Module 1 Lesson 11Place Value, Rounding, and Algorithms for Addition and

SubtractionTopic d: Multi-digit whole number addition

4.oa.3, 4.nbt.4, 4.nbt.1, 4 nbt.2

This PowerPoint was developed by Beth Wagenaar and Katie E. Perkins.The material on which it is based is the intellectual property of Engage NY.

Topic: Multi-Digit Whole Number

Addition•Objective: Use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm and apply the algorithm to solve word problems using tape diagrams

Lesson 11

Round to Different Place Values

5 Minutes

• 3,941 We are going to round to the nearest thousands• How many thousands are in 3,941?• I am going to label the lower endpoint with 3,000.• And 1 more thousand will be?

3,000

4,000

3,500

• What is halfway between 3,000 and 4,000?.• Label 3,500 on your number line as I do the

same.

<3,941

• Is 3,941 nearer to 3,000 or 4,000?• 3,941 ≈ _______ Write your answer on your

board.

• Label 3,941 on your number line.

Lesson 11

Round to Different Place Values• 74,621 We are going to round to the nearest ten

thousands• How many ten thousands are in 74,621?• I am going to label the lower endpoint with 70,000.• And 1 more ten thousand will be?

70,000

80,000

75,000

• What is halfway between 70,000 and 80,000?.• Label 75,000 on your number line as I do the

same.<74,621

• Is 74,621 nearer to 70,000 or 80,000?• 74,621 ≈ _______ Write your answer on your

board.

• Label 74,621 on your number line.

Lesson 11

Round to Different Place Values• 74,621 We are going to round to the nearest

thousands• How many thousands are in 74,621?• I am going to label the lower endpoint with 74,000.• And 1 more thousand will be?

74,000

75,000

74,500

• What is halfway between 74,000 and 75,000?.• Label 74,500 on your number line as I do the

same.

<74,621

• Is 74,621 nearer to 74,000 or 75,000?• 74,621 ≈ _______ Write your answer on your

board.

• Label 74,621 on your number line.

Lesson 11

Round to Different Place Values• 681,904 We are going to round to the nearest

hundred thousand• How many hundred thousands are in 681,904?• I am going to label the lower endpoint with 600,000. • And 1 more hundred thousand will be?

600,000

700,000

650,000

• What is halfway between 600,000 and 700,000?.• Label 650,000 on your number line as I do the

same.

<681,904

• Is 681,904 nearer to 600,000 or 700,000?• 681,904 ≈ _______ Write your answer on your

board.

• Label 681,904 on your number line.

Lesson 11

Round to Different Place Values• 681,904 We are going to round to the nearest ten

thousand• How many ten thousands are in 681,904?• I am going to label the lower endpoint with 680,000. • And 1 more ten thousand will be?

680,000

690,000

685,000

• What is halfway between 680,000 and 690,000?.• Label 685,000 on your number line as I do the

same.

<681,904• Is 681,904 nearer to 680,000 or 690,000?• 681,904 ≈ _______ Write your answer on your

board.

• Label 681,904 on your number line.

Lesson 11

Round to Different Place Values• 681,904 We are going to round to the nearest

thousand• How many thousands are in 681,904?• I am going to label the lower endpoint with 681,000. • And 1 more thousand will be?

681,000

682,000

681,500

• What is halfway between 681,000 and 682,000?.• Label 681,500 on your number line as I do the

same.

<681,904

• Is 681,904 nearer to 681,000 or 682,000?• 681,904 ≈ _______ Write your answer on your

board.

• Label 681,904 on your number line.

Lesson 11

Multiply by Ten(4 minutes)

10 x ____ = 100 10 x 1 ten = ______ 10 tens = ____hundred ____ ten x _____ ten = 1 hundred.

Say the multiplication sentence.On your boards, fill in the blank.

Lesson 11

Multiply by Ten(4 minutes)

Say the multiplication sentence.On your boards, fill in the blank.

Lesson 11

1 ten x 60 = ________ 10 x 6 tens = _______ 20 tens = _____ hundreds____ ten x _____ ten = 6 hundreds.

