4 mcaese210851 u06l01 -...
TRANSCRIPT
Family Letter
Fraction Comparisons
1–3
<1–2
Fraction Subtraction
5–5
-2–5
=3–5
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Unit 6 addresses the following standards from the Common Core Standards for Mathematics with California Additions: 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4a, 4.NF.4b, 4.NF.4c, and all Mathematical Practices.
Dear Family,
Your child has experience with fractions through measurements and in previous grades. Unit 6 of Math Expressions builds on this experience. The main goals of this unit are to:
• understand the meaning of fractions.
• compare unit fractions.
• add and subtract fractions and mixed numbers with like denominators.
• multiply a fraction by a whole number.
Your child will use fraction bars and fraction strips to gain a visual and conceptual understanding of fractions as parts of a whole. Later, your child will use these models to add and subtract fractions and to convert between improper fractions and mixed numbers.
Examples of Fraction Bar Modeling:
In later lessons of this unit, your child will be introduced to the number line model for fractions. Students name fractions corresponding to given lengths on the number line and identify lengths corresponding to given fractions. They also see that there are many equivalent fraction names for any given length.
Your child will apply this knowledge about fractions and fraction operations to solve real world problems.
If you have questions or problems, please contact me.
Sincerely, Your child’s teacher
Content Overview
UNIT 6 LESSON 1 Understand Fractions 209
Carta a la familia
Comparaciones de fracciones
1–3
<1–2
Resta de fracciones
5–5
-2–5
=3–5
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En la Unidad 6 se aplican los siguientes estándares auxiliares, contendidos en los Estándares estatales comunes de matemáticas con adiciones para California: 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4a, 4.NF.4b, 4.NF.4c y todos los de prácticas matemáticas.
Estimada familia:
Su niño ha usado fracciones al hacer mediciones y en los grados previos. La Unidad 6 de Math Expressions amplía esta experiencia. Los objetivos principales de la unidad son:
• comprender el significado de las fracciones.
• comparar fracciones unitarias.
• sumar y restar fracciones y números mixtos con denominadores iguales.
• multiplicar una fracción por un número entero.
Su niño usará barras y tiras de fracciones para comprender y visualizar el concepto de las fracciones como partes de un entero. Luego, usará estos modelos para sumar y restar fracciones y para convertir fracciones impropias y números mixtos.
Ejemplos de modelos con barras de fracciones:
Más adelante en esta unidad, su niño verá el modelo de la recta numérica para las fracciones. Los estudiantes nombrarán las fracciones que correspondan a determinadas longitudes en la recta numérica e identificarán longitudes que corresponden a fracciones dadas. También observarán que hay muchos nombres de fracciones equivalentes para una longitud determinada.
Su niño aplicará este conocimiento de las fracciones y operaciones con fracciones para resolver problemas cotidianos.
Si tiene alguna duda o algún comentario, por favor comuníquese conmigo.
Atentamente, El maestro de su niño
Un vistazo general al contenido
210 UNIT 6 LESSON 1 Understand Fractions
Class Activity
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VOCABULARY
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► Sums of FractionsA unit fraction represents one equal part of a whole. A unit fraction has a numerator of 1. The unit fraction 1 __
d is one of d equal parts.
The fraction bar below is divided into six equal parts, or sixths. Each part is 1 of 6 equal parts, or 1 __
6 .
A fraction is the sum of unit fractions. The fraction n __
d is the sum of n copies of 1 __
d .
numerator
denominator n __ d = number of unit fractions in the fraction ________________________________
number of equal parts in the whole
The fraction 5 __ 6 is the sum of five sixths.
5 __ 6 = 1 __
6 + 1 __
6 + 1 __
6 + 1 __
6 + 1 __
6 = 5 × 1 __
6
Fold your fraction strips to show each sum of unit fractions. Write the fraction each sum represents.
1. 1 __ 3 + 1 __
3 =
3. 1 __ 4 + 1 __
4 =
2. 1 __ 8 + 1 __
8 + 1 __
8 + 1 __
8 + 1 __
8 =
4. 1 __ 6 + 1 __
6 + 1 __
6 + 1 __
6 =
5. 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
=
6. 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
+ 1 ___ 12
=
7. 1 __ 8 + 1 __
8 + 1 __
8 + 1 __
8 + 1 __
8 + 1 __
8 + 1 __
8 =
unit fractionfractionnumeratordenominator
Content Standards 4.NF.3, 4.NF.3b, 4.NF.4a Mathematical Practices MP.2, MP.5, MP.7
Name Date
UNIT 6 LESSON 1 Understand Fractions 211
Class Activity
1 1
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► Patterns in Fraction Bars 8. Describe at least three patterns you see in the fraction
bars below.
Name Date
212 UNIT 6 LESSON 1 Understand Fractions
Class Activity
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► Sums of Unit FractionsShade the fraction bar to show each fraction. Then write the fraction as a sum of unit fractions and as a product of a whole number and a unit fraction. The first one is done for you.
