INVESTIGATION 1 Parts of Rectangles · INVESTIGATION 3 Working with Decimals Day Session Common Core Adaptation Common Core Standards 19 3.1 Representing Decimals MP5, MP6 4.NF.5,

Common Core

I N V E S T I G AT I O N 1

Parts of RectanglesDay Session Common Core Adaptation Common Core Standards

1 1.1 Fractions of an Area: Halves, Fourths, and Eighths

MP1, MP2 4.NBT.2, 4.NF.1, 4.NF.3.a, 4.NF.3.b

2 1.2 Fractions of an Area: Thirds and Sixths

MP1, MP2 4.NBT.2, 4.NF.3.a, 4.NF.3.b

3 1.3 Fractions of Groups of Things

MP4 4.NBT.2, 4.NF.3.d

4 1.4 Same Parts, Different Wholes

MP4 4.NBT.2, 4.NF.3.d

5 1.5 Assessment: Identifying and Comparing Fractions

MP1, MP2, MP4 4.NBT.2, 4.NF.1, 4.NF.3.a

6 1.6 Combinations That Equal 1

MP2 4.NBT.2, 4.NF.3.a, 4.NF.3.b

7 1.7 Adding Fractions MP2 4.NBT.2, 4.NF.2, 4.NF.3.a

8 1.8A Subtracting Fractions See p. CC48. MP1, MP4, MP5 4.NF.3.a, 4.NF.3.d

Mathematical Practices (MP)

Domains• Number and Operations in Base Ten (NBT)• Number and Operations–Fractions (NF)• Measurement and Data (MD)

Fraction Cards and Decimal Squares

Unit 6

Instructional Plan CC45

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Ordering FractionsDay Session Common Core Adaptation Common Core Standards

9 2.1 Fraction Cards MP3 4.NF.1, 4.NF.2SESSION FOLLOW-UP

Daily Practice and Homework

Daily Practice: In addition to Student Activity Book page 28, students complete Student Activity Book page 30 or C31 (Fraction Subtraction) for reinforcement of the content of this unit.

10 2.2 Fraction Cards, continued MP3 4.NF.2

11 2.3 Capture Fractions MP3 4.NF.1, 4.NF.2

12 2.4 Comparing Fractions to Landmarks

MP7 4.NF.2

13 2.5 Fractions on a Number Line

MP5 4.NF.1, 4.NF.2, 4.NF.3.a

14 2.6 Assessment: Comparing Fractions

MP5 4.NF.1, 4.NF.2

15 2.7A Adding and Subtracting Mixed Numbers

See p. CC52. MP5 4.NF.3.c, 4.MD.4

I N V E S T I G AT I O N 3A

Multiplying FractionsDay Session Common Core Adaptation Common Core Standards

16 3A.1 Multiplying Whole Numbers and Fractions

See p. CC57. MP4 4.NF.4.a, 4.NF.4.b, 4.NF.4.c

17 3A.2 Multiplying Whole Numbers and Fractions, continued


18 3A.3 Assessment: Multiplying with Fractions


CC46 UNIT 6 Fraction Cards and Decimal Squares

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Working with DecimalsDay Session Common Core Adaptation Common Core Standards

19 3.1 Representing Decimals MP5, MP6 4.NF.5, 4.NF.6, 4.NF.7, 4.MD.2

SESSION FOLLOW-UPDaily Practice and Homework

Daily Practice: In addition to Student Activity Book page 46, students complete Student Activity Book page 48 or C43 (Bug Collections) for reinforcement of the content of this unit.

20 3.2 Comparing Decimals MP5, MP6 4.NF.6, 4.NF.7

21 3.3 Representing and Combining Decimals

MP5, MP7 4.NF.5, 4.NF.6, 4.NF.7

22 3.4 Estimating and Adding Miles and Tenths of a Mile

MP4, MP5 4.NF.7, 4.MD.2

SESSION FOLLOW-UPDaily Practice and Homework

Daily Practice: In addition to Student Activity Book page 54, students complete Student Activity Book page 56 or C44 (Buying Fabric) for reinforcement of the content of this unit.

23 3.5 Comparing and Combining Decimals

MP4 4.NF.7, 4.MD.2

SESSION FOLLOW-UPDaily Practice

Daily Practice: In addition to Student Activity Book page 59, students complete Student Activity Book page 60A or C45 (Multiplying with Fractions) for reinforcement of the content of this unit.

24 3.6 Comparing and Combining Decimals, continued

MP4 4.NF.7, 4.MD.2

SESSION FOLLOW-UPDaily Practice

Daily Practice: In addition to Student Activity Book page 60, students complete Student Activity Book page 60B or C46 (Working Hard) for reinforcement of the content of this unit.

25 3.7 End-of-Unit Assessment MP1, MP2 4.NF.2, 4.NF.7

Instructional Plan CC47

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s e s s i o n 1 . 8 A

Activity

SubtractingFractions45 Min clAss

•Student Activity Book,p.26Aorc29, subtracting Fractions Makecopies.(asneeded)

Discussion

SubtractingFractions15 Min clAss

•Students’completedcopiesofStudent Activity Book,p.26AorC29(fromActivity1)

session Follow-up

DailyPractice •Student Activity Book,p.26Borc30, More subtracting Fractions Makecopies.(asneeded)

today’s plan Materials

SubtractingFractionsMath Focus points

Using visual representations to subtract fractions with like denominators

Subtracting fractions with like denominators

Ten-MinuteMathPracticing Place Value Write 3,850 on the board and have students practice saying it. Make sure all students can read, write, and say this number correctly. Ask students to write this number in expanded form. Then ask students to solve these problems mentally, if possible. • What is 3,850 – 300? 3,850 – 400? 3,850 + 300?

3,850 + 400? 3,850 + 500?Write each answer on the board. Have students compare each sum or difference with 3,850. Ask students: • Which places have the same digits? Which do not? Why?

cc48 investigAtion 1 parts of Rectangles

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DateNameFraction Cards and Decimal Squares

26A Unit 6 Session 1.8A

Subtracting FractionsSolve each problem and show your work. For the word problems, write an equation.

1. There was 7 _ 8 of a pan of brownies on the table. Some friends came over and ate 4 _ 8 of the pan of brownies. What fraction of the pan of brownies is left?

2. Marisol walks to school. The school is 6 __ 10 of a mile from her house. She has already walked 4 __ 10 of a mile. How much farther does Marisol have to walk?

3. There was 7 __ 12 of a gallon of milk in the refrigerator. The Jones family used 3 __ 12 of the gallon during breakfast. How much milk remains?

4. 4 __ 5 − 2 __

5 = 5. 9 ___

12 − 5 ___

12 =

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1 Activity 2 Discussion 3 Session Follow-Up

A C T I V I T Y

Subtracting FractionsClASS45 MIn

Ask students to draw a rectangle, shade 3 _ 4 , and check with a neighbor to make certain they have correctly shaded 3 _ 4 of the rectangle.

We’ve been adding fractions, and today we’re going to work on subtracting fractions. Let’s solve this problem:

Helena had 3 _ 4 of a bag of marbles and she gave 1 _ 4 of the bag of marbles to her little brother. How much of the bag did she have left?

Look at your rectangle. How could you show the 1 _ 4 Helena gave to her brother? What’s the answer to the problem?

Students might say:

“I just crossed out the 1 _ 4 of the marbles Helena gave away. That left me with 2 _ 4.”

What equation would you write to represent the problem?

Write the equation on the board: 3 _ 4 − 1 _ 4 ∙ 2 _ 4 .

[Damian] says he wrote 3 _ 4 − 1 _ 4 ∙ 1 _ 2 Are these answers equal? Is 1 _ 2 also correct?

Students should agree that 2 _ 4 and 1 _ 2 are equivalent fractions and that both answers are correct.

Students solve problems involving subtraction of fractions on Student Activity Book page 26A or C29.

As you work on these problems, think about what you know about fractions and about subtraction.

▲ Student Activity Book, Unit 6, p. 26A;Resource Masters, C29

Session 1.8A Subtracting Fractions CC49

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OngOing A SSeSSment: Obser ving Student s at Work

Studentsuserepresentationstosolvesubtractionproblemsinvolvingfractionswithlikedenominators.

• Howarestudentsusingrepresentationstosubtractfractions? Aretheyusingrectanglesormakingdrawingsthatmatchthecontextoftheproblem?Aretheymaintainingequal-sizedparts?

• Areanswersreasonable? Arestudentscontinuingtoreasonaboutthesizeoffractions?

DiFFerentiAtiOn: Suppor ting the range of Lear ner s

Somestudentsarestilldevelopingtheirideasaboutthemeaningoffractionsandmaybeunabletodrawrepresentationsforeachofthefractions.Helpthesestudentsdividearectangleintoequalparts,andthenshadeintheappropriatefraction.

Somestudentswillquicklyrecognizetheyonlyneedtosubtractthenumerator,andthedenominatorstaysthesame.Givethesestudentsproblemswithunlike,butrelatedfractions,suchas7 _ 8  – 1 _ 4  or 9 __ 10  – 3 _ 5 ,andaskthemtouserepresentationsandreasoningtosolvetheseproblems.

D i S c U S S i O n

Subtracting FractionscLASS15 min

math Focus Points for Discussion Subtractingfractionswithlikedenominators

Askoneortwostudentsforsolutions,includingdrawings,toProblem1onStudent Activity Bookpage26AorC29.Aftereachstudentexplainshisorhersolution,asktheclass:

Where is each of the fractions in the drawing? The 7 _ 8 ? 4 _ 8 ? 3 _ 8 ?

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DateNameFraction Cards and Decimal Squares Daily Practice

26BSession 1.8A Unit 6

More Subtracting Fractions Solve each problem and show your work. For the word problems, write an equation.

