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CHAPTER RESOURCES • Chapter 8Understand Fractions
INCLUDES • School-Home Letter • Vocabulary Game Directions • Daily Enrichment Activities • Reteach Intervention for every lesson • Chapter 8 Test • Chapter 8 Performance Task • Answer Keys and Individual Record Forms
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Contents Chapter 8 School-Home Letter (English) .......................................................8-1
Chapter 8 School-Home Letter (Spanish) ......................................................8-2
Vocabulary Game ..........................................................................................8-3
8.1 Reteach ..................................................................................................8-5
8.1 Enrich ......................................................................................................8-6
8.2 Reteach ..................................................................................................8-7
8.2 Enrich ......................................................................................................8-8
8.3 Reteach ..................................................................................................8-9
8.3 Enrich .................................................................................................... 8-10
8.4 Reteach ................................................................................................ 8-11
8.4 Enrich ....................................................................................................8-12
8.5 Reteach ................................................................................................8-13
8.5 Enrich ....................................................................................................8-14
8.6 Reteach ................................................................................................8-15
8.6 Enrich ....................................................................................................8-16
8.7 Reteach ................................................................................................8-17
8.7 Enrich ....................................................................................................8-18
iii Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company
8.8 Reteach ................................................................................................8-19
8.8 Enrich ....................................................................................................8-20
8.9 Reteach ................................................................................................8-21
8.9 Enrich ....................................................................................................8-22
Chapter 8 Test .............................................................................................8-23
Chapter 8 Performance Task .......................................................................8-29
Answer Keys ................................................................................................8-34
Individual Record Forms ..............................................................................8-41
iv Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company
Tips
School-HomeSchool-Home
LetterChapterChapter
STEP 3
Circle one of the groups to show 1 __
3 .
Then count the number of counters in that group.
There are 3 counters in 1 group.
So, 1 __ 3 of 9 = 3.
STEP 2
Since you want to find 1 __
3 of the group,
there should be 3 equal groups.
ActivityDisplay a group of 12 objects, such as crayons. Have your child find fractional parts of the
group by counting objects in equal groups. Ask your child to find these fractional groups of
12: 1 _ 2
(6), 1 _ 3
(4), 1 _ 4
(3), 1 _ 6
(2).
STEP 1
Find 1 __ 3 of 9.
Put 9 counters on your MathBoard.
This is how we will be finding how many are in a fractional part of a group.
Find How Many in a Fractional Part of a Group
Dear Family,
During the next few weeks, our math class will be learning about fractions. We will learn to identify, read, and write fractions as part of a whole and as part of a group.
You can expect to see homework that provides practice with fractions.
Here is a sample of how your child will be taught to use unit fractions to find a fractional part of a group.
denominator The part of a fraction below the line that tells how many equal parts are in the whole or in the group
equal parts Parts that are exactly the same size
fraction A number that names part of a whole or part of a group
numerator The part of a fraction above the line that tells how many equal parts are being counted
unit fraction A fraction that names 1 equal part of a whole. It has 1 as its top number, or numerator.
Equal Groups or Parts
Before you name a fraction, be sure there are equal groups or parts.
8
8-1Chapter Resources© Houghton Mifflin Harcourt Publishing Company
para la casaCartaCartaCapítulo
Pistas
8
PASO 2
Como quieres hallar 1 __ 3 del grupo, debe
haber 3 grupos iguales.
PASO 1
Halla 1 __ 3 de 9.
Coloca 9 fichas en el MathBoard.
ActividadMuestre un grupo de 12 objetos, como crayolas. Pida a su hijo que halle las partes fraccionarias del
grupo contando objetos en grupos iguales. Luego, pídale que halle estos grupos fraccionarios de 12: 1 __ 2
(6), 1 _ 3
(4), 1 __ 4
(3), 1 __ 6
(2).
Así es como hallaremos cuántos hay en una parte fraccionaria de un grupo.
Hallar cuántos hay en una parte fraccionaria de un grupo
Querida familia,
Durante las próximas semanas, en la clase de matemáticas aprenderemos sobre las fracciones. Aprenderemos a identificar, leer y escribir fracciones como parte de un todo y como parte de un grupo.
Llevaré a la casa tareas que sirven para practicar las fracciones.
Este es un ejemplo de la manera como aprenderemos a usar fracciones para hallar una parte fraccionaria de un grupo.
denominador La parte de una fracción que está debajo de la barra y que indica cuántas partes iguales hay en el entero o en el grupo
partes iguales Las partes que son exactamente del mismo tamaño
fracción Un número que representa una parte de un todo o una parte de un grupo
numerador La parte de una fracción que está arriba de la barra y que indica cuántas partes iguales del entero se están tomando en cuenta
fracción unitaria Una fracción que se refiere a 1 parte igual de un entero. Tiene un 1 en la parte de arriba o numerador.
