1 Teaching the Lesson materials - Ellis Familyellis2020.org/iTLG/iTLG Grade 4/U6.4.pdfTeaching the Lesson materials ... Students practice and maintain skills through Math Boxes and

Teaching the Lesson materials

Key ActivitiesStudents express remainders in division problems as fractions that become part of mixed-number answers or as decimals. They solve other division problems in which the remainder is either rounded up or ignored.

Key Concepts and Skills• Use multiples to solve division problems. [Number and Numeration Goal 3]

• Solve division number stories and interpret remainders. [Operations and Computation Goal 4]

• Use arrays to model division. [Operations and Computation Goal 7]

• Write number models to represent division number stories. [Patterns, Functions, and Algebra Goal 2]

• Write number models containing grouping symbols. [Patterns, Functions, and Algebra Goal 3]

Key Vocabulary mixed number

Ongoing Learning & Practice materials

Students play Division Dash to practice dividing 2- or 3-digit dividends by1-digit divisors.

Students practice and maintain skills through Math Boxes and Study Link activities.

Ongoing Assessment: Recognizing Student Achievement Use journal page 150.[Operations and Computation Goal 2]

Differentiation Options materials

Students read ARemainder of One,create arrays and recordnumber models based on the story.

Students solve a divisionnumber story by findingmultiples.

Students practice solvingdivision problems.

� Teaching Masters(Math Masters,pp. 183 and 184)

� 5-Minute Math,pp. 20 and 25

� A Remainder ofOne

� centimeter cubes;counters (optional)

EXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 1,p. 150

� Student ReferenceBook, p. 241

� Study Link Master(Math Masters,p. 182)

� Game Master (Math Masters,p. 471)

� per partnership: 4 each of numbercards 1–9

2

� Math Journal 1, pp. 148 and 149

� Study Link 6�3

� slate

� 13 sticks of gum (optional)

1

Objectives To introduce the expression of remainders as

fractions or decimals; and to provide practice interpreting

remainders in division problems.

Technology Assessment Management SystemMath Boxes, Problem 3

See the iTLG.

Additional InformationAdvance Preparation For the optional Readiness activity in Part 3, obtain the book A Remainder of One by Elinor J. Pinczes (Houghton Mifflin, 2002).

Lesson 6�4 419

See Advance Preparation

420 Unit 6 Division; Map Reference Frames; Measures of Angles

Adjusting the Activity

� Math Message Follow-UpPoint out that 4 R1 is a correct answer to the Math Messageproblem, but that this answer will not satisfy the three studentswho want to know who gets the last piece of gum.

Ask students to draw a simple picture to organize the informationin the problem. Have several volunteers draw their pictures on the board.

Ask: What do the quotient 4 and remainder 1 represent? Eachstudent can have 4 sticks of gum, and 1 stick will be left.Ask: Should the 1 stick be ignored? No. That would be a waste.The context of the problem indicates that the remainder should be made part of the answer.

One way to do this is to divide the remainder among the 3 students. Draw a rectangle to represent one stick of gum and divide it into thirds. Label each section �

13�.

ELL

Act out the problem using actual sticks of gum. Open the thirteenth stick

and break it into 3 equal pieces.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Getting Started

Study Link 6�3 Follow-Up Have students compare answers. Ask volunteers toshare different ways to solve the problems.

Math MessageThree students share 13 sticks of gum. How manysticks of gum does each student get if they receive equal shares?

Mental Math and Reflexes Pose division facts. Suggestions:

13

13

13

12 � 6 = 2

16 � 4 = 4

30 � 6 = 5

70 � 7 = 10

21 � 3 = 7

32 � 4 = 8

27 � 3 = 9

24 � 6 = 4

72 � 9 = 8

42 � 7 = 6

36 � 4 = 9

63 � 9 = 7

students sticks of gum per student sticks of gum in all

3 ? 13

13 sticks of gum shared

equally by 3 students

13 / 3 = x

13 sticks of gum.

3 students.

