Module 1 Lesson 11 Place Value Rounding and

Module 1 Lesson 11 Place Value, Rounding, and Algorithms for Addition and Subtraction Topic d: Multi-digit whole number addition 4. oa. 3, 4. nbt. 4, 4. nbt. 1, 4 nbt. 2 This Power. Point was developed by Beth Wagenaar and Katie E. Perkins. The material on which it is based is the intellectual property of Engage NY.

Lesson 11 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 4, 000 <3, 941 3, 500 3, 000 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? What is halfway between 3, 000 and 4, 000? . Label 3, 500 on your number line as I do the same. • Label 3, 941 on your number line. • Is 3, 941 nearer to 3, 000 or 4, 000? • 3, 941 ≈ _______ Write your answer on your board. • • •

Round to Different Place Values Lesson 11 80, 000 75, 000 <74, 621 70, 000 • 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? • What is halfway between 70, 000 and 80, 000? . • Label 75, 000 on your number line as I do the same. • Label 74, 621 on your number line. • Is 74, 621 nearer to 70, 000 or 80, 000? • 74, 621 ≈ _______ Write your answer on your board.

Round to Different Place Values Lesson 11 75, 000 <74, 621 74, 500 74, 000 • 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? • What is halfway between 74, 000 and 75, 000? . • Label 74, 500 on your number line as I do the same. • Label 74, 621 on your number line. • Is 74, 621 nearer to 74, 000 or 75, 000? • 74, 621 ≈ _______ Write your answer on your board.

Lesson 11 Round to Different Place Values 700, 000 <681, 904 650, 000 600, 000 • 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? • What is halfway between 600, 000 and 700, 000? . • Label 650, 000 on your number line as I do the same. • Label 681, 904 on your number line. • Is 681, 904 nearer to 600, 000 or 700, 000? • 681, 904 ≈ _______ Write your answer on your board.

Lesson 11 Round to Different Place Values 690, 000 685, 000 <681, 904 680, 000 • 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? • What is halfway between 680, 000 and 690, 000? . • Label 685, 000 on your number line as I do the same. • Label 681, 904 on your number line. • Is 681, 904 nearer to 680, 000 or 690, 000? • 681, 904 ≈ _______ Write your answer on your board.

Lesson 11 Round to Different Place Values 682, 000 <681, 904 681, 500 681, 000 • 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? • What is halfway between 681, 000 and 682, 000? . • Label 681, 500 on your number line as I do the same. • Label 681, 904 on your number line. • Is 681, 904 nearer to 681, 000 or 682, 000? • 681, 904 ≈ _______ Write your answer on your board.

Lesson 11 Multiply by Ten (4 minutes) Say the multiplication sentence. On your boards, fill in the blank. 10 x ____ = 100 10 x 1 ten = ______ 10 tens = ____hundred ____ ten x _____ ten = 1 hundred.

Lesson 11 Multiply by Ten (4 minutes) Say the multiplication sentence. On your boards, fill in the blank. 1 ten x 60 = ____ 10 x 6 tens = _______ 20 tens = _____ hundreds ____ ten x _____ ten = 6 hundreds.

Lesson 11 Multiply by Ten (4 minutes) Say the multiplication sentence. On your boards, fill in the blank. 1 ten x 30 = ____ hundreds 10 x 3 tens = ______. 30 tens = ______ hundreds ____ ten x _____ ten = 3 hundred

Lesson 11 Multiply by Ten (4 minutes) Say the multiplication sentence. On your boards, fill in the blank. 1 ten x _____ = 900 10 x 9 tens = ______ 90 tens = _____ hundred ____ ten x _____ ten = 9 hundred.

Lesson 11 Multiply by Ten (4 minutes) Say the multiplication sentence. On your boards, fill in the blank. 7 tens x 1 ten = _____ hundreds 70 x 1 tens = _______ 70 tens = _____ hundreds ____ ten x _____ ten = 7 hundreds

Add Common Units 3 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 Units 3 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 Units 3 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 Units Lesson 11 3 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?

Add Common Units 3 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 Problem Lesson 11 7 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. C 12, 490 Smaller Unit! Ten thousand –> Thousand -------> 14, 295 11, 116 10, 000 + 10, 000 = 30, 000 12, 000 + 14, 000 + 11, 000 = 37, 000

Lesson 11 Concept Development 35 Minutes Materials: Personal White Boards

Lesson 11 Problem 1 Add, 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. • What is the unknown? • Show the whole above the tape diagram using a bracket and label the unknown quantity a. a 3, 134 2, 493

Problem 1 Continued a = 5, 627 3, 134 Thousands Hundreds Tens Lesson 11 Ones === ==== = ===== 2, 493 • Draw disks into the place value chart to represent the first part, 3, 134. • Add 2, 493 by drawing more disks into your place value chart. • 4 ones plus 3 ones equals? • 3 tens plus 9 tens equals? • 1 hundred plus 4 hundreds plus 1 hundred equals? • We can bundle 10 tens as 1 hundred. • 3 thousand plus 2 thousands equals? • We can represent this in writing. Write 12 tens as 1 hundred, crossing the line, and 2 tens in the tens column, • Say the whole equation with me: • 3, 134 plus 2, 493 equals 5, 627. so that you are writing 12 and not 2 and 1 as separate • Label the whole in the tape diagram, above the bracket numbers. with a = 5, 627. 5 6 2 7

Lesson 11 Problem 2 Add, 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. B 40, 762 30, 473

Problem 2 Continued a = 71, 235 Ten Thousands llll 40, 762 30, 473 lll 7 lllll ll llll l 1 l • With your partner, write the problem and draw disks for the first addend in your chart. Then draw disks for the second addend. • 2 ones plus 3 ones equals? • 6 tens plus 7 tens equals? • We can group 10 tens to make 1 hundred. • Watch me as I record the larger unit. • 7 hundreds plus 4 hundreds plus 1 hundred equals 12 hundreds. Discuss with your partner how to record this. • Regroup and then record. Hundreds 1 2 Tens Lesson 11 Ones lllll lllll ll 3 5 • 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. • With your partner, add units right to left, regrouping when necessary. 336, 170 207, 426 +128, 744

Problem 4 Lesson 11 Solve 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? M 907 297 • 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. • 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? • Use a bracket to label the unknown as M for miles. • 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.

Problem Set (10 Minutes)

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• 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? Student Debrief Lesson 11 11 minutes 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.

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