PASO 3
Encierra en un círculo uno de los grupos para
mostrar 1 __ 3 . Luego
cuenta la cantidad de fichas en el grupo.
Hay 3 fichas en 1 grupo. Por lo tanto,
1 __ 3 de 9 = 3.
Grupos o partes iguales
Antes de que nombres una fracción, asegúrate de que haya grupos o partes iguales.
8-2Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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Going Places with words
Going to the Mint
Word Boxdenominatoreighthsequal partsfourthsfractionfraction greater than 1halvesnumeratorsixthsthirdsunit fractionwhole
For 2 to 4 players
Materials• 3 red connecting cubes
• 3 blue connecting cubes
• 3 green connecting cubes
• 3 yellow connecting cubes
• 1 number cube
How to Play1. Put your 3 connecting cubes in the START circle of the same
color.
2. To get a cube out of START, you must roll a 6.
• If you roll a 6, move 1 of your cubes to the same colored
circle on the path.
• If you do not roll a 6, wait until your next turn.
3. Once you have a cube on the path, toss the number cube to
take a turn. Move the connecting cubes that many tan spaces.
You must get all 3 of your cubes on the path.
4. If you land on a space with a question, answer it. If you are
correct, move ahead 1 space.
5. To reach FINISH, move your connecting cubes up the path that
is the same color as your cubes. Th e fi rst player to get all three
cubes on FINISH wins.
Chapter 8 442A
Chapter 6Vocabulary Game
8-3 Game DirectionsChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Equal Parts of a Whole
When you divide a shape into equal parts, each part must be exactly the same size.
This rectangle is divided into 2 equal parts, or halves.
This rectangle is divided into 3 equal parts, or thirds.
This rectangle is divided into 4 equal parts, or fourths.
Write the number of equal parts. Then write the name for the parts.
1. 2. 3.
equal parts
equal parts
equal parts
Write whether each shape is divided into equal parts or unequal parts.
4. 5. 6.
parts parts parts
Draw lines to divide the squares into equal parts.
7. 3 thirds 8. 6 sixths 9. 8 eighths
Lesson 8.1Reteach
8-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
4. Look back at Exercise 1. How did you decide where to divide each square?
5. Stretch Your Thinking How do you know the square is divided into equal parts even though they are not the same shape?
Way to Share!
Draw lines to divide each shape 3 different ways into the number of parts given.
1. 4 equal parts
2. 3 equal parts
3. 6 equal parts
Lesson 8.1Enrich
8-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Equal Shares
Six brothers share 5 sandwiches equally. How much does each brother get? Draw to model the problem.
Step 1 Draw 5 squares for the sandwiches.
Step 2 There are 6 brothers. Draw lines to divide each sandwich into 6 equal parts.
Step 3 Each brother will get 1 equal part from each sandwich.
So, each brother gets 5 sixths of a sandwich.
Draw lines to show how much each person gets. Write the answer.
1. 4 sisters share 3 pies equally. 2. 6 friends share 3 fruit bars equally.
Lesson 8.2Reteach
8-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
A Fair Share
Mary and her 3 friends go on a picnic. They share some food. Show how they can make the fewest cuts possible to share the food equally among 4 people. Shade your drawing to show one person’s share. Then write how much each person gets.
1. 4 sandwiches 2. 2 muffins
3. 3 small pizzas 4. 6 granola bars
5. How can you tell if an equal share is more than one whole? Use an example from above to explain your answer.
Lesson 8.2Enrich
8-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Unit Fractions of a Whole
A fraction is a number. It names part of a whole or part of a group.
The top number tells how many equal parts are being counted. The bottom number tells how many equal parts are in the whole. A unit fraction names 1 equal part of a whole. It always has 1 as its top number.
How much is 1 part of a fruit bar that is cut into 8 equal parts?
Step 1 Use fraction strips. Make a strip showing 8 equal parts, or eighths.
Step 2 Shade 1 of the parts and name it.
This fraction is called 1 _ 8 .
So, 1 part of a fruit bar that can be divided into 8 equal parts is 1 _ 8 .
Write the number of equal parts in the whole. Then write the fraction that names the shaded part.
1. 2. 3.
equal parts equal parts equal parts
Lesson 8.3Reteach
8-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
7. Stretch Your Thinking What unit fraction of the figure is shaded? Explain your answer.
Whole Lot of Fractions!
