NYS Math Module 2 Lesson 2 SWBAT multiply by 10, 100, and 1,000 (5.NBT.2) round to different place values (5.NBT.4) multiply by multiples of 10 (5.NBT.2) Objective: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.

Ready, Set, GO! Sprint 5 min. 5 min. **Multiply by 10, 100, and 1,000** Ready, Set, GO!

Round to Different Place Values Say this number: 48,625 50,000 Between which two ten thousands is 48,625? 48,625 What’s the midpoint for 40,000 and 50,000? 45,000 Would 48,625 fall above or below 45,000? above What’s 48,625 rounded to the nearest ten-thousand? 40,000 48,625 ≈ _________ 50,000

Show 48,625 on your number line and complete the number sentence. Round 48,625 to the thousands. Show 48,625 on your number line and complete the number sentence. 48,625 ≈ ______ 49,000 49,000 48,625 48,500 48,000

Show 48,625 on your number line and complete the number sentence. Round 48,625 to the hundreds. Show 48,625 on your number line and complete the number sentence. 48,625 ≈ ______ 48,600 48,700 Between which two hundreds is 48,625? What’s the midpoint for 600 and 700? 48,650 Would 48,625 fall above or below 48,650? 48,625 below 48,600

Show 48,625 on your number line and complete the number sentence. Round 48,625 to the tens. Show 48,625 on your number line and complete the number sentence. 48,625 ≈ ______ 48,630 48,630 48,625 48,625 48,620

Multiply by Multiples of 10 Say the multiplication sentence. 31 x 10 = ______ 310 310 x 2 = ______ 620 Write 310 x 20 as a three-step multiplication sentence, taking out the ten. 310 x 20 = ______ 6,200 2 x 10 310 x 2 x 10 = 6,200 620 x 10 = 6200

920 23 x 40 = ______ 23 X 4 92 Let’s do one more together. 4 x 10 First, we multiply 23 x 4. 23 X 4 92 Now, we can easily solve: 23 x 10 x 4 = 920

Do one on your own. Show it as a 3-step multiplication sentence. 32 x 30 = ______ 960 32 X 3 96 So, 32 x 10 x 3 = 960

Word Problem Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas. How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years? 365 x 2 = 730 730 x 2 = 1,460 hours 1460 x 60 = minutes practiced 146 x 10 x 10 x 6 = 87,600 Jonas Bradley 730 hours 730 hours 730 hours Bradley practices the guitar 87,600 minutes more than Jonas in 2 years.

Concept Development 30 students How many students do we have in class? Do all classes have exactly 28 students? There are 26 classes, but I’m not sure exactly how many students are in each class. What can I do to find a number that is close to the actual amount of students in our school? Great idea. We can estimate. What number could help me make an estimate for the number of students in each class? True, but 28 is difficult to multiply in my head. I’d like to use a number that I can multiply mentally. What can I round 27 to so it is easier to multiply? 30 students

Let’s estimate the number of classes. What could I round 26 to? How would I estimate the total number of students? multiply What would my estimate be? Show me your thinking. 26 x 28 30 x 30 So, 3 x 3 x 10 x 10 9 x 100 900 Yes, there are about 900 students. Estimates can help us understand a reasonable size of of a product when we multiply the original numbers.

456 x 42 ≈ _________ 20,000 500 x 40 Round to the tens. 460 x 40 Suppose I don’t need to know the exact product, just an estimate. How could I round the factors to estimate the product? Round to the tens. 460 x 40 If 460 x 40 is too hard, could you round to a different place value to make the product easier to find? 500 x 40 5 hundreds x 4 tens equals 20 thousands (5 x 100) x (4 x 10) = 20,000 That sounds easier! What would my estimate be? Can you give me the multiplication sentence in unit form?

4,560 x 42 ≈ _________ 200,000 Estimate your answer. Show your thinking by writing the multiplication sentence in unit form. 5,000 x 40 5 thousands x 4 tens equals 20 ten thousands (5 x 1000) x (4 x 10) = 200,000

4,560 x 420 ≈ _________ 2,000,000 Estimate your answer. Show your thinking by writing the multiplication sentence in unit form. 5,000 x 400 5 thousands x 4 hundreds equals 2 million (5 x 1000) x (4 x 100) = 2,000,000

1,320 x 88 ≈ _________ 90,000 Round the factors to estimate the product. Explain your thinking to your partner. 1,000 x 90 = 90,000

Compare this problem to the problem we just did. 13,205 x 880 ≈ _________ 9,000,000 Compare this problem to the problem we just did. What do you notice is different? The factors are greater. 13,205 is about 10 times as large as 1,320 and 880 is exactly 10 times as large as 88. What do you think that will do to our estimate? It will increase the product. The product should be about 100 times as large as the first one. Let’s test that prediction. Round and find the estimated product. 10,000 x 900 = 9,000,000 Was our prediction correct? Yes. 9 million is 100 times as large as 90,000.

3,120 x 880 ≈ _________ 2,700,000 Find a reasonable estimate. Show your work and answer in a complete sentence. 3,000 x 900 = 2,700,000 A reasonable estimate for 3,120 x 880 is 2,700,000.

31,200 x 880 ≈ ____ x _____ = _______ 30,000 900 27,000,000 Fill in the blanks. Show your work and answer in a complete sentence. A reasonable estimate for 31,200 x 880 is 27,000,000.

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