Illustrative Mathematics | v.360 Curriculum

9.1

Warm-up

Match each expression with its corresponding value and word.

expression

value
1,000,000,000,000

1,000
1,000,000,000
1,000,000

word
billion
milli-
million
thousand
centi-
trillion

For each of the numbers, think of something in the world that is described by that number.

9.2

Activity

Match each expression to one or more diagrams that could represent it. For each match, explain what the value of a single small square would have to be.
E
2 large squares each composed of 100 blocks, 10 by 10, 4 small squares each 1 block.

F
2 large squares each composed of 100 blocks, 10 by 10, 4 rectangles composed of 10 blocks, 10 by 1.

G
2 rectangles composed of 10 blocks, 10 by 1, 4 small squares, each 1 block.
1. Write an expression to describe the base-ten diagram if each small square represents . What is the value of this expression?
2. Write an expression to describe the base-ten diagram if each small square represents . What is the value of this expression?
3. Write an expression to describe the base-ten diagram if each small square represents . What is the value of this expression?
4. How does changing the value of the small square change the value of the expression? Explain or show your reasoning.

9.3

Activity

Your teacher will give you a card that tells you whether you are Partner A or B and gives you the information that is missing from your partner’s statements. Do not show your card to your partner.

Read each statement assigned to you, ask your partner for the missing information, and write the number your partner tells you.

Partner A’s statements:

Around the world, about pencils are made each year.
The mass of a proton is kilograms.
The population of Russia is about people.
The diameter of a bacteria cell is about meter.

Partner B’s statements:

Light waves travel through space at a speed of meters per second.
The population of India is about people.
The wavelength of a gamma ray is meters.
The tardigrade (water bear) is meters long.

Student Lesson Summary

Sometimes powers of 10 are helpful for expressing quantities, especially very large or very small quantities.

For example, the United States Mint has made over 500,000,000,000 pennies. To understand this number we can look at the number of zeros to know it is equivalent to 500 billion pennies. Since 1 billion can be written as , we can say that there are over pennies.

Sometimes we may need to rewrite a number using a different power of 10. We can say that . Since the factor was multiplied by 100 to get , the factor of 500 was divided by 100 to keep the value of the entire expression the same.

The same is true for very small quantities. For example, a single atom of carbon weighs about 0.0000000000000000000000199 grams. If we write this as a fraction we get . Using powers of 10, it becomes , which is a lot easier to write!

Just as we did with large numbers, small numbers can be rewritten as an equivalent value with a different power of 10. In this example we can divide the factor 199 by 100 and multiply the factor by 100 to get .

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Describing Large and Small Numbers Using Powers of 10

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Lesson 9

Describing Large and Small Numbers Using Powers of 10

Warm-up

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