Draw lines and shade each shape to show the fraction.
1. 1 __ 2
2. 1 __ 4
3. 1 __ 4
4. 1 __ 8
5. 1 __ 3
6. 1 __ 2
Lesson 8.3Enrich
8-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
1. Shade three parts out of eight equal parts. Write a fraction in words and in numbers to name the shaded part.
Read: eighths
Write:
Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.
2. 3. 4.
Each part is . Each part is . Each part is .
sixths fourths eighths
Fractions of a Whole
Some shapes can be cut into equal parts. A fraction can name more than 1 equal part of a whole.
Write a fraction in words and in numbers to name the shaded part.
How many equal parts make up the whole shape? 6 equal parts
How many parts are shaded? 3 parts
So, 3 parts out of 6 equal parts are shaded. Read: three sixths. Write: 3 _ 6
Lesson 8.4Reteach
8-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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Flag Fractions
Write a fraction to name the shaded part of each flag.
1. 2.
3. 4.
5. 6.
7. Draw your own flag. Divide it into equal parts. Shade some of the equal parts. Then write the fraction that names the shaded part of your flag.
Lesson 8.4Enrich
8-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
06
26
36
56
66
A
0 1
B
16
16
16
16
16
16
0 of 3equal lengths
0 1
33
23
13
03
13
13
13
1 of 3equal lengths
2 of 3equal lengths
3 of 3equal lengths
0 114
14
14
14
0 44
Name
2. point A 3. point B
Write the fraction that names the point.
1. Complete the number line. Draw a point to show 2 __ 4 .
Fractions on a Number Line
Use the fraction strips to help name the points on the number line.
Draw a point to show 1 _ 3 .
Step 1 The denominator is 3, so use fraction strips for thirds. Place the fraction strips above the number line. Use the fraction strips to divide the number line into three equal lengths.
Step 2 Label each mark on the number line. Think: The distance between each mark is 1 _
3 of the total
distance, so count the number of 1 _ 3 lengths.
Step 3 Draw a point on the number line to show 1 _ 3 .
Lesson 8.5Reteach
8-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
08
48
78
0 1
Name
Fraction Find
Write a fraction that names the shaded part of each whole. Then locate the fraction on the number line below. Write the letter of the model that represents the fraction.
A. B.
C. D.
E. F.
Lesson 8.5Enrich
8-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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04
24
34
44
0 1
1Jason
Tyra
113
33
63
13
13
13
13
13
Name
Relate Fractions and Whole Numbers
A fraction greater than 1 has a numerator greater than its denominator.
Jason ran 2 miles and Tyra ran 6 _ 3 miles. Did Jason and
Tyra run the same distance?
Step 1 Use fraction strips to show the distances. Use 2 whole strips to show Jason’s distance. Use six 1 _
3 -strips to show Tyra’s distance.
Step 2 Compare the fraction strips.Since the fraction strips for 2 and 6 _
3 are the same length,
they are equal.
So, Jason and Tyra ran the same distance.
Use the number line to find whether the two numbers are equal. Write equal or not equal.
1. 4 __ 4
and 1 2. 1 and 3 __ 4
3. 1 __ 4
and 4 __ 4
Lesson 8.6Reteach
8-15 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Fraction and Whole Number Match
For each model, write a fraction greater than 1 for the parts that are shaded. Then, for 1–3, write the letter of the model below the dashed line that shows the same whole number.
1.
2.
3.
A.
B.
C.
Lesson 8.6Enrich
8-16 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Think: 1 pan 5 1
Fractions of a Group
Adam has a collection of cars. What fraction names the shaded part of the collection?
Step 1 Count how many cars are shaded. There are 3 shaded cars. This number will be the numerator, or the top number of the fraction.
Step 2 Count the total number of cars. 8 This number will be the denominator, or the bottom number of the fraction.
Step 3 Read the fraction: three eighths, or three out of eight.
So, 3 _ 8 of Adam’s cars are shaded.
Write a fraction to name the shaded part of each group.
1.
2.
Write a whole number and a fraction greater than 1 to name the part filled.
3. Think: 1 can 5 1
4.
Lesson 8.7Reteach
8-17 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Fruit Fractions
Use the bowl of fruit to answer the questions. The bowl has 3 strawberries, 2 bananas, and 1 apple.
1. What fraction of the fruit in the bowl is bananas?
2. What fraction of the fruit in the bowl is apples?
3. What fraction of the fruit in the bowl is strawberries?
4. What fraction of the fruit in the bowl is bananas and strawberries?
5. Stretch Your Thinking Suppose 2 oranges are hidden under the fruit you can see in the bowl. What fraction of the fruit is oranges?
