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.

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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.

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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.

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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

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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

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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

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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

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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.

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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

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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

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6. Other Areas of Interest1) Science and Math Integration

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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.

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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:

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https://www.learningresources.com/home.do