1. There is 7 _ 8 of a carton of juice in the refrigerator. The Ortega family drank 5 _ 8 of the carton with their breakfast. What fraction of the carton remains?

2. Venetta was walking to the library, which is 3 _ 4 of a mile away. She has walked 1 _ 4 of a mile. How much farther does Venetta have to walk?

3. Richard had 4 _ 5 of a bag of carrots. He fed 2 _ 5 of the bag to his rabbit. What fraction of the bag did Richard have left?

4. 7 ___ 10

− 4 ___ 10

= 5. 6 __ 8 − 1 __

8 =

note Students solve subtraction problems involving fractions with like denominators.

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Write down the equations for Problems 1–3, and ask students to provide the answer for each.

1. 7 _ 8 – 4 _ 8 = 3 _ 8

2. 6 __ 10 – 4 __ 10 = 2 __ 10 (or 1 _ 5 )

3. 7 __ 12 – 3 __ 12 = 4 __ 12 (or 1 _ 3 )

As you were solving these problems, and now looking at the solutions, is there anything you noticed about these fractions? Which numbers changed and which stayed the same?

Collect a few responses, and focus on the idea of like denominators.

[Yuki] noticed that the denominator stays the same, unless we use an equivalent fraction for the answer. Why do you think this is true? Turn and discuss with a neighbor.

After a minute or two, collect some responses.

Students might say:

“The denominator tells how many pieces there are all together, so it stays the same.”

“I think that’s right. I’m not sure what you’d do if the denominators weren’t the same.”

[Amelia] brings up a good question. What if the problem were 3 _ 4 − 1 _ 2 ? Could we just subtract the numerators? Why or why not?

The purpose of this question is to highlight that the reason numerators can be subtracted in the problems students have been working on is because the denominators are the same.

S e S S i o n F o l l o w - U p

Daily Practice Daily Practice: For reinforcement of this unit’s content,

have students complete Student Activity Book page 26B or C30.

▲ Student Activity Book, Unit 6, p. 26B;Resource Masters, C30

Session 1.8A Subtracting Fractions CC51

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s e s s i o n 2 . 7 A

Ten-Minute MathCounting Around the Class Today we’re going to count around the class, but instead of using whole numbers, we’re going to count by fractions. Students count around the class by  1 _ 2  s until all students have counted once. Ask students to say each number as a fraction, not a mixed number (1 _ 2  ,  2 _ 2  ,   3 _ 2  ,  4 _ 2  , etc.). Draw a number line marked in halves, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line.• What number did the 6th person say? How do you write   6 _ 2   as a whole number? (3) • What number did the 9th person say? How do you write  9 _ 2   as a mixed number? (4  1 _ 2  )

Activity

Data on a Line Plot20 Min clAss individuAls

•Student Activity Book,p.44Aorc32, Butterfly Wingspans (page 1 of 2)Makecopies.(asneeded)

Activity

Butterfly Wingspans25 Min individuAls

•Student Activity Book,p.44Borc33, Butterfly Wingspans (page 2 of 2)Makecopies.(asneeded)

discussion

Adding and Subtracting Mixed Numbers 15 Min clAss

•Students’completedcopiesofStudent Activity Book,p.44BorC33(fromActivity2)

session FolloW-uP

Daily Practice •Student Activity Book,p.44Corc34, Pepper’s Puppies Makecopies.(asneeded)

today’s Plan Materials

Adding and Subtracting Mixed NumbersMath Focus Points

Making a line plot to display a data set of measurements involving fractions

Adding and subtracting mixed numbers with like denominators using representations and reasoning about fractions and the operations

cc52 investiGAtion 2 ordering Fractions

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Butterfly Wingspans (page 1 of 2)

Yuki went to the Natural History Museum to study butterflies. The information he has about some of the butterflies in the collection is shown below.

Name Wingspan (inches) Name Wingspan

(inches)

American Snout 1 1 _ 2 Pearl Crescent 1 5 _ 8

Giant Swallowtail 5 1 _ 4 Postman 2 1 _ 2

Julia 3 1 _ 2 Red Admiral 31 _ 8

Milbert’s Tortoiseshell 2 5 _ 8 Saturn 4 1 _ 4

Monarch 3 1 _ 2 Tiger Swallowtail 3 3 _ 4

Painted Lady 2 1 _ 2 Viceroy 2 7 _ 8

Record the measurements on the line plot below.

1 2 3 4 5 60

Butterfly Wingspans (inches)

Write three statements that describe the data.

Unit 6 Session 2.7A44A

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1 Activity 2 Activity 3 Discussion 4 Session Follow-Up

A c t i v i t y

Data on a Line PlotinDiviDUAlSclASS20 Min

Have students look at Student Activity Book page 44A or C32. Ask them what they notice about the data. If necessary, explain that wingspan refers to the longest distance possible across the wings of a butterfly. Draw the number line for the line plot on the board. Ask students what each of the tick marks between the whole numbers on the line plot represents; establish that each mark represents 1 _ 4 of an inch and that 2 _ 4 is equivalent to 1 _ 2 . Have volunteers label each of the tick marks (e.g., 1 _ 4 , 1 _ 2 , 3 _ 4 ,…).

You’re going to use the data in the table to create a line plot. Let’s start with the American Snout butterfly. Where would we put the X to show its wingspan on the line plot?

Once students have agreed, place an X above 1 1 _ 2 on the line plot on the board and have students do the same at their desks.

Now let’s look at the Milbert’s Tortoiseshell butterfly. Where would we put the X to show its wingspan? Talk to a neighbor and see if you can agree where the X would go.

Point to the location on the line plot that shows 2 5 _ 8 .

[Lucy] says the X should go here, and that’s correct. Why does the X go halfway between 2 1 _ 2 and 2 3 _ 4 ? There aren’t marks that show eighths on our line plot, so use what you know about fractions to correctly complete the line plot.

After students complete the line plot, tell them to write statements about the data. When they are done, they should check with a neighbor to make certain they have all the data correctly displayed.

When there are a few minutes remaining, call students back together. Ask how they would describe the shape of the data. Students are likely to mention that there are 12 pieces of data, most of the data are clumped between 2 and 4 inches, the lowest value is 1 1 _ 2 inches, and the highest is 5 1 _ 4 inches. (Some students may determine that the range is 3 3 _ 4 inches.)

▲ Student Activity Book, Unit 6, p. 44A; Resource Masters, c32

Session 2.7A Adding and Subtracting Mixed numbers cc53

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44BSession 2.7A Unit 6

Butterfly Wingspans (page 2 of 2)

Use the information on the previous page to solve the following problems. Show your work.

1. How much longer is the wingspan of the Viceroy butterfly than the wingspan of the Pearl Crescent butterfly?

2. How much longer is the wingspan of the Giant Swallowtail butterfly than the wingspan of the Tiger Swallowtail butterfly?

3. The American Snout butterfly and the Postman butterfly are side-by-side. What is the length of their combined wingspans?

4. How much longer is the wingspan of the Red Admiral butterfly than the wingspan of Milbert’s Tortoiseshell butterfly?

5. The Pearl Crescent butterfly and the Viceroy butterfly are side-by-side. What is the length of their combined wingspans?

6. The Saturn butterfly and the Tiger Swallowtail butterfly are side-by-side. What is the length of their combined wingspans?

INV12_SE04_U6.indd 2 6/1/11 3:10 PM

OngOing Assessment: Obser ving student s at Work

Studentsusetheinformationfromthetabletocompletethelineplot.

• Canstudentscorrectlyplotthedata?

• Arestudents’statementsaboutthedataaccurate?

DifferentiAtiOn: suppor ting the range of Lear ner s

Somestudentsarestillworkingonunderstandingfourthsandhalves.Helpthesestudentsputmarksonthelineplotforeighths.

A C t i V i t Y

Butterfly WingspansinDiViDuALs25 min

Let’s look at Problem 1 on Student Activity Book page 44B or C33, together. First find the wingspan of the Viceroy butterfly (27_8inches) and the Pearl Crescent butterfly (15_8 inches). Then work alone or with a partner to find the answer to the problem. Think about what you know about fractions and subtraction.

Givestudentsseveralminutestowork.Thenaskhowtheydeterminedthedifferenceinthewingspans.

Students might say:

“I just subtracted. 2 – 1 = 1, and 7 _ 8 – 5 _ 8 is 2 _ 8 , so it’s 1 2 _ 8 .”

“I sort of used the line plot as a number line. I started at 1 5 _ 8 . 3 _ 8 more is 2, then I have to go 7 _ 8 more to 2 7 _ 8 . That’s 10 __ 8 , or 1 2 _ 8 .”

[Andrew] says he thought of the line plot as a number line. Let’s take a look at that.

321 1 1 1 1 1 1 10 14_ 1

2_ 3

4_1

8_ 3

8_ 5

8_ 7

8_ 1

4_ 1

2_ 3

4_1

8_ 3

8_

38_

58_ 7

8_ 2 2 2 2 2 2 21

4_ 1

2_ 3

4_1

8_ 3

8_ 5

8_ 7

8_

78_

1 Activity 2 Activity 3 Discussion 4 session follow-up

▲ student Activity Book, unit 6, p. 44B; resource masters, C33

CC54 inVestigAtiOn 2 Ordering fractions

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What equation represents the problem?

Write 2 7 _ 8 – 1 5 _ 8 = 1 2 _ 8 (or 1 1 _ 4 ) on the board.

As you work on this page, read the problems carefully to decide whether they are addition or subtraction situations. When we come back together, we’re going to discuss Problems 2 and 5.

As students work, identify students who used different strategies, and ask them to be prepared to explain their solutions.

OngOing ASSeSSment: Obser ving Student s at Work

Studentsusetheinformationfromthetableandlineplottosolveadditionandsubtractionproblemsinvolvingmixednumberswithlikedenominators.

