1. annotated bibliography - markgregorylyons.weebly.com · web viewmathematics summative...
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Running head: MATHEMATICS SUMMATIVE ASSIGNMENT 1
Mathematics Summative Assignment
Mark Lyons
EDUC 5433 – Elementary School Math Methods
March 2, 2016
Dr. Shaunda Wood
MATHETMATICS SUMMATIVE ASSIGNMENT 2
1. Annotated Bibliography Area of Interest: Decimals, Fractions, and Percentages
Barmby, P., Bilsborough, L., Harries, T., & Higgins, S. J. (2009). Primary mathematics:
Teaching for understanding. Maidenhead, England: Open University Press. Retrieved
from: http://unb.worldcat.org.proxy.hil.unb.ca/title/primary-mathematics-teaching-for-
understanding/oclc/609854883&referer=brief_results
Barmby, Bilsborough, Harries, and Higgins all mention different methods for teaching
decimals in chapter 6 of this book. In particular they focus on how students can use volume to
represent decimals, with a base-ten thousands cube to represent 1, a hundreds square for 0.1, tens
for 0.01, and a ones cube for 0.001; this method also works when a teacher cuts up tubes to
represent these amounts. For adding or subtracting decimals they mention using a number line to
bring the decimal to the nearest unit. When a student needs to multiply or divide decimals they
can use the grid method. For example if a student is given 25.2 X 0.35 as a problem then they
can break it down to 20, 5, and 0.2 on top of the gird horizontally, while 0.3 and 0.05 are
vertically on the left side of the grid.
Methods such as these are useful because the manipulatives, number lines, and girds
allow a teacher to teach the students to break down the numbers into a simpler form. The
students can then put the numbers back together once they have solved each equation. These
methods can also be used for fractions with denominators by ten. This is because the decimals
and denominators by ten are related to each other, and work when converting decimals to
fractions or vice versa.
Beaman, B. (March 01, 2013). Sunny with a chance... of tenths! Using the familiar context of
temperature to support teaching decimals. Australian Primary Mathematics Classroom,
18, 1). Retrieved from:
http://unb.worldcat.org.proxy.hil.unb.ca/oclc/5817573658&referer=brief_results
Beaman explains how she taught decimals under the context of temperature, using tenths,
to her grade 5 class of 27 students. She states that students needed to learn using decimals to the
MATHETMATICS SUMMATIVE ASSIGNMENT 3
point where they comfortable and can apply them to real life context. From here Beaman’s class
began observing hourly changes in temperature outside for five days and placing their findings
on a line graph. After some time Beaman describes using the higher/lower game, where students
guessed what the temperature at 9 o’clock in the morning. When the class concluded that it was
above 15 degrees but below 16 degrees there was confusion until a student stated that the
temperature must be in tenths.
Decimals were then taught by Beaman acting as a weather lady, having students place
estimations on the temperature from the previous afternoon. This was done to get the students to
rationalize and explain their estimation. Students then would compare the numbers in
temperature by adding or subtracting the decimals to find the change in temperature from each
hour. This technique is useful because students need to learn how to tell temperature through
numbers and understand how a change in temperature can impact their wellbeing. It is a practical
way to approach teaching this portion of the curriculum.
Haylock, D. (2001). Numeracy for teaching. London: Paul Chapman. Retrieved from:
http://unb.worldcat.org.proxy.hil.unb.ca/title/numeracy-for-teaching/oclc/
297107750&referer=brief_results
Haylock, in chapter six of Numeracy for teaching, mentions strategies for getting students
to think of decimals as a number rather than focusing on the decimal point. Grouping into sets of
ten can be used to teach the students the numbers and terms involved with decimals. Students
can then be taught that in a number with decimals the number on the left is worth ten times more
than the number on the right. The number on the right is worth one tenth as much as the number
on the left.
To explain this students can think of it as arrows going to the right of a number as
dividing by 10, while an arrow to the left would be multiplied by 10. This basic method can be
elaborated upon by using manipulatives such as base ten blocks, ten-by-ten squares, and number
lines. It is useful to teach students this because it gets them to focus on an entire number rather
than focus on the decimal points.
