NYS Math Module 2 Lesson 1 SWBAT: multiply by 10, 100, and 1,000 (5.NBT.2) place value (5.NBT.3) round to different place values (5.NBT.4) Objective: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties.

Multiply by 10, 100, and 1,000 Say the product. 30 3 x 10 = _____ 300 3 x 100 = _____ 3,000 3 x 1000 = _____ 5,000 5 x 1,000 = _____ 5 0.005 x 1,000 = _____ 5,000 50 x 100 = _____ 5 0.05 x 100 = _____

Let’s do some more: 3,000 30 x 100 = _____ 30,000 30 x 1000 = ______ 32,000 32 x 1,000 = ______ 320 0.32 x 1,000 = _____ 5200 52 x 100 = _____ 520 5.2 x 100 = _____ 40 4 x 10 = _____ 4 0.4 x 10 = ______

Last group. 450 0.45 x 1,000 = ______ 30,450 30.45 x 1,000 = ______ 700 7 x 100 = _____ 7,200 72 x 100 = _____ 7,002 7.002 x 1000 = _____

Place Value 40 4 tens Zero ones 4 tens = ______ 4 tens How many tens do you see? There are 4 tens and how many ones? Zero ones 4 tens = ______ 40

7 4 4 2 Fill in the blank. 40,000 4 ten thousands = _____________ 400,000 4 hundred thousands = _____________ 7,000,000 7 million = _____________ 2,000 2 thousand = _____________

8 6 3 6 5 3 Show the answer in your place value chart. 5 hundreds = __________ 500 3 tens = ________ 30 53 tens = _____________ 530 6 ten thousands = _____________ 60,000 8 hundred thousands 36 thousands = _____________ 836,000

9,000 Round to Different Place Value 8,735 ≈ ______ Say this number: Let’s round to the thousands. Draw a vertical number line on your boards with two points and a midpoint between them. 9,000 Between which two thousands is 8,735? 8,735 ≈ ______ 9,000 8,735 Label your number line. Show 8,735 on your number line and complete the number sentence. What’s the midpoint for 8,000 and 9,000? 8,500 8,500 is the same as how many hundred? 85 hundreds How many hundreds are in 8,735? 8,000 87 hundreds

Show 8,735 on your number line and complete the number sentence. Round 8,735 to the hundreds. Show 8,735 on your number line and complete the number sentence. 8,735 ≈ ______ 8,700 8,800 8,750 8,735 8,700

Show 8,735 on your number line and complete the number sentence. Round 8,735 to the tens. Show 8,735 on your number line and complete the number sentence. 8,735 ≈ ______ 8,740 8,740 8,735 35 is between 30 and 40 8,735 8,735 40, so 35 ≈ 40 8,730

Show 7,458 on your number line and complete the number sentence. Round 7,458 to the thousands. Show 7,458 on your number line and complete the number sentence. 7,458 ≈ ______ 7,000 8,000 7,500 7,458 7,000

Show 7,458 on your number line and complete the number sentence. Round 7,458 to the hundreds. Show 7,458 on your number line and complete the number sentence. 7,458 ≈ ______ 7,500 7,500 7,458 458 is between 400 and 500 7,458 458 is closet to 500, so 458 ≈ 500 7,450 7,400

Show 7,458 on your number line and complete the number sentence. Round 7,458 to the tens. Show 7,458 on your number line and complete the number sentence. 7,458 ≈ ______ 7,460 7,460 7,458 7,455 7,450

Word Problem 14 56 - 4 16 DL DW 56 tenths ÷ 4 = 14 tenths The top surface of a desk has a length of 5.6 feet. The length is 4 times its width. What is the width of the desk? - 4 16 56 14 5.6 feet DL DW 56 tenths ÷ 4 = 14 tenths 14 tenths = 1.4 The width of the desk is 1.4 feet.

Concept Development 12 tens 120 12 0 4 x 30 4 x 3 tens = _______ Tip: To find the product, start by multiplying the whole numbers, remembering to state the unit in your product. Show 12 tens on your place value chart. 120 Write 12 tens in standard form. 12 0

1,200 1,200 4 tens x 3 tens = ___________ Solve with a partner. How did you use the previous problem to help you solve 4 tens x 3 tens? The place value unit of the first factor was different, so it was 12 hundreds. It’s the same as 4 threes times 10 times 10, which is 12 hundreds. I multiplied 4 x 3, which is 12. Then I multiplied tens by tens, so my new units are hundreds. Now, I have 12 hundreds, or 1,200. 1,200 4 tens x 3 tens = ___________ So, 10 x 10 = 100 (4 x 3) x 100 = 1200

Yes. We can multiply in any order, so they are the same. 4 tens x 3 hundreds = ___________ 12000 4 X 10 3 X 100 How is this problem different? We are multiplying tens and hundreds. 4 tens is the same as 4 times 10. 3 hundreds is the same as 3 times what? So, another way to write our problem would be (4 x 10) x (3 x 100). (4 x 3) x (10 x 100) What is 4 x3? 12 X 1000 What is 10 x 100? What is the product of 12 and 1,000? 12000 Are these expressions equal? Why or why not? Turn and talk. Yes. We can multiply in any order, so they are the same.

4,000 x 30 = _______ 120,000 (4 x 1,000) (3 x 10) What is another way to write 4 thousands? What is another way to write 3 tens? Rewrite the problem and solve. (4 x 3) x (1,000 x 10) 12 x 10,000 120,000

300 60 x 5 = ______ (6 x 10) x 5 (6 x 5) x 10 60 x 5 = 300 30 x 10 = 300 Are both of these equivalent to 60 x 5? Why or why not? Discuss with a partner. When we change the order of factors we are using the commutative property. 3 x 2 = 6 and 2 x 3 = 6, so 3 x 2 = 2 x 3 When we group factors differently we are using the associative property of multiplication. Solve the problems.

3,000 60 x 50 = ______ (6 x 10) x (5 x 10) (6 x 5) x (10 x 10) For this problem, use the properties and what you know about multiplying multiples of 10 to help you solve. Work with a partner to solve, and then explain. 3,000 60 x 50 = ______ (6 x 10) x (5 x 10) (6 x 5) x (10 x 10) 30 x 100 3,000 In our last problem set the number of zeros in the product has exactly the same number of zeros as our factors. That isn’t the case. Why is that? 60 x 50 = 3,000

Solve these problems independently. 60 x 500 = ______ 30,000 60 x 5,000 = ______ 300,000 (6 x 10) x (5 x 100) (6 x 5) x (10 x 100) 30 x 1000 30,000 (6 x 10) x (5 x 1000) (6 x 5) x (10 x 1000) 30 x 10,000 300,000

Find the product, using any method. 451 x 8 = ______ 3,608 Distributive Property Algorithm 400 x 8 = 3,200 50 x 8 = 400 1 x 8 = 8 Add products: 3,200 400 + 8 3,608 451 X 8 3,608 4 If you break the number apart, you can use basic facts to get the products. Different digits in three place values instead of zeros. Why is the distributive property useful here? Why does it help here, but we didn’t really use it in our other problems?

451 x 8 = ______ 3,608 451 x 80 = ______ 36,080 4,510 x 80 = _______ Turn and talk to your partner about how you can use 451 x 8 to help you solve these problems. Then solve. 451 x 8 = ______ 3,608 451 x 80 = ______ 36,080 4,510 x 80 = _______ 360,800 4,510 x 800 = _________ 3,608,000

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