• Whatstrategiesarestudentsusingtosolveadditionproblems?Aretheyusingavisualrepresentation,suchasextendingthenumberline?Aretheyreasoningandusingwhattheyknowaboutfractions?

• Whatstrategiesarestudentsusingtosolvesubtractionproblems?Aretheyusingthelineplotasanumberline?Aretheyreasoningandusingwhattheyknowaboutfractions?

• Howarestudentskeepingtrackofthenumbers?Aretheykeepingthewholenumbersandfractionsseparate,andthencombiningthemfortheiranswer?Iftheyareaddingup,dotheyrecognizewhentheyreachthenextwholenumber?


Somestudentshavedifficultytransferringdatafromthetableandlineplottothewordproblems.Helpthesestudentsidentifyeachofthenumbersneededtosolvetheproblem.Alsoconsidermodelinghowtouseanumberlinetosolvethesubtractionproblems.

Studentswhoeasilysolvetheseproblemscanbeaskedtomakeuptheirownproblemsusingthebutterflywingspanslistedinthetable.Encouragethemtousenumberswithunlikedenominators.

Session 2.7A Adding and Subtracting mixed numbers CC55

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44C Unit 6 Session 2.7A

Pepper’s PuppiesCheyenne’s dog, Pepper, had puppies. Cheyenne recorded their weights in the line plot below.

18

Weights of Pepper’s Puppies (pounds)

10

X X X X XX

14

38

12

58

34

78 11

8 11211

4 138

Solve each problem and show your work.

1. Two puppies weighed the same amount. What was the total weight of the two puppies?

2. How many more pounds did the heaviest puppy weigh than the lightest puppy?

3. The heaviest puppy gained 4 _ 8 of a pound in its first month. How much did it weigh after the first month?

note Students solve addition and subtraction problems involving fractions using data given in a line plot.

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D i S c U S S i o n

Adding and Subtracting Mixed Numbers

clASS15 Min

Math Focus Points for Discussion Addingandsubtractingmixednumberswithlike

denominatorsusingrepresentationsandreasoningaboutfractionsandtheoperations

As you discuss Problems 2 and 5 from Student Activity Book page 44B or C33, ask students you identified earlier to explain their solutions.

Let’s start with Problem 2. Was this an addition or subtraction situation? How did you know?

Students might say:“I knew I had to subtract to find the difference. It was 1 _ 4 more to 4 inches, and then another inch and 1 _ 4 . So that made it 1 2 _ 4 inches, or 1 1 _ 2 inches.”

Let’s look at Problem 5. Was this an addition or subtraction situation? How did you know?

Students might say:“I knew I was adding because I needed to find the total of both wingspans. I changed the 2 7 _ 8 to 3, because it’s only 1 _ 8 away. I added 1 5 _ 8 to 3 and got 4 5 _ 8 , but then I had to take the 1 _ 8 away so it’s 4 4 _ 8 , which is the same as 4 1 _ 2 .”

S E S S i o n F o l l o W - U P

Daily Practice DailyPractice: For reinforcement of this unit’s content,

have students complete Student Activity Book page 44C or C34.

▲ Student Activity Book, Unit 6, p. 44c; Resource Masters, c34

cc56 inVESTiGATion 2 ordering Fractions

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s e s s i o n 3 A . 1

Ten-Minute MathCounting Around the Class Students count around the class by 1 _ 3 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number (1 _ 3 , 2 _ 3 , 3 _ 3 , 4 _ 3 , etc.). Draw a number line marked in thirds, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line.• What number did the 6th person say? How do we write 6 _ 3  as a whole number? (2) • What number did the 10th person say? How do we write 10 __ 3 as a mixed number?

(3 1 _ 3 )

Today’s Plan MaterialsDiscussion

Counting Around the Class10 Min clAss

AcTiviTy

Multiplying Whole Numbers and Fractions 30 Min clAss inDiviDuAls

•Student Activity Book,p.44Dorc35, Multiplying Whole numbers and Fractions Makecopies.(asneeded)

Discussion

Strategies for Multiplying Fractions 20 Min clAss

•Students’completedcopiesofStudent Activity Book,p.44DorC35(fromActivity2)

session FolloW-uP

Daily Practice •Student Activity Book,p.44Eorc36, chunks of cheese Makecopies.(asneeded)

Multiplying Whole Numbers and FractionsMath Focus Points

Multiplying a whole number and a fraction

Using visual models to solve word problems involving multiplication of a whole number and a fraction

session 3A.1 Multiplying Whole numbers and Fractions cc57

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44DSession 3A.1 Unit 6

Multiplying Whole Numbers and FractionsUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was 3 _ 4 of each pizza left. How much pizza was left in all?

2. A class is counting by 2 _ 6 s. What number does the 7th person say?

3. 6 × 1 __ 3 =

4. 3 × 3 __ 8 =

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1 Discussion 2 Activity 3 Discussion 4 Session Follow-Up

Teaching Note1 MultiplyingWholeNumbersand

Fractions This Investigation focuses on multiplying whole numbers and fractions less than 1. Unless otherwise noted, the word “fraction” in this Investigation refers to numbers between 0 and 1.

2 Isit3× 3 _ 4 or 3 _ 4 ×3? Investigations has opted to show 3 groups of 3 _ 4 as 3 × 3 _ 4 , and 3 _ 4 group of 3 as 3 _ 4 × 3, using the same convention used for whole numbers. However, it is not necessary for students to follow this system rigidly. When students suggest a multiplication expression for a multiplication situation, what is important is that they understand what the numbers mean. For example, in the situation of the 3 pizzas, students need to understand that the 3 represents the number of groups and the 3 _ 4 represents the size of each group.

D i S c U S S i o N

Counting Around the Class

clASS10 MiN

Math Focus Points for Discussion Using visual models to solve problems involving

multiplication of a whole number and a fraction

Ask five students to count by 1 _ 4 s. Ask students to say each number as a fraction, not a mixed number ( 1 _ 4 , 2 _ 4 , 3 _ 4 , 4 _ 4 , 5 _ 4 , etc.). Keep track of the fractions on a number line.

What number did the 5th person say? How do we write 5 _ 4 as a mixed number? (1 1 _ 4 )

34_

44_10 2

4_ 21

4_ _7

4_64

54_

Five people counting by 1 _ 4 is five fourths, or five groups of 1 _ 4 . What is an equation that would represent 5 people counting by 1 _ 4 s? . . . Why would this be an equation for this situation?

If students are having trouble coming up with an equation, suggest that they think about whole numbers.

If we counted around by 7s instead, and 5 people counted, what equation would represent 5 people counting by 7s? Why would this be the equation? So, what is an equation that would represent 5 people counting by 1 _ 4 s?

A c T i v i T y

Multiplying Whole Numbers and Fractions

iNDiviDUAlSclASS30 MiN

Ask students to look at Problem 1 on Student Activity Book page 44D or C35 as you read it aloud. 1

Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was 3 _ 4 of each pizza left. How much pizza was left in all?

What equation could represent this problem? (3 × 3 _ 4 = ___) 2

▲ Student Activity Book, Unit 6, p. 44D;Resource Masters, c35

cc58 iNveSTigATioN 3A Multiplying Fractions

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Draw a square on the board.

One way to solve this problem would be to represent it on a number line like we did for counting around the class. Another way would be to draw a picture. How could we use squares to help us solve the problem?

Students might say:

“We could draw 3 squares to represent the 3 pizzas, divide them into fourths and color in 3 _ 4 of each.”

Those squares would be like the squares on the fraction cards. You only have one 3 _ 4 card, so you couldn’t actually use the fraction cards. But you could draw squares or rectangles and divide them into fractional pieces to help you solve this problem.

As you solve each problem on Student Activity book page 44D (or C35), think carefully about which number represents the number of groups and which represents the size of the group. 3

As students solve the problems, look for a variety of strategies used to solve Problem 1. Ask students to share these strategies during the discussion at the end of the session. Possible strategies are shown in the discussion section. 4 5

OngOing ASSeSSment: Obser ving Student s at Work

Studentssolveproblemsinwhichtheymultiplywholenumbersbyfractions.

• Whatrepresentationsandstrategiesdostudentsusetosolvetheproblems?Aretheyusingpicturesornumberlines?Howaretheykeepingtrackofeachpartoftheproblemandtheproduct?

• Canstudentswriteamultiplicationequationfortheproblem?Cantheyidentifywhichnumberintheequationandinthewordproblemrepresentsthenumberofgroupsandwhichrepresentsthesizeofthegroup?


Ifstudentsareunsurehowtostartsolvingtheproblem,suggestdrawingrectangles.Discusseachpartoftheproblemandhavethemshoweachpartontherectangles.

teaching note3 TeachingNote:TheCommutative

PropertyofMultiplication Students know from their work with whole numbers that multiplication is commutative. In this Investigation they may notice that, for example, 3 × 3_4=3_4× 3. If students do notice, use this opportunity to ask students whether they think multiplication is still commutative when one of the factors is a fraction: We’ve talked about how if you change the order of the factors in multiplication, the product doesn’t change. Do you think that is still the case when you’re multiplying a whole number and a fraction? While this is a good opportunity to consider this question, students do not yet have the tools to resolve this question during this Investigation: 3_4of a group of 3 can appear very different to them than 3 groups of3_4. For now, students need time to make sense of the operation of multiplication with fractions.

4 RepresentationsforMultiplyingFractions Both the number line and dividing rectangles into fractional pieces are useful representations to use when multiplying a whole number and a fraction. Even though students have used arrays for multiplication with whole numbers, arrays with a fraction as one or both dimensions of the rectangle is more challenging to understand. Students will use the array model in Grade 5 when they continue their work on multiplication of fractions.

