1 Teaching the Lesson - Everyday Math · Differentiation Options materials ... Teaching Master (Math Masters, p. 53; optional) base-10 blocks ... 4. Add the partial sums

Objectives To guide children as they make ballpark estimates;and to provide opportunities to model and practice the partial-sums algorithm for 2- and 3-digit numbers.

Teaching the Lesson materials

Key ActivitiesChildren add 2- and 3-digit numbers, discuss solution methods, and make ballpark estimates to check addition results.

Key Concepts and Skills• Model multi-digit numbers with base-10 blocks. [Number and Numeration Goal 1]• Use basic facts to solve extended fact problems with the partial-sums algorithm.

[Operations and Computation Goal 1]• Use base-10 blocks to extend the partial-sums algorithm to 3-digit addends.

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

[Operations and Computation Goal 5]

Key Vocabulary partial-sums algorithm • ballpark estimate • partial-sums methodOngoing Assessment: Recognizing Student AchievementUse journal page 45. [Operations and Computation Goal 2]

Ongoing Learning & Practice materials

Children play Target 50.Children practice and maintain skills through Math Boxes and Home Link activities.

Differentiation Options materials

Children use base-10 blocks to model 2-digit numbers.

Children make up andsolve 3-digit additionnumber stories based on a mileage map.

Children write ballparkestimate using the WordBank template.

� Student ReferenceBook, pp. 224 and225

� Teaching Aid Masters(Math Masters,pp. 407 and 411)

� DifferentiationHandbook

� base-10 blocks� number cards 0–9,

4 of each; paper

ELL SUPPORTENRICHMENTREADINESS

3

� Math Journal 1, p. 46� Student Reference

Book, p. 312� Home Link Master

(Math Masters, p. 52)

� Teaching Aid Master(Math Masters,p. 411)

� Game Master (MathMasters, p. 46 )

� number cards 0–9;base-10 blocks

2

� Math Journal 1, p. 45� Student Reference Book, pp. 190–194� Home Link 2�6� Teaching Master (Math Masters,

p. 53; optional)� base-10 blocks� overhead base-10 blocks, optional

1

Technology Assessment Management SystemJournal page 45See the iTLG.

Lesson 2�7 135

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5

136 Unit 2 Adding and Subtracting Whole Numbers

� Math Message Follow-UpAsk children how they calculated the answers. Record children’sdifferent strategies on the board. During the discussion, have children name the value in each place, not just the digits. In thefirst problem, for example, if a child says, “I added the 6 and the2” remind the class to say they added 60 and 20, or 6 tens and 2 tens.

Possible Strategies for 28 � 37

� 20 � 30 � 50; 8 � 7 � 15; and 50 � 15 � 65. This strategyuses the partial-sums algorithm.

� Take 2 from 37, getting 35, and add the 2 to 28; 28 � 2 � 30,and 30 � 35 � 65.

� Think of 37 as 30 � 7; 28 � 7 � 35; and 35 � 30 � 65.

� Making Ballpark Estimates(Student Reference Book, pp. 190–194)

Remind children that answers should always be checked to seewhether they make sense. This is true for number story problemsand for problems where there is no story like those in the MathMessage.

Children should make a close enough, or ballpark estimate ofthe answer either before or after calculating by changing theaddends to close but easier numbers and then adding them. Havechildren read about estimation on pages 190–194 in their StudentReference Books.

WHOLE-CLASS ACTIVITY

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Getting Started

Math MessageAdd.

63 � 24 � 8728 � 37 � 6549 � 18 � 67

Home Link 2�6 Follow-Up Review answers as necessary. Have a few childrenshare their strategies for solving the number stories.

Mental Math and Reflexes Ask such questions as the following:

Is 42 closer to 40 or 50? 40Is 56 closer to 50 or 60? 60Is 95 closer to 90 or 100? Same distance awayIs 150 closer to 100 or 200? Same distance awayIs 210 closer to 200 or 300? 200Is 998 closer to 900 or 1,000? 1,000Is 2,068 closer to 2,000 or 2,100? 2,100Is 3,243 closer to 3,240 or 3,250? 3,240Is 4,250 closer to 4,200 or 4,300? Same distance away

Unit

miles

NOTE Partial sums may be calculated ineither order—it does not matter whether you add the tens or the ones first. When discussing and using the partial-sums algorithm, emphasize the following paper-and-pencil method. EExxaammppllee:: 63 � 24

1. Add the tens:6 [tens] � 2 [tens] � 8 [tens] or 80. Write 80 below the line.

2. Add the ones:3 [ones] � 4 [ones] � 7 [ones] or 7.Write 7 below the 80.

3. Add the partial sums: Draw a second line beneath 80 and 7. Write 87 beneaththis line.

10s

6� 2

8

8

1s

34077

1. Add the 10s.

2. Add the 1s.

3. Add the partial sums.

EM07TLG1_G3_U02_L07.qxd 1/18/06 2:34 AM Page 136

Ask children to make ballpark estimates for the problems belowand tell how they arrived at their estimates. Note that there isoften more than one acceptable estimate.

