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©2016 Texas Education Agency. All Rights Reserved 2016 Mathematics Achievement Academy, Grade 2

Time for Cake Ms. Carol is sharing a cake with Samantha and Alan. Ms. Carol asks, “Do you want a slice of cake that is one-fourth of the cake or one-eighth of the cake?”

Samantha Alan

Do you agree with Samantha? Draw a picture to show why you agree or disagree with Samantha.

Do you agree with Alan? Draw a picture to show why you agree or disagree with Alan.

I would like to have a slice that is

one-fourth of the cake because fewer parts means bigger pieces!

I would like to have a slice that is

one-eighth of the cake because eight is more

than four!


Work Station 1 Materials:

Partitioning a Circle Partitioning a Rectangle Partitioning a Line Partitioning Wholes Station Summary Fraction circles — One set per group of four Cuisenaire® Rods — One set per group of four

Prompt students to work in groups of four to complete the activities. Use the Partitioning Wholes Station Summary to debrief the Work Station. Debriefing Questions:

How did you partition your model to represent the problem? Why? What happens as you share an item equally with more and more people? How did you label your model? Why?


Partitioning a Circle Cookie A There are 4 students who want to share a cookie. Use your fraction circles to partition the cookie into

4 equal parts. Outline and label one-fourth of the cookie.

Cookie B There are 8 students who want to share a cookie. Use your fraction circles to partition the cookie into

8 equal parts. Outline and label one-eighth of the cookie.

1 Which cookie has the most equal-sized parts? Cookie _____ 2 Does this cookie have the larger or smaller equal-sized part?


Partitioning a Rectangle Candy Bar A There are 2 students who want to share a candy bar. Determine the rod that is one-half of the whole. Use your rods to partition the candy bar into two equal parts. Outline and label one-half of the candy bar.

Candy Bar B There are 4 students who want to share a candy bar. Determine the rod that is one-fourth of the whole. Use your rods to partition the candy bar into four equal parts. Outline and label one-fourth of the candy bar.

Candy Bar C There are 8 students who want to share a candy bar. Determine the rod that is one-eighth of the whole. Use your rods to partition the candy bar into eight equal parts. Outline and label one-eighth of the candy bar.

1 Which candy bar has the fewest equal-sized parts? Candy Bar _____ 2 Does this candy bar have the larger or smaller equal-sized part?


Partitioning a Line Licorice Stick A There are 2 students who want to share a licorice stick. Determine the rod that is one-half of the whole. Use your rods to partition the licorice stick into two equal parts. Outline and label one-half of the licorice stick.

Licorice Stick B There are 4 students who want to share a licorice stick. Determine the rod that is one-fourth of the whole. Use your rods to partition the licorice stick into four equal parts. Outline and label one-fourth of the licorice stick.

Licorice Stick C There are 8 students who want to share a licorice stick. Determine the rod that is one-eighth of the whole. Use your rods to partition the licorice stick into eight equal parts. Outline and label one-eighth of the licorice stick.

1 Which licorice stick is partitioned into the most equal-sized parts? Licorice Stick _____ 2 Does this licorice stick have the larger or smaller equal-sized parts?

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Partitioning Wholes Station Summary Use the Word Bank to complete the sentence frames.

Word Bank

halves eighths fourths

smaller larger

1 The name of 2 equal parts that make a whole is _____________________.

It takes 2 _____________________ to make one whole.





4 The more fractional parts used to make a whole, the ________________________

the part.

5 The fewer the fractional parts used to make a whole, the _____________________

the part.



Identifying Examples and Non-examples Identifying Examples and Non-examples Cards—One set for group of two

students Scissors Tape or glue

Prompt students to work in groups of two to complete Identifying Examples and Non-examples. Debrief:

Did counting the number of parts help you determine whether the shape on the cards was an example or non-example of fourths or eighths?

How did you determine if the parts were equal after you decomposed the rectangle into smaller parts?

Do parts of an object have to have the same shape in order for the object to be equally partitioned? Why or why not?


Identifying Examples and Non-examples Sort the Identifying Examples and Non-examples Cards into two

groups: o Examples of fourths or eighths o Non-examples of fourths or eighths

Use your sort to answer the questions below. 1 Which card(s) are non-examples of fourths or eighths?

Card(s): _____________________ 2 Which card(s) are examples of fourths or eighths?

Card(s): _____________________ 3 Choose 1 of the cards you think is an example of fourths or eighths.

