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6-8 Grade 8 Unit 7 Lesson 12

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Lesson 12

12.1 Warm-up 12.2 Activity 12.3 Activity Student Lesson Summary

Unit 7, Lesson 12

Applications of Arithmetic with Powers of 10

Grade 8

12.1

Warm-up

What Information Do You Need?

What information would you need to answer these questions?

Which is taller, the Burj Khalifa or a stack of the money it cost to build the Burj Khalifa?
Which has more mass, the Burj Khalifa or the mass of pennies it cost to build the Burj Khalifa?

Are You Ready for More?

12.2

Activity

That’s a Tall Stack of Cash

In 2010, the Burj Khalifa became the tallest building in the world. It was very expensive to build.

Which is taller, the Burj Khalifa or a stack of the money it cost to build the Burj Khalifa? Ask your teacher for the information you need to be able to answer this question, and record the information here.
Answer the question “Which is taller, the Burj Khalifa or a stack of the money it cost to build the Burj Khalifa?” and explain or show your reasoning.
Decide what power of 10 to use to label the rightmost tick mark of the number line so that both the height of the stack of money and the height of the Burj Khalifa can be plotted on the same number line. Label the tick marks, and plot and label both values.
Which has more mass, the Burj Khalifa or the mass of the pennies it cost to build the Burj Khalifa? Ask your teacher for the information you need to be able to answer this question and record the information here.
Answer the question “Which has more mass, the Burj Khalifa or the mass of the pennies it cost to build the Burj Khalifa?” and explain or show your reasoning.
Decide what power of 10 to use to label the rightmost tick mark of the number line so that both the mass of the Burj Khalifa and the mass of the pennies it cost to build the Burj Khalifa can be plotted on the same number line. Label the tick marks and plot and label both values.

Are You Ready for More?

12.3

Activity

Meter Sticks to the Moon

How many meter sticks does it take to equal the mass of the Moon? Ask your teacher for the information you need to be able to answer this question, and record the information here.
Answer the question “How many meter sticks does it take to equal the mass of the Moon?” and explain or show your reasoning.
Label the number line and plot your answer for the number of meter sticks.
If you took all the meter sticks from the last question and lined them up end to end, would they reach the Moon? Would they reach beyond the Moon? If yes, how many times farther will they reach? Explain your reasoning.
One light year is approximately meters. How many light years away would the meter sticks reach? Label the number line, and plot your answer.

Are You Ready for More?

Student Lesson Summary

Powers of 10 can be helpful for making calculations with large or small numbers. For example, in 2014, the United States had 318,586,495 people who used the equivalent of 2,203,799,778,107 kilograms of oil in energy.

The amount of energy used per person is the total energy divided by the total number of people. We can use powers of 10 to estimate the total energy as and the population as . So the amount of energy per person in the U.S. is roughly . That is the equivalent of kilograms of oil in energy. That’s a lot of energy—the equivalent of almost 7,000 kilograms of oil per person!

In general, when we want to perform arithmetic with very large or very small quantities, estimating with powers of 10 and using exponent rules can help simplify the process. If we wanted to find the exact quotient of 2,203,799,778,107 by 318,586,495, then using powers of 10 would not simplify the calculation.

Glossary

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