9. 3 __ 4 = = 1 __
4 + 1 __
4 + 1 __
4 3 × 1 __
4
10. 3 __ 8 = =
11. 5 __ 5 = =
14. 7 __ 9 = =
13. 4 __ 7 = =
12. 2 ___ 12
= =
Name Date
UNIT 6 LESSON 1 Understand Fractions 213
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► Fractions as Parts of a WholeJon made a large sandwich for the 6 people in his family. He asked his father to help him cut it into 6 equal pieces. To do this, they made a paper cutting guide that is as long as the sandwich. Jon folded the paper into 6 equal parts, and his father used it to cut the sandwich into equal pieces.
Solve.
15. If each person ate 1 piece of the sandwich, what fraction of the sandwich did each person eat? Fold your 6-part fraction strip to show the fraction of the whole sandwich that each person ate.
16. How many pieces of the whole sandwich did Jon’s mother and father eat altogether? Fold your fraction strip to show the fraction of the whole sandwich Jon’s mother and father ate in all.
17. After Jon’s mother and father got their pieces, what fraction of the sandwich was left?
18. Jon and each of his sisters were each able to have one piece of the remaining sandwiches. How many sisters does Jon have?
19. What ideas about fractions did we use to answer the questions about Jon’s sandwich?
Name Date
Show your work.
214 UNIT 6 LESSON 1 Understand Fractions
Class Activity
1 whole = all of the books
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1 whole Jean‘s Maria‘s share share
5–5
–5
–5
= +
5–5
–5
–5
= +
5–5
–5
–5
= +
5–5
–5
–5
= +
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► Fifths that Add to OneEvery afternoon, student volunteers help the school librarian put returned books back on the shelves. The librarian puts the books in equal piles on a cart.
One day, Jean and Maria found 5 equal piles on the return cart. They knew there were different ways they could share the job of reshelving the books. They drew fraction bars to help them find all the possibilities.
1. On each fifths bar, circle two groups of fifths to show one way Jean and Maria could share the work. (Each bar should show a different possibility.) Then complete the equation next to each bar to show their shares.
Content Standards 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b Mathematical Practices MP.2, MP.3, MP.6
Name Date
UNIT 6 LESSON 2 Fractions that Add to One 215
Class Activity
1 whole = all of the books
1–6
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1–6
1–6
1–6
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1–6
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1–6
1–6
1–6
1–6
1–6
1–6
1–6
1–6
1–6
1–6
1–6
1 whole Liu‘s Henry‘s share share
6–6
–6
–6
= +
6–6
–6
–6
= +
6–6
–6
–6
= +
6–6
–6
–6
= +
6–6
–6
–6
= +
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► Sixths that Add to OneThe librarian put 6 equal piles of returned books on the cart for Liu and Henry to reshelve. They also drew fraction bars.
2. On each sixths bar, circle two groups of sixths to show one way that Liu and Henry could share the work. (Each bar should show a different possibility.) Then complete the equation next to each bar to show their shares.
► Find the Unknown AddendWrite the fraction that will complete each equation.
3. 1 = 7 __ 7 = 1 __
7 +
5. 1 = 8 __ 8 = 3 __
8 +
7. 1 = 3 __ 3 = 2 __
3 +
9. 1 = 6 __ 6 = 2 __
6 +
4. 1 = 4 __ 4 = 3 __
4 +
6. 1 = 5 __ 5 = 2 __
5 +
8. 1 = 10 ___ 10
= 6 ___ 10
+
10. 1 = 8 __ 8 = 5 __
8 +
Name Date
216 UNIT 6 LESSON 2 Fractions that Add to One
Class Activity
1 11
12
12
22
13
33
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14
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44
15
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► Discuss and Compare Unit FractionsUse these fraction bars to help you compare the unit fractions. Write > or <.
Name Date
11. 1 __ 6 1 __
8 12. 1 __
5 1 __
3 13. 1 ___
10 1 ___
12
14. 1 __ 7 1 __
4 15. 1 __
9 1 ___
12 16. 1 __
9 1 ___
11
17. Complete this statement:
When comparing two unit fractions, the fraction with the smaller denominator is .
UNIT 6 LESSON 2 Fractions that Add to One 217
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► Compare and Order Unit FractionsWrite the unit fractions in order from least to greatest.
Dear Math Students,
I had to compare 1 _ 4
and 1 _ 2 on my math homework.
I reasoned that 1 _ 4
is greater than 1 _ 2 because 4 is
greater than 2. My friend told me this isn’t right. Can you help me understand why my reasoning is wrong?
Your friend,Puzzled Penguin
► What’s the Error?
18. 1 __ 6 , 1 __
8 , 1 __
5
20. 1 __ 3 , 1 ___
10 , 1 __
7
19. 1 ___ 11
, 1 __ 4 , 1 __
8
21. 1 __ 4 , 1 __
7 , 1 __
9
Solve
22. Andi and Paolo both ordered small pizzas. Andi ate 1 __ 4 of
her pizza. Paolo ate 1 __ 6 of his pizza. Who ate more pizza?
23. Elena ordered a small pizza. Max ordered a large pizza. Elena ate 1 __
3 of her pizza. Max ate 1 __
4 of his pizza. Elena said
she ate more pizza because 1 __ 3 > 1 __
4 . Do you agree? Explain.