3 � x = 13

Lesson 6�4 421

///

////\///

////\///

////\///

////\///

14

14

14

14

14

14

14

14

14

14

14

14

25› 25› 25› 25›

$1.00

Therefore, each student will receive 4�13� sticks of gum. Another

way to say this is 4�13� sticks of gum per student. Explain that 4�

13� is

called a mixed number.

Students can check their answers by multiplying 3 � 4 and addingthe remainder of 1. (3 � 4) � 1 � 13

� Expressing Remaindersas Fractions or DecimalsTell students that in this lesson they will solve division numberstories in which something must be done with the remainder inorder to provide a useful answer. In the following examples, theremainder is expressed as a fraction or decimal.

Ask students to draw a simple picture to organize the informationfor each problem below.

Example 1: Four brothers are given 35 fruit bars. They agree toshare the bars equally. How many fruit bars will each boy get?

This is a division problem: 35 / 4 → 8 R3. If they each get 8 fruitbars, 3 fruit bars would still need to be divided.

Sketch the 3 fruit bars on the board. Divide each into fourths torepresent the 4 boys sharing each bar.

If each boy takes one piece of each bar, he will have 8�34� fruit bars.

Some students will discover the shortcut for writing a remainderas a fraction:

1. Make the remainder the numerator of the fraction.

2. Make the divisor the denominator of the fraction.

Then write the answer as a mixed number in which the remainderis now expressed as a fraction.

In some problems, especially those involving money, it may bepreferable to change the fraction to an equivalent decimal.

Example 2: Four people split the cost of a $15 present equally.What is each person’s share? 15 � 4 → 3 R3.

Using the remainder as the numerator of the fraction and thedivisor as the denominator leads to the answer $3�

34�, or $3.75.

Sketch a dollar bill on the board. Divide it into fourths to showthat �

34� of $1.00 = $0.75.

WHOLE-CLASSACTIVITY

35 fruit bars shared

equally by 4 brothers

35 / 4 = x

Each of the 4 brothers gets �34

�

of the remaining 3 bars.

Links to the FutureIn Unit 7 of Fourth Grade Everyday

Mathematics, students will continue their

exploration of mixed numbers in their work

with number lines, regions, and collections.


� Interpreting Remainders in Problem ContextsThe remainder in a division number story should not always be converted to a fraction or decimal and retained as part of theanswer. Depending on the situation, the remainder might beignored because it is a leftover amount that cannot be split upfurther. Or, it might indicate that the answer should be roundedup. Discuss examples that illustrate these other situations. Foreach problem, ask students to draw a simple picture to organizethe information.

Remainder that is ignored● Three children wish to divide a set of 16 toy cars equally. What

is each child’s share?

Each child can have 5 cars, and there is 1 car left over. Unlike the1 stick of gum in the Math Message problem that could be cut intoequal parts, the 1 remaining toy car cannot be divided up.Therefore, the remainder is considered a “leftover” amount.

Remainder that is ignored ● Ann has $18 to buy notebooks that cost $4 each. How many

notebooks can she buy?

The division is 18 � 4 → 4 R2. Ann can buy 4 notebooks and willhave $2 left. The remainder can be ignored. Note that Ann willhave $2 left, but the answer to the question is 4 (notebooks).

Remainder that indicates the answer should be rounded up ● Esteban has 29 photographs. He can fit 6 photos on each page

of his photo album. How many pages must he use to hold all 29 photos?

The division is 29 � 6 → 4 R5, or 4�56�. Esteban needs 4�

56� pages to

include all 29 photos. Four pages hold only 24 photos and are notenough. Esteban must use a fifth page to hold the last 5 photos.He must use 5 pages in all, which is 4�

56� rounded up to the next

whole number.

$4 $4

$4 $4$2

WHOLE-CLASSACTIVITY

149

Interpreting Remainders continuedLESSON

6�4

Date Time

3. Lateefah won 188 candy bars in a raffle.

She decided to share them equally with 7 of

her classmates and herself. How many

candy bars did each person receive?