6. Write your own problem about fractions of a group. Use the fruit in the bowl. Then write the answer.
Lesson 8.7Enrich
8-18 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Circle equal groups to solve. Count the number of shapes in 1 group.
1. 1 __ 4
of 8 5
2. 1 __ 3
of 9 5
3. 1 __ 4
of 16 5
4. 1 __ 6
of 18 5
Find Part of a Group Using Unit Fractions
Lauren bought 12 stamps for postcards. She gave Brianna 1 _ 6 of them.
How many stamps did Lauren give to Brianna?
Step 1 Find the total number of stamps. 12 stamps
Step 2 Since you want to find 1 _ 6 of the group, there should be
6 equal groups. Circle one of the groups to show 1 _ 6 .
Step 3 Find 1 _ 6
of the stamps. How many stamps are in 1 group? 2 stamps
So, Lauren gave Brianna 2 stamps. 1 _ 6 of 12 5 2
Lesson 8.8Reteach
8-19 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Name Number of Tickets Left
Evan
Omar
Kate
Jenny
Part of the Group
Evan and his friends go to a theme park. Each friend buys 24 tickets and rides only 1 ride. Solve the problem.
1. Evan uses 1 __ 3
of his tickets to ride
the Loop-D-Loop. How many tickets does he use?
2. Omar uses 1 __ 6
of his tickets to ride
the water slide. How many tickets does he use?
3. Kate uses 1 __ 2
of her tickets to ride
the roller coaster. How many tickets does she use?
4. Jenny uses 1 __ 4
of her tickets to ride
the merry-go-round. How many tickets does she use?
5. Stretch Your Thinking Use the information in 1–4 to find the number of tickets each friend has left.
6. The friends now want to go on the Loop-D-Loop and the roller coaster. Explain why only 1 of the friends can go on both of these rides.
Lesson 8.8Enrich
8-20 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
1. Max has 3 beta fish in his fish tank. One half of his fish are beta fish. How many fish does Max have in his tank?
2. Two boys are standing in line. One sixth of the students in line are boys. How many students are standing in line?
Problem Solving • Find the Whole Group Using Unit Fractions
There are 3 apple juice boxes in the cooler. One fourth of the juice boxes in the cooler are apple juice. How many juice boxes are in the cooler?
Read the Problem Solve the Problem
What do I need to find?
I need to find are in the cooler.
Describe how to draw a diagram to solve.
The denominator in 1 _ 4 tells you
that there are parts in the whole group. Draw 4 circles to show parts.
Since 3 juice boxes are 1 _ 4 of
the group, draw counters
in the first circle.
Since there are counters in the first circle, draw counters in each of the remaining circles. Then count all of the counters.
So, there are juice boxes in the cooler.
What information do I need to use?
There are apple juice boxes.
of the juice boxes are apple juice.
How will I use the information?
I will use the information in the problem to draw a diagram.
Lesson 8.9Reteach
12
33
3
4
4how many juice boxes
One fourth
3
8-21 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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What Part of the Group?
Draw a quick picture to solve.
1. Lisa’s dog has 4 squeaky toys. Two thirds of the dog’s toys are squeaky toys. How many dog toys does Lisa’s dog have in all?
2. Sam has 9 yellow pencils in his desk. Three fourths of his pencils are yellow. How many pencils does Sam have in his desk?
3. Julia has 8 red barrettes. Two fourths of her barrettes are red. How many barrettes does Julia have?
4. Antonio has 15 pennies in his pocket. Five eighths of his coins are pennies. How many coins does Antonio have in his pocket?
5. Stretch Your Thinking One half of the birds at a pet store are yellow. Tara buys one of the yellow birds. Then one third of the birds at the store are yellow. How many yellow birds were at the pet store before Tara bought one? Explain how you know.
Lesson 8.9Enrich
8-22 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chapter 8 TestPage 1
1. Each shape is divided into equal parts. Select the shapes that show fourths. Mark all that apply.
A B C D
2. What fraction names the shaded part of the shape?
A 3 eighths
B 5 eighths
C 6 eighths
D 8 eighths
3. The shaded part of the model shows what part of a garden is planted with peas. What fraction names the shaded part? Explain how you know how to write the fraction.
8-23Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 2
4. What fraction names point A on the number line?
__
5. Kwan divided this circle into equal parts. Circle the word that makes the sentence true.
The circle is divided into
sixths
eighths
fourths
.
