1 Teaching the Lesson materials - Everyday Math - Login · PDF filethe partial-sums algorithm and make ballpark estimates to check their answers. ... [Operations and Computation Goal

294 Unit 4 Addition and Subtraction

Teaching the Lesson materials

Key ActivitiesChildren are introduced to the partial-sums algorithm using base-10 blocks and paper-and-pencil computation. Children practice adding 2- and 3-digit numbers usingthe partial-sums algorithm and make ballpark estimates to check their answers.

Key Concepts and Skills• Identify the value of digits in multidigit numbers. [Number and Numeration Goal 2]• Use base-10 blocks and fact extensions to add two 2-digit whole numbers.

[Operations and Computation Goal 2]• Use ballpark estimates. [Operations and Computation Goal 3]• Show understanding of addition and subtraction symbols.

[Patterns, Functions, and Algebra Goal 2]

Key Vocabulary algorithm

Ongoing Assessment: Recognizing Student Achievement Use Mental Mathand Reflexes. [Operations and Computation Goal 2]

Ongoing Learning & Practice materials

Children answer questions about the times before or after a given time of an event.

Children practice fact extensions by playing the Fact Extension Game.

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

Differentiation Options materials

Children use base-10blocks to review place-value concepts.

Children explain additionstrategies.

Children solve problemsusing multiples of 10.

� Teaching Masters(Math Masters,pp. 114 and 115)

� Teaching Aid Master(Math Masters, p. 428)

� Minute Math®+, p. 42

� number cards� base-10 blocks:

9 cubes, 9 longs, 9 flats

� number grid

EXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 1,pp. 109 and 110

� My Reference Book,pp. 134 and 135

� Home Link Master(Math Masters, p. 113)

� per partnership:number cardslabeled 0–5 (optional: 0–9 number cards)

� 1 die per partnership

2

� Math Journal 1, pp. 107 and 108� Home Link 4�8� base-10 blocks: 2 flats, 18 longs, 18 cubes� overhead base-10 blocks (optional): 8 longs,

13 cubes� slate (optional)

See Advance Preparation

1

Objective To introduce and practice the partial-sums addition algorithm.

Technology Assessment Management SystemMental Math and ReflexesSee the iTLG.

Additional InformationBackground Information The problems in Mental Math and Reflexes give children practicewith quickly solving mental addition. This skill is needed for making ballpark estimates and carrying out the partial-sums algorithm.

Advance Preparation Plan to spend three days on this lesson. Decide how you will demonstrate the partial-sums algorithm using base-10 blocks—on a flat surface with childrengathered around or with blocks on the overhead projector.

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� 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 added mentally. For example:● 37 � 58 is close to 40 � 60, or 100, or 30 �50, or 80. The

exact answer to 37 � 58 should be close to 100.● 473 � 234 is close to 500 � 200, or 700, or 400 � 200, or 600.

The exact answer should be near 700. Or notice that 400 � 200is 600. That leaves 73 � 34, which is close to 70 � 30, or 100.Thus, 473 � 234 is close to 600 � 100, or 700.

� Introducing the Partial-SumsAddition Algorithm Using Base-10 BlocksToday children will learn and practice a single strategy for addition. (Encourage children to continue using other favoritestrategies they may have for adding numbers.)

WHOLE-CLASSDISCUSSION


1 Teaching the Lesson

Lesson 4�9 295

Getting Started

Home Link 4�8Follow-Up Review answers and ask volunteers toexplain the strategies they used to addand to make ballpark estimates.Problems 11 and 12 involve adding 3-digit numbers.

Math Message Make a ballpark estimatefor each answer. Write anumber model for each estimate.

37 � 58 � ? 40 � 60 � 100

473 � 234 � ? 500 � 200 � 700

Mental Math and Reflexes Pose pairs of problems, suchas the following:

30 � 40 � ? 70300 � 400 � ? 700? � 20 � 50 70? � 200 � 500 70090 � 30 � ? 120900 � 300 � ? 1,200

Unit

people

● On Day 1 of this lesson, children shouldcomplete the Math Message Follow-Up andbe introduced to and practice the partial-sums addition algorithm using base-10 blocks. Then children should playthe Fact Extension Game in Part 2.

● On Day 2 of this lesson, children should beintroduced to and practice the partial-sumsalgorithm as a paper-and-pencil method.Then children should complete journal page109 in Part 2.

