NYS Math Module 1Lesson 11

I can…take out the unit 5.NBT.1add, 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 UnitSay this number: 1.234 = ____ thousandths

Think about how many thousandths are in 1.234.

1234

How much is one thousand, thousandths?

1.000 = 1One thousand thousandths = 1 whole

Say this number:

65.247 = _________________ 65 ones 247 thousandths

On your board, fill in the blank.

76.358 = 7 tens ____ thousandths6358

Let’s try another one.

6 358

76.358 = 763 tenths ____ thousandths58 58

What do you notice? Discuss with your partner.

Last one.

76.358 = ____ hundredths 8 thousandths7635 76 35

Add and Subtract DecimalsWrite 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

4 ones 8 hundredths – 2 ones = _______

4.08 - 2 = 2.08

Write the subtraction sentence in decimal form.

9 tenths 7 thousandths – 4 thousandths = _______

4 ones 582 thousandths – 3 hundredths = _______

0.907 - 0.004 = 0.903

4.582 – 0.3 = 4.552

9 ones 708 thousandths – 4 tenths = _______

9.708 – 0.4 = 9.308

4 ones 73 thousandths – 4 hundredths = _______

4.073 – 0.4 = 3.673

Word ProblemAfter school, Marcus ran 3.2km and Cindy ran

1.95km. Who ran farther? How much farther?

3.201.95-1.25

2 11 10

Concept DevelopmentShow 2 tenths on your place value chart.

ones

tenths

Make 3 copies of 2 tenths. How many tenths to you have in all? 6 tenths

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

0.2 + 0.2 + 0.2 = 0.6

3 copies of 2 tenths is ____________6 tenths

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.

ones tenths

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

12 tenths is the same as _______________.

12 tenths makes a number greater than 1 whole

1 and 2 tenths

9 tenths

ones tenths

12 tenths

4 copies of 3 tenths is _______________.12 tenths

2 x 0.43 = _______

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

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

0.86

Read what your place value chart shows.

Two groups of 4 tenths = 0.8 Two groups of 3 hundredths= 0.06

4 x 0.423 = _______

Solve this problem using your disks.

1.692

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

0.423X 41.692How 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.

1 6 9 2

6 x 1.21 = _______

Solve this problem using an area model.

7.26

Draw an area model.

How many sections do we have? 3; ones, tenths, and hundredths

I am multiplying each number by what? 6

6

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

6 12 tenths 6 hundredths

6 + 1.2 + 0.06 = 7.26

1.21X 67.26

7 x 2.41 = _______

Solve this problem using an area model and an equation.

16.87

7 14 28 tenths 7 hundredths

14 + 2.8 + 0.07 = 16.87

2.41 X 716.87

8 x 2.34 = _______

Last one..

18.72

8 16 24 tenths 32 hundredths

16 + 2.4 + 0.32 = 18.72

2.34 X 818.72

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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