Module 1 Lesson 9 Place Value, Rounding, and Algorithms for Addition and Subtraction Topic c: Rounding multi-digit whole numbers 4.nbt.3 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: Rounding Multi-Digit whole Numbers Objective: Use place value understanding to round multi-digit number to any place value. I can do this! Lesson 9

Multiply by Ten (5 minutes) 10 x 10 = ________ Say the multiplication sentence. 10 x ____ ten = 100 On your boards, fill in the blank. ____ ten x _____ ten = 100 On your boards, fill in the blank. ____ ten x _____ ten = _____ hundred. Fill in the blank. Lesson 9

Multiply by Ten (5 minutes) Lesson 9 10 x 20 = ________ Say the multiplication sentence. 10 x _____tens = 200 On your boards, fill in the blank. ____ ten x _____ tens = 200 On your boards, fill in the blank. ____ ten x _____ tens = _____ hundreds. Fill in the blank.

Multiply by Ten (5 minutes) Lesson 9 10 x 40 = ________ Say the multiplication sentence. 10 x _____tens = 400 On your boards, fill in the blank. ____ ten x _____ tens = 400 On your boards, fill in the blank. ____ ten x _____ ten = _____ hundreds. Fill in the blank.

Multiply by Ten (5 minutes) Lesson 9 10 x ______ = 700 Say the multiplication sentence. 10 x _____tens = 700 On your boards, fill in the blank. ____ ten x _____ tens = 700 On your boards, fill in the blank. ____ ten x _____ tens = _____ hundreds. Fill in the blank.

Multiply by Ten (5 minutes) Lesson 9 4 tens x 1 ten = _____ hundreds. Say the multiplication sentence. 40 x _____ten = 400 On your boards, fill in the blank. ____ tens x _____ ten = 400 On your boards, fill in the blank. ____ tens x _____ ten = _____ hundreds. Fill in the blank.

Multiply by Ten (5 minutes) Lesson 9 10 x ______ = 1,900 Say the multiplication sentence. 10 x _____tens = 1,900 On your boards, fill in the blank. ____ ten x _____ tens = 1,900 On your boards, fill in the blank. ____ ten x _____ tens = _____ hundred. Fill in the blank.

Round to Different Place Values 7 Minutes 47,261 Say the number Between what 2 thousands is 47,261? Write a vertical number line with 47,000 and 48,000 as endpoints. What is halfway between 47,000 and 48,000? Label 47,500 as the midpoint on your number line. 47,000 48,000 47,500 Label 47,261 on your number line. <47,261 47,261 ≈ _______ On your boards, fill in the blank, rounding 47,261 to the nearest thousand. Lesson 9

Round to Different Place Values 7 Minutes 63,941 Say the number Between what 2 ten thousands is 63,941? Write a vertical number line with 60,000 and 70,000 as endpoints. What is halfway between 60,000 and 70,000? Label 65,000 as the midpoint on your number line. 60,000 70,000 65,000 Label 63,941 on your number line. <63,941 63,941 ≈ _______ On your boards, fill in the blank, rounding 63,941 to the nearest ten thousand. Lesson 9

Round to Different Place Values 7 Minutes 63,941 Say the number Between what 2 thousands is 63,941? Write a vertical number line with 63,000 and 64,000 as endpoints. What is halfway between 63,000 and 64,000? Label 63,500 as the midpoint on your number line. 63,000 64,000 63,500 Label 63,941 on your number line. <63,941 63,941 ≈ _______ On your boards, fill in the blank, rounding 63,941 to the nearest thousand. Lesson 9

Round to Different Place Values 7 Minutes 47,261 Say the number Between what 2 ten thousands is 47,261? Write a vertical number line with 40,000 and 50,000 as endpoints. What is halfway between 40,000 and 50,000? Label 45,000 as the midpoint on your number line. 40,000 50,000 45,000 Label 47,261 on your number line. <47,261 47,261 ≈ _______ On your boards, fill in the blank, rounding 47,261 to the nearest ten thousand. Lesson 9

Round to Different Place Values 7 Minutes 618,409 Say the number Between what 2 hundred thousands is 618,409? Write a vertical number line with 600,000 and 700,000 as endpoints. What is halfway between 600,000 and 700,000? Label 650,000 as the midpoint on your number line. 600, , ,000 Label 618,409 on your number line. <618, ,409 ≈ _______ On your boards, fill in the blank, rounding 618,409 to the nearest hundred thousand. Lesson 9

Round to Different Place Values 7 Minutes 618,409 Say the number Between what 2 thousands is 618,409? Write a vertical number line with 618,000 and 619,000 as endpoints. What is halfway between 618,000 and 619,000? Label 618,500 as the midpoint on your number line. 618, , ,500 Label 618,409 on your number line. <618, ,409 ≈ _______ On your boards, fill in the blank, rounding 618,409 to the nearest thousand. Lesson 9

Application Problem 5 Minutes 34,123 people attended a basketball game. 28,310 people attended a football game. About how many more people attended the basketball game than the football game? Round to the nearest ten thousands to find the answer. Does your answer make sense? What might be a better way to compare attendance? First you round Then you subtract! Lesson 9

