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MATH_3_A_1 FRACTIONS SECTION 1 COMPOSE DECOMPOSE 2014_LES

Third Grade CurriculumFractionsSection: 1

Composing and Decomposing Fractions

Suggested Number of Days: 5 days

The suggested number of days includes instruction, practice, and mixed review time. Please review materials in advance to

allocate days based on the resources provided.

Topic TEKS Page

Composing and

Decomposing Fractions

Day 1:Part I-II

Day 2:Part III-V

Day 3:VI-VII

Day 4:Part VIII

Day 5:XIII

Day 6:Rotation Review

(found in additional resources)

Part I: Experience Before Label - Snowball ShowdownSnowball Showdown Record Sheet

Part II: Naming Fractions to Compose a Whole Object – ConcreteFraction Pieces IMN StripFocus Questions to DisplayFraction Record Sheet 1

Part III: Composing and Decomposing a Whole Object Using Unit Fractions – PictorialFraction Record Sheet 2

Part IV: Composing and Decomposing a Whole Object – ConcreteFraction Record Sheet A

Part V: Composing and Decomposing a Whole Object - PictorialFraction Record Sheet B

Part VI: Composing and Decomposing a Fraction - ConcreteFraction Record Sheet C

Part VII: Composing and Decomposing Fractions - PictorialFraction Rotation Record Sheet

Part VIII: Composing and Decomposing a Set of Objects - ConcreteParts of a Set Record Sheet

Part IX: Fractions on a Number Line to 1 WholeFractions on a Number Line Record Sheet

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Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-2015

Additional Resources:

MATH_3_A_2 FRACTIONS SECTION 1 of 4 PRACTICE 1 2014_RESMATH_3_A_3 FRACTIONS SECTION 1 of 4 PRACTICE 2 2014_RESMATH_3_A_4 FRACTIONS SECTION 1 of 4 PRACTICE 3 2014_RESMATH_3_A_5 FRACTIONS SECTION 1 of 4 FRACTION BOOK 2014_RESMATH_3_A_6 FRACTIONS SECTION 1 of 4 MINI 1 2014_RES


NOTE: **Target Questions** are included for use in conjunction with the Teacher Notes. In the Practice Problems, some are marked with an “*”. It is suggested that you include these problems in your unit. There is also a model window pane problem on some target problems to use as a Guided Practice. Additional problems are also included as needed.

Note: Bolded sentences are teacher talk and () are student talk.

Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-2015 1

Additional Resources:

MATH_3_A_2 FRACTIONS SECTION 1 of 4 PRACTICE 1 2014_RESMATH_3_A_3 FRACTIONS SECTION 1 of 4 PRACTICE 2 2014_RESMATH_3_A_4 FRACTIONS SECTION 1 of 4 PRACTICE 3 2014_RESMATH_3_A_5 FRACTIONS SECTION 1 of 4 FRACTION BOOK 2014_RESMATH_3_A_6 FRACTIONS SECTION 1 of 4 MINI 1 2014_RES


Fractions – Representing, Composing and Decomposing

TEKS 3.3 A: The student is expected to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines; (supporting)TEKS 3.3 C: The student is expected to explain that unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero number; (supporting)TEKS 3.3D: The student is expected to compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b. (supporting) Vocabulary: fraction, numerator, denominator, fraction bar, part, total, whole, half, thirds, fourths, sixths, eighths, partition, equal, number line, strip diagramStudent Background: In second grade, students had experiences with fractions. They identified numerators and denominators for parts of a whole object and parts of a set of objects. They also had experiences with describing fractions on a number line as closer to

0, 12, or 1.

Teacher Background: Rational numbers can include whole numbers and numbers between whole numbers. A rational number can be written as a fraction comprised of a numerator and a denominator other than zero. The numerator represents the number of equal parts described. The denominator represents the number of equal parts the whole or unit is partitioned into. The terms whole and unit should be used interchangeably. A unit fraction ( 1b ) is 1 part of a whole

partitioned into (b) equal parts. For example, 14 is the unit fraction that 44 is comprised of.