24. Write a response to Puzzled Penguin.
Name Date
218 UNIT 6 LESSON 2 Fractions that Add to One
Class Activity
1–7
1–7
1–7
1–7
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1–7
1–7
1–7
1–7
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► Add FractionsThe circled parts of this fraction bar show an addition problem.
1. Write the numerators that will complete the additionequation.
__ 7 + __
7 = + _____
7 = __
7
Solve each problem. Write the correct numerator to complete each equation.
2. 3 __ 9 + 4 __
9 = + _____
9 = __
9 3. 1 __
5 + 3 __
5 = + _____
5 =
__ 5 4. 2 __ 8 + 5 __
8 = + _____
8 =
__ 8
5. What happens to the numerators in each problem?
6. What happens to the denominators in each problem?
► Subtract FractionsThe circled and crossed-out parts of this fraction bar show a subtraction problem.
7. Write the numerators that will complete the subtraction equation.
__ 7 - __
7 = - _____
7 = __
7
Content Standards 4.NF.3a, 4.NF.3d, 4.MD.2 Mathematical Practices MP.2, MP.3, MP.4, MP.6
Name Date
UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators 219
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► Subtract Fractions (continued)Solve each problem. Write the correct numerators to complete each sentence.
8. 5 __ 6 - 4 __
6 = - _____
6 = __
6 9. 9 ___
10 - 5 ___
10 = - _____
10 =
__ 10. 14 ___ 16
- 9 ___ 16
= - _____ 16
= __
11. What happens to the numerators in each problem?
12. How is subtracting fractions with like denominators similar to adding fractions with like denominators?
► Mixed Practice with Addition and SubtractionSolve each problem. Include the “circled” step in Exercises 16–21.
22. 7 __ 9
- 5 __ 9
_
25. 2 ___ 11
+ 7 ___ 11
_
23. 4 __ 5
- 3 __ 5
_
26. 5 __ 6
- 1 __ 6
_
24. 1 __ 3
+ 2 __ 3
_
27. 1 __ 8
+ 1 __ 8
_
13. 1 __ 4 + 2 __
4 = + ______
4 =
16. 4 ___ 10
+ 5 ___ 10
=
19. 5 __ 7 + 2 __
7 =
14. 3 __ 9 + 5 __
9 = + _____
9 =
17. 2 __ 5 + 4 __
5 =
20. 7 ___ 11
- 4 ___ 11
=
15. 6 __ 6 - 2 __
6 = - _____
6 =
18. 8 ___ 12
- 3 ___ 12 =
21. 8 __ 8 - 5 __ 8 =
Solve.
Name Date
220 UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators
2–2
1–2
1–2
1–3
1–3
1–3
3–3
1–6
1–6
1–6
1–6
1–6
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10—10
1—10
1—10
1—10
1—10
1—10
1—10
1—10
1—10
1—10
1—10
1–1one whole
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1—12
1—12
1—12
1—12
1—12
1—12
1—12
1—12
1—12
1—12
1—12
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► Fractions Bars
UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators 220A
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220B UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators
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28. Write a response to Puzzled Penguin.
29. Write a response to Puzzled Penguin.
Dear Math Students,
My friend said, “If you catch 3 fish and then 2 more fish, how many fish will you have?” Of course, I know I will have 5 fish! She said, “This is the same problem, but you have fifths instead of fish!”
Can you help me understand what my friend meant and help me find the right answer?
Your friend,Puzzled Penguin
Dear Math Students,
My friend said my answer for this problem is wrong too.
She said “Think about fish again. If you have 4 fish and then eat 3, how many will you have?” What does she mean? What should the answer be?
Your friend,Puzzled Penguin
► What’s the Error?
3 __ 5
+ 2 __ 5
= 5 ___ 10
4 __ 5
- 3 __ 5
= 1 __ 0
Name Date
UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators 221
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► Real World ProblemsDraw a model. Then solve.
30. Wayne had 7 __ 8 cup of trail mix. He ate 3 __
8 cup
as he was hiking. How many cups does he have now?
31. Reese had 2 __ 4 cup of orange juice. She added
pineapple juice to make a total of 3 __ 4 cup of
juice. How much pineapple juice did she add?
Write an equation. Then solve.
32. Nasira walks 4 __ 5 mile to school each day. This is 2 __
5 mile
farther than Kat walks. How far does Kat walk to school?
33. A puppy is now 5 weeks old. It has gained 8 ___ 16
pound since it was born. The puppy weighs 11 ___
16 pound now.
How much did the puppy weigh when it was born?
34. The water in a tub was 7 ___ 12
foot deep. Then Dom added water until it was 4 ___
12 foot deeper. How deep
is the water now?
35. Jesse had some flour. She used 3 __ 4 cup in a recipe
and had 1 __ 4 cup of flour left. How much flour did
she have to start with?
Name Date
Show your work.
222 UNIT 6 LESSON 3 Add and Subtract Fractions with Like Denominators
Class ActivityVOCABULARY
Regular (serves 2)Friendship (serves 4)Super (serves 10)Magna (serves 18)
$3.00 $5.00
$12.00 $20.00
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mixed number
► Mixed Numbers in the Real World
Nineteen friends decide to camp in the park. They order two Super sandwiches. Each camper eats 1 serving.