5 FractionsGreaterthanOneorMixedNumbers When students solve these problems they may come up with answers that are mixed numbers (e.g., 2 1_4 ) or fractions greater than 1 (e.g., 9_4 ). Either answer is fine, and the fact that the answers are equivalent is discussed further in the discussion at the end of this session.

Session 3A.1 multiplying Whole numbers and Fractions CC59

INV12_TE04_U06_S3A.1.indd 59 6/3/11 5:15 PM


D i S c U S S i o n

Strategies for Multiplying Fractions

clASS20 Min

Math Focus Points for Discussion Multiplyingawholenumberandafraction

Usingvisualmodelstosolvewordproblemsinvolvingmultiplicationofawholenumberandafraction

Refer students to Problem 1 on Student Activity Book page 44D or C35.

What multiplication equation fits this problem? ( 3 × 3 _ 4 = )

Ask students to share the strategies you identified during the last activity. These strategies may include the following:

Diagram A

24_3

4_ 1

4_210

Diagram B

There are three 1 _ 4 s left in each pizza. There are 3 pizzas. So that is 3 × 3 × 1 _ 4 pieces. That’s nine 1 _ 4 pieces left, which means there is 9 _ 4 of a pizza left.

Diagram C

14_ 2

4_ 3

4_ 1

4

1 2 3

_ 24_ 3

4_ 3

4_1

4_ 2

4_

three 3 _ 4 pizzas = 2 wholes and 1 _ 4 = 2 1 _ 4

cc60 inveStigAtion 3A Multiplying Fractions

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44E Unit 6 Session 3A.1

Chunks of CheeseMorris Mouse’s Cheese House sells chunks of cheese. Each chunk weighs 3 _ 4 of a pound. Find the total weight of each kind of cheese. Use a representation to solve each problem. Also, write a multiplication equation that represents the problem. Show your work.

1. 5 chunks of cheddar cheese 2. 10 chunks of Swiss cheese

Total weight Total weight

3. 4 chunks of American cheese 4. 8 chunks of parmesan cheese


note Students solve problems involving multiplication of a whole number and a fraction.

INV12_SE04_U6.indd 5 6/1/11 3:15 PM▲ Student Activity Book, Unit 6, p. 44E;Resource Masters, C36


We said the equation for this problem is 3 × 3 _ 4 = ____. Which number tells us the number of groups? Which number tells us the size of the group? Where do you see the number of groups and the size of the groups in these representations?

In Diagram A, the number of groups is the number of jumps, and the size of the group is the size of the jump. In Diagram B, the number of groups is the number of squares, and the size of the group is the amount shaded on each square. In Diagram C, the number of groups is the number of times you can count off 1 _ 4 , 2 _ 4 , 3 _ 4 , and the size of the group is the amount shaded in each group you count.

Discuss students’ answers to the problem. Some may have an answer of 9 _ 4 and some may have an answer of 2 1 _ 4 . Ask students about these two answers.

[Terrell] said the answer to this problem is 9 _ 4 . [Jill] said the answer is 2 1 _ 4 . Are these answers equal?

Encourage students to use one of the representations to explain their ideas.

Discuss that one way to think about multiplying fractions and whole numbers is to think of 3 _ 4 as 3 × 1 _ 4 . Then 3 × 3 _ 4 = 3 × 3 × 1 _ 4 .

In our representation of 3 pizzas with 3 _ 4 of each pizza shaded, we can think about this as being three 1 _ 4 s shaded in each pizza. We notate this as 3 × 3 × 1 _ 4 = 9 _ 4 . You can change this to 2 1 _ 4 , which helps you see that there are between 2 and 3 pizzas left.

S E S S i o n F o l l o w - U p


have students complete Student Activity Book page 44E or C36.

Session 3A.1 Multiplying whole numbers and Fractions CC61

INV12_TE04_U06_S3A.1.indd 61 6/3/11 2:53 PM

s e s s i o n 3 A . 2

Today’s Plan Materials

Ten-Minute MathCounting Around the Class Students count around the class by 2 _ 5 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number (2 _ 5 , 4 _ 5 , 6 _ 5 , etc.). Draw a number line marked in fifths, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line.• What number did the 6th person say? How do we write 12 __ 5  as a mixed

number? (22 _ 5 ) • What number did the 12th person say? How do we write 24 __ 5  as a mixed

number? (44 _ 5 )• What is a multiplication equation that would represent 12 people counting

by 2 _ 5 s? (12 × 2 _ 5  = 24 __ 5 , or 44 _ 5 )

Discussion

Multiplying Whole Numbers and Fractions 20 Min clAss

•Chartpaper(Copythestoryproblemsandtableshowninthediscussionsection.)

MATh WorkshoP

Multiplying with Fractions2A Multiplying Fractions and Whole Numbers2B More Multiplying Fractions and Whole

Numbers

40 Min 2A •Student Activity Book,p.44For

c37, Multiplying Fractions and Whole numbers Makecopies.(asneeded)

2B •Student Activity Book,p.44Gorc38, More Multiplying Fractions and Whole numbers Makecopies.(asneeded)

session FolloW-uP

Daily Practice •Student Activity Book,p.44Horc39, Multiplying with Fractions Makecopies.(asneeded)

•Student Math Handbook,p.55

Multiplying Whole Numbers and Fractions, continued Math Focus Points

Multiplying a fraction and a whole number

Using visual models to solve word problems involving multiplication of a fraction and a whole number

cc62 invesTigATion 3A Multiplying Fractions

INV12_TE04_U06_S3A.2.indd 62 6/14/11 2:24 PM

1 Discussion 2 Math Workshop 3 Session Follow-Up

D i S c U S S i o n

Multiplying Whole Numbers and Fractions

claSS20 Min

Math Focus Points for Discussion Multiplyingafractionandawholenumber

Usingvisualmodelstosolvewordproblemsinvolvingmultiplicationofafractionandawholenumber

Call attention to the following two stories you have written on chart paper:

(1) Eggs come in cartons of 12. Richard was making cakes for a party and used 2 cartons of eggs. How many eggs did he use?

(2) Sabrina was making a cake for herself. She used 1 _ 4 of a carton of eggs. There are 12 eggs in each carton. How many eggs did she use?

Give students some time to work with a partner to solve each problem.

Below the stories make a table to record the information from each problem.

Number of Cartons

Number of Eggs in a

CartonNumber of

Eggs Equation(1)(2)

Work with the class to fill out the table. As you ask students the following questions, they should refer back to the problem or to the table to answer the questions.

What multiplication equation represents action in the first problem? Which number represents the number of groups and which represents the size of the group?

What multiplication equation, using 1 _ 4 , 12, and 3, represents what is happening in the second problem? Which number represents the number of groups and which represents the size of the group? 1

We came up with multiplication equations for both problems. What makes them both multiplication problems? 2

Teaching note1 PartsofaGroup: Students may find it

confusing to think about 1 _ 4 of a group as being the “number of groups”. Consider these two phrases: 2 groups of 12 and 1 _ 4 group of 12. In each, the 12 is the number in the group. In the first phrase, 2 tells us how many full groups of 12, and in the second phrase, 1 _ 4 tells us how much of a group of 12.

Math note2 DivisionEquation Some students

may say that the second problem seems like a division situation and suggest 12 ÷ 4 = 3 as an equation that represents the problem. This division equation does represent what is happening in the problem and is equivalent, but the focus in this session is on multiplying a whole number and a fraction. Students are specifically asked to write a multiplication equation using 1 _ 4 , 12, and 3.

Session 3.a2 Multiplying Whole numbers and Fractions, continued cc63

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44FSession 3A.2 Unit 6

Multiplying Fractions and Whole NumbersUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. A grocery store sells bags of 9 apples. Anna used 2 _ 3 of the apples in a bag in an apple pie. How many apples did she use in the pie?

2. Steve was in a 7 mile race. He ran 1 _ 2 of it and walked the rest. How many miles did he run?

3. 2 __ 3 × 12 =

4. There are 10 boys in class. 4 _ 5 of them have brown hair. How many boys have brown hair?

5. 5 __ 8 × 16 =

6. 1 __ 2 × 11 =

INV12_SE04_U6.indd 6 6/3/11 10:27 AM

Math Note3 NumberLine It is likely going to be

more difficult for students to use a number line to represent 2 _ 3 group of 9. Rather than “skip counting” by 2 _ 3 on the number line, as they have done previously, to represent this problem they would mark the number line from 0 to 9, and then have to figure out how to divide that distance into thirds.


Students might say:

“They are multiplication problems because they talk about groups of things.”

WriteProblem1fromStudent Activity Bookpage44Fontheboard:

A grocery store sells bags of 9 apples. Anna used 2 _ 3 of the apples in a bag in an apple pie. How many apples did she use in the pie?

What equation could we write using 9 and 2_3 that represents the problem? ( 2_3 × 9 = __ )

Ifstudentsareunsurewhattheequationforthisproblemwouldbe,thenaskthefollowingquestions:

What would the equation be if Anna used 5 bags of 9 apples? So then, what would the equation be for this problem?

What representations might you use to help you solve this problem?

Studentsarelikelytosaytheycouldstartbydrawing9apples.Somestudentsmaysuggestusinganumberline. 3

M at h W o r k S h o p

Multiplying with Fractions 40 MiN

Studentscontinuetoworkonproblemsinwhichtheymultiplywithfractions.Theycontinueusingrepresentations(drawingsoranumberline)toshowsolutions.StudentswillcontinuetoworkontheseactivitiesinSession3A.3.

2a Multiplying Fractions and iNDiviDUalS

Whole NumbersStudentssolveproblemsonStudent Activity Bookpage44ForC37inwhichtheymultiplyfractionsandwholenumbers.Ifstudentsseemuncertainabouthowtosolvetheseproblems,remindthemtheysolvedsimilarproblemsinInvestigation1,andthestrategiestheyusedthenalsoworkfortheseproblems.