Part I: Experience before Label – Snowball Showdown

The following activity is designed to help students understand the need for rational numbers (fractions and decimals).

Materials: cotton balls (1 per table), equally cut paper strips (10 per table), painters tape or masking tape.

Directions:Use tape to create a start line next to each student table.

1. As a table group, students will take turns tossing the snow ball (cotton ball) from the start line. The results of each student toss will be marked with tape. Students will work together to measure the distance of the farthest student toss. To measure the distance, students will use the pre-cut paper strips (non-standard unit of measure). Encourage groups to raise their hands when they have questions about their measurements. Students will quickly discover that the pre-cut strips, or wholes, are not precise enough accurately measure the marked distance. Facilitate a discussion with each group, or the entire class, to help them decide how to divide their last strip.

2. The group must agree on the measured distances and how to record each distance on the record sheet. The table with the longest recorded toss will win the snowball showdown.

3. Discuss the record sheet questions as a class.



Snowball Showdown Record SheetStudent Name Furthest Toss

Measure the distance of the winning toss. Distance: ______________

1. Did you need to make changes to your measurement tool to measure your snow ball toss? If so, explain the changes you made? ________________________________________________________________________________________________________________

2. Why did you need to make changes to your measurement tool?________________________________________________________________________________________________________________

3. Are there numbers between the whole numbers 1 and 2? How do you know?________________________________________________________________________________________________________________



Part II: Naming Fractions to Compose a Whole Object – Concrete

The following activity is designed to help students develop an understanding of a whole or unit, and introduce the relationship between the denominator and the size of each part or unit fraction. Materials: fraction circles: halves, thirds, fourths, sixths and eighths, focus questions (1 to display), Record Sheet 1, dry marker and eraser, paper plates (2 different sizes),

Directions:1. Display the following question: Colby made several pizzas that were the same size. He cut each pizza into a different number of slices. Each pizza's slices were equal in size. How can you use the fraction circles to show different ways Colby could cut his pizzas?

2. “Arrange your fraction pieces to show different ways Colby could have cut his pizzas.” Student fraction pieces may look like this.

3. “Let’s take a look at the pizzas you have created. What do you notice?” (the pizzas are all the same size, cut into different amounts: halves, thirds, fourths, sixths, eighths; made of equal sized pieces, some pieces are big, some pieces are small) Fraction pieces should remain together for the duration of the activity.



4. “Look at the pizza cut into 3 equal sections and the pizza cut into 8 equal sections. What do you notice? Are the pizzas the same size?” (yes) “What about the equal sections? What do you notice?” (the pizza cut into 3 equal sections has larger pieces, the pizza cut into eight equal sections has smaller pieces) “Why?” (the first pizza is only cut into 3 pieces, so the pieces are larger. The second pizza is cut into 8 pieces, so the pieces are small there are smaller) “Look at all of the pizzas you have created? What do you notice about the pieces? (the more pieces the whole is divided into, the smaller the piece)

5. Students will apply their knowledge of this new concept to complete The Fraction Pieces IMN strip.

6. “Now let’s focus on the pizza that is cut into 3 pieces, or thirds.” Display the following scenario:

Colby decided to eat some of this pizza, so he put 1 slice on his plate. How can you show that he put 1 piece of pizza on his plate with your fraction circles?”

“Let’s draw a plate with our dry erase markers. What do we need to do with our fraction circles?” (put 1 piece on the plate) “Ok, let’s put 1 piece of pizza on the plate. “Let’s

show this on the first model on Record Sheet 1 by shading in 1 piece to show that 1 of 3 pieces, or one-third of the pizza is on the plate.”

