Eureka Math

5th: Module 1 Lesson 5

Objective: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

Fluency (12 min)

• Sprint: Multiply by 4 3.OA.7 (10 minutes)
• Unit Skip-Counting 4.NBT.1 (2 minutes)
• Place Value 4.NBT.2 (2 minutes)

Sprint: Multiply Decimals by 10, 100, and 1,000

(8 minutes) Materials: (S) Multiply Decimals by 10, 100, and 1,000 Sprint

Multiply and Divide by Exponents (2 minutes)

Materials: (S) personal white board, Millions to thousandths place value chart

Write 54 tenths as a decimal.

Say the decimal.

five and four tenths

Multiply it by 10².

Say the product.

five hundred forty

,

,

5

4

5

4

0

Write 6 tenths as a decimal.

Say the decimal.

six tenths

Multiply it by 10².

Say the product.

sixty

,

,

6

6

0

Write 6 tenths as a decimal.

Say the decimal.

six tenths

Divide it by 10².

Say the quotient.

Six thousandths

,

,

6

6

0

0

Write 2 and 784 thousandths as a decimal.

Say the decimal.

Two and seven hundred eighty-four thousandths

Multiply it by 10³.

Say the product.

Two thousand seven hundred eighty-four

,

,

2

2

4

8

7

4

8

7

Write 6 thousands 583 ones.

Say the number.

Six thousand, five hundred eighty-three.

Divide it by 10³.

Say the quotient.

Six and five hundred eighty-three thousandths.

,

,

6

6

3

8

5

3

8

5

Multiplying Metric Units (2 minutes)

Materials: (S) Millions to thousandths place value chart (Lesson 1 Template), personal white board

3 m = ___ cm

Show 3 on your place value chart.

How many centimeters are in 1 meter?

100 centimeters.

Show how many centimeters equal 3 meters on your place value chart.

How many centimeters are in 3 meters?

300 centimeters.

7 kg = ____ g

Show 7 on your place value chart.

How many grams are in 1 kilogram?

1000 grams.

Show how many grams equal 7 kilograms on your place value chart.

How many grams are in 7 kilograms?

7000 grams.

7000 mL = ____ L

Show 7 thousands on your place value chart.

How many milliliters are in 1 liter?

1000 milliliters.

Show how many liters equal 7000 milliliters on your place value chart.

How many liters are in 7000 milliliters?

7 liters.

7500 m = ____ km ____ m

Show 7 thousands 5 hundreds on your place value chart.

How many meters are in 1 kilometer?

1000 meters.

Show how many kilometers and meters equal 7500 meters on your place value chart.

How many kilometers and meters equal 7500 meters?

7 kilometers 500 meters.

8350 g = ____ kg ____ g

Show 8 thousands 3 hundreds 5 tens on your place value chart.

How many grams are in 1 kilogram?

1000 grams.

Show how many kilograms and grams equal 8350 grams on your place value chart.

How many kilograms and grams equal 8350 meters?

8 kilograms 350 grams

Application Problem (8 minutes)

Jordan measures a desk at 200 cm.

James measures the same desk in millimeters, and Amy measures the same desk in meters.

What is James’s measurement in millimeters?

What is Amy’s measurement in meters?

Show your thinking using a place value chart or an equation with exponents.

James:

200 cm = ______ mm

200 x 10 = 2000 mm

​

Amy:

200 cm = _____ m

200 ÷ 10² = 2 m

Concept Development (30 minutes)

Materials: (S) Personal white board, thousands through thousandths place value chart

Three thousand, forty-seven

On your personal board, write this number in standard form, expanded form, and unit form.

Standard form: 3,047

Expanded form: 3,000 + 40 + 7

Unit form: 3 thousands 4 tens 7 ones

Explain to your partner the purpose of writing this number in these different forms.

• Standard form shows us the digits that we are using to represent that amount. 3,047
• Expanded form shows how much each digit is worth and that the number is a total of those values added together. 3,000 + 40 + 7
• Unit form helps us see how many of each size unit are in the number. 3 thousands 4 tens 7 ones

Write 1 thousandth using digits on your place value chart.

Standard form for 1 thousandth: 0.001

How many ones, tenths, hundredths, thousandths?