▲ Student activity Book, Unit 6, p. 44F;resource Masters, C37

CC64 iNveStigatioN 3a Multiplying Fractions

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44G Unit 6 Session 3A.2

More Multiplying Fractions and Whole NumbersUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. Sabrina walks to school. Her house is 3 _ 8 of a mile from school. How many miles would she walk to and from school in 5 days?

2. 6 × 2 __ 5 =

3. Damian has a recipe that calls for 2 _ 3 of a cup of flour. He wants to make 4 times the recipe. How much flour does he need?

4. 3 × 3 __ 4 =

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44HSession 3A.2 Unit 6

note Students solve problems involving multiplication of whole numbers and fractions.

Multiplying with FractionsUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. 4 × 1 __ 5 = 2. 3 __

4 ×16 =

3. 1 __ 6 ×9 = 4. 12 × 1 __

2 =

5. Mr. Garcia has 15 grandchildren. 2 _ 3 of them are girls. How many are girls?

6. Helena needs 8 pieces of wire. Each piece needs to be 3 _ 4 of a foot long. What is the total length of the wire Helena needs?

INV12_SE04_U6.indd 8 6/1/11 3:18 PM▲ Student Activity Book, Unit 6, p. 44HResource Masters, C39

▲ Student Activity Book, Unit 6, p. 44G;Resource Masters, C38


OnGOinG ASSeSSMent: Obser ving Student s at Work

Students solve problems in which they multiply fractions and whole numbers.

• Whatstrategiesdostudentsusetosolvetheproblems? Are they using pictures or number lines? How are they keeping track of each part of the problem and the product?

• Canstudentswriteamultiplicationequationfortheproblem? Can they identify which number in the equation and in the word problem represents the number of groups and which represents the size of the group?

• Canstudentsdecidewhethertheiranswerstotheproblemsarereasonable?

DiFFeRentiAtiOn: Suppor ting the Range of Lear ner s

If students are unsure how to start solving a problem, suggest drawing the objects in the problem. Discuss each part of the problem and have them illustrate each part of the problem in the picture.

If students easily solve both sets of problems, encourage them to use a number line to represent each problem as well.

2B More Multiplying Fractions and inDiviDUALS

Whole NumbersStudents solve problems on Student Activity Book page 44G or C38 in which they multiply fractions and whole numbers.

S e S S i O n F O L L O W - U p


have students complete Student Activity Book page 44H or C39.

StudentMathHandbook: Students and families may use Student Math Handbook page 55 for reference and review. See pages 170–176 in the back of Unit 6.

Session 3.A2 Multiplying Whole numbers and Fractions, continued CC65

INV12_TE04_U06_S3A.2.indd 65 6/14/11 2:29 PM

s e s s i o n 3 A . 3

Today’s Plan Materials

Ten-Minute MathCounting Around the Class Students count around the class by 4 _ 6 s until all students have counted once. Ask students to say each number as a fraction, not a mixed number (4 _ 6 , 8 _ 6 , 12 __ 6 , etc.). Draw a number line marked in sixths, but not numbered. As students count, ask them to help you figure out where to put each fraction on the number line.• What number did the 7th person say? How do we write 28 __ 6  as a mixed

number? (44 _ 6 ) • What number did the 9th person say? How do we write 36 __ 6  as a whole

number? (6)• What is a multiplication equation that would represent 9 people counting

by 4 _ 6 s? (9 × 4 _ 6 = 36 __ 6  , or 6)

MATh WorkshoP

Multiplying with Fractions2A Multiplying Fractions and Whole Numbers2B More Multiplying Fractions and

Whole Numbers2C Multiplying with Fractions

20 Min

2A •Students’copyofStudent Activity Book,p.44ForC37(fromSession3A.2)

2B •Students’copyofStudent Activity Book,p.44GorC38(fromSession3A.2)

2C •Student Activity Book,p.44IorC40, Multiplying Fractions Makecopies.(asneeded)

DisCussion

Multiplying with Fractions20 Min ClAss

•Students’completedcopiesofStudent Activity Bookp.44IorC40(fromMathWorkshop2C)

AssessMenT ACTiviTy

Multiplying with Fractions20 Min inDiviDuAls

•C41, Assessment: Multiplying with Fractions Makecopies.(oneperstudent)

session FolloW-uP

Daily Practice •Student Activity Book,p.44JorC42, All kinds of nuts Makecopies.(asneeded)

•Student Math Handbook,p.55

Assessment: Multiplying with FractionsMath Focus Points

Multiplying fractions and whole numbers

Using visual models to solve word problems involving multiplication of a fraction and a whole number

CC66 invesTiGATion 3A Multiplying Fractions

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44I Unit 6 Session 3A.3

Multiplying FractionsUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. In the store Damian found pretzels that came in 1 _ 3 -pound bags. He bought 5 bags of pretzels. How many pounds of pretzels did he buy?

2. 3 × 6 __ 8 =

3. There were 25 students in class. One day, 3 _ 5 of them wore sneakers. How many students wore sneakers?

4. 7 ___ 10

× 4 =

5. Jill used stones that were each 3 _ 4 of a foot high to build a wall. She piled 6 stones on top of each other. How many feet high was her wall?

6. 5 __ 6 × 12 =

INV12_SE04_U6.indd 9 6/1/11 4:40 PM

1 Math Workshop 2 Discussion 3 Assessment Activity 4 Session Follow-Up

M At h W o r k S h o p

Multiplying with Fractions20 Min

In addition to the activities students worked on in Session 3A.2, students solve another set of problems in which they multiply fractions and whole numbers.

2A Multiplying Fractions and Whole Numbers inDiviDUAlS

Students continue to work on Student Activity Book page 44F or C37. For complete details of this activity, see Session 3A.2, pages CC64 and CC65.

2B More Multiplying Fractions and inDiviDUAlS

Whole NumbersStudents continue to work on Student Activity Book page 44G or C38.

2C Multiplying with Fractions inDiviDUAlS

Students solve problems on Student Activity Book page 44I or C40 in which they multiply fractions and whole numbers.

ongoing ASSeSSMent: obser ving Student s at Work

Students multiply whole numbers and fractions.

• Whatstrategiesdostudentsusetosolvetheproblems? Are they using pictures or number lines? How are they keeping track of each part of the problem and the product?

• Canstudentswriteamultiplicationequationfortheproblem? Can they identify which number in the equation and in the word problem represents the number of groups and which represents the size of the group?

• Canstudentsdecidewhethertheiranswerstotheproblemsarereasonable?

DiFFerentiAtion: Suppor ting the range of lear ner s

If students are unsure how to start solving a problem, suggest drawing the objects in the problem. Discuss each part of the problem and have them show each part of the problem in the picture.

▲ Student Activity Book, Unit 6, p. 44i;resource Masters, C40

Session 3A.3 Assessment: Multiplying with Fractions CC67

INV12_TE04_U06_S3A.3.indd 67 6/14/11 2:32 PM


Some students may notice that to solve a problem that involves multiplying a fraction and a whole number you can multiply the numerator by the whole number and put that product over the denominator. Ask the students to show why this works and then encourage them to use this method to solve the problems using just numbers.

D i S c U S S i o n

Multiplying with FractionsclASS20 Min

Math Focus Points for Discussion Multiplying fractions and whole numbers

Ask students to bring Student Activity Book page 44I or C40 with them to the discussion.

Ask students what product they got for each problem. Write the equation for each problem on the board. Record each product as both a fraction and a mixed number or whole number.

1. 5 × 1 _ 3 = 5 _ 3 , or 1 2 _ 3 4. 7 __ 10 × 4 = 28 __ 10 , or 2 8 __ 10 , or 2 4 _ 5

2. 3 × 6 _ 8 = 18 __ 8 , or 2 2 _ 8 , or 2 1 _ 4 5. 6 × 3 _ 4 = 18 __ 4 , or 4 2 _ 4 , or 4 1 _ 2

3. 3 _ 5 × 25 = 75 __ 5 , or 15 6. 5 _ 6 × 12 = 60 __ 6 , or 10

You solved a variety of problems which involved multiplying fractions and whole numbers. What do you notice about multiplying fractions and whole numbers?

Ideas to highlight include:

• Unlike multiplication with nonzero whole numbers, where the product is larger than either factor, the product of a fraction less than one and a nonzero whole number is larger than the fraction and smaller than the whole number.

• The product is equal to the numerator of the fraction multiplied by the whole number, placed over the denominator of the fraction. (4 × 4 _ 5 = 4 × 4 × 1 _ 5 = 4 × 4 × 1 ______ 5 )

• If your class has discussed the commutative property, this idea could also be included. (3 × 3 _ 4 = 3 _ 4 × 3)

Ask students to use representations to show and support their thinking.

cc68 inveStigAtion 3A Multiplying Fractions

INV12_TE04_U06_S3A.3.indd 68 6/3/11 3:22 PM

C41 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unit 6 Session 3A.3

Assessment: Multiplying with Fractions Use a representation to solve each problem. For the word problem, write an equation that represents the problem.

1. Ursula bought 30 apples. 3 _ 5 of them are green. How many of the apples are green?

2. 5 × 2 __ 3 =


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44JSession 3A.3 Unit 6

note Students solve problems involving multiplication of whole numbers and fractions.

All Kinds of Nuts Use a representation to solve each problem. Also, write an equation that represents the problem.

1. Emaan bought 6 bags of walnuts. Each bag contained 3 _ 4 of a pound of walnuts. What was the total weight of the walnuts?

2. A man bought 12 boxes of nuts. He took 1 _ 6 of the boxes to his office. How many boxes of nuts did he take to the office?