● On Day 3 of this lesson, children shouldcontinue to practice the partial-sums algorithm. Then have children complete the other Part 2 activities.

Ongoing Assessment:Recognizing Student Achievement

Use Mental Math and Reflexes to assess children’s progress toward solvingproblems involving addition of multidigit multiples of ten. Children are makingadequate progress if they are able to successfully complete Level 1. Somechildren may be able to solve problems that have a 4-digit number as a sum.

[Operations and Computation Goal 2]

Mental Math and Reflexes�

�

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Write these two problems on the board, in vertical form:

45 26

Ask children to gather around as you demonstrate how to usebase-10 blocks. You may wish to use an overhead. Refer to thelongs as tens and the cubes as ones. For each problem, model addition as a three-part operation: adding the 10s, adding the 1s,and then adding the partial sums.

Example 1: Model 45 � 22 with base-10 blocks.

1. Make a ballpark estimate before or after solving the problem.Sample answers: 50 � 20; 45 � 20; 40 � 20

2. Count out 4 tens and 5 ones to represent 45. Count out 2 tensand 2 ones to represent 22.

3. Arrange the blocks so that they resemble the vertical additionproblem. (See the first model in the margin.)

4. Collect the tens into one pile. Collect the ones into a second pile.

5. Count the tens. 6 tens, or 60

6. Count the ones. 7 ones, or 7

7. Add the counts of tens and ones. 60 � 7 � 67 Record theanswer on the board. The ballpark estimates are close to thisanswer, so the answer is reasonable.

Example 2: Model 26 � 57 with base-10 blocks.

For the second example, follow the same procedure. When youcount the ones, some children may notice that 10 cubes in the ones pile can be replaced by 1 long; you can make this substitution.There are still two piles of blocks: the tens pile (with 8 tens), andthe revised ones pile (with 3 ones).

Summary

These examples using base-10 blocks illustrate the steps of thepartial-sums method for addition:

1. Add the tens.

2. Add the ones.

3. Add the partial sums of tens and ones to obtain the final answer.

Children do several problems at their desk. Have them describeexactly what they are doing at each step.

� Practicing Addition Using Base-10 Blocks(Math Journal 1, p. 107)

Partners use base-10 blocks to practice the partial-sums algorithm.

PARTNER ACTIVITY

� 57� 22

�

70 � 13 � 83

�

60 � 7 � 67

Tens Ones

Partial-Sums Addition Using Base-10 BlocksLESSON

4 � 9

Date Time

Draw base-10 blocks and write the number sentence to solve each problem.

1. Example: Unit

books

23� 46

Answer: 69 books

� 960

2.Unit

41� 35

Answer: 76

� 670

Tens Ones

3.Unit

67� 38

Answer: 105

� 1590

Tens Ones

4.Unit

46� 36

Answer: 82

� 1270

Tens Ones

Math Journal 1, p. 107

Student Page

Example 1:

Example 2:


� Introducing the Partial-Sums Algorithm as a Paper-and-Pencil MethodReview the partial-sums addition with base-10 blocks using thesame two problems: 45 � 22 and 26 � 57.

Next, on the board or overhead, demonstrate the paper-and-pencilmethod for solving these problems. As a reminder of place value,write “10s” and “1s” above the columns and use the samelanguage to describe 10s and 1s.

Example: 45 � 22

1. Find a ballpark estimate. 50 � 20; 45 � 20; 40 � 20

2. Add the tens. 4 tens � 2 tens � 6 tens, or 60. Write 60 belowthe line.

3. Add the ones. 5 ones � 2 ones � 7 ones, or 7. Write 7 below 60.

4. Add the partial sums. Draw a second line beneath 60 and 7.Write 67 beneath this line.

In this example, the tens were added first. However, the partialsums may be calculated in either order—it does not matterwhether the tens or the ones are added first.

For the second example, follow the same procedure again to findand add the partial sums 70 and 13, checking the answer againsta ballpark estimate.

Tell children that the method illustrated by these examples is called an algorithm. An algorithm is a step-by-step set ofinstructions for doing something. Write algorithm on the board.

� Practicing the Partial-Sums AlgorithmWrite several multidigit addition problems on the board. Start byadding together a 2-digit and a 1-digit number. Most problemsshould have 2-digit addends. Using slates or paper, have childrendescribe exactly what they are doing at each step. Correct errorsin calculation and in method, making sure the numbers arealigned in columns.

