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Engage NY Module 1. Lesson 5 Objective: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. MULTIPLY AND DIVIDE BY EXPONENTS. Write 54 tenths as a decimal. Say the decimal. Multiply it by 10². Say the product. 5.4 x 10² = 540. - PowerPoint PPT Presentation
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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
MULTIPLY AND DIVIDE BY EXPONENTS
Write 6 tenths as a decimal. Say the decimal. Divide it by 10². Say the quotient.
◦ 0.6 ÷10² = 0.006
MULTIPLY AND DIVIDE BY EXPONENTS
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
MULTIPLY AND DIVIDE BY EXPONENTS
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
MULTIPLYING METRIC UNITS
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
MULTIPLYING METRIC UNITS
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
MULTIPLYING METRIC UNITS
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
MULTIPLYING METRIC UNITS
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.
CONCEPT DEVELOPMENT – Problem 1
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.
CONCEPT DEVELOPMENT – Problem 1
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
CONCEPT DEVELOPMENT – Problem 2
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
CONCEPT DEVELOPMENT – Problem 2
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
CONCEPT DEVELOPMENT – Problem 2
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.
CONCEPT DEVELOPMENT – Problem 3
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
Write it as a mixed number, then in expanded form.
CONCEPT DEVELOPMENT – Problem 3
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
Write it as a mixed number, then in expanded form.
CONCEPT DEVELOPMENT – Problem 3
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.
CONCEPT DEVELOPMENT – Problem 4
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.
CONCEPT DEVELOPMENT – Problem 4
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
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