3. Kimberly is making 3 loaves of nut bread. For each loaf, she needs 3 _ 4 of a cup of pecans. How many cups of pecans does she need? Circle the best answer below.

between 3 and 4 cups



INV12_SE04_U6.indd 10 5/13/11 11:06 AM▲ Student Activity Book, Unit 6, p. 44J;Resource Masters, C42

▲ Resource Masters, C41


A S S e S S M e n t A C t i v i t y

Multiplying with Fractions20 Min inDiviDUAlS

Students work on Assessment: Multiplying with Fractions (page C41) to assess their understanding of multiplication of whole numbers and fractions. They solve one word problem and are asked to write an equation for it, and they solve one number problem. 1

OngOing ASSeSSMent: Obser ving Student s at Work

Students solve problems in which they multiply fractions and whole numbers.

• Whatstrategiesdostudentsusetosolvetheproblems?Do they use visual models? Do they draw pictures or use a number line?

• Canstudentswriteamultiplicationequationfortheproblem?

S e S S i O n F O l l O W - U p


have students complete Student Activity Book page 44J or C42.

StudentMathHandbook: Students and families may use Student Math Handbook page 55 for reference and review. See pages 170–176 in the back of Unit 6.

professional Development 1 TeacherNote: Assessment: Multiplying

with Fractions, p. CC70

Session 3A.3 Assessment: Multiplying with Fractions CC69

INV12_TE04_U06_S3A.3.indd 69 6/3/11 3:24 PM

Teacher Note

Benchmarks addressed:

Multiply a fraction (less than 1) and a whole number.

In order to meet the benchmark, students’ work should show that they can:

• Use a visual representation to solve a multiplication problem involving a fraction (less than 1) and a whole number;

• Determine the correct product, either as a fraction (greater than 1), or as a mixed number or whole number.

Meeting the BenchmarkStudents who meet the benchmark are able to correctly multiply the fraction and whole number by using visual representations such as a number line, rectangles divided into equal parts, or other types of drawings. Students find the correct product for both problems and their representations clearly show their thinking. For Problem 1, students write an equation that matches their representation.

Partially Meeting the BenchmarkStudents who partially meet the benchmark show some knowledge of fractions and multiplication, but solve only one problem correctly. Students are likely to have more difficulty with Problem 1. They might draw 30 apples/objects, but are unsure how to determine 3 _ 5 of 30. They also may not be able to write an equation. For Problem 2, students draw a correct representation of 5 × 2 _ 3 , such as showing 5 jumps of 2 _ 3 on a number line, or drawing 5 wholes and correctly shading in 2 _ 3 of each. They are likely to get 3 1 _ 3 (or 10 __ 3 ) as an answer, but some students may be unable to determine what the product is.

Not Meeting the BenchmarkStudents who do not meet the benchmark may draw a separate representation for each of the numbers in the problems and/or manipulate the numbers in some way that is not based on an understanding of the problem (e.g., by adding the numbers). They might not draw any representation. They might treat each of the numbers as whole numbers, and randomly multiply two or all three of those numbers (e.g., 5 × 2 × 3).

Assessment: Multiplying with Fractions

CC70 INvestIgatIoN 3a Multiplying Fractions

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C29 Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved. 4


Unit 6 Session 1.8A

Subtracting FractionsSolve each problem and show your work. For the word problems, write an equation.

1. There was 7 _ 8 of a pan of brownies on the table. Some friends came over and ate 4 _ 8 of the pan of brownies. What fraction of the pan of brownies is left?

2. Marisol walks to school. The school is 6 __ 10 of a mile from her house. She has already walked 4 __ 10 of a mile. How much farther does Marisol have to walk?

3. There was 7 __ 12 of a gallon of milk in the refrigerator. The Jones family used 3 __ 12 of the gallon during breakfast. How much milk remains?

4. 4 __ 5 − 2 __

5 = 5. 9 ___

12 − 5 ___

12 =

INV12_BLM04_U6.indd 29 6/22/11 4:19 PM



C30

Daily Practice

More Subtracting Fractions Solve each problem and show your work. For the word problems, write an equation.

1. There is 7 _ 8 of a carton of juice in the refrigerator. The Ortega family drank 5 _ 8 of the carton with their breakfast. What fraction of the carton remains?

2. Venetta was walking to the library, which is 3 _ 4 of a mile away. She has walked 1 _ 4 of a mile. How much farther does Venetta have to walk?

3. Richard had 4 _ 5 of a bag of carrots. He fed 2 _ 5 of the bag to his rabbit. What fraction of the bag did Richard have left?

4. 7 ___ 10

− 4 ___ 10

= 5. 6 __ 8 − 1 __

8 =

notE Students solve subtraction problems involving fractions with like denominators.

Unit 6 Session 1.8A

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C31

Daily Practice

Unit 6 Session 2.1

notE Students solve subtraction problems involving fractions with like denominators..

Fraction Subtraction Solve each problem and show your work. For the word problems, write an equation.

1. There is 5 _ 6 of a pot of soup on the stove. The Kim family ate 4 _ 6 of the pot of soup. What fraction of the pot of soup remains?

2. Nadeem is walking to the park, which is 9 __ 10 of a mile away. He has walked 4 __ 10 of a mile. How much farther does Nadeem have to walk?

3. Tonya had 10 __ 12 of a yard of fabric. She used 5 __ 12 of a yard of fabric to make a lamp shade. What fraction of a yard of fabric is left?

4. 7 __ 8 − 2 __

8 = 5. 3 __

5 − 1 __

5 =

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Unit 6 Session 2.7A

Butterfly Wingspans (page 1 of 2)Yuki went to the Natural History Museum to study butterflies. The information he has about some of the butterflies in the collection is shown below.

Name Wingspan (inches) Name Wingspan

(inches)

American Snout 1 1 _ 2 Pearl Crescent 1 5 _ 8

Giant Swallowtail 5 1 _ 4 Postman 2 1 _ 2

Julia 3 1 _ 2 Red Admiral 3 1 _ 8

Milbert’s Tortoiseshell 2 5 _ 8 Saturn 4 1 _ 4

Monarch 3 1 _ 2 Tiger Swallowtail 3 3 _ 4

Painted Lady 2 1 _ 2 Viceroy 2 7 _ 8

Record the measurements on the line plot below.

1 2 3 4 5 60

Butterfly Wingspans (inches)

Write three statements that describe the data.

INV12_BLM04_U6.indd 32 6/20/11 11:10 AM



Unit 6 Session 2.7A

Butterfly Wingspans (page 2 of 2)Use the information on the previous page to solve the following problems. Show your work.

1. How much longer is the wingspan of the Viceroy butterfly than the wingspan of the Pearl Crescent butterfly?

2. How much longer is the wingspan of the Giant Swallowtail butterfly than the wingspan of the Tiger Swallowtail butterfly?

3. The American Snout butterfly and the Postman butterfly are side-by-side. What is the length of their combined wingspans?

4. How much longer is the wingspan of the Red Admiral butterfly than the wingspan of Milbert’s Tortoiseshell butterfly?

5. The Pearl Crescent butterfly and the Viceroy butterfly are side-by-side. What is the length of their combined wingspans?

6. The Saturn butterfly and the Tiger Swallowtail butterfly are side-by-side. What is the length of their combined wingspans?

INV12_BLM04_U6.indd 33 6/17/11 11:04 AM



C34

Daily Practice

Unit 6 Session 2.7A

notE Students solve addition and subtraction problems involving fractions using data given in a line plot.

Pepper’s PuppiesCheyenne’s dog, Pepper, had puppies. Cheyenne recorded their weights in the line plot below.

18


10

X X X X XX

14

38

12

58

34

78 11

8 11211

4 138

Solve each problem and show your work.

1. Two puppies weighed the same amount. What was the total weight of the two puppies?

2. How many more pounds did the heaviest puppy weigh than the lightest puppy?

3. The heaviest puppy gained 4 _ 8 of a pound in its first month. How much did it weigh after the first month?

INV12_BLM04_U6.indd 34 6/22/11 4:26 PM



Unit 6 Session 3A.1

Multiplying Whole Numbers and FractionsUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was 3 _ 4 of each pizza left. How much pizza was left in all?

2. A class is counting by 2 _ 6 s. What number does the 7th person say?

3. 6 × 1 __ 3 =

4. 3 × 3 __ 8 =

INV12_BLM04_U6.indd 35 6/17/11 11:04 AM



C36

Daily Practice

Unit 6 Session 3A.1

notE Students solve problems involving multiplication of a whole number and a fraction.

Chunks of CheeseMorris Mouse’s Cheese House sells chunks of cheese. Each chunk weighs 3 _ 4 of a pound. Find the total weight of each kind of cheese. Use a representation to solve each problem. Also, write a multiplication equation that represents the problem. Show your work.

1. 5 chunks of cheddar cheese 2. 10 chunks of Swiss cheese


3. 4 chunks of American cheese 4. 8 chunks of parmesan cheese


INV12_BLM04_U6.indd 36 6/23/11 4:01 PM



Unit 6 Session 3A.2

Multiplying Fractions and Whole NumbersUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. A grocery store sells bags of 9 apples. Anna used 2 _ 3 of the apples in a bag in an apple pie. How many apples did she use in the pie?

2. Steve was in a 7 mile race. He ran 1 _ 2 of it and walked the rest. How many miles did he run?

3. 2 __ 3 × 12 =

4. There are 10 boys in class. 4 _ 5 of them have brown hair. How many boys have brown hair?

5. 5 __ 8 × 16 =

6. 1 __ 2 × 11 =

INV12_BLM04_U6.indd 37 6/17/11 11:05 AM



Unit 6 Session 3A.2

More Multiplying Fractions and Whole NumbersUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. Sabrina walks to school. Her house is 3 _ 8 of a mile from school. How many miles would she walk to and from school in 5 days?

2. 6 × 2 __ 5 =

3. Damian has a recipe that calls for 2 _ 3 of a cup of flour. He wants to make 4 times the recipe. How much flour does he need?