6. “Now, let’s write the fraction of the pizza that Colby has on our record sheet. How many total slices were in the whole pizza?” (3) “This is our denominator. What do you think the denominator represents?” (the denominator tells the total number of pieces in the whole) “Yes, and the denominator is always recorded underneath the fraction bar. Let’s record our denominator under the fraction bar.”


3

Numerator

(fraction bar)

Denominator


7. How many slices did we shade in to represent the pizza Colby took? (1) “This is our Numerator. What do you think the numerator represents?” (the numerator tells how many equal parts are being described) The question above asked, how can you show that he put 1 piece of pizza on his plate with your fraction circles? We are describing 1 piece of pizza, so our numerator is 1. We always record the numerator above the fraction bar.”

8. So, Colby has 1 of 3 pieces of pizza, or one-third of the pizza. 13 is a unit fraction, because it represents 1 equal part of the whole fraction. Take a look at the pizzas on your table. Can you find another unit fraction?” (one-half, one-fourth, one- sixth, one-eighth)

9. “Now, let’s refocus on the pizza cut into thirds.” Display the following scenario:

Colby was very hungry, so he decided to take 2 pieces of pizza. What fraction of the pizza did he take?

“What do we need to do with our fraction circles?” (put another piece on the plate) “Ok, put 2 pieces of pizza on the plate. Let’s show this on the second model of Record Sheet 1 by shading in 2 pieces to show that 2 of 3 pieces, or two-thirds of the pizza are on the plate.”

10. “How many total slices were in the whole pizza?” (3) “What is this number called in the fraction?” (the denominator) “Where do we write the denominator in our fraction? (underneath the fraction bar) “Write the denominator under the


3

1 Numerator

(fraction bar)

Denominator


second shaded model.”

10. How many pieces of pizza did Colby take? (2) “What is this number called?” (the numerator) “Where do we write the numerator in our fraction?” (above the fraction bar) “Write the numerator under the shaded model. How many pieces did Colby take?” (2 of the 3 pieces or two-thirds of the pizza)

11. “Let’s continue to use the pizza cut into thirds.” Display the following scenario:

Colby was actually starving, and decided to take 3 slices of pizza. What fraction of the pizza did Colby take?

“How many total slices were in the whole pizza?” (3) “What is this number called in a fraction?” (the denominator) “Where do we write the denominator in our fraction?” (underneath the fraction bar) “Write the denominator under the third shaded model.”

12. “How many pieces of pizza did Colby take?” (3) “What is this number called?” (the numerator) “Where do we write the numerator in our fraction?” (above the fraction bar) “Write the numerator under the third shaded model. How many pieces of pizza did Colby take?” (3 of 3 pieces or three-thirds of the pizza)

13. “Let’s take a look at the last model. What do you see? What do you notice? (the numerator and denominator are the same, the whole pizza is shaded) “So, 33 = 1. When the numerator and the denominator are equal you have 1 whole.”

14. Show students a small plate and a large plate to represent a small and large pizza. Both plates should be partitioned into fourths and all fourths should be shaded in.



“Take a look at these two plates. What do you see? What do you notice?” (one is larger, one is smaller) “Yes, they are different sizes. Which one could represent a whole pizza?” (both pizzas) “Why?” (they both represent a whole because all four parts are shaded, 4 of 4 parts, or 44 are shaded, so they represent 1 whole) “So, what does this tell us about the size of a whole?” (wholes can come in different sizes)

15. “What if we look at only one out of four pieces of pizza? What fraction does that represent? (14 )

“Are the 14 pieces the same size on each of the pizzas?” (no, they are not the same size because the wholes are different sizes)


14 1

4


Fraction Pieces IMN Strip

You can choose 1 piece of cookie to eat. Shade in the piece you want to eat. Why did you choose that piece?

________________________________________________________

Tell me more about that.

________________________________________________________

You can choose 1 piece of cookie to eat. Shade in the piece you want to eat. Why did you choose that piece?

________________________________________________________

Tell me more about that.