6. Sophie uses 16 beads to make a necklace. One fourth of the beads are purple. How many of the beads are purple?
__ beads
7. Four brothers work together to mow 3 equal-sized fields. Each brother mows the same amount.
How much does each brother mow? Mark all that apply.
A 4 thirds of a field
B 1 whole and 1 third of a field
C 3 fourths of a field
D 2 thirds of a field
E 1 fourth of a field
08
0 1
88
A
18
18
18
18
18
18
18
18
8-24Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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Chapter 8 Test
Chapter 8 TestPage 3
8. Bailey shaded this model.
Select one number from each column to show the part of the model Bailey shaded.
Numerator Denominator
1 2
2 4
4 5
6 6
9. Jayson baked a pan of cornbread for a family dinner. He cut the cornbread into equal size pieces. At the end of the dinner, there were 2 pieces left. Explain how you find the number of pieces in the whole pan of cornbread if Jayson told you that 1 _ 6 of the pan was left. Use a drawing to show your work.
8-25Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 4
10. The model shows one whole. What fraction of the model is NOT shaded?
__
11. Michael replaced 1 _ 3 of the buttons on his coat. If he
replaced a total of 3 buttons, how many buttons are on his coat? Show your work.
__ buttons
12. Four teachers share 3 gallons of paint equally. How much paint does each teacher get?
13. Each shape is 1 whole.
For numbers 13a–13e, choose Yes or No to show whether the number names the parts that are shaded.
13a. 3 Yes No
13b. 4 Yes No
13c. 12
__ 3 Yes No
13d. 12
__ 4 Yes No
13e. 3 __ 12
Yes No
8-26Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 5
14. A store sold 6 fruit trees. Five of the trees were apple trees. What fraction of the trees were apple trees?
__
15. Christina and Erin made vegetable trays for a neighborhood picnic.
Part A
Christina put 15 vegetables on her tray. If 1 _ 5 of the vegetables were carrots, how many carrots were on the tray? Make a drawing to show your work.
__ carrots
Part B
Erin put 20 vegetables on her tray. If 1 _ 4 of them were carrots, how many carrots were on Christina's and Erin's trays? Explain how you found your answer.
16. Maria has 8 tulip bulbs. She gives 5 of the tulip bulbs to her neighbor. What fraction of her tulip bulbs does she give to her neighbor?
__
8-27Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 6
17. Lucy rode her bike around the block 4 times for a total of 1 mile yesterday. Today she wants to ride her bike 3
_ 4 of
a mile. How many times will she need to ride her bike around the block?
__ times
18. Jackson colored some shapes.
Select one number from each column to show a fraction greater than 1 that names the parts Jackson colored.
Numerator Denominator
1 1
2 2
3 3
6 6
19. Samira ran around a park loop that was 1 _ 3 mile long. She
ran around the loop 9 times. Samira says she ran 9 _ 3 miles.
Her brother Amal says she ran 3 miles. Who is correct? Use words and drawings to explain how you know.
04
0 1
44
14
14
14
14
8-28Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Name Chapter 8
In the Kitchen
Rana and Yoshi are cooking food for a party. They need to cut up the food so people can share.
1. Yoshi makes 3 small pepperoni pizzas. There are 4 people who will share the pizzas. Draw a picture to show how much each person will get. Explain your answer.
2. Rana makes a large vegetable pizza. She cuts the pie into 8 equal parts. Three people each eat a slice of the pie.
a. Draw a picture to show the pie. Shade the missing parts.
b. Write a fraction to show how much of the pie is left.
8-29 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
3. Yoshi makes a large sandwich. He cuts the sandwich into 8 equal parts. He wants to put 5 _ 8 of the sandwich on a plate. How many pieces of the sandwich does he need? Draw a number line to solve the problem. Then write your answer.
4. Rana puts 12 pieces of fruit in a bowl. 1 _ 4 of the fruit pieces are apples. a. Draw a fraction strip to show how many apple pieces are in the
bowl.
b. Write a fraction to show how many pieces are apples.
5. Yoshi and Rana serve muffins. There are 3 muffins with nuts. 1 _ 6 of the muffins have nuts.
a. How many muffins do they serve in all? Draw a number line to solve. Explain how you solved the problem.
b. Write a fraction to show how many muffins do not have nuts.
8-30 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chapter 8Understanding Fractions
In the KitchenCOMMON CORE STANDARDS
3.NF.A.1 Understand a fraction 1 _ b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a _ b as the quantity formed by a parts of size 1 _ b .
