1 teaching the lesson materials - everyday math...answers vary. 1,000 answers vary. 200 answers...

Objectives To review making ballpark estimates; and to reviewthe counting-up and trade-first subtraction algorithms.

Teaching the Lesson materials

Key ActivitiesChildren make ballpark estimates for 2-digit subtraction problems. They review the counting-up and trade-first subtraction algorithms.

Key Concepts and Skills• Use place-value concepts to apply the counting-up and trade-first algorithms.

[Number and Numeration Goal 1]• Use basic facts to solve extended fact problems involved in trade-first subtraction.

[Operations and Computation Goal 1]• Use base-10 blocks to model and solve subtraction problems.

[Operations and Computation Goal 2]• Make ballpark estimates as a check for reasonableness of answers.

[Operations and Computation Goal 5]

Key Vocabularycounting-up method • trade-first method

Ongoing Assessment: Informing Instruction See page 143.

Ongoing Assessment: Recognizing Student Achievement Use journal page 50.[Operations and Computation Goal 2]

Ongoing Learning & Practice materials

Children write equivalent names for numbers in name-collection boxes.

Children play Number-Grid Difference.

Children practice and maintain skills through Math Boxes and Home Link activities.

Differentiation Options materials

Children play Base-10 Trading Game. Children make posters showing a variety of subtraction strategies.

� Teaching Aid Master (Math Masters, p. 411)� base-10 blocks; dice� large paper; crayons

ENRICHMENTREADINESS

3

� Math Journal 1, pp. 48 and 49� Student Reference Book, p. 301� Home Link Master (Math Masters, p. 54)� Teaching Master (Math Masters, p. 21)� Game Master (Math Masters, p. 452)� number cards 0–9, 4 of each� 2 pennies or counters; calculator

2

� Math Journal 1, pp. 47 and 50� Home Link 2�7� Teaching Master (Math Masters, p. 55)� base-10 blocks� overhead base-10 blocks (optional)� Number-Grid Poster (optional)

See Advance Preparation

1

Technology Assessment Management SystemJournal page 50See the iTLG.

Additional InformationAdvance Preparation Plan to spend a total of two days on this lesson.

Lesson 2�8 141

EM07TLG1_G3_U02_LOP08.qxd 1/18/06 3:02 AM 41

142 Unit 2 Adding and Subtracting Whole Numbers

� Math Message Follow-UpRemind children that one way to make a ballpark estimate is tochange the numbers in the problem to close-but-easier numbersthat can be subtracted mentally. For example:

� 56 � 24 is close to 60 � 20, so the exact answer should be close to 40.

� 71 � 46 is close to 70 � 50 or 75 � 45, so the exact answershould be near 20 or 30.

� 45 � 18 is close to 40 � 20 or 50 � 20, so the exact answershould be near 20 or 30.

NOTE There can often be more than one acceptable answer when making ballpark estimates.

� Reviewing the Counting-Up Method for 2-Digit SubtractionHave children find exact answers to the Math Message problems,using the counting-up method from Second Grade EverydayMathematics, and check them against their ballpark estimates.Children share their answers and procedures while you keep arecord on the board. This is called the counting-up methodbecause children count up from the smaller number to the largernumber, using a combination of multiples of 10s and 1s.

WHOLE-CLASS ACTIVITY

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Getting Started

Home Link 2�7 Follow-UpHave partners share theirsolution strategies.

Math Message Make ballpark estimates.On a half-sheet of paper, write the number sentence you used for each estimate.

Sample answers:

1. 56 � 24 � ? 60 � 20 � 40

2. 71 � 46 � ? 70 � 50 � 20; 75 � 45 � 30

3. 45 � 18 � ? 40 � 20 � 20; 50 � 20 � 30

Mental Math and Reflexes Pose fact-extension problems.Suggestions:

10 � � 100 9030 � � 70 4090 � � 30 6040 � � 120 80150 � � 143 7160 � � 151 91,050 � � 900 150795 � � 820 25993 � � 1,010 17

Unit

books

� On Day 1 of this lesson, children shouldcomplete the Math Message Follow-Up,review counting up for 2-digit subtraction,subtract 3-digit numbers, and write equivalent names for numbers.

� On Day 2 of this lesson, children shouldmodel trade-first subtraction, subtract 3-digit numbers, and play Number-GridDifference.

Make a ballpark estimate. Write a number model to show yourestimate. Choose at least two problems to solve using the counting-upmethod and show your work. You may choose any method you wishto solve the other problems.

Date Time

Unitlunches

Example: Ballpark estimate:

Counting-Up Method

230�200 � 30

1. Ballpark estimate:

6 3� 3 7

26


9 1� 4 6

45


7 5 2� 3 8 7

365


2 8 3� 2 5 6

27


1 2 9� 1 1 2

17

Subtraction Methods LESSON

2�8

187� 3190

� 10200

� 30230� 4234

3 � 10 � 30 � 4 � 47

60 � 40 � 20

280 � 260 � 20130 � 110 � 20 750 � 400 � 350

90 � 50 � 40

Sample estimates given.