________________________________________________________



Focus Questions

1. Colby decided to eat some of this pizza, so he put 1 slice on his plate. How can you show that he put 1 piece of pizza on his plate with your fraction circles?”

2. Colby was very hungry, so he decided to take 2 pieces of pizza. What fraction of the pizza did he take?

3. Colby was actually starving, and decided to take 3 slices of pizza. What fraction of the pizza did Colby take?




Fraction Record Sheet 1

numerator

denominator

(fraction bar)


Part III: Composing a Whole with Unit Fractions: Partner Activity

Materials: fraction pieces (you may use circles, squares, or fraction towers. This lesson is shown using the fraction circles), student Record Sheet 3

1. Students will work with a partner to complete row 1 on Record Sheet 3. They will shade and label all of the unit fractions on row 1.

2. Students will work with a partner to complete row 2 on their student record sheet. Students will shade a different unit fraction in each model and label each picture until they have shaded and labeled the whole.

3. Students will work together to answer questions 1 and 2 on Fraction Record Sheet 3.


18

14

12

16

13

14

14

14

14+ + + = 4

4


1. How can you determine how many unit fractions are needed to make a whole? ___________________2. What happens to the size of the unit fractions as the denominator gets bigger? ___________________


Fraction Record Sheet 2


Part IV: Composing and Decomposing a Whole Object – Concrete

The following activity is designed to give students hands on experiences with composing and decomposing fractions. Fraction towers are recommended for this activity as they are similar to the pictorial strip diagrams.Materials: fraction towers for each student, dry erase boards, markers and erasers, teacher Record Sheet ADirections:

1. “Let’s compose a fraction. Let’s compose 66 using the unit

fractions or 16

pieces out of the fraction towers. Take out a

whole and place it on the dry erase board laying it horizontally.

Why did we take out the whole?” (because it represents 66 )

2. “Let’s compose 66 using

16 fraction pieces, or unit fractions.

Use

your dry erase marker to label each piece until you make a whole.”

16

16

16

16

16

16

66 1

3. “What stayed the same throughout our number sentence?” (the denominator) “Why?” (because our whole is cut into 6 equal pieces) “In this situation, our numerator stayed the same as

well because each piece was 16 of the whole. In our solution,


+ + + + + = =


however, our solution our numerator is 6 because we put

together 6 unit fractions, or

16 ‘s to make

66 or 1 whole.

4. “We composed 66 using all unit fractions. Can you think of

another way to compose 66 ? Work with students at your table

to manipulate your fraction pieces into groups to show a

different way to compose 66 and record the number sentence

under your fraction pieces on your dry erase board.”

5. Have each table share their number sentences one at a time. Each

table should be creative in composing 66 . If a table has the same

number sentence as one that is shared aloud, they must try to create a

different number sentence to compose66 . A each table shares, the

teacher will record each number sentence on Record Sheet A using different colored pencils to show each fraction that is being used to

compose66 .

If a table shares the following:

26

26

26

66

The teacher’s record sheet will look as follows:


+ + = =

==

1

1


26

26

26

66

66

Notice each group of fractions is a different color. Teacher will model partitioning into sixths using the last strip diagram on Record Sheet A.

Fraction Record Sheet A


+ +


Part V: Composing and Decomposing a Whole Object: Pictorial

The following activity is designed to give students pictorial experiences with composing and decomposing fractions. Materials: fraction towers for each student, dry erase boards, markers and erasers, Record Sheet B

1. “Work with your table to manipulate your fraction pieces into

groups to show a different way to compose 88 and record the

number sentence under your fraction pieces on your dry erase board.”

2. Have each table share their number sentences one at a time. If a table has the same number sentence as one that is shared aloud, they must

try to create a different number sentence to compose 88 . As each

table shares, the teacher and students will record each number sentence on the record sheet using different colored pencils to show

each fraction used to compose88 .

