
Shows a partial understanding of the problem and the
major concepts necessary for its solution
Addresses some, but not all, of the mathematical
components presented in the task
Incomplete solution, indicating that parts of the
problem are not understood
Uses a strategy that is partially useful,
leading some way toward a solution, but not
to a full solution of the problem
Some evidence of mathematical reasoning
Some parts may be correct, but a correct
answer is not achieved
Incomplete explanation; may not be clearly
presented
Some use of appropriate mathematical
representation
Some use of mathematical terminology and
notation appropriate to the problem
1 (N)
Has difficulty, even
with support
Shows limited understanding of the problem and the
major concepts necessary for its solution
Inappropriate concepts are applied and/or
inappropriate procedures are used
May address some of the mathematical components
presented in the task
Little or no evidence of a strategy or
procedure or uses a strategy that does not
help solve the problem
Little or no evidence of mathematical
reasoning
So many mathematical errors that the
problem could not be resolved
No explanation of the solution, the
explanation cannot be understood or it is
unrelated to the problem
No use, or mostly inappropriate use, of
mathematical terminology and notation
I DON’T KNOW WHAT TO SAY . . . I WANT TO
JOIN THE CONVERSATION
THINK MORE DEEPLY
Could you explain your answer?
I have a different opinion because . . .
What is your proof?
Say more about that . . .
Where do you see that?
I’d like to add to what _______ said.
Why do you think that?
I have a different opinion because . . .
Something else I noticed was . . .
I agree with what _____ said because .
. .
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