3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1 _ b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1 _ b and that the endpoint of the part based at 0 locates the number 1 _ b on the number line.
b. Represent a fraction a _ b on a number line diagram by marking off a lengths 1 _ b from 0. Recognize that the resulting interval has size a _ b and that its endpoint locates the number a _ b on the number line.
PURPOSETo assess the ability to use fractions to describe how much or how many
TIME25–30 minutes
GROUPINGIndividuals
MATERIALS• Performance Task, paper, pencil
• Fraction bars (optional)
PREPARATION HINTS• Review dividing an object into equal parts by folding paper into halves, then into halves again,
before assigning the task.
• Review showing parts of a group using counters before assigning the task.
IMPLEMENTATION NOTES• Read the task aloud to students and make sure that all students have a clear understanding
of the task.
• Students may use manipulatives to complete the task.
• Allow students as much paper as they need to complete the task.
• Allow as much time as students need to complete the task.
• Students must complete the task individually, without collaboration.
• Collect all student work when the task is complete.
8-31 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
TASK SUMMARYStudents draw pictures to show fraction concepts including parts of a whole, equal shares, fractions of a whole, fractions on a number line, and finding unit fractions.
REPRESENTATION In this task, teachers can…
• Provide options for comprehension by pre-teaching critical prerequisite concepts through models such as fraction strips.
• Provide options for comprehension by using cues and prompts to draw attention to big ideas and critical fraction concepts.
ACTION and EXPRESSION In this task, teachers can…
• Provide options for physical action by offering fraction strips for students to use as they draw fractional parts.
• Provide options for monitoring progress by asking students questions to guide self-monitoring.
ENGAGEMENT In this task, teachers can…
• Help students meet goals and objectives by helping them organize long-term goals into short-term objectives.
• Optimize relevance by asking students to give examples of fractions at home, in school and in their personal lives.
EXPECTED STUDENT OUTCOMES• Complete the task within the time allowed
• Reflect engagement in a productive struggle
• Solve problems using fractions
SCORING Use the associated Rubric to evaluate each student’s work.
8-32 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Performance Task Rubric
IN THE KITCHEN
A level 3 response • Indicates that the student has made sense of the task, modeled accurately, and persevered
• Shows the ability to accurately solve fraction problems by using parts of a whole, equal shares, fractions of a whole, fractions on a number line, and finding unit fractions
• Demonstrates an understanding of a fraction as part of a whole
• Addresses all aspects of the task including representing fractions with drawings and explaining mathematical reasoning
A level 2 response • Indicates that the student has made sense of the task, modeled accurately, and persevered
• Shows the ability to accurately solve fraction problems by using parts of a whole, equal shares, fractions of a whole, fractions on a number line, and finding unit fractions
• Demonstrates an understanding of a fraction as part of a whole
• Addresses all or most elements of the task including representing fractions with drawings and explaining mathematical reasoning
• May include minor errors of omission
A level 1 response • Shows that the student has made sense of at least some elements of the task
• Shows evidence of understanding some basic concepts of fractions
• May not include accurately drawn fractions or explanations of mathematical reasoning
A level 0 response • Shows little evidence that the student has made sense of the task
• Reflects a lack of understanding of fractions as part of a whole or unit
• Shows little evidence of addressing the elements of the task
• May include incorrectly or inappropriately applied mathematical reasoning
8-33 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chap
ter 8
Tes
tPa
ge 2
4
. W
hat
fraction n
am
es
poin
t A
on t
he n
um
ber
line?
__
5
. K
wan d
ivid
ed t
his
cir
cle
into
equal part
s. C
ircle
the w
ord
th
at
makes
the s
ente
nce t
rue.
The c
ircle
is
div
ided into
sixt
hs
eig
hth
s
fourt
hs
.
6
. Sophie
use
s 1
6 b
eads
to m
ake a
neckla
ce. O
ne f
ourt
h o
f th
e b
eads
are
purp
le. H
ow
many
of
the b
eads
are
purp
le?
__
beads
7
. Four
bro
thers
work
togeth
er
to m
ow
3 e
qual-
size
d f
ield
s.
Each b
roth
er
mow
s th
e s
am
e a
mount.
How
much d
oes
each b
roth
er
mow
? M
ark
all
that
apply
.
A 4
thir
ds
of
a f
ield
B 1
whole
and 1
thir
d o
f a f
ield
C 3
fourt
hs
of
a f
ield
D 2
thir
ds
of
a f
ield
E 1
fourt
h o
f a f
ield
0 801 8 8
A
1 81 8
1 81 8
1 81 8
1 81 8
4
7 _ 8
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Chap
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Tes
t
Chap
ter 8
Tes
tPa
ge 1
1
. Each s
hape is
div
ided into
equal part
s. S
ele
ct
the s
hapes
that
show
fourt
hs.