3. Again, the teacher will model partitioning into eighths using the last strip diagram on Record Sheet B.



Fraction Record Sheet B



Part VI: Composing and Decomposing a Fraction – Concrete

Each student will need a set of fraction towers for the following activity.

1. “Let’s compose the fraction 58 . What unit fraction pieces will

you need to compose 58 ?” (

18 ‘s) “Why?” (because the

denominator is 8)

2. “Make 58 with your fraction towers.”

3. “How many18 ‘s, or unit fractions did it take to make

58 ?” (5)

“Why?” (because our numerator is 5.)

4. “Let’s decompose 58 . How do we decompose a number?” (break

it apart) “We could decompose 58 using unit fractions like this:”

18

18

18

18

18

58

5. “Work with your partner and use your fraction pieces to find

multiple ways to decompose 58 . Record your representations

on Record Sheet C. Partition the last strip diagram into

eighths, and shade the model to show how you composed 58 in

a different way.”


+ + =+ +


6. As students work, teacher should walk around the classroom to check for understanding.

Fraction Record Sheet C



Part VII: Composing and Decomposing a Fraction – Pictorial

The following rotation is designed to give students multiple experiences with composing and decomposing a fraction. This activity is written to be completed as 2 simultaneous, 3 way rotations.

Materials: fraction towers, Rotation Record Sheet (1 per table- the record sheets will stay at each table, and students will build apon what other students have already started)

Home Table:

1. As a table group, students will use unit fractions to label the shaded model and identify the number they will continue compose and decompose during the rotation activity.

2. After the group has named 56 using unit fractions, they will work

together to show a different way to compose 56 and shade the second

model in the Home Table section to show how they composed 56 .

Example representations include:


16

16

16

16

16+ + + + = 5

6

1

Home2

1

Home2


Rotation 1:

3. After the group has composed 56 using different groups of fractions,

they will rotate to the next table and review the multiple ways 56 is

composed at this table. Then, they will work together to show a

different way to compose 56 and shade the third model to show how

they composed 56 in a different way.


+ +OR

26

26

16

56=

+ 16 = 5

616++ 2

616

OR

36 = 5

626+


Rotation 2:

4. Finally, the group will rotate to the last table and review the multiple

ways 56 is composed at this table. Then, they will work together to

show a different way to compose 56 . They will partition the strip

diagram into sixths and shade the model to show how they composed 56 in a different way.

5. The group will return to their home table and review the multiple

representations of 56 on the record sheet.



Fraction Rotation Record SheetHome Table

Rotation 1

Rotation 2



Part VIII: Composing and Decomposing - Whole Set of Objects: Fruit Loops

The following rotation is designed to give students hands on experiences With composing and decomposing a set.

Materials: Fruit Loops or circle cut outs (8 per student), Parts of a Set Record Sheet

Directions:

1. Display the problem below.

2. Pass out 8 Fruit Loops to each student, and have students place them in the circle at the top of the record sheet.

3. Students will count the total number of Fruit Loops they have. Ask them where they should record this number in their fraction. (the denominator) Why? (because it is the total number of parts that are in the whole or group)Students will label the denominator for all colors. Ask students why they are doing this. (because the total amount of Fruit Loops will not change)


Scottlynn grabbed a handful of Fruit Loops on the way to school. She

grabbed yellow, red, green, purple, blue and orange Fruit Loops. What

fraction of each color did she grab?

Red = ❑8 Green = ❑8

Purple = ❑8 Blue = ❑8 Orange = ❑8

Yellow = ❑8


4. Now students will decompose the fraction by color and place the Fruit Loops in the corresponding box on their record sheet.

5. Ask students how many of their Fruit Loops are yellow. Ask students where they should put this number in their fraction. (the numerator) Why? (the numerator tells how many parts are being described) Discuss with students that ___ of 8 parts are yellow. If students do not have yellow Fruit Loops they

will label their fraction 08 to show that they have 0 of 8 Fruit Loops are

yellow.