Multiply by Ten(4 minutes)

Say the multiplication sentence.On your boards, fill in the blank.

Lesson 11

1 ten x 30 = ____ hundreds10 x 3 tens = ______.30 tens = ______ hundreds____ ten x _____ ten = 3 hundred

Multiply by Ten(4 minutes)

Say the multiplication sentence.On your boards, fill in the blank.

Lesson 11

1 ten x _____ = 900 10 x 9 tens = ______ 90 tens = _____ hundred____ ten x _____ ten = 9 hundred.

Multiply by Ten(4 minutes)

Say the multiplication sentence.On your boards, fill in the blank.

Lesson 11

7 tens x 1 ten = _____ hundreds70 x 1 tens = _______ 70 tens = _____ hundreds____ ten x _____ ten = 7 hundreds

Add Common Units3 Minutes

• 303 Say the number in unit form.• 303 + 202 = ______ Say the addition sentence

and answer in unit form.• Did you say, ‘ 3 hundreds 3 ones + 2 hundreds 2

ones = 5 hundreds 5 ones?• Write the addition sentence on your personal

white boards.• Did you write 303 + 202 = 505?

Lesson 11

Add Common Units3 Minutes

• 505 Say the number in unit form.• 505 + 404 = ______ Say the addition sentence

and answer in unit form.• Did you say, ‘ 5 hundreds 5 ones + 4 hundreds 4

ones = 9 hundreds 9 ones?• Write the addition sentence on your personal

white boards.• Did you write 505 + 404 = 909?

Lesson 11

Add Common Units3 Minutes

• 5,005 Say the number in unit form.• 5,005 + 5,004 = ______ Say the addition

sentence and answer in unit form.• Did you say, ‘ 5 thousands 5 ones + 5 thousands

4 ones = 10 thousands 9 ones?• Write the addition sentence on your personal

white boards.• Did you write 5,005 + 5,004 = 10,009?

Lesson 11

Add Common Units3 Minutes

• 7,007 Say the number in unit form.• 7,007 + 4,004 = ______ Say the addition

sentence and answer in unit form.• Did you say, ‘ 7 thousands 7 ones + 4 thousands

4 ones = 11 thousands 11 ones?• Write the addition sentence on your personal

white boards.• Did you write 7,007 + 4,004 = 11,011?

Lesson 11

Add Common Units3 Minutes

• 8,008 Say the number in unit form.• 8,008 + 5,005 = ______ Say the addition

sentence and answer in unit form.• Did you say, ‘ 8 thousands 8 ones + 5 thousands

5 ones = 13 thousands 13 ones?• Write the addition sentence on your personal

white boards.• Did you write 8,008 + 5,005 = 13,013?

Lesson 11

Application Problem7 Minutes

Meredith kept track of the calories she consumed for 3 weeks. The first week, she consumed 12,490 calories, the second week 14,295 calories, and the third week 11,116 calories. About how many calories did Meredith consume altogether? Which of these estimates will produce a more accurate answer: rounding to the nearest thousand or rounding to the nearest ten thousand? Explain.

12,490 14,295 11,116

C

Ten thousand –> 10,000 + 10,000 + 10,000 = 30,000 Thousand -------> 12,000 + 14,000 + 11,000 = 37,000Smaller Unit!

Lesson 11

Concept Development 35 Minutes

Materials: Personal White Boards

Lesson 11

Problem 1Add, renaming once using disks in a place value chart

• 3,134 + 2,493 Say this problem with me.

• Draw a tape diagram to represent this problem.

• What are the two parts that make up the whole?

• Record that in the tape diagram.3,134 2,493• What is the unknown?

• Show the whole above the tape diagram using a bracket and label the unknown quantity a.

a

Lesson 11

Problem 1 Continueda

3,134 2,493• Draw disks into the place value chart to represent the

first part, 3,134.

Thousands Hundreds Tens Ones

===

==

=

=====

===

=========

====

===

• Add 2,493 by drawing more disks into your place value chart.• 4 ones plus 3 ones equals?