� Continuing Practice with the Partial-Sums Algorithm(Math Journal 1, p. 108)

Review the partial-sums algorithm. Most problems should have 2-digit addends, but include at least one with 3-digit addends.When you discuss the problem with 3-digit addends, write “100s,”“10s,” and “1s” above the columns as a reminder of place value.Most children will realize that the partial-sums method works thesame way for 3-digit numbers as for 2-digit numbers.




Unit

Addition PracticeLESSON

4 � 9

Date Time

Write a number model to show your ballpark estimate. Solve the problem.Show your work. Use the ballpark estimate to check whether your exactanswer makes sense. Sample estimates:

59� 8

Ballpark estimate:

60 � 10 � 70

Ballpark estimate:

70 � 10 � 80

Ballpark estimate:

50 � 30 � 80

Ballpark estimate:

60 � 30 � 90

Ballpark estimate:

120 � 50 � 170

Ballpark estimate:

140�160�300

67

67� 774

47� 3279

58� 2684

122� 53175

136� 157293

1. 2. 3.

4. 5. 6.


Student Page

Lesson 4�9 297

10s

4� 2

6�

6

1s

52077

10s

2� 5

7� 1

8

1s

67033

NOTE Provide base-10 blocks for children touse when working on journal page 108. Thisconcrete experience is essential to preparechildren for the transition from concrete toabstract thought.

100s

4� 2

61

� 7

10s

7300

0

1s

340077

Links to the FutureThis is the first time that children have been exposed to a formal paper-and-pencil addition algorithm. They will have plenty ofopportunities to practice the partial-sumsalgorithm throughout the year. Do not expectall children to be able to perform the algorithmat the conclusion of this lesson.



The Time of DayLESSON

4 � 9

Date Time

For Problems 1–4, draw the hour hand and the minute hand to show the time.

1. Luz got up at 7:00. She had breakfast an hour later. Show the time when she had breakfast.

2. The second graders went on a field trip.They left school at 12:30.They got back 2 hours later.Show the time when they got back.

3. Tony left home at 8:15.It took him half an hour to get to school. Show the time whenhe arrived at school.

4. Ming finished reading a story at 10:30.It took her 15 minutes. Show the timewhen she started reading.

5. The clock shows when Bob went to bed.He went to sleep 15 minutes later.At what time did he go to sleep?

: 309

12 12

3

4567

8

9

1011

12 12

3

4567

8

9

1011

12 12

3

4567

8

9

1011

12 12

3

4567

8

9

1011

12 12

3

4567

8

9

1011


Student Page

� Reviewing Telling Time(Math Journal 1, p. 109)

Children answer questions in which they determine the timesbefore or after the given time of an event.

This activity is related to the partial-sums algorithm. In adding aninitial time and an elapsed time, a common strategy is to add thehours and minutes separately and then trade 60 minutes for anhour if the total number of minutes is 60 or greater.

� Playing the Fact Extension Game(My Reference Book, pp. 134 and 135)

Children practice fact extensions through the Fact ExtensionGame first introduced on page 292 in Lesson 4-8.

� Math Boxes 4�9(Math Journal 1, p. 110)

Mixed Practice Math Boxes in this lesson are linked withMath Boxes in Lessons 4-5 and 4-7. The skill in Problem6 previews Unit 5 content.

Writing/Reasoning Have children draw, write, or verbalize their answers to the following: In Problem 4,what time will it be in 12 hours? Explain how you solved

this problem. Sample answer: 6:15. I counted up 12 hours. 7:15,8:15, 9:15, 10:15, and so on.

� Home Link 4�9(Math Masters, p. 113)

Home Connection Children use the partial-sums algorithm to solve multidigit addition problems.

� Reviewing Place-Value Concepts(Math Masters, pp. 114 and 428)

To provide experience with place value, have children use base-10blocks to explore a strategy for using the fewest base-10 blocks.

30+ Min

PARTNER ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

PARTNER ACTIVITY

INDEPENDENTACTIVITY

2 Ongoing Learning & Practice

Math BoxesLESSON

4 �9

Date Time

1. I bought a radio for $67.00. I paid with $100.00.How much change did I get? $33.00

3. Write three even and threeodd 2-digit numbers. Circle theeven numbers.

237439683122

Sample answers:

6. Use your Pattern-BlockTemplate. Draw the triangles.

What is the difference betweenthe triangles?