Application Problem 5 Minutes 34,123 people attended a basketball game. 28,310 people attended a football game. About how many more people attended the basketball game than the football game? Round to the nearest ten thousands to find the answer. Does your answer make sense? What might be a better way to compare attendance? First you round Then you subtract! Lesson 9

Application Problem 5 Minutes First you round Then you subtract! Lesson 9

Concept Development 35 Minutes Materials: Personal White Boards Lesson 9

Problem 1 4,333 ≈ ____. Between what two thousands is 4,333? What is halfway between 4,000 and 5,000? Is 4,333 less than or more than halfway? So 4,333 is less than halfway. Rounding to the nearest thousand without using a number line Lesson 9

Problem 1 18,753 ≈ ____. Between what two thousands is 18,753? What is halfway between 18 thousand and 19 thousand? Round 18,753 to the nearest thousand. Tell your partner if 18,753 is more or less than halfway. 18,753 ≈ ____. Rounding to the nearest thousand without using a number line Lesson 9

Problem 1 Continued 346,560 ≈ ____. Between what two thousands is 346,560? What is halfway between 346 thousand and 347 thousand? Round 346,560 to the nearest thousand. Tell your partner if 346,500 is more or less than halfway. 346,560 ≈ ____. Lesson 9

Problem 2 Rounding to the nearest ten thousand or hundred thousand without using a vertical line. 65,600 ≈ ____. Between what two ten thousands is 65,600? What is halfway between 60,000 and 70,000? Is 65,600 less or more than halfway? Tell your partner what 65,600 is when rounded to the nearest ten thousand. 65,600 ≈ ____.

Problem 2 Continued Rounding to the nearest ten thousand or hundred thousand without using a vertical line. 548,253 ≈ ____. Between what two ten thousands is 548,253? What is halfway between 540,000 and 550,000? Is 548,253 less or more than halfway? Tell your partner what 548,253 is when rounded to the nearest ten thousand. 548,253 ≈ ____. Lesson 9

Problem 2 Continued Rounding to the nearest ten thousand or hundred thousand without using a vertical line. 676,000 ≈ ____. Round 676,000 to the nearest hundred thousand. First tell your partner what your endpoints will be. Determine the halfway point. Is 676,000 more or less than the halfway point? Tell your partner what 676,000 is when rounded to the nearest hundred thousand. 676,000 ≈ ____. Lesson 9

Problem 2 Continued Rounding to the nearest ten thousand or hundred thousand without using a vertical line. 203,301 ≈ ____. Work with your partner to round 203,301 to the nearest hundred thousand. Explain to your partner how we use the midpoint to round without a number line. Lesson 9

Problem 3 Rounding to any value without using a number line. 147,591 ≈ ____. Whisper read this number to your partner in standard form. Now round 147,591 to the nearest hundred thousand. 147,591 ≈ 100,000 Hundred thousands Ten thousandsThousands HundredsTensOnes Lesson 9

Problem 3 Rounding to any value without using a number line. 100,000 has no ones in the ones place, no tens in the tens place, no hundreds in the hundreds place, no thousands in the thousands place, and no ten thousands in the ten thousands place. I could add, subtract, multiply, or divide with this rounded number much easier than with 147,591. True? But what if I want a more accurate estimate? Give me a number closer to 147,591 that has a zero in the ones, tens, hundreds, and thousands. Hundred thousands Ten thousandsThousands HundredsTensOnes Lesson 9

Problem 3 Rounding to any value without using a number line. Why isn’t 140,000 the best choice? 147,591 rounded to the nearest ten thousand is 150,000. Now let’s round 147,591 to the nearest thousand. Hundred thousands Ten thousandsThousands HundredsTensOnes Lesson 9

Problem 3 continued Rounding to any value without using a number line. Work with your partner to round 147,591 to the nearest hundred and then the nearest ten. Compare estimates of 147,591 after rounding to different units. What do you notice? When might it be better to round to a larger unit? When might it be better to round to a smaller unit? Hundred thousands Ten thousandsThousands HundredsTensOnes Lesson 9

Problem Set (10 Minutes)

Lesson 9

Student Debrief 7 minutes Explain the reasoning behind your answer for Problems 2(e) and 3(e). In Problem 2(e), you and your partner probably wrote different numbers that rounded to 30,000. Explain why your numbers were different. What is the smallest possible number that could round to 30,000 when rounded to the nearest ten thousand? What is the largest possible number that could round to 30,000 when rounded to the nearest ten thousand? Explain your reasoning. Was there any difficulty in solving Problem 3(d)? Explain your strategy when solving this problem. In Problem 4(b), the newspaper rounded to the nearest hundred thousand inappropriately. What unit should the newspaper rounded to and why? How is rounding without a number line easier? How is it more challenging? How does knowing how to round mentally assist you in everyday life? What strategy do you use when observing a number to be rounded? Objective: Use place value understanding to round multi-digit numbers to any place value. Lesson 9

Exit Ticket Lesson 9

Home work! !

Lesson 9