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NYS Math Module 1 Lesson 11. I can… take out the unit 5.NBT.1 add, subtract, and multiply decimals 5.NBT.7.

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NYS Math Module 1

Lesson 11

I can…

take out the unit 5.NBT.1

add, subtract, and multiply decimals 5.NBT.7

Objective: Multiply a decimal fraction by single-digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used.


Take Out the Unit

Say this number:

1.234 = ____ thousandths

1234

Think about how many thousandths are in 1.234.

How much is one thousand, thousandths?

1.000 = 1

One thousand thousandths = 1 whole

Say this number:

65.247 = _________________

65 ones 247 thousandths


On your board, fill in the blank.

76.358 = 7 tens ____ thousandths

6 358

6358

Let’s try another one.

76.358 = 763 tenths ____ thousandths

58

58

What do you notice? Discuss with your partner.


Last one.

7635

76.358 = ____ hundredths 8 thousandths

7635


Add and Subtract Decimals

Write the addition sentences in decimal form.

7258 thousandths + 1 thousandth = _______

7.258 + 0.001= 7.259

7 ones 258 thousandths + 3 hundredths = _______

7.258 + 0.03= 7.288

7 ones 258 thousandths + 4 tenths = _______

7.258 + 0.4= 7.658


Let’s try some more…

6 ones 453 thousandths + 4 hundredths = _______

6.453 + 0.04= 6.493


2 ones 37 thousandths + 5 tenths = _______

2.037 + 0.5 =2.537

Tell your partner how you are solving these problems.

You add the number to the corresponding place value.

2.037 + 0.5 =2.537

Both the “0” and “5” are in the tenths place, so you add 0 +5 = 5. All the other place values did not change.


6 ones 35 hundredths + 7 thousandths = _______

6.35 + 0.007 = 6.357


Write the subtraction sentence in decimal form.

4 ones 8 hundredths – 2 ones = _______

4.08 - 2 = 2.08

9 tenths 7 thousandths – 4 thousandths = _______

0.907 - 0.004 = 0.903

4 ones 582 thousandths – 3 hundredths = _______

4.582 – 0.3 = 4.552


9 ones 708 thousandths – 4 tenths = _______

9.708 – 0.4 = 9.308



Word Problem

After school, Marcus ran 3.2km and Cindy ran 1.95km. Who ran farther? How much farther?

2 11 10

3.20

1.95

-

1.25


Concept Development

Show 2 tenths on your place value chart.

How many tenths to you have in all?

6 tenths

Make 3 copies of 2 tenths.

Write a number sentence to express how we made 6 tenths.

0.2 + 0.2 + 0.2 = 0.6

6 tenths

3 copies of 2 tenths is ____________

3 x 0.2 = 0.6

Read the equation in unit form.


Find the value of 3 x 0.3 and 4 x 0.3.

12 tenths

9 tenths

How was 4 x 3 tenths different from 3 x 3 tenths?

12 tenths makes a number greater than 1 whole

4 copies of 3 tenths is _______________.

12 tenths

12 tenths is the same as _______________.

1 and 2 tenths


How can we use our knowledge from the previous problems to solve this?

2 x 0.43 = _______

0.86

We make copies of hundredths like we make copies of tenths. Hundredths is a different unit, but we can multiply it just like tenths.

Use your place value chart to find the product. Complete the sentence, “2 copies of 43 hundredths is __________.”

0.86

Read what your place value chart shows.

Two groups of 3 hundredths= 0.06

Two groups of 4 tenths = 0.8


Solve this problem using your disks. solve this?

4 x 0.423 = _______

1.692

0.423

X 4

1.692

1 6 9 2

Read the product that is shown on your place value chart.

How was this problem different?

We had to bundle 10 thousandths to make 1 hundredth.

Did any other units have to be regrouped?

Yes, the tenths. We had to regroup 10 tenths to make 1 whole.

Show how you found the product using an area model and equation.


Solve this problem using an area model. solve this?

6 x 1.21 = _______

7.26

Draw an area model.

3; ones, tenths, and hundredths

How many sections do we have?

1.21

X 6

7.26

6

6

12 tenths

6 hundredths

6 + 1.2 + 0.06 = 7.26

6

I am multiplying each number by what?

With a partner, solve the equation using an area model and an equation.


Solve this problem using an area model and an equation. solve this?

16.87

7 x 2.41 = _______

7

14

28 tenths

7 hundredths

14 + 2.8 + 0.07 = 16.87

2.41

X 7

16.87


Last one.. solve this?

18.72

8 x 2.34 = _______

8

16

24 tenths

32 hundredths

16 + 2.4 + 0.32 = 18.72

2.34

X 8

18.72


Thank you for your purchase solve this?.

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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


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