MATHETMATICS SUMMATIVE ASSIGNMENT 4
May, L. (February 01, 1995). Using Models to Extend the Meaning of Decimals. Teaching Prek-
8, 25, 5, 24-25. Retrieved from: http://unb.worldcat.org.proxy.hil.unb.ca/title/using-
models-to-extend-the-meaning-of-decimals/oclc/19530425775658?referer=brief_results
May uses money in this article as a way to teach decimals, with the dollar value
representing the ones, tens, hundreds, thousands, and so on. The cents can at least represent the
tenths and hundredths place in a number. She also mentions using a meter stick for teaching
students decimals through meters, centimetres, and millimeters. Students can also learn through
base ten blocks by representing the ones, tenths, hundredths place, and so on. This method of
teaching decimals is useful because money is common factor in everyday life and many careers
depend on this and measurement.
May, L. (April 01, 2000). Another Look at Decimals and Percent. Teaching Pre K-8, 30, 7).
Retrieved from:
http://unb.worldcat.org.proxy.hil.unb.ca/oclc/4601501880&referer=brief_results
May describes decimals as a subset of fractions in this article. She mentions the technique
where fractions with denominators at the power of 10 can be written as a decimal. A place value
chart can be used to get students to properly read the answer that is a decimal. Next May stresses
the importance of changing decimals to percent and vice versa because of the amount of
computing that is done in our world. From here she uses a triangle example as a method to use
all three types of the percent problems, with the order of the method being the top (is), bottom
left (of), and bottom right (percent).
For example, if the top is 80 and the bottom left is 320 then the question would be 80 is
what percent of 320? (25%). This method of using a shape to solve the three types of percent
problems is useful because the three types are related to each other and it connects decimals,
percents, and whole numbers together. By connecting these factors together students will be able
to relate this connection with the triangle visual. After they are used to making this connection a
MATHETMATICS SUMMATIVE ASSIGNMENT 5
teacher can then use manipulatives and other forms of visuals to reinforce this method since it is
associated with shapes.
Sweeney, E. S., & Quinn, R. J. (January 01, 2000). Concentration: Connecting Fractions,
Decimals, and Percents. Mathematics Teaching in the Middle School, 5, 5, 324-28.
Retrieved from: http://unb.worldcat.org.proxy.hil.unb.ca/title/concentration-connecting-
fractions-decimals-and-percents/oclc/19530425079816?referer=brief_results
Sweeney and Quinn both describe a lesson covering decimals, fractions, and percentages
that can be taught over three separate days. Students are given a preassessment sheet to define
these factors and to use the language associated with each factor. Next it is recommended to
show the class cards of circles that are half shaded or shaded in one quarter. The main idea is to
get students to use language that would describe the way it is shaded. Next the students are given
a geoboard and two rubber bands, with a region on the geoboard shaded. One band represents a
whole number and the other a partition number. Students explain their answers in a similar
fashion to before.
Students can then create their own game of concentration by creating 32 cards, with four
sets matching in value (i.e. 0.5, 50%, 1/2, visual, and so on). Once all students have written and
cut out their cards a teacher can then collect the cards and mix them up on a large table. Students
then gather around the table and take turns flipping them until the find a match, until all
matching pairs have been flipped. When the students have completed this game they can try a
version where the pairs found are linked together (now four), flipped, and then the student must
find the four cards that match. This activity can also be done in sets of numbers on smaller, four-
by-eight trays so individual students or smaller groups can play.
A post assessment quiz can then be provided to the students with questions that are the
same are the preassessment sheet to see what they have learned. These activities are useful
because they associate the values of decimals, fractions, percentages, and visuals all together,
getting the students familiar with the terms and making connections between these factors. It also
gets the students out of their seats, cooperating and communicating with their peers, and creating
their own materials.
MATHETMATICS SUMMATIVE ASSIGNMENT 6
2. STEM: Full Lessons
School of Education
Lesson (2 Classes)
Grade Level: 4
Subject: Mathematics
Date: March 4, 2016
I. Provincial Curriculum Outcome(s):
GCOs
N: Develop number sense
SCOs
N8: Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representationsto:
- name and record fractions for the parts of a whole or a set- compare and order fractions- model and explain that for different wholes, two identical fractions may not represent the
same quantity- provide examples of where fractions are used.