Solve.
1. How many campers does one Super sandwich serve?
3. What fraction of the second sandwich is left over?
2. What fraction of the second sandwich is needed to serve the rest of the campers?
4. What number tells how many Super sandwiches the campers ate in all?
A mixed number is a number that consists of a whole number and a fraction.
A fraction greater than 1 has a numerator greater than its denominator.
1 4 __ 6 3 4 __
5
10 ___ 6 19 ___
5
Mellie’s Deli makes sandwiches. This is the price list.
Content Standards 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3d Mathematical Practices MP.2, MP.5, MP.7
Name Date
UNIT 6 LESSON 4 Mixed Numbers and Fractions Greater Than 1 223
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► Convert Between Mixed Numbers and Fractions Greater Than 1
Change each mixed number to a fraction and each fraction to a mixed number.
5. 5 2 __ 3 =
7. 6 6 ___ 10
=
9. 2 7 __ 8 =
11. 8 3 __ 5 =
13. 40 ___ 6 =
15. 23 ___ 7 =
17. 22 ___ 4 =
19. 29 ___ 7 =
21. 4 6 __ 9 =
6. 3 3 __ 7 =
8. 9 1 __ 4 =
10. 4 5 __ 9 =
12. 7 4 __ 6 =
14. 11 ___ 2 =
16. 28 ___ 3 =
18. 25 ___ 8 =
20. 6 4 __ 8 =
22. 16 ___ 3 =
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224 UNIT 6 LESSON 4 Mixed Numbers and Fractions Greater Than 1
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1–8
1–8
1–8
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1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
1–5
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► Understand Fractions Greater Than 1 and Mixed Numbers
UNIT 6 LESSON 4 Mixed Numbers and Fractions Greater Than 1 224A
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
1 whole
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► Understand Fractions Greater Than 1 and Mixed Numbers (continued)
224B UNIT 6 LESSON 4 Mixed Numbers and Fractions Greater Than 1
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► Practice Addition and Subtraction with Fractions Greater Than 1
Add or subtract.
► Add Mixed Numbers with Like DenominatorsAdd.
► Subtract Mixed Numbers with Like DenominatorsSubtract.
Explain each solution.
7. 8. 9. 10.
11. 12. 13. 14.
15. 16. 17.
2 3 __ 5
+ 1 1 __ 5
_
5 6 __ 8
- 3 3 __ 8
_
6 2 __ 7 = 5 9 __
7
- 1 5 __ 7 = 1 5 __
7
__
4 4 __ 7
6 2 __ 6 = 5 8 __
6
- 1 5 __ 6 = 1 5 __
6
__
4 3 __ 6
6 2 ___ 11
= 5 13 ___ 11
- 1 5 ___ 11
= 1 5 ___ 11
___
4 8 ___ 11
3 5 __ 8
+ 1 3 __ 8
_
4 1 __ 5
- 1 3 __ 5
_
5 2 __ 3
+ 2 2 __ 3
_
5 1 __ 6
- 3 4 __ 6
_
1 2 __ 5
+ 3 4 __ 5
_
6 2 __ 8
- 4 5 __ 8
_
7 + 2 = 9 6 + 2 = 8 11 + 2 = 13
Content Standards 4.NF.3a, 4.NF.3c Mathematical Practices MP.3, MP.6
Name Date
1. 8 __ 5 + 3 __
5 =
4. 10 ___ 8 + 7 __
8 =
2. 6 __ 9 + 12 ___
9 =
5. 9 __ 6 - 4 __
6 =
3. 10 ___ 7 - 3 __
7 =
6. 19 ___ 10
- 7 ___ 10
=
555
UNIT 6 LESSON 5 Add and Subtract Mixed Numbers with Like Denominators 225
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18. Write a response to Puzzled Penguin.
Dear Math Students,
Here is a subtraction problem that I tried to solve.
Is my answer correct? If not, please help me understand why it is wrong.
Your friend,Puzzled Penguin
7 3 __ 8
- 1 5 __ 8
_
6 2 __ 8
► What’s the Error?
► Compare and SubtractCompare each pair of mixed numbers using > or <. Then subtract the lesser mixed number from the greater mixed number.
Name Date
19. 3 2 __ 5 ; 1 4 __
5
21. 14 ___ 11
; 1 6 ___ 11
23. 3 2 __ 6 ; 4 3 __
6
20. 8 __ 9 ; 2 2 __
9
22. 4 1 __ 8 ; 2 7 __
8
24. 10 1 __ 3 ; 7 2 __
3
226 UNIT 6 LESSON 5 Add and Subtract Mixed Numbers with Like Denominators
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► Practice with Fractions and Mixed NumbersWrite the fraction that will complete each equation.