Card ____

a) Cut the parts along the solid black lines to justify that the parts cover the same area. Tape or glue the parts below.

b) The rectangle I chose has ___ parts that cover the same area. One of

these parts is one-____________.

c) Do parts of an object have to have the same shape in order for the object to be equally partitioned? Why or why not?


Identifying Examples and Non-Examples Cards Cut along the dotted lines.

Card A

Card B

Card C

Card D



Sharing Candy Straws Candy Straws Cuisenaire® Rods Scissors

Prompt students to complete Sharing Candy Straws. Debrief:

What is the name of each part when you share equally between two people? Four people? Eight people?

How can you prove these are halves? Fourths? Eighths? How many halves did it take to make the whole? Fourths? Eighths?


Sharing Candy Straws

One strip of paper represents one candy straw. Use the rods to show how you can share one candy straw equally

between two people. Label each share of the candy straw with its size. Use your representation of a candy straw to complete the “Sharing with

Two People” section of the table. Repeat by sharing a candy straw equally among four people then eight

people. What is the size

of one share called?

Complete the statement

Sharing with Two People

one-________

The size is “one-________.” It takes exactly

_____ one-________ to make the whole.

Sharing with Four People

one-________



Sharing with Eight People

one-________




Candy Straws

Cut along the dotted lines. Six sets of candy straws are provided.


Small-Group Instruction Teacher Notes Materials:

Example and Non-Example Cards Paper Strips—three strips per student, cut Fraction circles—one set per student Cuisenaire® Rods—one set per student

Step A: Partitioning Using Fraction Circles or Cuisenaire® Rods 1. Distribute a set of fraction circles to each student. 2. Prompt students to identify the fraction circle that represents the whole. 3. Prompt students to use the fraction circles to partition the whole into two equal shares.

Note: The objective is for students to place the two half pieces on top of the whole. What is the name of one part? How many one halves represent the whole?

4. Repeat steps 2-3 to partition a whole fraction circle into fourths then eighths. 5. Does it take more fourths or eights to make a whole? Why? 6. Display a circle model showing halves, fourths, and eighths, then debrief the activity.

Which fraction part needs the smallest number of equal-sized parts to make one whole? Which fraction part needs the largest number of equal-sized parts to make one whole? What did you notice about the size of the part when more equal-sized parts are needed to

make one whole? What did you notice about the size of the part when fewer equal-sized parts are needed to

make one whole? Step B: Examples and Non-Examples Option I: Display one Example and Non-Example Card at a time.

1. Does the picture correctly model ______? How do you know? Option II: Prompt students to sort the cards into two groups: examples and non-examples.

1. How did you determine in which group to place this card? 2. Look at the example cards.

Into how many equal-sized parts is the whole partitioned? What is the name of each of these parts?

Step C: Exploring Iteration 1. Distribute three Paper Strips and a set of Cuisenaire® Rods to each student. Each paper strip

represents one whole. 2. Prompt students to model halves with the Cuisenaire® Rods and to use the Cuisenaire® Rods

to determine the placement of a line to partition the paper strip into halves. How do you know your model represents halves?

3. Prompt students to label each section of the paper strip with the words “one half.” 4. Repeat steps 2-5 to partition the paper strips into fourths then eighths using iteration. 5. Display a paper strip showing halves, fourths, and eighths then debrief the activity.

Which model needs the smallest number of equal-sized parts to equal one whole? Which model needs the largest number of equal-sized parts to equal one whole? What did you notice about the size of the part when more equal-sized parts are needed to

equal one whole? What did you notice about the size of the part when fewer equal-sized parts are needed to

equal one whole?


Example and Non-Example Cards Cut along the dotted lines.

Card A Card B

Card C Card D

Card E Card F


Paper Strips

Cut along the dotted lines. Six sets of paper strips are provided.


G/T Modeling and Describing Multiplication Situations

Materials: G/T Modeling and Describing Multiplication Situations

Prompt students to complete G/T Modeling and Describing Multiplication Situations. Debriefing Questions:

How did you use the number line to represent the situation? How did you use the number line to solve the problem? How did you decide which model to use to represent and solve the problem?


G/T Modeling and Describing Multiplication Situations

Use a number line to model each situation. Describe the model by filling in the blanks or by writing your own

description. Answer each question. 1 Ms. White placed the cupcakes in 5 rows. Each row had 5 cupcakes. How

many cupcakes did Ms. White have altogether? Number Line:

Description:

________ rows of ________ cupcakes is equal to ________ cupcakes.

Answer: Ms. White had _____ cupcakes.