N9: Describe and represent decimals (tenths and hundredths) concretely, pictorially and symbolically.
N10: Relate decimals to fractions (to hundredths).
II. NCTM Outcome(s):
Number and Operations—Fractions 4.NFUnderstand decimal notation for fractions, and compare decimalfractions.6. Use decimal notation for fractions with denominators 10 or 100. Forexample, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate0.62 on a number line diagram.
MATHETMATICS SUMMATIVE ASSIGNMENT 7
III. Materials & Resources (Teacher Materials, Student Materials etc.):- Flipchart- Base-ten grids- Weighing Scale- Pennies- Beads (necklaces)- Duotang math journals- Markers- String for necklaces- A set of weights (approximate weight)
o 0.45 kgo 0.90 kg o 0.135 kgo 0.18 kgo 0.225 kg
IV. Technology Used (if appropriate): (Text, Audio, Video-based Resources, Web address, Maps, Charts etc.)- None
V. Plan:
Engagement (15 Minutes)
At the start of class tell the students that percentages, fractions, and decimals are all
numbers but each word is a different way of writing values. Explain that each one can
just be different names for the same quantity value.
Record this information on the whiteboard. Next define the meaning of the word cent
and percent. Ask students to write these list of terms below in their math journals.
List of terms:
Percent – means out of 100, using the % sign as a way to write percent.
Fraction – part or proportion of a whole value.
Decimal – relating to “base 10”, number in tenth parts, and powers of ten.
Cent - a hundredth part of the unit of the money system
Have the students then stand up and line up for a mock attendance. Ask one student
MATHETMATICS SUMMATIVE ASSIGNMENT 8
volunteer to step out and be “absent” from class. Write the class amount on the board as
a fraction and include all the students who are present in class. Ask the students what
the amounts are for percent, decimal, and fraction.
Exploration (20 minutes)
Have a jar of pennies and ask each group to place a number of pennies on a base ten
grid (not exceeding 30) and ask them to write that as a percent, a fraction, and a decimal
(see appendix A).
Then distribute bead necklaces of different colors and ask the students to count the
beads and write their answers next to the corresponding colors. Then ask the students to
add all the beads up and write the total on the chart under the correct column (see
appendix B).
Next ask the students to find the percent of beads in each necklace from the total.
Remind them that the percentages should total to one hundred and to double check their
answers.
Explanation (15 Minutes)
Now have each student weigh their necklace on the scale and have them record the
weight on the chart. Add total weight of the beads and then find the percent of each.
Tell the students that it costs a manufacturer approximately $1.50 to produce one bead
(hypothetically high quality beads, explain to the students that these are not the real
prices for the beads). Write these amounts for each of their colours on the chart. Then
ask the students to find the total cost for the manufacturer.
Write store prices for the beads to be $2.50 each. Let them find the profit the store
makes and find the profit as a percent of the cost.
Expansion (10 Minutes) – Class may end halfway through this section or before
MATHETMATICS SUMMATIVE ASSIGNMENT 9
this section of the lesson.
Have students look at the store price and calculate the amount of sales tax (15%) for all
of the beads. Then have the students add the amount of sales tax to the store price.
Explain to the students that this is the total cost for the consumer purchasing a necklace
with these beads
Give each student a necklace string and have the students test how much weight they
can hold. Make sure the students write down the breaking point on their Designing a
Necklace sheet (see appendix B).
Evaluation (15 Minutes)
Ask students to come up with seven or eight titles of Disney movie classics. Have them
vote on their favorite movie and then find the percent of student votes each title
received. Have the students construct a chart using multi-colored bar graphs to show
those percentages on flip chart paper in pairs of three. Assign the students a number
from 1-5 on and pair up based on the number they receive. Each group will design their
own graph for this part of the lesson.
Students will write an exit slip on a piece of paper for the follow question:
“How could you apply what you have learned to a real situation? What situations can
you think of aside from designing necklaces?”