Picture:

Number model:

Answer: candy bars

What did you do about the remainder?

Circle the answer.

A. Ignored it

B. Reported it as a fraction or decimal

C. Rounded the answer up

Why?

evenly among the 8 people.

be cut into halves and shared

remaining 4 candy bars can

Sample answer: The

23�48

� or 23�12

�

188 � 8 ∑ 23 R4

Sample picture:

8 equal groups

188candybars

Write each answer as a mixed number by

rewriting the remainder as a fraction.

4. 2�2�7�

5. 10�8�8�3�

6. 16�2�5�2�

Write each answer as a decimal.

7. 39 � 2 � 19 R1

8. 183 � 12 � 15 R3

9. 2,067 � 5 � 413 R2 413.4

15.25

19.5

15 �11

26�

88 �130�

13 �12

�

Try This

13 R1

88 R3

15 R12

Math Journal 1, p. 149

Student Page

148

Interpreting RemaindersLESSON

6�4

Date Time

1. Jackson is buying balloons for a party.

Balloons cost $6 per bunch. How many

bunches can he buy with $75?

Picture:

Number model:

Answer: bunches


Circle the answer.

A. Ignored it



Why?

to buy another bunch.

three dollars left isn’t enough

Sample answer: The

12

75 � 6 ∑ 12 R3

$6 $6 $6 $6 $6

$6 $6

$6 $6

$6 $6 $6

2. Rosa is buying boxes to hold all 128 of her

CDs. Each box holds 5 CDs. How many

boxes are needed to store all of her CDs?

Picture:

Number model:

Answer: boxes


Circle the answer.

A. Ignored it



Why?

to store the remaining 3 CDs.

additional box was needed

Sample answer: An

26

128 � 5 ∑ 25 R3

5 5 5 5 55 5 5 5 55 5 5 5 5553

5 5 5 55 5 5 5

For each number story:

� Draw a picture.

� Write a number model.

� Use a division algorithm to solve the problem.

� Decide what to do about the remainder.

179

Sample pictures:


Student Page

Adjusting the Activity

� Solving Division Problems and Interpreting Remainders(Math Journal 1, pp. 148 and 149)

Encourage students to think about each remainder and thedifferent ways in which it should be interpreted as they completejournal pages 148 and 149.

� Playing Division Dash(Student Reference Book, p. 241; Math Masters, p. 471)

Students play Division Dash to practice dividing 2- or 3-digit dividends by 1-digit divisors.

Use this game variation as appropriate:

Have students place only the 2 and 5 cards in the divisor pile.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

� Math Boxes 6�4(Math Journal 1, p. 150)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-2. The skill in Problem 5previews Unit 7 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess students’ ability to solve decimal

addition and subtraction problems. Students are making adequate progress if

they compute the correct sums and differences. Some students may be able to

explain how to use ballpark estimates or the relationship between addition and

subtraction to check their answers.

[Operations and Computation Goal 2]

� Study Link 6�4(Math Masters, p. 182)

Home Connection Students practice using a divisionalgorithm and interpreting the remainder.

INDEPENDENTACTIVITY

Math Boxes

Problem 3 �

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

PARTNER ACTIVITY

150

Math Boxes LESSON

6�4

Date Time

4. How many centimeters are in 12 meters?

Circle the best answer.

A. 0.12

B. 1.2

C. 120

D. 1,200

5. Circle the fractions equivalent to �1

2�.

�1

8

6� �

5

6� �

1

6

2�

�2

3� �

1

2

2

4� �

1

8

5�

1. Joe ordered 72 plants for his patio garden.

Each pot holds 4 plants. How many pots

are needed to hold all of the plants?