2 3 4� 1 8 7

Math Journal 1, p. 47

Student Page

EM07TLG1_G3_U02_L08.qxd 1/18/06 2:34 AM Page 142

Lesson 2�8 143

�2 �40 �100 �40 �3158 160 200 300 340 343

2 � 40 � 100 � 40 � 3 = 185343 � 158 = 185

158 � 2 � 160160 � 40 � 200200 � 100 � 300300 � 40 � 340340 � 3 � 343

longs10s67/

� 42

cubes1s111/65

46� 4

50�10

60�10

70� 1

71

Longs and cubes to represent 71

Trade 1 ten for 10 ones.

Subtract 46 by removing 4 tens and 6 ones. 25 (2 tens, 5 ones) remaining.

Example: 71 � 46

Write the problem on the board in horizontal form. Then write 46next to the problem. Model counting up from 46 to 71. Circle eachnumber as you count up. Remind children that they may beginwith the 100s, 10s, or 1s in any order when adding mentally.Then model the mental addition of the circled numbers.

4 � 10 � 10 � 1 � 25. So 71 � 46 � 25.

Ongoing Assessment: Informing InstructionWatch for children who are having difficulty using multiples of 10s and 1s tocount up. You may want to use the number grid to model the counting-upmethod.

� Subtracting 3-Digit Numbers(Math Journal 1, p. 47)

Write the following problem on the board in horizontal format:343 – 158

Have children solve the problem and then share their solutionstrategies. If no one mentions it, model the counting-up method.See the margin for other ways to record the counting-up method.

Children solve the problems on the journal page. Remind them tomake ballpark estimates. Provide access to the number grid andother manipulatives.

Children may share their answers with a partner. If there is adisagreement, encourage them to discuss their strategies witheach other and do the problem again until they agree on ananswer.

� Modeling the Trade-First Algorithm for 2-Digit SubtractionRemind children that in Second Grade Everyday Mathematicsthey used the trade-first method to subtract 2-digit numbers.Model solving the problem using the trade-first method.

Example: 71–46

Write the problem on the board in vertical format.

Draw a picture on the board of 7 longs and 1 cube to represent thenumber 71. Ask: Are there enough blocks to remove 46 (4 longs and6 cubes)? No Trade 1 long for 10 cubes. Mark the problem toreflect this action: Draw a slash through the 7 and write 6; draw aslash through the 1 and write 11.

Subtract 4 tens by erasing 4 longs from the picture. Subtract 6 ones by erasing 6 cubes from the picture. That leaves 25 (2 longs and 5 cubes). Record this answer on the board.





23/

� 11

133

4/58

133/85

Show 343 with 3 hundreds, 4 tens, and 3 ones.

Trade 1 hundred for 10 tens.

Trade 1 ten for 10 ones.

Subtract 158 by removing 1 hundred, 5 tens, and 8 ones. 185 (1 hundred, 8 tens, and 5 ones)remaining.

Links to the Future

� Subtracting 3-Digit NumbersWrite this problem on the board in vertical form:

343�158

Ask children to solve the problem and share their solution strategies. If no one mentions it, model the trade-first method. Seethe margin for representations of the base-10 block trades for thesolution. Try several more 2- and 3-digit subtraction problems asneeded.

� Practicing Subtraction Algorithms(Math Journal 1, p. 50; Math Masters, p. 55)

Children solve the problems on the journal page. Remind them tomake ballpark estimates to check answers and look for mistakes.Make sure children have access to manipulatives. Children mayshare their answers with a partner. If there is a disagreement,encourage them to discuss their strategies with each other and dothe problem again until they agree on an answer. Use MathMasters, page 55 to create additional practice problems as needed.

Abundant practice with 3-digit subtraction problems will be found on Math Boxesand Home Links in future lessons.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 50, Problems 1 and 2 to assess children’s ability to solvemultidigit subtraction problems. Children are making adequate progress if theyare able to solve Problems 1 and 2 correctly. Some children may be able tocomplete the remaining problems with or without manipulatives.

[Operations and Computation Goal 2]

� Writing Equivalent Names for Numbers(Math Journal 1, p. 48)

Children complete name-collection boxes. Name-collection boxeswere reviewed in Lesson 1-6.

INDEPENDENTACTIVITY

2 Ongoing Learning & Practice

Journal Page 50Problems 1 and 2 �

INDEPENDENTACTIVITY



� Playing Number-Grid Difference(Math Masters, pp. 21 and 452; Student Reference Book,p. 301)

Children practice finding differences by playing Number-GridDifference. If necessary, review game directions on page 301 of theStudent Reference Book.

� Math Boxes 2�8(Math Journal 1, p. 49)

Mixed Practice Math Boxes in this lesson are paired withMath Boxes in Lesson 2-6. The skill in Problem 6 previews Unit 3 content.