2 Ms. Grey made 3 bracelets. Each bracelet had 7 beads. What is the total

number of beads on the bracelets? Number Line:

Description:

________ bracelets with ________ beads is equal to ________ beads.

Answer: Ms. Grey had _____ beads.


3 Mr. Green planted 4 rows of corn. Each row had 10 corn stalks. What is the total number of corn stalks Mr. Green planted? Number Line:

Description:

Answer: Mr. Green planted _____ stalks of corn.

4 Mr. Black made 2 bowls of soup. He placed 8 crackers with each bowl. What is the total number of crackers Mr. Black placed with the bowls of soup? Number Line:

Description:

Answer: Mr. Black placed _____ crackers with 2 bowls of soup.


Modeling and Describing Multiplication Situations

Materials: Modeling and Describing Multiplication Match Modeling and Describing Multiplication Match Cards

Prompt students to complete Modeling and Describing Multiplication Match. Debriefing Questions:

How did you determine which model represented each situation? How did you determine which sentence best described each situation? Look at the two soccer ball situations. What is the total number of soccer balls in

each situation? Why does the model look different for each situation? Look at the two donut situations. What is the total number of donuts in each

situation? Why does the model look different for each situation? Look at the two flower situations. What is the total number of flowers in each

situation? Why does the model look different for each situation?


Modeling and Describing Multiplication Match

Match the picture that models each situation. Match and complete the description for each situation.

1 Terrance had 6 bags. He placed

5 soccer balls in every bag. How many total soccer balls did Terrance have?

Model:

Description:

2 Alexandria planted 7 rows of flowers in the garden. She planted 4 flowers in each row. How many flowers were planted in the garden?

Model:

Description:


3 Robert placed 10 donuts on every tray in the display cabinet. There were 3 trays in the display cabinet. How many total donuts did Robert place in the display cabinet?

Model:

Description:

4 Sylvia had 5 bags. She placed 6 soccer balls in every bag. How many total soccer balls did Sylvia have?

Model:

Description:


5 Robert planted 4 rows of flowers in the garden. He planted 7 flowers in each row. How many flowers were planted in the garden?

Model:

Description:

6 Emma placed 3 donuts on every tray in the display cabinet. There were 10 trays in the display cabinet. How many total donuts did Emma place in the display cabinet?

Model:

Description:


Modeling and Describing Multiplication Match Cards

Cut along the dotted lines.

_____ rows of _____ flowers is equal to _____ flowers.

_____ bags, each with ____ soccer balls, is equal to _____ soccer balls.

_____ trays with _____ donuts each is equal to _____ donuts.

_____ rows of _____ flowers is equal to _____ flowers.

_____ trays with _____ donuts each is equal to _____ donuts.

_____ bags with _____ soccer balls per bag is equal to _____ soccer balls.



Materials: Modeling and Describing Multiplication Situations Counters

Prompt students to complete Modeling and Describing Multiplication Situations. Debriefing Questions:

How did you use the counters to represent the situation? How did you use the counters to solve the problem? What shape does 5 rows of 5 cupcakes look like? 4 rows of 10 corn stalks? Why does putting objects in rows look like squares and rectangles?



Use counters to model each situation. Draw a picture of your model. Describe the model by filling in the blanks or by writing your own

description. Answer each question. 1 Ms. White placed the cupcakes in 5 rows. Each row had 5 cupcakes.

How many cupcakes did Ms. White have altogether? Picture:

Description:

________ rows of ________ cupcakes is equal to ________ cupcakes.

Answer: Ms. White had _____ cupcakes.


2 Ms. Grey made 3 bracelets. Each bracelet had 7 beads. What is the total number of beads on the bracelets? Picture:

Description: ________ bracelets with ________ beads is equal to ________ beads.

Answer: Ms. Grey had _____ beads on the 3 bracelets.

3 Mr. Green planted 4 rows of corn. Each row had 10 corn stalks. What is the total number of corn stalks Mr. Green planted? Picture:

Description:

Answer: Mr. Green planted _____ stalks of corn.


4 Mr. Black made 2 bowls of soup. He placed 8 crackers with each bowl. What is the total number of crackers Mr. Black placed with the bowls of soup? Picture:

Description:

Answer: Mr. Black placed _____ crackers with 2 bowls of soup.