Content Standards 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.MD.2, 4.MD.4 Mathematical Practices MP.1, MP.3, MP.4, MP.6
Name Date
1. 1 = 4 __ 4 = 1 __
4 + 2. 1 = 10 ___
10 = 9 ___
10 + 3. 1 = 8 __
8 = 4 __
8 +
4. 5 __ 6
6. 6 __ 8
5. 8 ___ 10
7. 10 ___ 6
8. 11 ___ 8 = 9. 15 ___
6 = 10. 32 ___
5 =
11. 3 2 __ 5 = 12. 1 1 __
4 = 13. 2 11 ___
12 =
14. 2 __ 5 + 1 __
5 =
17. 5 __ 7 - 2 __
7 =
20. 9 __ 4 + 5 __
4 =
15. 3 __ 9 + 6 __
9 =
18. 7 ___ 12
+ 1 ___ 12
=
21. 23 ___ 8 - 12 ___
8 =
16. 4 __ 6 - 3 __
6 =
19. 10 ___ 10
- 4 ___ 10
=
22. 5 __ 2 + 3 __
2 =
Write each fraction as a sum of fractions in two different ways.
Write each fraction as a mixed number.
Write each mixed number as a fraction.
Add or subtract.
UNIT 6 LESSON 6 Practice with Fractions and Mixed Numbers 227
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► Practice with Fractions and Mixed Numbers (continued)Add or subtract.
23. 3 1 __ 4
+ 5 2 __ 4
_
26. 4 1 __ 3
- 1 2 __ 3
_
24. 4 6 __ 8
- 3 3 __ 8
_
27. 2 5 ___ 10
+ 4 9 ___ 10
__
25. 1 3 __ 5
+ 1 2 __ 5
_
28. 10 5 __ 8
- 3 7 __ 8
_
29. Write a response to Puzzled Penguin.
Dear Math Students,
This is a problem from my math homework. My friend says my answer is not correct, but I can’t figure out what I did wrong. Can you help me find and fix my mistake?
Your friend,Puzzled Penguin
► What’s the Error?
4 9 __ 8
4 1 __
8
− 1 5 __8
_3 4 __
8
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228 UNIT 6 LESSON 6 Practice with Fractions and Mixed Numbers
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► Real World ProblemsWrite an equation. Then solve.
30. Daniel spent 1 1 __ 4 hours playing soccer on Saturday
and 3 __ 4 hour playing soccer on Sunday. How much
time did he spend playing soccer over the weekend?
31. A pitcher contains 4 3 __ 8 cups of juice. Antonio pours
5 __ 8 cup into a glass. How much juice is left in the pitcher?
32. Shayna walked from school to the library. Then she walked 1 3 ___
10 miles from the library to her apartment.
If she walked 2 1 ___ 10
miles in all, how far did she walk from school to the library?
33. The vet said Lucy’s cat Mittens weighs 7 1 __ 4 pounds.
This is 1 2 __ 4 pounds more than Mittens weighed last year.
How much did Mittens weigh last year?
34. The width of a rectangle is 3 5 __ 6 inches. The length of the
rectangle is 1 4 __ 6 inches longer than the width. What is the
length of the rectangle?
35. Choose one of the problems on this page. Draw a model to show that your answer is correct.
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Show your work.
UNIT 6 LESSON 6 Practice with Fractions and Mixed Numbers 229
Class Activity
Distance (inches)
0 114
12
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114
112
314
2 124
122
324
3 4134
132
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► Make a Line Plot 36. Make a mark anywhere on this line segment.
37. Measure the distance from the left end of the segment to your mark to the nearest quarter inch.
38. Collect measurements from your classmates and record them in the line plot below.
39. The range is the difference between the greatest value and the least value. What is the range of the data?
40. Which distance value was most common?
41. Describe any interesting patterns in the data values. For example, are there any large gaps? Are there clusters of values?
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230 UNIT 6 LESSON 6 Practice with Fractions and Mixed Numbers
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► A Whole Number Multiplied by a Unit Fraction
The lunchroom at Mandy’s school serves pizza every Friday. Each slice is 1 __
4 of a pizza. Mandy eats one slice
every week.
To find the fraction of a pizza she eats in three weeks, you can add or multiply.
1 __ 4 + 1 __
4 + 1 __
4 = 3 __
4 or 3 ⋅ 1 __
4 = 3 __
4
Solve each problem, first by adding and then by multiplying. Show your work.
1. What fraction of a pizza does she eat in five weeks?
2. What fraction of a pizza does she eat in eleven weeks?
Draw a model for each problem. Then solve.
Draw a model for each fraction. Then write each fraction as the product of a whole number and a unit fraction.
Content Standards 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c Mathematical Practices MP.1, MP.2, MP.3, MP.4, MP.6
Name Date
3. 2 ⋅ 1 __ 3 = 4. 6 ⋅ 1 __
5 = 5. 10 ⋅ 1 __
8 =
6. 3 __ 5 = ⋅ 1 __
5 7. 8 __
3 = ⋅ 8. 12 ___
7 = ⋅
UNIT 6 LESSON 7 Multiply a Fraction by a Whole Number 231
Class Activity
Week 1 Week 2 Week 3 Week 1 Week 2 Week 3
Week 4 Week 5
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► A Whole Number Multiplied by a Non-Unit Fraction
The lunchroom at Joe’s school serves sub sandwiches every Thursday. Each slice is 1 __
6
of a sub. Joe eats two pieces, or 2 __ 6 of a
sandwich, every week.
Solve each problem, first by adding and then by multiplying. Write your answer as a fraction. Show your work.