One is larger.

2. What is the temperature? Circle the best answer.

A. 34�F

B. 36�F

C. 32�F

D. 4�F

4. What time is it?

:

What time will it be in 15 minutes?

: 306

156

5. Find the rules.

711

�4 �6

1391511

°F

20

30

40

12 12

3

4567

8

9

1011

97

98 99 54


Student Page


For each problem, draw a new set of base-10 blocks that usesthe fewest possible number of flats, longs, and cubes.

LESSON

4 �9

Name Date Time

Base-10 Blocks

1.

2.

3.

4.

5.

6.

Math Masters, p. 114

Teaching Master

Use base-10 blocks: Partners shuffle number cards, place the deckfacedown between them, and draw two cards. They place the firstcard in the ones column on the Place-Value Mat (Math Masters,page 428) and the second card in the tens column. They use thefewest base-10 blocks possible to build the number. On a sheet ofpaper, they record the number shown, as well as the number oftens (longs) and the number of ones (cubes).

Then partners switch the two cards on the mat and repeat theprocedure. Vary the activity by having children draw three cardsto make 3-digit numbers.

Use Math Masters, page 114: For each group of base-10 blocks,children represent the same number using the fewest flats, longs,and cubes possible.

� Using Addition Strategies(Math Masters, p. 115)

To apply children’s understanding of multidigit addition, havethem determine the steps of an addition strategy on Math Masters,page 115. Have children explain how the strategies work. Brieflydiscuss which strategy they thought was easier and why.

� Minute Math+Children practice adding multiples of 10. Model this, using thenumber grid to find the answer. See the following page in MinuteMath�: p. 42.

5–15 Min

SMALL-GROUP ACTIVITYEXTRA PRACTICE

15–30 Min

INDEPENDENTACTIVITYENRICHMENT

Lesson 4�9 299

Name Date Time

Your child is learning a method for addition that focuses on place value. The child is asked tofirst find a ballpark estimate. (For more on ballpark estimates see page 92 in the My ReferenceBook.)

Find 68 � 24

Ballpark estimate: 70 � 20 � 90

FamilyNote

HOME LINK

4 �9 Place Value

Write a number model for your ballpark estimate. Find each sum.

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

53 27 45� 36 � 81 � 38

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

18 154 126� 76 � 31 � 237

36318594

8310889

130 � 240 � 370150 � 30 � 18020 � 80 � 100

40 � 40 � 8030 � 80 � 11050 � 40 � 90

Encourage your child to use the correct place-value language when using this method. Forexample, when adding tens in the example, say “60 � 20 � 80,” not “6 � 2 � 8.” We onlyrecently introduced this method, so allow plenty of time for practice before expecting yourchild to be able to use it easily.

Please return this Home Link to school tomorrow.

Add the tens (60 � 20 � 80) and write the sum.

Add the ones (8 � 4 �12) and write the sum.

Combine the tens and ones (80 � 12 � 92) to find the final sum.

10s

6� 2

8� 1

9

1s

84022

Unit

10

Try This


Home Link Master

Addition Strategies

Look at the two addition strategies below. See if you can figureout how they work.

Louisa’s Strategy Li’s Strategy

37 � 44 � ? 37 � 44 � ?

37 � 40 � 77 40 � 44 � 84

77 � 4 � 81 84 � 3 � 81

37 � 44 � 81 37 � 44 � 81

Now try to use either Louisa’s Strategy or Li’s Strategy to solvethe problems below.

29 � 56 � ? 65 � 27 �Sample answers:Louisa’s Strategy Li’s Strategy29 � 50 � 79 65 � 30 � 9579 � 6 � 85 95 � 3 � 9229 � 56 � 85 65 � 27 � 92Which strategy do you think is easier? Explain.

the ones. She doesn’t have to subtract anything.because she is adding the tens and then addingSample answer: Louisa’s strategy is easier

LESSON

4 �9

Name Date Time

Addition Strategies


Teaching Master


1 Teaching the Lesson materials - Everyday Math - Login · PDF filethe partial-sums algorithm and make ballpark estimates to check their answers. ... [Operations and Computation Goal

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