Check Point: Modeling and Describing Multiplication Situations • Use your counters to model each situation. • Draw a picture of your model. • Describe the model. • Answer the question.

1 Manny has 4 rows of star stickers. Each row has 5 star stickers.

How many star stickers does Manny have altogether?

Picture:

Description: ________ rows of ________ star stickers is equal to ________ star stickers. Answer: Manny has ________ star stickers altogether.

2 Triana decorated 8 cupcakes. Each cupcake has 4 candies. How many total

candies did Triana use? Picture:

Description: Answer:


Modeling and Describing Division Situations: How Many Groups? Materials:

Counters or base-10 blocks Bonnie’s Birthday Bash

Prompt students to complete Bonnie’s Birthday Bash. Debriefing Questions:

How did you use the counters to represent the situation? How did you use the counters to solve the problem? How are all three problems similar to each other?


Bonnie’s Birthday Bash Use counters to model each situation. Draw a picture of your model. Fill in the blanks to describe your model. Answer each question.

1 Bonnie is having a birthday party. She is making treat bags to give to her

friends at the party.

Bonnie has 18 toy cars for the treat bags. She puts exactly 2 toy cars in each treat bag.

How many treat bags can Bonnie make? Picture: Description: 18 toy cars separated into groups of 2 toy cars makes ________ groups of toy cars. Answer: Bonnie can make ________ treat bags.


2 Bonnie is filling vases with flowers to place on the tables at the party. She has 27 flowers. She uses exactly 9 flowers for each vase. How many vases can Bonnie fill with flowers? Picture: Description: 27 flowers separated into groups of ________ flowers makes ________ groups of flowers. Answer: Bonnie can fill ________ vases with flowers.

3 Bonnie has 24 balloons to use as party decorations. She will place

bunches of balloons around the party room. She uses exactly 6 balloons to make each bunch. How many bunches of balloons can Bonnie make? Picture: Description:

________ balloons separated into groups of ________ balloons makes

________ groups of balloons.

Answer: Bonnie can make ________ bunches of balloons.


Modeling and Describing Division Situations: How Many In Each Group?

Materials:

Counters Julian’s Sticker Collection

Prompt students to complete Julian’s Sticker Collection. Debriefing Questions:

How did you use the counters to represent the situation? How did you use the counters to solve the problem? How are all three problems similar to each other?


Julian’s Sticker Collection Use counters to model each situation. Draw a picture of your model. Fill in the blanks to describe your model. Answer each question.

1 Julian is organizing his sticker collection.

Julian has 18 superhero stickers. He has 2 pages in his sticker book for the superhero stickers. Julian places the same number of stickers on each page.

How many superhero stickers does Julian place on each page? Picture: Description: 18 superhero stickers separated into 2 groups makes

________ superhero stickers in each group.

Answer: Julian places ________ superhero stickers on each page.


2 Julian has 27 airplane stickers. He has 9 pages in his sticker book for the airplane stickers. Julian places the same number of airplane stickers on each of these pages. How many airplane stickers does Julian place on each page? Picture: Description: 27 airplane stickers separated into ________ groups makes ________ airplane stickers in each group. Answer: Julian places ________ airplane stickers on each page.

3 Julian has 24 monster truck stickers. He has 6 pages in his sticker book

for the monster truck stickers. Julian places the same number of monster truck stickers on each of these pages. How many monster truck stickers does Julian place on each page? Picture:

Description:

________ monster truck stickers separated into ________ groups makes

________ monster truck stickers in each group.

Answer: Julian places ________ monster truck stickers on each page.


Check Point: Don’s Bakery Don had 36 donuts to place in his bakery’s display cases. He divided the donuts equally among 3 display cases. How many donuts did he place in each display case? 1 Does the question ask for the number of equal-sized groups or the

number in each group? 2 Use counters to model the situation. Draw a picture of your model. 3 Don placed ________ donuts in each display case. Don had 24 mini-cupcakes to display in the bakery. He could fit exactly 8 mini-cupcakes on one bakery tray. How many bakery trays did Don need to display the mini-cupcakes? 4 Does the question ask for the number of equal-sized groups or the

number in each group? 5 Use counters to model the situation. Draw a picture of your model. 6 Don needs ________ bakery trays for the mini-cupcakes.