Draw a model for each problem. Then solve.
Solve. Write your answer as a fraction.
1 __ 6 + 1 __
6 = 2 __
6 or 2 ⋅ 1 __
6 = 2 __
6
Name Date
14. 8 ⋅ 3 __ 4 =
17. 4 ⋅ 5 __ 7 =
15. 18 ⋅ 2 __ 3 =
18. 15 ⋅ 3 ___ 10
=
16. 10 ⋅ 5 __ 6 =
19. 7 ⋅ 8 __ 9 =
11. 4 ⋅ 3 __ 8 = 12. 2 ⋅ 4 __
5 = 13. 5 ⋅ 2 __
3 =
9. What fraction of a sandwich does Joe eat in three weeks?
10. What fraction of a sandwich does Joe eat in five weeks?
232 UNIT 6 LESSON 7 Multiply a Fraction by a Whole Number
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► Real World ProblemsDraw a model for each problem. Then solve.
20. The five members of the Sanchez family each drank 3 __ 4 cup orange juice for breakfast. How much juice
did the family drink for breakfast altogether?
21. Stella ran 1 __ 2 mile. Brian ran 7 times as far as Stella.
How far did Brian run?
Write an equation. Then solve.
22. A banner has a length of 3 yards and a width of 2 __ 3 yard.
What is the area of the banner?
23. The 12 members of a volleyball team had a pizza party. Each pizza was divided into 8 equal slices and each player ate 3 slices. What fraction of a pizza did the team eat altogether?
24. It took Eli’s mother 1 __ 6 hour to drive him to school. It
took Alex 4 times as long as this to walk to school. How long did it take Alex to walk to school?
Name Date
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UNIT 6 LESSON 7 Multiply a Fraction by a Whole Number 233
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► Real World Problems (continued)Write an equation. Then solve.
25. Ami has building bricks that are 5 __ 8 inch thick. She
makes a stack of 15 bricks. How tall is the stack?
26. A crepe recipe calls for 3 __ 4 cups of flour. A bread
recipe calls for four times this much flour. How much flour is in the bread recipe?
27. The path around a park is 7 ___ 12
mile long. Nicolas ran around the park 6 times along the path. How far did he run?
28. Write a response to Puzzled Penguin.
Dear Math Students,I have so much homework! I have assignments in math, science, and reading. I think each subject will take 1 _ 2 hour. I tried to multiply to find the total time.
3 • 1 _ 2 = 3 _ 6
That can’t be right! I know 3 _ 6 is the same as 1 _ 2 , so
that is only 1 _ 2 hour.
What did I do wrong? How long will my homework really take?
Your friend,Puzzled Penguin
► What’s the Error?
Name Date
Show your work.
234 UNIT 6 LESSON 7 Multiply a Fraction by a Whole Number
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► Multiplication PracticeWrite each fraction as a sum of unit fractions and as the product of a whole number and a unit fraction.
Draw a model for each problem. Then solve.
Multiply. Write your answer as a mixed number or a whole number, when possible.
Content Standards 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c, 4.MD.2 Mathematical Practices MP.4, MP.5
Name Date
1. 4 __ 7 =
4 __ 7 =
3. 2 __ 3 =
2 __ 3 =
2. 5 __ 2 =
5 __ 2 =
4. 6 __ 4 =
6 __ 4 =
5. 6 ⋅ 1 __ 4 = 6. 6 ⋅ 2 __
3 =
9. 20 ⋅ 3 ___ 10
= 10. 36 ⋅ 5 __ 9 =
7. 3 ⋅ 2 __ 9 = 8. 4 ⋅ 4 __
5 =
11. 2 ⋅ 2 ___ 12
= 12. 21 ⋅ 1 __ 3 =
13. 16 ⋅ 3 __ 8 = 14. 11 ⋅ 7 ___
10 =
UNIT 6 LESSON 8 Practice Multiplying a Fraction by a Whole Number 235
Class Activity6-8
► Real World ProblemsDraw a model for each problem. Then solve. Write your answer as a mixed number or a whole number, when possible.
15. Michelle has three textbooks. Each weighs 5 __ 8 pound.
What is the total weight of her textbooks?
16. Mark lived in a house in the suburbs with 2 __ 3 acre of land.
Then he moved to a farm in the country that had 6 times this much land. How much land is on Mark’s farm?
Write an equation. Then solve. Write your answer as a mixed number or a whole number, when possible.
17. A restaurant served quiche for lunch today. Each quiche was cut into six pieces. The restaurant sold 59 pieces. How many quiches is this?
18. Zahra’s dog Brutus weighed 7 __ 8 pound when he was
born. Now he weighs 60 times this much. How much does Brutus weigh now?
19. Calvin made posters to advertise the school play. The posters are 2 feet long and 11 ___
12 foot wide.
What is the area of each poster?
Name Date
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Show your work.
236 UNIT 6 LESSON 8 Practice Multiplying a Fraction by a Whole Number
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► Practice Fraction OperationsWrite each fraction as a sum of fractions in two different ways.
Add or subtract.
Multiply. Write your answer as a mixed number or a whole number, when possible.
8. 9. 10.
11. 12. 13.