4. 3 × 3 __ 4 =

INV12_BLM04_U6.indd 38 6/17/11 11:05 AM



C39

Daily Practice

notE Students solve problems involving multiplication of whole numbers and fractions.


1. 4 × 1 __ 5 = 2. 3 __

4 × 16 =

3. 1 __ 6 × 9 = 4. 12 × 1 __

2 =

5. Mr. Garcia has 15 grandchildren. 2 _ 3 of them are girls. How many are girls?

6. Helena needs 8 pieces of wire. Each piece needs to be 3 _ 4 of a foot long. What is the total length of the wire Helena needs?

Unit 6 Session 3A.2

INV12_BLM04_U6.indd 39 6/22/11 4:32 PM



Unit 6 Session 3A.3

Multiplying FractionsUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. In the store Damian found pretzels that came in 1 _ 3 -pound bags. He bought 5 bags of pretzels. How many pounds of pretzels did he buy?

2. 3 × 6 __ 8 =

3. There were 25 students in class. One day, 3 _ 5 of them wore sneakers. How many students wore sneakers?

4. 7 ___ 10

× 4 =

5. Jill used stones that were each 3 _ 4 of a foot high to build a wall. She piled 6 stones on top of each other. How many feet high was her wall?

6. 5 __ 6 × 12 =

INV12_BLM04_U6.indd 40 6/22/11 4:33 PM

C41 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unit 6 Session 3A.3

Assessment: Multiplying with Fractions Use a representation to solve each problem. For the word problem, write an equation that represents the problem.

1. Ursula bought 30 apples. 3 _ 5 of them are green. How many of the apples are green?

2. 5 × 2 __ 3 =


INV12_BLM04_U6.indd 41 6/1/11 3:54 PM



C42

Daily Practice

Unit 6 Session 3A.3


All Kinds of Nuts Use a representation to solve each problem. Also, write an equation that represents the problem.

1. Emaan bought 6 bags of walnuts. Each bag contained 3 _ 4 of a pound of walnuts. What was the total weight of the walnuts?

2. A man bought 12 boxes of nuts. He took 1 _ 6 of the boxes to his office. How many boxes of nuts did he take to the office?

3. Kimberly is making 3 loaves of nut bread. For each loaf, she needs 3 _ 4 of a cup of pecans. How many cups of pecans does she need? Circle the best answer below.




INV12_BLM04_U6.indd 42 6/22/11 4:33 PM



C43

Daily Practice

Unit 6 Session 3.1

notE Students solve addition and subtraction problems involving fractions using data given in a line plot.

Bug CollectionsThe science class collected crickets and beetles. The students made line plots to show the lengths of the insects.

18

Lengths of Crickets (inches)

10

X X X X X X X XX XX

14

38

12

58

34

78 11

8 114 13

8 112 15

8 134 1 27

8

18

Lengths of Beetles (inches)

10

X X X X X XX X

X X XXX

X

14

38

12

58

34

78 11

8 114 13

8 112 15

8 134 1 27

8

1. How much longer is the longest cricket than the shortest cricket?

2. How much longer is the longest beetle than the shortest beetle?

3. The cricket Benson found is 1 1 _ 8 inches long. How much longer is this cricket than the shortest one in the collection?

4. The beetle Tonya found is 1 1 _ 4 inches long. How much shorter is this beetle than the longest one in the collection?

INV12_BLM04_U6.indd 43 6/22/11 4:34 PM



C44

Daily Practice

Unit 6 Session 3.4

notE Students solve problems involving multiplication of a whole number by a fraction.

Buying FabricUse a representation to solve each problem. For each word problem, write a multiplication equation that represents the problem.

1. Bill bought 6 pieces of yellow fabric. Each piece was 1 _ 3 of a yard long. How many yards of fabric did Bill buy in all?

2. Kimberly bought 2 pieces of blue fabric. Each piece was 7 _ 8 of a yard long. How many yards of fabric did Kimberly buy in all?

3. Alejandro bought 7 pieces of red fabric. Each piece was 3 _ 4 of a yard long. How many yards of fabric did Alejandro buy in all?

4. 2 × 3 ___ 10

= 5. 9 × 1 __ 6 =

INV12_BLM04_U6.indd 44 6/22/11 4:34 PM



C45

Daily Practice

Unit 6 Session 3.5



1. 1 __ 5 × 8 = 2. 6 × 2 __

3 =

3. 2 × 5 __ 6 = 4. 7 __

8 × 8 =

5. LaTanya had a piece of fabric that was 3 yards long. She used 1 _ 2 of it to make a skirt. How much of the fabric did she use?

6. Benson had 16 marbles. He gave 3 _ 8 of them away. How many marbles did he give away?

INV12_BLM04_U6.indd 45 6/22/11 4:35 PM



C46

Daily Practice

Unit 6 Session 3.6


Working Hard Use a representation to solve each problem. Also, write an equation that represents the problem.

1. Last week, Ms. Cortez sold 24 computers. 5 _ 8 of them were laptops. How many laptops did Ms. Cortez sell?

2. An office building has 14 offices, all the same size. A painter uses 3 _ 4 of a gallon of paint to paint one office ceiling. How much paint will the painter need to paint all of the office ceilings?

3. Mr. Stein bikes to work. The roundtrip distance he bikes each day is 7 _ 8 of a mile. What is the total distance he bikes in 5 days? Circle the best answer below.

between 6 and 7 miles



INV12_BLM04_U6.indd 46 6/22/11 4:36 PM

C29 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

FechaNombreTarjetas de fracciones y cuadrados de decimales

Unidad 6 Sesión 1.8A

Restas de fraccionesResuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación.

1. Había 7 _ 8 de una bandeja de brownies sobre la mesa. Vinieron algunos amigos y se comieron 4 _ 8 de la bandeja de brownies. ¿Qué fracción de la bandeja de brownies queda?

2. Marisol camina a la escuela. La escuela está a 6 __ 10 de milla de su casa. Ya ha caminado 4 __ 10 de milla. ¿Cuánto más tiene que caminar Marisol?

3. Había 7 __ 12 de un galón de leche en el refrigerador. La familia Jones usó 3 __ 12 del galón durante el desayuno. ¿Cuánta leche queda?

4. 4 __ 5 − 2 __

5 = 5. 9 ___

12 − 5 ___

12 =

INV12_SP_BLM04_U6.indd 29 7/21/11 7:21 AM


FechaNombre

C30

Práctica diaria

Más restas de fraccionesResuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación.

1. Hay 7 _ 8 de un envase de jugo en el refrigerador. La familia Ortega bebió 5 _ 8 del envase en el desayuno. ¿Qué fracción queda del envase?

2. Venetta caminaba a la biblioteca, que está a 3 _ 4 de milla de distancia. Ha caminado 1 _ 4 de milla. ¿Cuánto más tiene que caminar Venetta?

3. Richard tenía 4 _ 5 de una bolsa de zanahorias. Alimentó a su conejo con 2 _ 5 de la bolsa. ¿Qué fracción de la bolsa le queda a Richard?

4. 7 ___ 10

− 4 ___ 10

= 5. 6 __ 8 − 1 __

8 =

notA Los estudiantes resuelven problemas de resta que incluyen fracciones con el mismo denominador.


Tarjetas de fracciones y cuadrados de decimales

INV12_SP_BLM04_U6.indd 30 6/20/11 9:33 PM


FechaNombre

C31

Práctica diaria Tarjetas de fracciones y cuadrados de decimales

Unidad 6 Sesión 2.1

notA Los estudiantes resuelven problemas de resta que incluyen fracciones con el mismo denominador.

Restas de fraccionesResuelve cada problema y muestra tu trabajo. Para los problemas verbales, escribe una ecuación.

1. Hay 5 _ 6 de una olla de sopa sobre la estufa. La familia Kim comió 4 _ 6 de la olla de sopa. ¿Qué fracción queda de la olla de sopa?

2. Nadeem camina al parque, que está a 9 __ 10 de milla de distancia. Ha caminado 4 __ 10 de milla. ¿Cuánto más tiene que caminar Nadeem?

3. Tonya tenía 10 __ 12 de yarda de tela. Usó 5 __ 12 de la yarda de tela para hacer una pantalla de lámpara. ¿Qué fracción queda de la yarda de tela?

4. 7 __ 8 − 2 __

8 = 5. 3 __

5 − 1 __

5 =





Envergaduras de mariposas (página 1 de 2)Yuki fue al Museo de Historia Natural a estudiar las mariposas. Abajo se muestra la información que tiene sobre algunas mariposas de la colección.

Nombre Envergadura (pulgadas) Nombre Envergadura

(pulgadas)

Picuda 1 1 _ 2 Perla creciente 1 5 _ 8

Mariposa macaón gigante

5 1 _ 4 Cartero 2 1 _ 2

Julia 3 1 _ 2 Almirante rojo 31 _ 8

Mariposa concha de Milbert

2 5 _ 8 Saturn 4 1 _ 4

Monarca 3 1 _ 2 Mariposa de cola de golondrina

3 3 _ 4

Vanesa de los cardos 2 1 _ 2 Virrey 2 7 _ 8

Anota las medidas en el diagrama de puntos de abajo.

1 2 3 4 5 60

Envergaduras de mariposas (pulgadas)

Escribe tres enunciados que describan los datos.





Envergaduras de mariposas (página 2 de 2)Usa la información de la página anterior para resolver los siguientes problemas. Muestra tu trabajo.

1. ¿Cuánto más larga es la envergadura de la mariposa virrey que la envergadura de la mariposa perla creciente?

2. ¿Cuánto más larga es la envergadura de la mariposa macaón gigante que la envergadura de la mariposa de cola de golondrina?

3. La mariposa picuda y la mariposa cartero están una junto a la otra. ¿Cuál es la longitud de sus envergaduras combinadas?