Mark
all
that
apply
.
A
B
C
D
2
. W
hat
fraction n
am
es
the s
haded p
art
of
the s
hape?
A 3
eig
hth
s
B 5
eig
hth
s
C 6
eig
hth
s
D 8
eig
hth
s
3
. The s
haded p
art
of
the m
odel sh
ow
s w
hat
part
of
a
gard
en is
pla
nte
d w
ith p
eas.
What
fraction n
am
es
the
shaded p
art
? E
xpla
in h
ow
you k
now
how
to w
rite
the
fraction.
1 _ 6 ; Po
ssib
le e
xpla
nat
ion
: Th
ere
are
6 eq
ual
par
ts a
nd
1 p
art
is s
had
ed, s
o I
wri
te 1
on
th
e to
p a
nd
6 o
n t
he
bo
tto
m.
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Chap
ter 8
Tes
t
8-34 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chap
ter 8
Tes
tPa
ge 4
10
. The m
odel sh
ow
s one w
hole
. W
hat
fraction o
f th
e m
odel
is N
OT s
haded?
__
11
. M
ichael re
pla
ced 1
_
3 o
f th
e b
utt
ons
on h
is c
oat. If
he
repla
ced a
tota
l of
3 b
utt
ons,
how
many
butt
ons
are
on
his
coat?
Show
your
work
.
__
butt
ons
12
. Four
teachers
share
3 g
allo
ns
of
pain
t equally
. H
ow
m
uch p
ain
t does
each t
eacher
get?
13
. Each s
hape is
1 w
hole
.
For
num
bers
13
a–1
3e, choose
Yes
or
No t
o s
how
w
heth
er
the n
um
ber
nam
es
the p
art
s th
at
are
shaded.
13a.
3
Y
es
N
o
13b.
4
Y
es
N
o
13c.
1
2
__
3
Y
es
N
o
13d.
1
2
__
4
Y
es
N
o
13e.
3
__
12
Y
es
N
o
9
Po
ssib
le a
nsw
ers:
3 fo
urt
hs,
or
1 h
alf
and
1 fo
urt
h o
f a
box
Ch
eck
stu
den
ts' w
ork
.
3 __
4
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Chap
ter 8
Tes
t
Chap
ter 8
Tes
tPa
ge 3
8
. B
aile
y sh
aded t
his
model.
Sele
ct
one n
um
ber
from
each c
olu
mn t
o s
how
the p
art
of
the m
odel B
aile
y sh
aded.
Nu
mer
ato
rD
eno
min
ato
r
1
2
2
4
4
5
6
6
9
. Ja
yson b
aked a
pan o
f corn
bre
ad f
or
a f
am
ily d
inner. H
e
cut
the c
orn
bre
ad into
equal si
ze p
ieces.
At
the e
nd o
f th
e d
inner, t
here
were
2 p
ieces
left
. Exp
lain
how
you f
ind
the n
um
ber
of
pie
ces
in t
he w
hole
pan o
f corn
bre
ad if
Jays
on t
old
you t
hat
1
_
6 o
f th
e p
an w
as
left
. U
se a
dra
win
g
to s
how
your
work
.
6 ov
als.
Sin
ce 2
pie
ces
are
1 _ 6 of
the
pan
, I d
rew
2 c
ou
nte
rs
in e
ach
ova
l. 6 ×
2 =
12,
so
th
ere
wer
e 12
pie
ces
in t
he
Po
ssib
le e
xpla
nat
ion
: Th
e d
eno
min
ato
r in
1 _ 6 is
6, s
o I
dre
w
wh
ole
pan
of
corn
bre
ad.
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Chap
ter 8
Tes
t
8-35 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chap
ter 8
Tes
tPa
ge 6
17
. Lucy
rode h
er
bik
e a
round t
he b
lock 4
tim
es
for
a t
ota
l of
1 m
ile y
est
erd
ay.
Today
she w
ants
to r
ide h
er
bik
e 3
_
4 o
f a m
ile. H
ow
many
tim
es
will
she n
eed t
o r
ide h
er
bik
e
aro
und t
he b
lock?
__
tim
es
18
. Ja
ckso
n c
olo
red s
om
e s
hapes.
Sele
ct
one n
um
ber
from
each c
olu
mn t
o s
how
a f
raction
gre
ate
r th
an 1
that
nam
es
the p
art
s Ja
ckso
n c
olo
red.
