Math 3 a 1 Fractions Section 1Compose Decompose 2014 Les

MATH_3_A_1 FRACTIONS SECTION 1COMPOSE DECOMPOSE 2014_LES

Third Grade Curriculum

Fractions

Section: 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.

NOTE: **Target Questions** are included for use inconjunction 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.

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 diagram

Student 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, , 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 ( ) is 1 part of a whole partitioned into (b) equal parts. For example, is the unit fraction that 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 tomeasure the

distance of the fartheststudent 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, arenot 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

eachdistance 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 Sheet

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 waysColby

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 equalsections 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 3equal sections has larger pieces,

the pizza cut into eight equal sectionshas smaller pieces) “Why?”

(the first pizza is only cut into 3 pieces, so the pieces are larger.

The second pizzais 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 pizzathat 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 fractioncircles?”

“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

thison the first model onRecord Sheet 1 by shading in 1

piece to show that 1 of 3 pieces, or one-thirdof 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 ofpieces in the whole) “Yes, and the denominator is

always recorded underneath thefraction bar. Let’s record

ourdenominator under the fraction bar.”

7. How many slices did we shade in to represent the pizza

Colbytook? (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.

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:

Colbywas 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 of3 pieces, or

two-thirdsof 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

secondshaded 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 ortwo-thirds of the pizza)

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

following scenario:

Colbywas 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 afraction?” (the denominator) “Where

do we write the denominator in our fraction?” (underneath the

fraction bar) “Write the denominator under the thirdshaded

model.”

12.“How many pieces of pizza did Colby take?” (3) “What is

thisnumber 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 of3 pieces orthree-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, = 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 onecould represent a whole pizza?”

(both pizzas)“Why?” (they both represent a whole because

all four parts are shaded, 4 of 4 parts, or are shaded, so they

represent 1 whole) “So, what does this tell us about the size

of a whole?” (wholes cancome in different sizes)

15. “What if we look at only one out offour pieces of pizza?

What fraction does that represent? ()

“Are the pieces the same size on each of the pizzas?”(no,

they are not the same size because the wholes are different sizes)

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 fractioncircles?”

2.Colbywas very hungry, so he decided to take 2 pieces of pizza.

What fraction of the pizza did he take?

3.Colbywas actually starving, and decided to take 3 slices of pizza.

What fraction of the pizza did Colby take?

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

MATH_3_A_1 FRACTIONS SECTION 1COMPOSE DECOMPOSE 2014_LES

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

MATH_3_A_1 FRACTIONS SECTION 1COMPOSE DECOMPOSE 2014_LES

Part III: Composing a Wholewith 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

andlabel 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.

Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-20151

MATH_3_A_1 FRACTIONS SECTION 1COMPOSE DECOMPOSE 2014_LES

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? ______

Property of Cy-Fair ISD Elem. Math Dept. (3rd grade) 2014-20151

MATH_3_A_1 FRACTIONS SECTION 1COMPOSE DECOMPOSE 2014_LES

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 thisactivity as they are similar to the pictorial strip diagrams.

Materials:fraction towers for each student, dry erase boards, markers and erasers, teacherRecord Sheet A

Directions:

1. “Let’s compose a fraction. Let’s composeusing the unit fractions orpieces 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 )

2.“Let’s compose usingfraction pieces, or unit fractions. Use

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

whole.”

1

1. “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 of the whole. In our solution, however,our solution our numerator is 6 because we put together 6 unit fractions, or ‘s to makeor 1 whole.
2. “We composed using all unit fractions.Can you think of another way to compose ? Work with students at your table to manipulate your fraction pieces into groups to show a different wayto compose and record the number sentence under your fraction pieces on your dry erase board.”

1. Have each tableshare their number sentences one at a time. Each table should be creative in composing .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. A each table shares, the teacher will record each number sentence onRecord SheetA using different colored pencils to show each fraction that is being used to compose.

If atable shares the following:

The teacher’s record sheet will look as follows:

Notice each group of fractions is a different color. Teacher will model

partitioninginto 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 and record the number sentence under your fraction pieces on your dry erase board.”

1. Have each tableshare 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. 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 compose.
2. Again, the teacher will model partitioning into eighths using the last strip diagram on Record Sheet B.

Fraction Record Sheet B