6 7 ___ 10
- 1 4 ___ 10
__
5 2 __ 3
+ 4 1 __ 3
_
7 1 __ 6
- 3 2 __ 6
_
12 4 __ 9
+ 10 5 __ 9
__
1 4 __ 5
+ 1 3 __ 5
_
7
- 1 1 __ 4
_
Content Standards 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c Mathematical Practices MP.1
Name Date
5. 5 __ 8 + 3 __
8 = 6. 2 ___
10 + 1 ___
10 = 7. 7 __
9 - 3 __
9 =
14. 7 ⋅ 1 ___ 10
= 15. 4 ⋅ 2 __ 9 = 16. 5 ⋅ 3 __
5 =
17. 12 ⋅ 3 __ 4 = 18. 7 ⋅ 5 __
8 = 19. 10 ⋅ 5 __
6 =
1. 3 ___ 10
=
3. 4 __ 5 =
2. 7 __ 7 =
4. 5 ___ 12
=
UNIT 6 LESSON 9 Mixed Practice 237
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► Real World ProblemsWrite an equation. Then solve.
20. Dimitri rode his bike 32 miles yesterday. He rode 12 4 __ 5 miles
before lunch and the rest of the distance after lunch. How far did he ride after lunch?
21. Ms. Washington is taking an accounting class. Each class is 3 __
4 hour long. If there are 22 classes in all, how many
hours will Ms. Washington spend in class?
22. Elin bought a large watermelon at the farmer’s market. She cut off a 5 5 __
8 -pound piece and gave it to her
neighbor. She has 11 5 __ 8 pounds of watermelon left.
How much did the whole watermelon weigh?
23. A recipe calls for 3 __ 4 cup of whole wheat flour, 1 2 __
4 cups of white
flour, and 3 __ 4 cup of rye flour. How much flour is this in all?
24. Henri spent a total of 3 2 __ 6 hours working on his science
project. Kali spent 1 5 __ 6 hours working on her science
project. How much longer did Henri work on his project?
25. Mr. Friedman’s baby daughter is 5 __ 9 yard long. Mr. Friedman’s
height is 4 times this much. How tall is Mr. Friedman?
26. A track is 1 __ 4 mile long. Kenny ran around the track 21 times.
How far did Kenny run in all?
Name Date
Show your work.
238 UNIT 6 LESSON 9 Mixed Practice
Class Activity
vegetables wheat
vegetablesItalianherbs
vegetables
dairycows
fruit
fruit
6-10
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► Math and Vegetarian Pizza FarmsA pizza farm is a circular region of land divided into eight pie-shaped wedges or slices, such as those you would see in a pizza. There are hundreds of such farms across the United States. At a vegetarian pizza farm, each wedge or slice grows a different vegetarian ingredient used to make a pizza. Some things you might find on a vegetarian pizza farm include wheat, fruit, vegetables, Italian herbs, and dairy cows.
Write an equation to solve.
A farmer created a vegetarian pizza farm with these wedgesor slices: 3 __
8 for vegetables, 1 __
8 for wheat, 2 __
8 for fruit,
1 __ 8 for dairy cows, and 1 __
8 for Italian herbs.
1. What fraction of the farm is made up of fruitor vegetables?
2. What fraction of the farm is not made up of wheat?
3. Which wedge of the farm is bigger, the wedge forfruit or the wedge for Italian herbs? Explain.
Show your work.
Content Standards 4.NF.2, 4.NF.3c, 4.NF.3d, 4.NF.4, 4.NF.4c Mathematical Practices MP.1, MP.5
Name Date
UNIT 6 LESSON 10 Focus on Mathematical Practices 239
Class Activity
Time Spent ResearchingDuring Study Time (in hours)
51
52
53
54
55
6-10
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Write an equation to solve.
4. On Monday, two of the workers at the pizza farm each filled a basket with ripe tomatoes. Miles picked 15 1 __
6 pounds of tomatoes, and Anna picked
13 5 __ 6 pounds of tomatoes. How many more pounds
of tomatoes did Miles pick than Anna?
For Problems 5–6, use the line plot to solve.
After a field trip to a vegetarian pizza farm, Mrs. Cannon asked each of her students to use some of their study time to research different vegetarian ingredients for pizzas. The line plot below shows the amount of time each student spent researching during study time.
Show your work.
5. How many students spent at least 3 __ 5 hour
researching? Explain how you know.
6. How many hours in all did the students who researched for 2 __
5 hour spend researching?
Write a multiplication equation to solve.
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240 UNIT 6 LESSON 10 Focus on Mathematical Practices
Review/Test
18
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1. Represent the shaded part of the fraction bar as the product of a whole number and a unit fraction.
2. In the morning Naomi jumps rope for 1 __ 4 hour. After lunch she jumps rope for another 2 __ 4 hour. How long does Naomi jump rope? Write an equation. Then solve.
