NYS Grade 5 Module 1 Lesson 12

NYS Math Module 1

Lesson 12Objective: Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point.

I can:

Add decimals 5NBT.7Find the product 5.NBT.7

Sprint – Adding Decimals

**** 8 minutes ****

On your mark,

get set,

GO!

Find the Product

4 x 2 ones = _____

Let’s keep going. Say the multiplication in unit form.

8 ones

Yes, 4 times 2 ones equals 8 ones.

Say the multiplication in unit form.

4 x 0.2 = _______8 tenths

4 x 0.02 = _________8hundredths

Let’s continue to say the entire multiplication sentence.

5 x 3 = _______15 ones

5 x 0.3 = _______15 tenths

5 x 0.03 = ___________15 hundredths

Look carefully. Write the answer on your white board.3 x 0.2 = _______ 0.6

3 x 0.03 = ______ 0.09

3 x 0.23 =_______0.69

2 x 0.14 =_______0.28

Word ProblemPatty buys 7 juice boxes a month for lunch. If one juice box costs $2.79, how much money does Patty spend on juice each month? If necessary, use an area model to solve.

2.79 7X

19.53

ExtensionPatty would spend $19.53 a month on juice. How much would she spend in 10 months? In 12 months? Work with a partner.

19.53 10X

195.30

19.53 12X

3906 19530

+

234.36

Concept Development** Write on your white boards.**

31 x 4 = __________

3.1 x 4 = __________

0.31 x 4 = __________

How are these 3 problems the same?

Yes, they are the same numbers. Use area models to solve, if necessary.

12.4

124

1.24

How are all three problems alike?

So, if all three problems have the same digits in the problem and in the product, do they have the same value? Turn and talk with your partner.

Okay, so the digits are all have a different value to begin with, but they are in the same order for the product. Therefore, I can multiply first and then worry about where to place the decimal.

31 x 4 = __________

3.1 x 4 = __________

0.31 x 4 = __________

12.4124

1.24

5.1 x 6 = _______

How many tenths are there in 5.1?

Right, there are 51, so multiply 51 x 6 first.

51 6X

306306 What? Tenths.

Tenths

So, 306 tenths = 30.6

Here we see that we can multiply first and then worry about where to place the decimal. Let’s try it.

306 Tenths.

11.4 x 4 = ____

What is the smallest unit in 11.4? Tenths

114 tenthsX

456 tenthsNow, let’s think about where to place the decimal. If we multiply 11 x 4 it’s 44. So our answer has to be close to 44. It would make sense to put the decimal between the 5 and 6.

Okay, so lets convert 11.4 into tenths. How many tenths are there in 11.4?

4

456 tenths

3.12 x 4 = ____

312 tenthsX

1248 tenths 0r 12.48

4

What’s the product?

+

3.22 x 5 = ____

3.22X

16.105

What’s the product?

2 numbers after the decimal in the problem, so there are 2 numbers after the decimal in the product.

+

3.42 x 6 = ____

3.42X

20.526

What’s the product?

20.52

I’m going to write four possible products. Talk to your partner about which one would be reasonable. Be ready to share your thinking.

4.12 x 7 =

2.88428.840.2884288.4

4.12X

28.847

You know 4 x 7 =28, so your answer has to be around 28 ones.

Which of the following would be the most reasonable product?

15.8 x 3 =

47.44.740.474474

47.4, because 15 x 3= 45, my answer has to be around 45

ones

47.4

What is 0.733 renamed using its smallest unit?

0.733 x 4 =

2.93229.32293.22932

2.932, because 1 x4 =4, my answer has to be around 4

ones

733 thousandths

Now multiply vertically by 4. What is the product?2932 thousandths

Which of these is the most reasonable product?

Rename 10.733 using its smallest units and multiply by 4. What is the product?

10.733 x 4 =

4.293242.932429.324293.2

42.932, because 10 x 4 = 40, my answer has to be around 40

ones

42932 thousandths

Which of these is the most reasonable product?

5.733 x 4 =

5.733X

22.9324

Problem Set Review

Example 1: Pick the most reasonable product. Explain your reasoning.

3.5 x 2 7 70 700 0.7

3 x 2= 6, 7 is closest to 6. or 35 x 2= 70 tenths which is the same as 7 ones.

The rest of the problems are word problems. Be sure to show your reasoning by showing all of your work!

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Worksheets in this file are from NYS Math Module 1 Grade 5. I have simply minimized the pages to reduce the use of paper. For the entire module visit:

www.engageny.org/resource/grade-5-mathematics-module-2