VI. Accommodation(s) for Diverse Learner(s):
Differentiation
If students are in need of enrichment then provide different types of string for students to
test, such as leather, yarn, hemp, steel, etc. Allow these students to make detailed hypotheses
about what each necklace could hold in kilograms and allow these students to test their
theories with the weights. This could also apply to students who struggle with understanding
MATHETMATICS SUMMATIVE ASSIGNMENT 10
the content of this lesson. Allow students who struggle to move around the room, trying
different types of string and to make point-form hypotheses.
VII. Evaluation/Assessment of Student Progress:
Exit Slip
How could you apply what you have learned to a real situation? What situations can you
think of aside from designing necklaces?
VIII. Lesson Plan Reflection:
1. Preparation and Research – Was I well prepared? What could I have done differently?
2. Written Plan – Was I organized? What did I learn that will help me in the future?
3. Presentation – Were the students involved? Was I clear in my presentation? How was the pacing?
4. Assessment – What did the class do? How do I know if they were successful? What should I change for next time?
IX. Appendices
MATHETMATICS SUMMATIVE ASSIGNMENT 11
Appendix A
Base Ten Grid
Percent:______________
Decimal:______________
Fraction:______________
Appendix B
MATHETMATICS SUMMATIVE ASSIGNMENT 12
Designing a Necklace
Please fill out the chart according the category
ColourCategory Blue Green Red Yellow Orange TotalColour Amount
Percentage of Beads
As a Fraction
Production Price
Store Price
Sales Tax
Total Price
Cost to produce one bead: $1.50
Store price per bead: $2.50
Sales Tax: 15%
Weight of beads (Total in kg):
Weight of single bead (kg):
Necklace weight breaking point (kg):
3. Review of Manipulatives or other resources
MATHETMATICS SUMMATIVE ASSIGNMENT 13
1) Cube Links
Description
Cube links are good for getting students to practice making geometric shapes, create
patterns, practice counting on, making estimations, sorting, designing objects, and so on. In
standard math curriculum they can be applied to measurement and data, number and operations,
algebraic thinking, and counting. They are a common classroom math manipulative and
generally most students enjoy using them for math problems, since they can select colours that
they prefer to use. This manipulative was selected by me because it requires little instruction to
be said to the students, and it is adaptable to be used across grades and the math curriculum. For
example, if a class were learning to create patterns that increase or decrease then a student could
start with a basic shape. From here the students could build upon the shape by creating two other
shapes that indicate a pattern increase or decrease.
MATHETMATICS SUMMATIVE ASSIGNMENT 14
2) Two Colour Counters
Description
Counters are great for counting on, creating concrete graphs, creating patterns, and much
more. This applies to operations and algebraic thinking, numbers and operations, and counting.
For creating patterns two colour counters can be used to create basic patterns such as AB, AAB,
ABB, ABA, and so on. Students can use the red side as the A pattern and yellow side as the B
pattern. This helps students get into the habit of identifying and recognizing patterns that are in
their everyday life.
MATHETMATICS SUMMATIVE ASSIGNMENT 15
3) Square Colour Tiles
Description
Square colour tiles can be used as counters, making patterns with one attribute, or used
for teaching fractions. They can also help students with poor conceptual abilities. For example
when counting or doing basic operations students can use the tiles as a physical representation of
numbers if they have trouble counting in their head. These tiles can also be used for teaching
geometry or even graphing data. An example could be creating a graph, with the colour tiles
representing the different categories, and a teacher could ask what the graph tells about the data.
MATHETMATICS SUMMATIVE ASSIGNMENT 16
4) Base Ten Blocks
Description
Base ten blocks can be used to teach basic mathematical concepts like place value,
addition, subtraction, number sense, and counting. Student can manipulate the blocks in different
ways to display numbers and patterns. Since they can be applied to whole numbers, decimals,
fractions, and percentages, I feel that they are a useful visual for students to use and manipulate. I
find that they are appropriate because these factors apply to life after primary schooling, with
students dealing with currency and most careers require a basic understanding on percentages,
decimals, and fractions. It can apply to voting in politics, collecting data for scientific statistics,
and so on.
MATHETMATICS SUMMATIVE ASSIGNMENT 17
5) Transparent Geoboards
Description
A transparent geoboard is a great manipulative because a student can create shapes, apply
area and perimeter, fractions, and transformations at all grade levels. I have selected transparent
geoboards because they can be seen clearly when held up in the air or can even be placed under a
projector due to its transparency. An activity could be designing a shape on one half of the
geoboard and constructing its reflection on the other half. Since they are a common math tool
students can become familiar with it by using elastic bands to create images, giving them a visual
for mathematical theories.