� 42 � 89 is close to 40 � 90 � 130

� 23 � 71 is close to 20 � 70 � 90

� 148 � 51 is close to 150 � 50 � 200

� 213 � 468 is close to 200 � 500 � 700 or 210 � 470 � 680

� 35 � 63 is close to 30 � 60 � 90 or 40 � 60 � 100. Point outthat because 35 is halfway between 30 and 40 on the numberline, either 30 or 40 may be used as an easier substitute for 35.

� Modeling the Partial-Sums Method for 3-Digit Addends(Math Masters, p. 53)

Remind children that in Second Grade Everyday Mathematicsthey used the partial-sums method to add 2-digit addends.Today you will show them that the partial-sums method works inthe same way with 3-digit addends.

Write these problems on the board in vertical form:

145 169� 322 � 175

Ask children to gather in a circle as you demonstrate with base-10blocks, or use base-10 blocks on the overhead projector. Refer toflats as hundreds, longs as tens, and cubes as ones. For eachproblem, model addition as a four-part operation: add the 100s,add the 10s, add the 1s, and then add the partial sums.

Example 1: Model 145 � 322 with base-10 blocks.

� Count out 1 flat, 4 longs, and 5 cubes to represent 145. Countout 3 flats, 2 longs, and 2 cubes to represent 322.

� Arrange the blocks like the addition problem in vertical form.

� Gather the hundreds into one pile, the tens into a second pile,and the ones into a third pile.

� Count the hundreds. 4 hundreds, or 400 Count the tens. 6 tens,or 60 Count the ones. 7 ones, or 7

� Add the hundreds, tens, and ones. 400 � 60 � 7 � 467

� Ask children how they would record this procedure on paper.You may use Math Masters, page 53 if you wish.

WHOLE-CLASS ACTIVITY

Lesson 2�7 137

LESSON

2�7

Name Date Time

Addition: The Partial-Sums Method

100s3

� 4

7

�7

10s21

031 4

1s98

0077

Example: Ballpark estimate:

1. Ballpark estimate:




300 � 400 � 700

100s 10s 1s 100s 10s 1s

100s 10s 1s 100s 10s 1s

Math Masters, p. 53

Teaching Master

400 � 60 � 7 � 467

100s

1� 3

4

4

10s

4206

6

1s

520077

1. Add the 100s.

2. Add the 10s.

3. Add the 1s.


+



200 � 130 � 14 � 344

+

1. Add the 100s.

2. Add the 10s.

3. Add the 1s.


100s

1� 1

21

3

10s

670314

1s

950044

Date Time

Make a ballpark estimate. Write a number model to show your estimate.Choose at least two problems to solve using the partial-sums methodand show your work. You may choose any method you wish to solve the other problems.

Unitmiles

Example:

Ballpark estimate:

Partial-Sums Method






300�400 � 700 9 0� 3 7

127

Addition MethodsLESSON

2�7

4 3� 2 6

69

� �Sample estimates given.

40 � 30 � 70

380 � 400 � 780 170 � 110 � 280 90 � 110 � 200

90 � 40 � 130

+

100s3

� 4

7

7

10s21

031 4

1s98

0077

1 7 2� 1 0 9

2813 7 8

� 4 0 1

7798 7

� 1 1 3

200

Math Journal 1, p. 45

Student Page

Adjusting the ActivityWrite each addend in expanded notation before adding. For example, in

145 � 322 rewrite each number in expanded notation.

145 � 100 � 40 � 5322 � 300 � 20 � 2

Write out each partial sum based on the expanded notation.100 � 300 � 40040 � 20 � 605 � 2 � 7

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

Example 2: Model 169 � 175 with base-10 blocks.

� Count out and arrange the blocks as before. Gather the hundreds, tens, and ones into separate piles.

� Children might notice that the 13 tens can be replaced by 1 hundred and 3 tens. The 14 ones can be replaced by 1 ten and 4 ones. Make these substitutions, but leave the 1 hundredand 3 tens in the tens pile, and leave the 1 ten and 4 ones in theones pile.

� Add the hundreds, tens, and ones: 200 � 130 � 14 � 344.Show children how to record this procedure on paper.

Try more 3-digit addition problems as needed.

� Practicing the Partial-Sums Algorithm and Other Addition Methods(Math Journal 1, p. 45; Math Masters, p. 53)

Children should show their work on the journal page. Remindthem to make ballpark estimates for checking their answers andfor finding mistakes if an answer seems unreasonable. Providebase-10 blocks for children to use. Children may share theiranswers with a partner. If there is a disagreement, encouragethem to discuss their strategies with each other and do theproblem again until they both can agree on an answer. Abundantpractice will be found on Home Link and Math Boxes pages infuture lessons. Additional problems may be created on MathMasters, page 53.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 45, Problems 1 and 2, to assess children’s ability to solve multidigit addition problems. Children are making adequate progress if they areable to solve Problems 1 and 2 correctly, with or without the use of manipulatives.Some children may be able to solve the rest of the problems on the page, with orwithout manipulatives.