Check Point: What Is the Problem? Tameka represented a math problem using counters. She drew a picture of her counters as shown below.

What could Tameka’s problem have been? Write a problem that could be modeled with Tameka’s counters.


Comparing and Contrasting Division Situations Materials:

Bonnie’s Birthday Bash (previously completed) Julian’s Sticker Collection (previously completed) Bonnie and Julian Comparing Cards – One set per group of 3-4 students

1. Prompt students to sort the comparison cards so that each statement is either true of

Bonnie’s Birthday Bash or is true for Julian’s Sticker Collection. Students may find it helpful to have their completed activities for reference as they sort the cards.

2. If a statement is true for both activities, prompt students to place the card in between the two sets of sorted cards. A sample is provided below:

Debriefing Questions:

How did you use the counters to represent each type of situation? How was the way in which you used the counters to solve Bonnie’s problems

different from the way you used the counters to solve Julian’s problems? How can you summarize the similarities in all of Bonnie’s problems? How can you summarize the similarities in all of Julian’s problems? What makes all of Bonnie’s problems different from all of Julian’s problems?

Bonnie’s Birthday Bash Julian’s Sticker Collection

Statement true of Bonnie activity

Statement true of Julian

activity

Statement true of both

activities


Bonnie and Julian Comparing Cards

Bonnie’s Birthday Bash

Julian’s Sticker Collection

The information in the problem told me the total amount of something.

The information in the problem told me the number of objects in each group.

To solve the problem, I had to determine the number of objects in each group.

To solve the problem, I had to determine the number of equal-sized groups.

The information in the problem told me the number of equal-sized groups.


Creating Multiplication and Division Situations Materials:

Creating Situations Cards – One set per group of three students Counters Blank paper or construction paper – One piece per group of two students

1. Prompt students to distribute the cards so each person has a different card. 2. Prompt students to fill in the blanks on their card to create a problem. 3. Prompt students to trade their completed cards within their group so each person has a

new card. 4. Prompt students to use counters to model the problem and to draw a picture of the

model on the back of the card. Students should use their model to determine the answer to the question being asked in the problem.

5. Prompt students to take turns explaining their models and solutions to their groups. 6. Select one or two examples of each problem card to share with the class. 7. Prompt students to work together with their group to create a new problem, using a

context of their choosing. The problem should either describe a situation where equivalent groups are being joined together or a set of objects is being separated into equivalent sets. Students should write their new problem on construction paper.

8. Select a few problems to share with the class. Prompt students to model and solve each problem as it is shared.

Debriefing Questions:

Are equivalent groups being joined together in this situation? Is a set of objects being separated into equivalent groups in this situation? Does this situation describe the number of equal-sized groups or the number of

objects in each group? How do you know? How did you use the counters to represent the situation? How did you use the counters to solve the problem? When you solved the problem, did you have any counters leftover? How could you

adjust the numbers in the problem to avoid leftovers?


Creating Situations Cards

Jack’s Candy Jack has __________ bags of candy. There are __________ pieces of candy

in each bag. How many pieces of candy does Jack have?

Laura’s Beads Laura has __________ beads to make bracelets. She needs __________

beads to make each bracelet. How many bracelets can she make?

Piper’s Buttons Piper has __________ buttons. She has __________ containers to keep all

of the buttons. She places the same number of buttons in each container.

How many buttons will go in each container?


Counting and Naming Fractional Parts

Materials: Counting and Naming Fractional Parts

Prompt students to work in groups of two to complete the Counting and Naming Fractional Parts. Students should use words to describe the fractional parts. Debrief:

How many halves equal one whole? If two halves equal one whole, how many half pieces were shown? How many half pieces does

it take to equal two wholes? How many fourths equal one whole? If two fourths equal one whole, how many fourth pieces were shown? How many fourth pieces

would it take to equal two wholes?


Counting and Naming Fractional Parts One whole equals:

1 What fractional part of the whole is shaded? _____________________________

2 What fraction is represented by the shaded parts? ________________________






Check Point: Fraction Prediction

1 Circle the piece you predict to be one-fourth of the bar shown above.

2 Use the Cuisenaire® Rods to check your estimate.

3 Complete the statement to describe the part of the strip circled above.

The size is “one-________” because it takes exactly _____ equal parts to

make the whole.

time for cakejukebox.esc13.net/psgateway/k3math/gr2_teacher/g2_teacherresources_d3.pdftime for cake...

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