MATHETMATICS SUMMATIVE ASSIGNMENT 18
4. Mathematics Technology product to assist with teaching math concepts
1) Integrating Tech: Recording and Formatting Data
Below is a screenshot of a Microsoft Excel document. In my year as a Business Analyst
at New Brunswick Community of Fredericton I learned how to format and document information
on programs such as excel. With this in mind I will be able to teach students how create formulas
and equations for programs. This is good practice for careers that are always in high demand,
such as accounting or programming. If my students learn the basics of IF statements,
VLOOKUP’s, or RATE’s then they will begin to grasp basic concepts of programming and
mathematics.
2) Shapes and Spins Overview
Shapes and spins is an example of creating a basic math game that combines SmartBoard
technology and a board game. It was develop by Emily MacInnis and myself for teaching basic
geometric shapes to associate shapes with images. The main idea is that it will have students
reflect on results based on their move and make connections with past experiences. The students
MATHETMATICS SUMMATIVE ASSIGNMENT 19
may be able to develop a deeper understanding of relationships between numbers and shapes, as
well as identify the patterns associated with these factors.
Rules
Three to five students per board.
Shapes around board, players take turn spinning the spinner. There are twelve different
possible options on the spinner.
o The spinner has four shapes on it. Each shape is coloured, some shapes have
randomly assigned numbers (see Spinner Wheel picture below).
When a student lands on a shape they will first go to that shape. If the shape has a number
they go to the shape plus the additional number.
MATHETMATICS SUMMATIVE ASSIGNMENT 20
Once they get to the spot there may be additional tasks required. i.e. Trade places with
someone of your choosing.
Wheel Spinner Picture
MATHETMATICS SUMMATIVE ASSIGNMENT 21
Wordless Video Demonstration
3. Prezi on SMART Notebook
Here is a link for a Prezi on basic activities you can create or find for SMART Notebook.
Link: http://prezi.com/i-7paslrspbp/?utm_campaign=share&utm_medium=copy
MATHETMATICS SUMMATIVE ASSIGNMENT 22
6. Other Areas of Interest1) Science and Math Integration
MATHETMATICS SUMMATIVE ASSIGNMENT 23
Description
During my time at St. Thomas University, in the Bachelor of Education program, I
learned how to apply a science observation journal into an academic setting. This was useful for
my first field placement, particularly with You and Your World. I felt it was important to
integrate math and science together by having my students record the temperature, measuring the
rain amount (mm), and the time. These facts can be documented to compare data on line graphs
and students can begin to understand the importance of collecting information. Unfortunately I
did not get the chance to do this in my practicum but I was able to get the students in a habit of
gathering the information necessary for gathering data and analyzing it. Now I plan on
improving upon this in the future for my teaching practices.
2) Game Websites: ABCya.com
ABCya.com is a free to use website that allows students to improve their mathematical
skills by playing games related to this subject. It offers many different games that apply to
different grade levels and even has games related to the literacy.
One game in particular is a version of Pac-man, now retitled Math-man, where students
can choose to use the game to solve addition, subtraction, multiplication, or division equations.
MATHETMATICS SUMMATIVE ASSIGNMENT 24
Each time the user makes Math-man eat a question mark an equation will appear on the screen
and one correct answer will appear on the ghost. Math-man must eat each ghost with the correct
answer in order to proceed to the next level.
These games are great because they draw the students into using math without relating it
to the typical anxiety that some students associate with it. Since they are divided by grade each
game will have levels that increase in difficulty as they solve problems and equations.
7. References
ABCya.com, L.L.C. (2016). The Leader in Educational Games for Kids!. Retrieved from:
http://www.abcya.com/
Illinois Institute of Technology. (2013). Smile Program Mathematics Index. Retrieved from:
http://stem-works.com/external/lesson_plan/103
Learning Resources. (2016). Explore the World of STEM. Retrieved from:
MATHETMATICS SUMMATIVE ASSIGNMENT 25
https://www.learningresources.com/home.do