[Operations and Computation Goal 2]

Journal Page 45Problems1 and 2 �

INDEPENDENTACTIVITY


� Playing Target: 50(Student Reference Book, p. 312; Math Masters,

pp. 411 and 465)

Children practice multidigit addition and subtraction with base-10blocks by playing Target: 50. Go over the rules for Target: 50 onpage 312 in the Student Reference Book.

NOTE The Target: 50 Record Sheet on Math Masters, page 465 may be used as

an assessment tool. Have children record one series of turns taken to reach 50.

� Math Boxes 2�7(Math Journal 1, p. 46)

Mixed Practice Math Boxes in this lesson are linked withMath Boxes in Lessons 2-5 and 2-9. The skill in Problem6 previews Unit 3 content.

Writing/Reasoning Have children write an answer to thefollowing: Explain how you found the length of the fencein Problem 6. Sample answer: I added all of the sides.

� Home Link 2�7(Math Masters, p. 52)

Home Connection Children solve addition problemsusing 2- and 3-digit numbers. Since the partial-sums algorithm might not be familiar to parents, you mightwant to send home the Student Reference Book.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

SMALL-GROUP ACTIVITY

2 Ongoing Learning & Practice

Lesson 2�7 139

5. Austin read his book for 45 minuteson Monday and for 25 minutes onTuesday. How many more minutesdid he read on Monday?

minutes 20

3. In 1,532,

the 1 means

the 5 means

the 3 means

the 2 means 230500

1,000

Date Time

2. “What’s My Rule?”

4. Write at least 5 names for 1,000.

6. How long is the fence around theflowers?

feet10

1. Use addition or subtraction tocomplete these problems on yourcalculator.Enter Change to How?

173 873

4,501 1,501

5,604 6,604

9,646 9,346 �300�1,000�3,000�700

18, 19,264

258

18 19

in out

4 133 12

0 912 21

1,000

10 � 100 1,000 � 12,000 � 1,000�100 � 1,100500 � 500

Sample answers:

14 15

Math BoxesLESSON

2�7

Answers vary.

3 feet

3 feet

2 feet2 feet

150 151

Quantity

Quantity

Difference

45

25 ?

203 204

Rule

out

in

Add 9

Math Journal 1, p. 46

Student Page

Name Date Time

The Partial-Sums Addition MethodHOME LINK

2�7

Today your child learned about adding two 3-digit numbers using a procedure called thepartial-sums method. Your child may choose to use this method or may prefer a differentprocedure. For more information, see pages 57 and 58 in the Student Reference Book.

Please return this Home Link to school tomorrow.

FamilyNote

57 58

Solve each addition problem. You may want to use the partial-sums method. Use a ballpark estimate to check that your answer makes sense. Write a number model to show your estimate. Sample estimates given.







250 � 100 � 350

400 � 200 � 600 460 � 200 � 660 800 � 400 � 1,200

100 � 200 � 300 250 � 300 � 550

124� 2152 4 5

� 9 2

100s 10s 1s 245� 317

366� 208

459� 168

769� 445

337

574 627 1,214

339 562

Math Masters, p. 52

Home Link Master

e

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� Modeling 2-Digit Numbers With Base-10 Blocks(Math Masters, p. 411)

To explore place-value concepts using a concrete model, have children build numbers with base-10 blocks. Children draw twocards and place them on a Place-Value Mat to make a 2-digitnumber. They put longs in the tens column to show the tens digit and cubes in the ones column to show the ones digit. On ahalf-sheet of paper, children draw a picture to show what they did.They write the number in standard notation and in expandednotation under the picture. (See margin.)

� Making Up Addition Problems from a Mileage Map(Student Reference Book, pp. 224 and 225; Math Masters, p. 407)

Social Studies Link To apply children’s understanding ofaddition, have them write and solve addition number

stories. Children study the U.S. mileage map in theStudent Reference Book, on pages 224 and 225. Pose

problems like the following to be sure that children understandhow to read the map.● Find Minneapolis, Minnesota. Which city on the map is 501

miles from Minneapolis? Bismarck, North Dakota● Find Seattle, Washington. How would you determine the

number of miles from Seattle to Salt Lake City, Utah, by wayof Boise, Idaho? Add the distance from Seattle to Boise to thedistance from Boise to Salt Lake City. Children pose new addition problems to each other using the mileage map.Children may record one or two of their stories on MathMasters, page 407.

� Building a Math Word Bank(Differentiation Handbook)

To provide language support for estimation, have children use the Word Bank template found in the Differentiation Handbook.Ask children to write the term ballpark estimate, draw a picturerepresenting the term, and write other related words. See theDifferentiation Handbook for more information.

5–15 Min


ELL SUPPORT

5–15 Min


ENRICHMENT

5–15 Min

INDEPENDENTACTIVITYREADINESS

3 Differentiation Options

NOTE The numbers indicate distancesbetween cities based on routes usually followed by motorists, except for Hawaii andAlaska, which are distances by air.

30 � 4 � 34


Documents

1 Teaching the Lesson - Everyday Math · Differentiation Options materials ... Teaching Master (Math Masters, p. 53; optional) base-10 blocks ... 4. Add the partial sums