Download - Engage NY Module 1

Engage NY Module 1Lesson 5

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

Write 54 tenths as a decimal. Say the decimal. Multiply it by 10². Say the product.

◦ 5.4 x 10² = 540

MULTIPLY AND DIVIDE BY EXPONENTS

Write 6 tenths as a decimal. Say the decimal. Multiply it by 10². Say the product.

◦ 0.6 x 10² = 60


Write 6 tenths as a decimal. Say the decimal. Divide it by 10². Say the quotient.

◦ 0.6 ÷10² = 0.006


Write 2 and seven hundred eighty-four thousandths as a decimal.◦ 2.784

Multiply it by 10³. Say the product.

◦ 2.784 x 10³ = 2784 Write six thousand five hundred eighty three.

◦ 6583 Divide it by 10³. Say the quotient.

◦ 6583 ÷ 10³ = 6.583


3 m = ____ cm Show 3 in your place value chart. How many centimeters are in 1 meter? Show how many centimeters are in 3 meters on your place value

chart.◦ 3 m = 300 cm

MULTIPLYING METRIC UNITS

3

3 0 0

7 kg = ____ g Show 7 in your place value chart. How many grams are in 1 kilogram? Show how many grams are in 7 kilograms on your place value

chart.◦ 7 kg = 7000 g


7

0 0 07

7000 ml = ____ l Show 7000 in your place value chart. How many milliliters are in 1 liter? Show how many liters are in 7000 milliliters on your place value

chart.◦ 7000 ml = 7 l


0 0 07

7

7500 m = ____ km ____ m Show 7500 in your place value chart. How many meters are in 1 km? Show how many kilometers are in 7500 meters on your place

value chart.◦ 7500 m = 7 km 500 m


5 0 07

7 5 0 0

8350 g = ____ kg ____ g Show 8350 in your place value chart. How many grams are in 1 kilogram? Show how many kilograms are in 8350

grams on your place value chart.◦ 8350 g = 8 kg 350 g


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’ measurement in millimeters? What is Amy’s measurement in meters? Show your thinking using a place value mat or an equation with exponents. Include a statement of solution.

◦ James: 200 cm = ____ mm 2000 mm

◦ Amy: 200 cm = ____ m 2 m

APPLICATION PROBLEM

Three thousand forty seven

◦ Write this number in standard form, expanded form, and unit form.

Standard form: 3,047 Expanded form: 3,000 + 40 + 7 Unit form: 3 thousand, 4 tens, 7 ones

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

CONCEPT DEVELOPMENT

Write one thousandth using digits on your place value chart. How many ones, tenths, hundredths, thousandths? This is the standard form of the decimal for 1 thousandth.

CONCEPT DEVELOPMENT – Problem 1

00 0 1

We write 1 thousandth as a fraction like this.

1 thousandth is a single copy of a thousandth. I can write the expanded form using a fraction like this, 1 x ( or using a decimal like this 1 x 0.001.

The unit form of this decimal looks like this 1 thousandth. We use a numeral (1) and the unit (thousandth) written as a word for the unit form.


One thousandth = 0.001 =

= 1 x (

0.001 = 1 x 0.001

1 thousandth

Imagine 3 copies of 1 thousandths. How many thousandths is that?

Write in standard form and as a fraction. Standard form: 0.003 Fraction form:

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 =

= 3 x (

0.003 = 3 x 0.001

3 thousandths

Write thirteen thousandths in standard form, and expanded form using fractions and then using decimals.

Turn and share with your partner.

Standard form: 0.013 Expanded forms: 1 x ( + 3 x (

1 x 0.01 + 3 x 0.001

Now write this decimal in unit form. 1 hundredth 3 thousandths = 13 thousandths


Thirteen thousandths = 0.013 =

= 0.013 = 1 x 0.01 + 3 x 0.001

1 hundredth 3 thousandths

13 thousandths

Write two hundred seventy-three thousandths in standard form, and expanded form using fractions and then using decimals.

