Unit 7, Lesson 2
Multiplying Powers of 10
Accelerated 7
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The purpose of this activity is for students to develop a sense of visual scale between powers of 10. Students should understand that multiplying by 10 corresponds to increasing the exponent by 1.
This activity prompts students to make sense of quantities and their relationships (MP2). For example, even though the notation for
In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.
The purpose of this discussion is to make sure students understand that increasing the exponent of a power of 10 by 1 corresponds to multiplying by 10, and decreasing the exponent by 1 corresponds to dividing by 10.
Ask students the following questions:
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The goal of this activity is to help students flexibly transition between different notations for powers of 10 and to introduce the property of multiplication of values with the same base. Students observe patterns in the notations and generalize that
Give students 1 minute of quiet think time to complete the first unfinished row in the table before inviting 1–2 students to share and explain their answers. When it is clear that students understand how to complete the table, explain that they can skip one entry in the table, but they have to be able to explain why they skipped it. Give students 5–6 minutes to complete the remaining questions before a whole-class discussion.
| expression | expanded | single power of 10 |
|---|---|---|
The goal of this discussion is to reinforce the exponent rule for multiplying exponential expressions with the same base. Introduce and explain the visual display prepared earlier. This display should be kept visible to students throughout the remainder of the unit.
Continue to reinforce student understanding of this rule by writing out the expanded form of each expression and counting the total number of factors of 10 when discussing the following questions:
MLR2: Collect and Display
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In this activity, students explore patterns to discover the property
Give students 1 minute of quiet think time to complete the first unfinished row in the table before inviting 1–2 students to share and explain their answers. When it is clear that students understand how to complete the table, explain to them that they can skip one entry in the table, but they have to be able to explain why they skipped it. Give students 5–6 minutes to complete the remaining questions before a whole-class discussion.
Complete the table to explore patterns in the exponents when raising a power of 10 to a power. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.
| expression | expanded | single power of 10 |
|---|---|---|
The goal of this discussion is to reinforce the exponent rule for raising powers of 10 to another power. Introduce and explain the visual display prepared earlier. This display should be kept visible to students throughout the remainder of the unit.
Continue to reinforce student understanding of this rule by writing out an expanded form of each expression when discussing the following questions:
In this lesson, we developed a rule for multiplying powers of 10: Multiplying powers of 10 corresponds to adding the exponents together.
To see this, multiply
This will work for other powers of 10, too. For example,
We also developed a rule for raising a power of 10 to another power: Taking a power of 10 and raising it to another power is the same as multiplying the exponents.
To understand this, take
This works for any power of 10 raised to another power. For example,
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