Writing/Reasoning Have children write an answer to thefollowing: Explain how you figured out what the timewould be in 30 minutes in Problem 3. Sample answer:

Starting at the minute hand, I counted in 5 min intervals until Iadded 30 min to find the new time.

� Home Link 2�8(Math Masters, p. 54)

Home Connection Children solve subtraction problems.Since some of the methods children use may not be familiar to parents, you may want to send home theStudent Reference Book.

� Playing Base-10 Trading Game(Math Masters, p. 411)

To provide experience with place-value exchanges, have childrenplay Base-10 Trading Game. The following materials are neededper partnership: 2 flats, 20 longs, 40 cubes; 2 dice; and 2 Place-Value Mats. Each partner pair needs to begin with a bank of 20longs and 40 cubes. Each partner places 1 flat on the Place-ValueMat. (See the next page for game directions.)

5–15 Min

PARTNER ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

PARTNER ACTIVITY

Lesson 2�8 145

Date Time

3. Write at least 10 names for 200.

2. Write at least 10 names for 40.

4. Write at least 10 names for 1,000.

1. Three names do not belong. Markthem with a big X.

100

25 � 25 � 25

1,680 � 1,580

1,000 �100

9,999 �9,899

48 � 52

80�3030 � 70

2 fifties

63�37

Name-Collection BoxesLESSON

2�8

40

Answers vary.

1,000

Answers vary.

200

Answers vary.

14 15


Student Page

Date Time

100s12

�1

10s14

48

6

1s

76

1

Subtraction MethodsLESSON

2�8Make a ballpark estimate. Write a number model to show yourestimate. Choose at least two problems to solve using the trade-firstmethod and show your work. You may choose any method you wishto solve the other problems.

Unitdollars

Example:Ballpark estimate:

Trade-First Method

250�200 � 50


7 4� 2 9

45


9 6� 3 7

59


8 2 6� 1 7 2

654


2 7 1� 2 4 8

23


2 0 8� 1 0 6

102

Sample estimates given.

70 � 30 � 40

200 � 100 � 100 270 � 250 � 20 800 � 200 � 600

100 � 40 � 60� �


Student Page



Directions:

Take turns. On each turn, a player does the following:

1. Roll the dice and find the sum of the dice dots.

2. Return that number of cubes to the bank. (Whenever thereare not enough individual cubes, make exchanges.)

3. The player who is not rolling the dice checks the accuracy ofthe transactions.

4. The first player to clear his or her Place-Value Mat wins thegame.

� Making Subtraction PostersTo further explore subtraction algorithms, have children makesubtraction posters. Small groups work together to write a 2- or 3-digit subtraction problem. They use as many methods asthey can to solve the problem. Then children create postersshowing their methods. Possible methods include using thenumber grid, number line, base-10 blocks, counting-up, partial-differences, trade-first, and the U.S. traditional algorithms.Children may use other methods as well. Display the posters.

15–30 Min

SMALL-GROUP ACTIVITY

ENRICHMENT

3-Digit Place-Value Mat

Name Date Time

Hun

dred

sTe

nsO

nes

Math Masters, p. 411

Teaching Aid MasterName Date Time

Subtraction MethodsHOME LINK

2�8

Over the past 2 days, your child practiced subtracting two 3-digit numbers using thecounting-up method and the trade-first method. For more information, see pages 60, 61,and 63 in the Student Reference Book.

Please return this Home Link to school tomorrow.

FamilyNote

60 6163

Fill in the unit. Solve the problems. You may use any method you wish. Use a ballpark estimate to check that your answer makes sense. Write a number model for yourestimate. On the back of this Home Link, explain how you solved one of the problems.Sample estimates given.

531�329

468�274

331�209

925�486

724�237

194 202 122

653�447

206 439 487

Unit

1. Ballpark estimate: 2. Ballpark estimate: 3. Ballpark estimate:

300 � 200 � 100500 � 300 � 200500 � 300 � 200

4. Ballpark estimate: 5. Ballpark estimate: 6. Ballpark estimate:

700 � 200 � 500900 � 500 � 400650 � 450 � 200

Math Masters, p. 54

Home Link Master

Date Time

5. Corey had $75. He bought a newbaseball for $18. How much moneydoes he have now?

Number model:

75 � 18 � 57

$57

3. What time doesthe clock show?

What time will itbe in 30minutes?

2:55

2:25

2. Fill in the blanks.

� 53 � 60

90 � 3 �

132 � 140 �

198 � � 210128

877

4. Find the rule and complete the table.

6. Measure the line segment to thenearest �

12� centimeter.

cm4�12�

1. Complete the fact extensions.

6 � 5 � 11

16 � 5 �

26 � 5 �

86 � 5 �

126 � 5 � 131913121

Unit Unitdays

12 12

3

4567

8

9

1011

203 204

137–139

Start EndChange

75 �18 57

Math BoxesLESSON

2�8

Rule

out

in

Add 20

in out

102 122

130 150164 184

173 193

188 208


Student Page


1 teaching the lesson materials - everyday math...answers vary. 1,000 answers vary. 200 answers...

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