Equation: ____________
Solution: ____________ hour
3. For numbers 3a–3d, write a fraction from the tiles to make a true equation.
1 ___ 10
2 ___ 10
3 ___ 10
4 ___ 10
3a. 10 ___ 10
= 5 ___ 10
+ 3 ___ 10
+
3b. 1 = 1 ___ 10
+ 5 ___ 10
+
3c. 7 ___ 10
= 1 ___ 10
+ 1 ___ 10
+ 1 ___ 10
+ 1 ___ 10
+
3d. 4 ___ 10
= 1 ___ 10
+ 1 ___ 10
+ 1 ___ 10
+
Name Date
UNIT 6 TEST 241
Review/TestUNIT 6
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4. Caesar buys dog treats and cat treats. He buys 7 __ 8 pound of dog
treats. This is 5 __ 8 pound more than the weight of the cat treats
he buys. How many pounds of cat treats does Caesar buy? Write an equation. Then solve.
Equation: ____________
Solution: ____________ pound
5. A recipe calls for 2 __ 3 cup of mushrooms. Dae uses 3 times as
much mushrooms. Choose the number of cups of mushrooms he uses. Mark all that apply.
A 5 __ 3 cup C 2 cups
B 6 __ 3 cups D 3 cups
6. Complete the table to show the fraction as a product of a whole number and a unit fraction.
Fraction Product
5 ___ 12
2 __ 3
4 __ 7
7. For 7a–7d, choose the operation that makes the equation true.
7a. 6 3 __ 4 = 4 2 __ 4
7b. 3 2 __ 5 = 2 3 __ 5
7c. 4 3 3 __ 5 = 7 3 __ 5
7d. 7 1 __ 3 = 2 1 __
3
+
-
×
+
-
×
+
-
×
+
-
×
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242 UNIT 6 TEST
Review/TestUNIT 6
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8. Multiply the expression to complete the table.
Expression Written as a Fraction
Written as a Mixed Number
7 ⋅ 1 __ 6
12 ⋅ 1 __ 5 2 2 __ 5
3 ⋅ 5 __ 8
9. For numbers 9a–9f, choose True or False for the equation.
9a. 2 __ 8 + 1 __
8 = 3 ___
16 True False
9b. 4 __ 5 - 1 __ 5 = 3 __ 5 True False
9c. 9 __ 4 + 2 __ 4 = 2 3 __ 4 True False
9d. 5 ___ 12
+ 4 ___ 12
= 9 ___ 24
True False
9e. 8 5 __ 6 - 6 4 __
6 = 2 1 __
6 True False
9f. 2 7 ___ 10
+ 3 3 ___ 10
= 5 10 ___ 20
True False
10. Elias says this problem can be solved using addition. Vladmir says it can be solved using multiplication. Explain why both boys are correct.
Milo practices piano 3 __ 5 hour every day. How many hours does
he practice in 5 days?
Name Date
UNIT 6 TEST 243
Review/TestUNIT 6
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11. For 11a and 11b, find the sum or difference. Write your answer as a mixed number or a whole number, when possible.
11a. 11b.
12. On Saturday, Jesse plays basketball for 2 __ 3 hour. Then he plays
some more. He plays 2 1 __ 3 hours in all. How much longer did
Jesse play basketball?
Part A
Draw a model to represent the problem. Then solve. Explain how your model helps you solve the problem.
Part B
On Sunday, Jesse played basketball for 1 2 __ 3 hours. How many
total hours did he play basketball on Saturday and Sunday? Show your work.
9 3 __ 8
- 3 7 __ 8
5 2 __ 3
+ 4 2 __ 3
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244 UNIT 6 TEST
Review/TestUNIT 6
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13. Rebecca’s soup recipe calls for 3 __ 4 cup milk. She needs 3 times as much milk to make a triple batch of soup. How many cups of milk does Rebecca need?
Part A
Draw a model for the problem.
Part B
Use your model to write two equations for the problem. Then solve.
14. For numbers 14a–14e, choose Yes or No to tell whether the fraction is correctly expressed as the sum of other fractions.
14a. 8 ___ 13
= 5 ___ 13
+ 3 ___ 13
Yes No
14b. 4 __ 5 = 1 __ 5 + 1 __ 5 + 1 __ 5 + 1 __ 5 + 1 __ 5 Yes No
14c. 6 ___ 11 = 4 __ 6 + 2 __ 5 Yes No
14d. 3 __ 8 = 1 __
8 + 1 __
8 + 1 __
8 Yes No
14e. 10 ___ 17 = 5 ___ 17 + 5 ___ 17 Yes No
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UNIT 6 TEST 245
Review/Test
Trail Lengths (miles)
158
68
78 1 1
21 381 2
81 18
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15. The line plot shows the lengths of trails Andrea hiked last month at a state park.
Andrea hiked 3 miles last week. She could have hiked two 1 1 __
2 -mile trails. Describe two other combinations
of trails she could have hiked.
16. Select the expression that is equivalent to 2 2 __ 7 . Mark all that apply.
A 1 __ 7 + 1 __ 7 + 2 __ 7 D 7 __ 7 + 7 __ 7 + 1 __ 7 + 1 __ 7
B 1 + 1 + 2 __ 7 E 20 ___ 7 + 2 __ 7
C 2 __ 7 + 2 __ 7 + 2 __ 7 F 7 __ 7 + 4 __ 7 + 3 __ 7 + 2 __ 7
17. Explain how to change 11 ___ 4 to a mixed number.
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246 UNIT 6 TEST