6. Students will repeat step 5 and label the numerators until all colors are written as fractions.

7. Ask students how many total Fruit Loops they had. (8)

8. Ask students how they can check to see if they used all of their Fruit Loops when making the fractions for each color.

9. Finally, students will color and label the strip diagram to compose their factions to check to see if they composed a whole. Students should add their

numerators to see that they total 8. When students see a total of 88 , they

should recognize that by putting all of their fractions together they have

composed a whole, or that88 = 1 whole set of Fruit Loops.



Parts of a Set Record Sheet

Parts of a Set

Composing a Whole


Scottlynn grabbed a handful of Fruit Loops on the way to school. She grabbed yellow, red,

green, purple, blue and orange Fruit Loops. What fraction of each color did she grab?

Yellow = ❑❑

Orange = ❑❑Blue = ❑❑Purple = ❑❑

Green = ❑❑Red = ❑❑

Fruit Loops

= ❑❑


Part IX: Fractions on a Number Line to 1 Whole

The following activity is designed to give students hands on experiences with representing fractions using number lines and strip diagrams.

Materials: fraction towers (1 per pair of students), fraction book for each student (MATH_3_A_FRACTION BOOK 2014_RES.doc), Number Line Record SheetNote: It is suggested that the fraction book for students be pre-assembled.Directions:

1. Students will use fraction towers to help them create number lines and strip diagrams in the fraction book.

2. Pass out the fraction book to each student and have them use the edge of the flaps to draw the number lines in the fraction book.

3. Have students take the whole from the fraction towers and place on the number line. Have students notice that the number line starts with 0 and does not have an end number. Have students discuss with a partner what they predict the end number will be on the number line.

4. Now, have students put the whole fraction tower away and take out both halves. Keep the halves connected so they equal a whole.



5. Students can place the halves on the top portion of the fraction book.

6. Students can then place a ‘tick’ mark on the number line after the first half and label that mark 12. Then, ask students what fraction

they think they should label at the end of the number line. (22)

7. Ask students what 22 represents. (1 whole) Students can show that 22 = 1.



8. After labeling the number line, raise the top flap and use the ‘tick’ mark to partition the strip above the number line. Students can also label 12 or 1 of the 2 pieces in the strip diagram they have now created for halves.

9. Now, have students get the fraction towers out that represent thirds. Again, keep the 3 thirds together as a whole. Students will place the thirds on the next number line.

10. Repeat steps 6 – 8 to have students label the number line and strip diagram into thirds.

11. Continue to have students label the number lines and strip diagrams in the fraction book using fourths, sixths, and eighths.

12. Discuss with students that fractions do have other denominators besides 2, 3, 4, 6 and 8. However, in third grade we are only focusing on those.

13. Also, have students look at all of the fractions that represent 1 whole in their fraction book. Have students discuss why those all equal 1 whole.



Using the Number Line Record Sheet, students are going to practice labeling number lines by creating a strip diagram.

14. Have students look at the second number line. Circle two whole numbers that are neighbors. Ask students why they would be circling whole numbers that are neighbors. (because we want to look at the fractions that are between them).

15. Then draw a line from each whole number and extend lines to partition into sections. Number each section of the strip diagram.

16. Now, label each ‘tick’ mark on the number line with a 3 in the denominator, including the 1 (whole).

17. Ask students if this looks familiar? (Yes, we did this in our fraction book) Have students shade in the first section of the strip diagram and label the numerator.


33

321

10

3

33

13

321

10


18. Have students share with a partner what they think they should shade next. (shade the second section now) Ask students what they think the numerator will be. (2) Ask, why? (because we’ve shaded 2 equal pieces.

19. Let’s shade the third section and label the numerator.

20. Students can try to label the first number line with a partner using the same strategy. Depending on how students label the number line, you may want to do another one as guided practice or let them continue on working with a partner.


33

23

13

321

10

3

23

13

321

10



10

10

10

10

Fractions on a Number Line Record Sheet

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