7• 3 tens plus 9 tens equals?• We can bundle 10 tens as 1 hundred.

2

• We can represent this in writing. Write 12 tens as 1 hundred, crossing the line, and 2 tens in the tens column, so that you are writing 12 and not 2 and 1 as separate numbers.

• 1 hundred plus 4 hundreds plus 1 hundred equals?

6

• 3 thousand plus 2 thousands equals?

5

• Say the whole equation with me:• 3,134 plus 2,493 equals 5,627. • Label the whole in the tape diagram, above the bracket with

a = 5,627.

= 5,627

Lesson 11

Problem 2Add, renaming in multiple units using the standard algorithm and the

place value chart.

• 40,762 + 30,473 Say this problem with me.

• With your partner, draw a tape diagram to represent this problem labeling the two known parts and the unknown whole, using B to represent the whole.

40,762 30,473

B

Lesson 11

Problem 2 Continueda = 71,235

40,762 30,473

Ten Thousands Thousands Hundreds Tens Ones

• With your partner, write the problem and draw disks for the first addend in your chart. Then draw disks for the second addend.

llll lllllll

llllll

ll

lll llll lllllll

lll

• 2 ones plus 3 ones equals?

5• 6 tens plus 7 tens equals?• We can group 10 tens to make 1 hundred.

l

• Watch me as I record the larger unit.

1

3

• 7 hundreds plus 4 hundreds plus 1 hundred equals 12 hundreds. Discuss with your partner how to record this.

• Regroup and then record.

l

217

• Say the whole equation with me.• 40,762 plus 30,473 equals 71,235. Label the whole

in the bar diagram with 71,235, and write 71,235.

Lesson 11

Problem 3

• 207,426 + 128,744• Draw a tape diagram

to model this problem.

207,426 128,744

• With your partner, add units right to left, regrouping when necessary.

207,426+128,744

336,170

Lesson 11

Problem 4Solve one-step word problem using standard algorithm modeled with a tape

diagram.

The Lane family took a road trip. During the first week, they drove 907 miles. The second week they drove the same amount as the first week plus an additional 297 miles. How many miles did they drive during the second week?

• What information do we know?• What is the unknown information?• Draw a tape diagram to represent the

amount of miles in the first week, 907 miles.

907

• Since the Lane family drove an additional 297 miles in the second week, extend the bar for 297 more miles. What does the bar represent?

297

• Use a bracket to label the unknown as M for miles.

M

• How do we solve for M?• Solve. What is M?• Write a sentence that tells your answer.• The Lane family drove 1,204 miles during

the second week.

Lesson 11

Problem Set(10 Minutes)

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Student Debrief

11 minutes

• When we are writing a sentence to express our answer, what part of the original problem helps us to tell our answer using the correct words and context?

• What purpose does a tape diagram have? How does it support your work?• What does a variable, like the letter B in Problem 2, help us do when

drawing a tape diagram? • I see different types of tape diagrams drawn for Problem 3. Some drew

one bar with two parts. Some drew one bar for each addend, and put the bracket for the whole on the right side of both bars. Will these diagrams result in different answers? Explain.

• In Problem 1, what did you notice was similar and different about the addends and the sums for Parts (a), (b), and (c)?

• If you have 2 addends, can you ever have enough ones to make 2 tens, or enough tens to make 2 hundreds, or enough hundreds to make 2 thousands? Try it out with your partner. What if you have 3 addends?

• In Problem 1, each unit used the numbers 2, 5, and 7 once, but the sum doesn’t show repeating digits. Why not?

• How is recording the regrouped number in the next column of the addition algorithm related to bundling disks?

• Have students revisit the Application Problem and solve for the actual amount of calories consumed. Which unit when rounding provided an estimate closer to the actual value?

Objective: Use place value understanding to fluently

add multi-digit whole numbers using the standard

addition algorithm and apply the algorithm to solve word problems using tape

diagrams.

Lesson 11

Exit TicketLesson 11

Home

work!!

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