Zero ones, zero tenths, zero hundredths, one thousandth

​

We write 1 thousandth as a fraction like this:

Problem 1

_1_

1000

​

• Expanded form with a decimal: 1 x 0.001

​

• Unit form: 1 thousandth

​

Each form shows how many copies of a unit there are.

1 thousandth is a single copy of a thousandth.

Problem 1

​

• Expanded form with a fraction: 1 x

Imagine 3 copies of 1 thousandth.

How many thousandths is that?

​

__3__

1000

3 thousandths is 3 copies of 1 thousandth.

​

Turn and talk to your partner about how this would be written in expanded form using a fraction and using a decimal.

three thousandths = 0.003 =

Problem 1

three thousandths = 0.003 =

__3__

1000

• Expanded form with fraction:

= 3 x

__3__

1000

Problem 1

• Expanded form with decimal: 0.003 = 3 × 0.001

​

• Unit form: 3 thousandths

__3__

1000

Write 13 thousandths in standard form.

Turn and share with your partner.

thirteen thousandths = 0.013 =

​

__13__

1000

= 1 x + 3 x

__13__

1000

Problem 2

Write 13 thousandths in expanded form using fractions.

thirteen thousandths = 0.013 =

Write 13 thousandths in expanded form using decimals.

​

0.013 = 1 x 0.01 + 3 x 0.001

0.013 = (1 x 0.01 ) + (3 x 0.001)

__13__

1000

Problem 2

Now, write this decimal in unit form.

thirteen thousandths = 0.013 =

__13__

1000

13 thousandths =

1 hundredth 3 thousandths

OR

13 thousandths

Problem 2

Write 273 thousandths in standard form.

Turn and share with your partner.

= 2 x + 7 x + 3 x

Two hundred seventy-three thousandths = 0.273 =

_273_

1000

Write 273 thousandths in expanded form using fractions.

_273_

1000

Problem 2

_1_

10

_1_

100

_1_

1000

two hundred seventy-three thousandths = 0.273 =

_273_

1000

Write 273 thousandths in expanded form using decimals.

​

0.273 = 2 x 0.1 + 1 x 0.01 + 3 x 0.001

0.273 = (2 x 0.1) + (1 x 0.01) + (3 x 0.001)

​

Problem 2

two hundred seventy-three thousandths = 0.273 =

Now, write this decimal in unit form.

_273_

1000

273 thousandths =

2 tenths 7 hundredths 3 thousandths OR

2 tenths 73 thousandths OR

27 hundredths 3 thousandths OR

273 thousandths

Problem 2

Write 25.413 in word form on your board.

Twenty-five and four hundred thirteen thousandths.

Write 25.413 in unit form on your board.

2 tens 5 ones 4 tenths 1 hundredth 3 thousandths OR

25 ones 413 thousandths OR

254 tenths 13 hundredths OR

25,413 thousandths OR….

​

Problem 2

Standard form: 25.413

Write 25.413 as a mixed number.

Compare your work with your partner’s.

_413_

1000

Problem 3

Twenty-five and four hundred thirteen thousandths = 25

Twenty-five and four hundred thirteen thousandths =

25.413 = 25

​

​

Write the fraction in expanded form.

Compare your work with your partner’s.

Expanded form using fractions:

_413_

1000

25 = 2 x 10 + 5 x 1 + 4 x + 1 x + 3 x

Problem 3

_413_

1000

_1_

10

_1_

100

_1_

1000

Twenty-five and four hundred thirteen thousandths =

25.413 = 25

​

_413_

1000

Write the decimal in expanded form.

Compare your work with your partner’s.

Expanded form using decimals:

25.413 = 2 x 10 + 5 x 1 + 4 x 0.1 + 1 x 0.01 + 3 x 0.001

25.413 = (2 x 10) + (5 x 1) + (4 x 0.1) + (1 x 0.01) + (3 x 0.001)

Problem 3

Twenty-five and four hundred thirteen thousandths =

25.413 = 25

​

2 tens 5 ones 4 tenths 1 hundredth 3 thousandths OR

25 ones 413 thousandths

Problem 3

_413_

1000

Write the decimal in unit form.

Compare your work with your partner’s.

Unit form:

Write the standard, expanded, and unit forms of

four hundred four thousandths AND

four hundred and four thousandths

Problem 4

Write the standard, expanded, and unit forms of

four hundred four thousandths AND

four hundred and four thousandths

Problem 4