Nu
mer
ato
rD
eno
min
ato
r
1
1
2
2
3
3
6
6
19
. Sam
ira r
an a
round a
park
loop t
hat
was
1
_
3 m
ile long. S
he
ran a
round t
he loop 9
tim
es.
Sam
ira s
ays
she r
an 9
_
3 m
iles.
H
er
bro
ther
Am
al sa
ys s
he r
an 3
mile
s. W
ho is
corr
ect?
U
se w
ord
s and d
raw
ings
to e
xpla
in h
ow
you k
now
.
0 401 4 4
1 41 4
1 41 4
3
Bo
th a
re c
orr
ect.
Po
ssib
le e
xpla
nat
ion
: Th
e d
ista
nce
aro
un
d P
oss
ible
dra
win
g:
the
loo
p is
1 _ 3 mile
, so
if s
he
ran
aro
un
d it
9 t
imes
, th
at is
nin
e
thir
ds
or
9 _ 3 . I d
rew
a c
ircl
e, d
ivid
ed it
in t
hir
ds
and
sh
aded
3 _ 3 .
I th
en d
rew
tw
o m
ore
cir
cles
an
d s
had
ed e
ach
th
e sa
me
to
sho
w 9 _ 3 . M
y d
raw
ing
sh
ow
s th
at 9 _ 3 =
3, s
o b
oth
are
co
rrec
t.
8-28
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Chap
ter 8
Tes
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Chap
ter 8
Tes
tPa
ge 5
14
. A
sto
re s
old
6 f
ruit t
rees.
Fiv
e o
f th
e t
rees
were
apple
tr
ees.
What
fraction o
f th
e t
rees
were
apple
tre
es?
__
15
. C
hri
stin
a a
nd E
rin m
ade v
egeta
ble
tra
ys f
or
a
neig
hborh
ood p
icnic
.
Par
t A
Chri
stin
a p
ut
15
vegeta
ble
s on h
er
tray.
If
1
_
5 o
f th
e
vegeta
ble
s w
ere
carr
ots
, how
many
carr
ots
were
on
the t
ray?
Make a
dra
win
g t
o s
how
your
work
.
__
carr
ots
Par
t B
Eri
n p
ut
20
vegeta
ble
s on h
er
tray.
If
1
_
4 o
f th
em
were
carr
ots
, how
many
carr
ots
were
on C
hri
stin
a's
and E
rin's
tr
ays
? E
xpla
in h
ow
you f
ound y
our
answ
er.
16
. M
ari
a h
as
8 t
ulip
bulb
s. S
he g
ives
5 o
f th
e t
ulip
bulb
s to
her
neig
hbor. W
hat
fraction o
f her
tulip
bulb
s does
she g
ive t
o h
er
neig
hbor?
__
3
5 _ 6
Po
ssib
le w
ork
: 1 _ 5 o
f 15
is 3
. 1 _ 4 of
20 is
5. 3
+ 5
= 8
, so
th
ere
wer
e a
tota
l of
8 ca
rro
ts o
n b
oth
tra
ys.
5 _ 8
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Chap
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Tes
t
8-36 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 3 Response
8-37 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 2 Response
8-38 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 1 Response
8-39 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 0 Response
8-40 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Student’s Name Date
Individual Record Form 8-41© Houghton Mifflin Harcourt Publishing Company
Chapter Resources
Item Lesson Standard Content Focus Intervene With
Personal Math Trainer
1, 5 8.1 3.NF.A.1 Identify and name equal parts of a whole. R—8.1 3.NF.1
2, 8, 10 8.4 3.NF.A.1 Name a fraction of a whole. R—8.4 3.NF.1
3 8.3 3.NF.A.1 Write a unit fraction to name part of a whole. R—8.3 3.NF.1
4, 17 8.5 3.NF.A.2a, 3.NF.A.2b
Represent and locate fractions on a number line. R—8.5 3.NF.2a, 3.NF.2b
6, 15 8.8 3.NF.A.1 Find part of a group using unit fractions. R—8.8 3.NF.1
7, 12 8.2 3.NF.A.1 Make equal shares. R—8.2 3.NF.1
9, 11 8.9 3.NF.A.1 Find the whole group using unit fractions. R—8.9 3.NF.1
13, 18, 19 8.6 3.NF.A.3c Relate fractions and whole numbers. R—8.6 3.NF.3c
14, 16 8.7 3.NF.A.1 Name a fraction of a group. R—8.7 3.NF.1
Key: R—Reteach
Chapter 8 Test