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.
Topic / TEKS / PageComposing 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 Showdown
Snowball Showdown Record Sheet
Part II: Naming Fractions to Composea Whole Object– Concrete
Fraction Pieces IMN Strip
Focus Questions to Display
Fraction Record Sheet 1
Part III: Composing and Decomposinga Whole ObjectUsing Unit Fractions – Pictorial
Fraction Record Sheet 2
Part IV: Composing and Decomposing a Whole Object – Concrete
Fraction Record Sheet A
Part V: Composing and Decomposing a Whole Object - Pictorial
Fraction Record Sheet B
Part VI: Composing and Decomposing a Fraction - Concrete
Fraction Record Sheet C
Part VII: Composing and Decomposing Fractions - Pictorial
Fraction Rotation Record Sheet
Part VIII: Composing and Decomposing a Set of Objects - Concrete
Parts of a Set Record Sheet
Part IX: Fractions on a Number Line to 1 Whole
Fractions on a Number Line Record Sheet / 3
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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
Student Name / Furthest TossMeasure 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:
- “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
- “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.
- “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.”
- 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
- “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.”
- 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.
- Again, the teacher will model partitioning into eighths using the last strip diagram on Record Sheet B.
Fraction Record Sheet B