lesson 4 objective: use exponents to denote powers of 10 with application to metric conversions....
TRANSCRIPT
Lesson 4
Objective: Use exponents to denote powers of 10 with application to metric conversions.
MODULE 1
Multiply and Divide Decimals by 10, 100, and 1000
• Say the value as a decimal.• Write the number and multiply it by 10.
• 32.4 x 10 = 324• Now show 32.4 divided by 10.
• 32.4 ÷ 10 = 3.24
Multiply and Divide Decimals by 10, 100, and 1000
• Using your place value chart, show 32.4 x 100.• 32.4 x 100 = 3240
• Now show 32.4 ÷ 100.• 32.4 ÷ 100 = 0.324
Multiply and Divide Decimals by 10, 100, and 1000
•Using your place value chart, show 837 ÷ 1000.
•837 ÷ 1000 = 0.837
•Now show 0.418 x 1000.•0.418 x 1000 = 418
Write the Unit as a Decimal
• 9 tenths = _____• 10 tenths = ____• 20 tenths = ____• 30 tenths = ____• 70 tenths = ____• 9 hundredths = ____• 10 hundredths = ____• 11 hundredths = ____• 17 hundredths = ____
• 57 hundredths = ____
• 42 hundredths = ____• 9 thousandths = ____• 10 thousandths = ____
• 20 thousandths = ____
• 60 thousandths = ____
• 64 thousandths = ____
• 83 thousandths = ____
Write in Exponential Form
• 100 = 10?
Write 100 in exponential form.• 100 = 10²
• 1,000 = 10?
Write 1,000 in exponential form.• 1,000 = 10³
• 10,000 = 10?
Write 10,000 in exponential form.• 10,000 = 10⁴
• 1,000,000 = 10?
Write 1,000,000 in exponential form.• 1,000,000 = 10⁶
Converting Units
• 1 km = _____ mFill in the missing number.
• 1000 m
• 1 kg = _____ gFill in the missing number.
• 1000 g
• 1 liter = ____ mlFill in the missing number.
• 1000 ml
• 1 m = _____ cmFill in the missing number.
• 100 cm
APPLICATION PROBLEM
Mr. Brown wants to withdraw $1,000 from his bank and in ten dollar bills. How many ten dollar bills should he receive? Explain how you arrived at your answer.
Concept Development – Problem 1
Draw a line 2 meters long.
0 m 2 m
• With your partner, determine how many centimeters equal 2 meters.
• 2 m = 200 cm• How is it that the same line can measure both 2 meters and
200 centimeters?• Discuss with a partner how we convert from 2 meters to 200
centimeters.• Multiply by 100
• Why didn’t the length of our line change? Discuss that with your partner.
Concept Development – Problem 1
Draw a line 2 meters long.
0 m 2 m
• With your partner, determine how many millimeters equal 2 meters.
• 2 m = 2000 mm• How is it that the same line can measure both 2 meters and
2000 millimeters?• Discuss with a partner how we convert from 2 meters to
2000 millimeters.• Multiply by 1000
• Why didn’t the length of our line change? Discuss that with your partner.
• Can we represent the conversion from meters to centimeters or meters to millimeters with exponents? Discuss this with your partner.
Concept Development – Problem 1
• When we convert from centimeters to meters, we multiplied by 10², while to convert from meters to millimeters we multiplied by 10³.
• However, if we convert from centimeters to meters we divide by 10² and to convert from millimeters to meters we divide by 10³.
Concept Development – Problem 2
Draw a line 1 meter 37 centimeters long.
0 m 0.5 m 1 m 1 m 37 cm 1.5 m 2 m
• What fraction of a whole meter is 37 centimeters?• 37 hundredths
• Write 1 and 37 hundredths as a decimal fraction.• 1.37
• With your partner, determine how many centimeters is equal to 1.37 meters both by looking at your meter strip and line and writing an equation using an exponent.
• What is the equivalent measure in meters?• 137 centimeters
• Show the conversion using an equation with an exponent. • 1.37 meters =1.37 x 10² = 137 centimeters
• What is the conversion factor?• 10² or 100
Concept Development – Problem 2
• Convert 1.37 meters to millimeters. Explain how you got your answer.• 1.37 meters = 1370 millimeters
• Convert 2.6 m to centimeters. Explain how you got your answer.• 2.6 m = 260 centimeters
• Convert 12.08 millimeters to meters.• 12.08 mm = 0.01208 meters
Concept Development – Problem 3
A cat weighs 4.5 kilograms. Convert its weight to grams. A dog weighs 6700 grams. Convert its weight to kilograms.
• Work with a partner to find both the cat’s weight in grams and the dog’s weight in kilograms. Explain your reasoning with an equation using an exponent for each problem.• 4.5 kg x 10? = ______ g• 6700 g ÷ 10? = ______ kg
• What is the conversion factor for both problems?
• Now convert 2.75 kg to g and 6007 g to kg.• 2.75 kg x 10? = ______ g• 6007 g ÷ 10? = ______ kg
• What is the conversion factor for both problems?• Let’s relate our meter to millimeter measurements to our
kilogram to gram conversions.
Concept Development – Problem 4
• The baker uses 0.6 liter of vegetable oil to make brownies. How many millimeters of vegetable oil did he use.
• 0.6 l x 10³ = 600 ml
• He is asked to make 100 batches for a customer. How many liters of oil will he need?
• 0.6 l x 10² = 60 l
• After gym class, Mei Ling drank 764 milliliters of water. How many liters of water did she drink?• 764 ml ÷ 10³ = 0.764 l
• What do you notice with measurement conversions thus far?
Place Values of Metric Prefixes
Thousand
Hundred Ten One Tenth
Hundredth
Thousandth
kmkgkL
hmhghL
dkmdkgdkL
mgL
dmdgdL
cmcgcL
mmmgmL
Concept Development – Problem 4
• Convert 1,045 ml to liters.• 1,045 ml ÷ 10³ = 1.045 l
• Convert 0.008 liters to milliliters.• 0.008 l x 10³ = 8 ml