4. ¿Cuánto más larga es la envergadura de la mariposa almirante rojo que la envergadura de la mariposa concha de Milbert?

5. La mariposa perla creciente y la mariposa virrey están una junto a la otra. ¿Cuál es la longitud de sus envergaduras combinadas?

6. La mariposa saturn y la mariposa de cola de golondrina están una junto a la otra. ¿Cuál es la longitud de sus envergaduras combinadas?



FechaNombre

C34



notA Los estudiantes resuelven problemas de suma y resta que incluyen fracciones usando los datos proporcionados en un diagrama de puntos.

Los cachorros de PepperLa perra de Cheyenne, Pepper, tuvo cachorros. Cheyenne anotó sus pesos en el siguiente diagrama de puntos.

18


10

X X X X XX

14

38

12

58

34

78 11

8 11211

4 138

Pesos de los cachorros de Pepper (libras)

Resuelve cada problema y muestra tu trabajo.

1. Dos cachorros pesaban la misma cantidad. ¿Cuál fue el peso total de los dos cachorros?

2. ¿Cuántas libras más pesaba el cachorro más pesado que el cachorro más liviano?

3. El cachorro más pesado aumentó 4 _ 8 de libra durante su primer mes. ¿Cuánto pesaba después del primer mes?




Unidad 6 Sesión 3A.1

Multiplicar números enteros no negativos y fraccionesUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. Jake compró tres tipos de pizza para una fiesta. Cada pizza era del mismo tamaño. Las personas no tenían mucha hambre y al final de la fiesta quedaron 3 _ 4 de cada pizza. ¿Cuánta pizza quedó en total?

2. Una clase está contando de 2 _ 6 en 2 _ 6 . ¿Qué número dice la séptima persona?

3. 6 × 1 __ 3 =

4. 3 × 3 __ 8 =



FechaNombre

C36



notA Los estudiantes resuelven problemas que incluyen la multiplicación de un número entero no negativo y una fracción.

Trozos de quesoLa Casa de queso Morris Mouse vende trozos de queso. Cada trozo pesa 3 _ 4 de libra. Halla el peso total de cada tipo de queso. Usa una representación para resolver cada problema. También, escribe una ecuación de multiplicación que represente el problema. Muestra tu trabajo.

1. 5 trozos de queso cheddar 2. 10 trozos de queso suizo

Peso total Peso total

3. 4 trozos de queso americano 4. 8 trozos de queso parmesano

Peso total Peso total





Multiplicar fracciones y números enteros no negativosUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. Una tienda de abarrotes vende bolsas de 9 manzanas. Ana usó 2 _ 3 de las manzanas de una bolsa en una tarta de manzana. ¿Cuántas manzanas usó en la tarta?

2. Steve participó en una carrera de 7 millas. Corrió durante 1 _ 2 de la carrera y caminó el resto. ¿Cuántas millas corrió?

3. 2 __ 3 × 12 =

4. Hay 10 chicos en la clase. 4 _ 5 de ellos tienen cabello café. ¿Cuántos chicos tienen cabello café?

5. 5 __ 8 × 16 =

6. 1 __ 2 × 11 =





Multiplicar más fracciones y números enteros no negativosUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. Sabrina camina a la escuela. Su casa está a 3 _ 8 de milla de la escuela. ¿Cuántas millas caminará de ida y vuelta, entre su casa y la escuela, en 5 días?

2. 6 × 2 __ 5 =

3. Damián tiene una receta que requiere 2 _ 3 de taza de harina. Quiere preparar 4 porciones más de la receta. ¿Cuánta harina necesita?

4. 3 × 3 __ 4 =



FechaNombre

C39


notA Los estudiantes resuelven problemas que incluyen la multiplicación de números enteros no negativos y fracciones.

Multiplicar con fraccionesUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. 4 × 1 __ 5 = 2. 3 __

4 ×16 =

3. 1 __ 6 ×9 = 4. 12 × 1 __

2 =

5. El Sr. García tiene 15 nietos. 2 _ 3 de ellos son niñas. ¿Cuántas son niñas?

6. Elena necesita 8 pedazos de alambre. Cada pedazo debe medir 3 _ 4 de pie de largo. ¿Cuál es la longitud total del alambre que necesita Elena?






Multiplicar fraccionesUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. En la tienda, Damián buscó pretzels que vienen en bolsas de 1 _ 3 de libra. Compró 5 bolsas de pretzels. ¿Cuántas libras de pretzels compró?

2. 3 × 6 __ 8 =

3. En la clase había 25 estudiantes. Un día, 3 _ 5 de ellos llevaron tenis. ¿Cuántos estudiantes llevaron tenis?

4. 7 ___ 10

× 4 =

5. Para construir una pared, Jill usó piedras que medían 3 _ 4 de pie de alto cada una. Apiló 6 piedras una sobre otra. ¿Cuántos pies de alto medía su pared?

6. 5 __ 6 × 12 =



© Pearson Education, Inc., or its affiliates. All Rights Reserved. 4Unidad 6 Sesión 3A.3

Evaluación: Multiplicar con fracciones escritu

ra

Usa una representación para resolver cada problema. Para el problema verbal, escribe una ecuación que represente el problema.

1. Úrsula compró 30 manzanas. 3 _ 5 de ellas son verdes. ¿Cuántas de las manzanas son verdes?

2. 5 × 2 __ 3 =

C41



FechaNombre

C42




Todo tipo de frutos secosUsa una representación para resolver cada problema. También, escribe una ecuación que represente el problema.

1. Emaan compró 6 bolsas de nueces. Cada bolsa contenía 3 _ 4 de libra de nueces. ¿Cuál era el peso total de las nueces?

2. Un hombre compró 12 cajas de frutos secos. Llevó 1 _ 6 de las cajas a su oficina. ¿Cuántas cajas de frutos secos llevó a la oficina?

3. Kimberly está preparando 3 panes de frutos secos. Para cada pan, necesita 3 _ 4 de taza de pacanas. ¿Cuántas tazas de pacanas necesita? Encierra en un círculo la mejor respuesta.

entre 3 y 4 tazas

entre 2 y 3 tazas

entre 1 y 2 tazas



FechaNombre

C43



Colecciones de insectosLa clase de ciencias recolectó grillos y escarabajos. Los estudiantes hicieron diagramas de puntos para mostrar las longitudes de los insectos.

18

Longitudes de los grillos (pulgadas)

10

X X X X X X X XX XX

14

38

12

58

34

78 11

8 114 13

8 112 15

8 134 1 27

8

18

Longitudes de los escarabajos (pulgadas)

10

X X X X X XX X

X X XXX

X

14

38

12

58

34

78 11

8 114 13

8 112 15

8 134 1 27

8

1. ¿Cuánto más largo es el grillo más largo que el grillo más corto?

2. ¿Cuánto más largo es el escarabajo más largo que el escarabajo más corto?

3. El grillo que encontró Benson mide 1 1 _ 8 pulgadas de longitud. ¿Cuánto más largo es este grillo que el más corto de la colección?

4. El escarabajo que encontró Tonya mide 1 1 _ 4 pulgadas de longitud. ¿Cuánto más corto es este escarabajo que el más largo de la colección?

notA Los estudiantes resuelven problemas de suma y resta que incluyen fracciones usando los datos proporcionados en un diagrama de puntos.



FechaNombre

C44



notA Los estudiantes resuelven problemas que incluyen la multiplicación de un número entero no negativo por una fracción.

Comprar telaUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. Bill compró 6 pedazos de tela amarilla. Cada pedazo medía 1 _ 3 de yarda de longitud. ¿Cuántas yardas de tela compró Bill en total?

2. Kimberly compró 2 pedazos de tela azul. Cada pedazo medía 7 _ 8 de yarda de longitud. ¿Cuántas yardas de tela compró Kimberly en total?

3. Alejandro compró 7 pedazos de tela roja. Cada pedazo medía 3 _ 4 de yarda de longitud. ¿Cuántas yardas de tela compró Alejandro en total?

4. 2 × 3 ___ 10

= 5. 9 × 1 __ 6 =



FechaNombre

C45




Multiplicar con fraccionesUsa una representación para resolver cada problema. Para cada problema verbal, escribe una ecuación de multiplicación que represente el problema.

1. 1 __ 5 × 8 = 2. 6 × 2 __

3 =

3. 2 × 5 __ 6 = 4. 7 __

8 × 8 =

5. LaTanya tenía un pedazo de tela que medía 3 yardas de longitud. Usó 1 _ 2 de la tela para hacer una falda. ¿Cuánta tela usó?

6. Benson tenía 16 canicas. Regaló 3 _ 8 de las canicas. ¿Cuántas canicas regaló?



FechaNombre

C46




Trabajar duro Usa una representación para resolver cada problema. También, escribe una ecuación que represente el problema.

1. La semana pasada, la Srta. Cortez vendió 24 computadoras. 5 _ 8 de ellas eran computadoras portátiles. ¿Cuántas computadoras portátiles vendió la Srta. Cortez?

2. Un edificio de oficinas tiene 14 oficinas, todas del mismo tamaño. Un pintor usa 3 _ 4 de galón de pintura para pintar el techo de una oficina. ¿Cuánta pintura necesitará el pintor para pintar los techos de todas las oficinas?

3. El Sr. Stein va en bicicleta al trabajo. La distancia del viaje de ida y vuelta en bicicleta cada día es de 7 _ 8 de milla. ¿Cuál es la distancia total que anda en bicicleta en 5 días? Encierra en un círculo la mejor respuesta.

entre 6 y 7 millas

entre 5 y 6 millas

entre 4 y 5 millas


Documents

INVESTIGATION 1 Parts of Rectangles · INVESTIGATION 3 Working with Decimals Day Session Common Core Adaptation Common Core Standards 19 3.1 Representing Decimals MP5, MP6 4.NF.5,