Standard form: 0.273 Expanded forms: 2 x ( + 7 x ( + 3 x (

2 x 0.1 + 7 x 0.01 + 3 x 0.001

Now write this decimal in unit form. 2 tenths 7 hundredths 3 thousandths = 2 tenths 73 thousandths = 27

hundredths 3 thousandths = 273 thousandths


Two hundred seventy three thousandths

= 0.273 =

= 0.273 = 2 x 0.1 + 7 x 0.01 + 3 x 0.001

2 tenths 7 hundredths 3 thousandths

273 thousandths

Write one and six hundred eight thousandths in standard form, and expanded form using fractions and then using decimals.

Standard form: 1.608 Expanded forms: 1 + 6 x ( + 8 x (

1 + 6 x 0.1 + 8 x 0.001

Now write this decimal in unit form. 1 one 6 tenths 8 thousandths = 1 one 60 hundredths 8 thousandths = 1

one 608 thousandths


One and six hundred eight thousandths= 1.608 =

1

1 = 1.608 = 1 + 6 x 0.1 + 8 x 0.001

1 one 6 tenths 8 thousandths = 1 one 60

hundredths 8 thousandths = 1 one 608

thousandths

Write 25.413 in word form.◦ Twenty-five and four hundred thirteen thousandths

Now write this decimal in unit form.◦ 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths

What are other unit forms of this number?◦ 25 ones 413 thousandths◦ 254 tenths 13 hundredths◦ 25,413 thousandths

Write it as a mixed number, then in expanded form.


Twenty-five and four hundred thirteen thousandths= 25.413

= 25

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

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

2 tens 5 ones 4 tenths 1 hundredths 3 thousandths

25 ones 413 thousandths

Write 12.04 in word form.◦ Twelve and four hundredths

Now write this decimal in unit form.◦ 1 ten 2 ones 4 hundredths

What are other unit forms of this number?◦ 12 ones 4 hundredths◦ 1, 204 hundredths



Twelve and four hundredths= 12.04 = 12

12 = 1 x 10 + 2 x 1 + 4 x

12.04 = 1 x 10 + 2 x 1 + 4 x 0.01

1 ten 2 ones 4 hundredths = 12 ones 4 hundredths =

1,204 hundredths

Write 9.495 in word form.◦ Nine and four hundred ninety-five thousandths

Now write this decimal in unit form.◦ 9 ones 4 tenths 9 hundredths 5 thousandths



Nine and four hundred ninety-five thousandths = 9.495 =

9

9 = 9 x 1 + 4 x + 9 + 5

9.495 = 9 x 1 + 4 x 0.1 + 9 x 0.01 + 5 x 0.001

9 ones 4 tenths 9 hundredths 5 thousandths = 9,495 thousandths

Write four hundred four thousandths in standard form. ◦ 0.404

Now write four hundred and four thousandths in standard form.◦ 400.004

Tell the digits you used to write four hundred four thousandths. How did you know where to write the decimal in each of the standard

forms? Now write the expanded and unit forms for each of these numbers.


Four hundred four thousandths = 0.404 = 4 x ( ) + 4 ()

0.404= 4 x 0.1 + 4 x 0.001

4 tenths 4 thousandths

Four hundred and four thousandths = 400 = 4 x 100 + 4 () =

400.004 = 4 x 100 + 4 x 0.001

4 hundreds and 4 thousandths

Write two hundred two thousandths in standard form. ◦ 0.202

Now write nine hundred nine tenths in standard form.◦ 900.9

How did you know where to write the decimal in each of the standard forms?

Now write the expanded and unit forms for each of these numbers.


Two hundred two thousandths = 0.202 =

2 x () + 2 ()

0.202= 2 x 0.1 + 2 x 0.001

2 tenths 2 thousandths

Nine hundred and nine tenths = 900 = 9 x 100 + 9 () =

900.9 = 9 x 100 + 9 x 0.1

9 hundred and 9 tenths

Download - Engage NY Module 1

Top Related