2. Solve each open sentence.

a. (6 � 9) � (3 � A) � 30 A �

b. 24 � 8 � 21 � B B �

c. 72 � (2 � C) � 9 C �

d. 6.2 � 0.79 � D D �

e. 8.91 � E � 2.72 E � 6.196.99

475

pots plants per plantspot in all

? 4 72

35–37148

34–37

51129

3. Use a paper-and-pencil algorithm to add or subtract.

a. 0.37 b. 2.9 c. 6.79 d. 7.80

� 0.26 � 5.01 � 6.55 � 3.65

Number model:

Answer: 18 pots

72 / 4 � 18

0.63 7.91 0.24 4.15�


Student Page

STUDY LINK

6�4

Name Date Time

Interpreting Remainders

1. Mrs. Patel brought a box of 124

strawberries to the party. She wants to

divide the strawberries evenly among

8 people. How many strawberries will

each person get?

Picture:

Number model:

Answer: strawberries


Circle the answer.

A. Ignored it



Why?

2. Mr. Chew has a box of 348

pens. He asks Maurice to

divide the pens into groups

of 16. How many groups

can Maurice make?

Picture:

Number model:

Answer: groups


Circle the answer.

A. Ignored it



Why?

to form another group of 16.

aren’t enough remaining pens

Sample answer: There

21

348 � 16 ∑ 21 R12

into halves.

cut the remaining strawberries

Sample answer: You can

15�48

� or 15�12

�

124 � 8 ∑ 15 R4

Practice

3. 68 � 7 � 4. � 74 � 4

5. �46

9

8� � 6. 3��9�5� � 31 R252

18 R29 R5

15 15 15 15

15 15 15 15

161616161616161616161616161616161616161616

Sample picture: Sample picture:

179

Math Masters, p. 182

Study Link Master

Lesson 6�4 423


LESSON

6�4

Name Date Time

A Remainder of One

Use 25 centimeter cubes to represent the 25 ants in the story A Remainder of One.

1. Divide the cubes into 2 equal rows.

Draw what you did.

How many cubes are in each row?

cubes

How many cubes are left over?

cube(s)


Draw what you did.


cubes


cube(s)


Draw what you did.


cubes


cube(s)


Draw what you did.


cubes


cube(s)0

5

1

8

1

6

1

12

Math Masters, p. 183

Teaching Master

� Exploring Remaindersin Literature(Math Masters, p. 183)

Literature Link To explore the concept of remainders, havestudents read and discuss the book A Remainder of One

by Elinor J. Pinczes (Houghton Mifflin, 2002). For each situationin the story, ask students to create arrays using centimeter cubesand record their work on Math Masters, page 183. Have studentsdescribe the arrays and tell how they determined the number ofrows. Encourage the use of vocabulary from this unit.

� Solving a Multiples Number Story(Math Masters, p. 184)

To apply students’ understanding of multiples, factors,and division and remainders, have them solve a marble-sharing number story. Encourage students tomodel the problem with counters if necessary.

� 5-Minute MathTo offer students more experience with division, see 5-MinuteMath, pages 20 and 25.

5–15 Min

SMALL-GROUP ACTIVITY

EXTRA PRACTICE

5–15 Min

INDEPENDENTACTIVITY

ENRICHMENT

15–30 Min

SMALL-GROUP ACTIVITY

READINESS

3 Differentiation Options

LESSON

6�4

Name Date Time

Multiples Number Story

Paolo has fewer than 40 marbles in a bag. If he splits up the marbles among his 4 friends,

he’ll have 3 left over.

If he divides them among his 7 friends, he’ll have 2 left over.

1. How many marbles are in the bag? marbles

2. Show or explain how you got your answer.

divided by 4. 23 � 4 ∑ 5 R3; 23 � 7 ∑ 3 R2.

2 left over. Only 23 gives a remainder of 3 when it is

divides the marbles evenly among his 7 friends there are

than a multiple of 7 (9, 16, 23, 30, 37) because when Paolo

Sample answer: The number of marbles has to be 2 more

23MARBLES

Math Masters, page 184

Documents

1 Teaching the Lesson materials - Ellis Familyellis2020.org/iTLG/iTLG Grade 4/U6.4.pdfTeaching the Lesson materials ... Students practice and maintain skills through Math Boxes and