The purpose of this Warm-up is to introduce the idea of raising a value with an exponent to another power. Computing the volume of a cube whose side lengths are themselves powers of 10 introduces the basic structure of a power to a power, which will lead to a general exponent rule in later activities.
Monitor for students who use different strategies, such as counting zeros to keep track of place value or writing 10,000 as 104 and then using exponent rules.
Give students 1–2 minutes of quiet work time followed by a brief whole-class discussion.
What is the volume of a giant cube that measures 10,000 km on each side? Be prepared to explain your reasoning.
1,000,000,000,000 km3. Sample reasoning: 104⋅104⋅104=10(4+4+4)=1012
The purpose of this discussion is to introduce the idea that 104⋅104⋅104=(104)3, which is equal to 1012 before this pattern is generalized in a following activity.
Invite previously identified students to share their strategies for computing the volume. If not brought up in students’ explanations, show students the strategy of re-writing 10,000 as a power of 10 and raising 104 to the power of 3. Ask students what patterns they notice between (104)3 and 1012. If students mention the strategy of counting zeros to multiply powers of 10, emphasize that the exponent describes the number of factors that are multiplied together and not necessarily the number of zeros.
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The purpose of this Warm-up is to introduce the idea of raising a value with an exponent to another power. Computing the volume of a cube whose side lengths are themselves powers of 10 introduces the basic structure of a power to a power, which will lead to a general exponent rule in later activities.
Monitor for students who use different strategies, such as counting zeros to keep track of place value or writing 10,000 as 104 and then using exponent rules.
Give students 1–2 minutes of quiet work time followed by a brief whole-class discussion.
What is the volume of a giant cube that measures 10,000 km on each side? Be prepared to explain your reasoning.
1,000,000,000,000 km3. Sample reasoning: 104⋅104⋅104=10(4+4+4)=1012
The purpose of this discussion is to introduce the idea that 104⋅104⋅104=(104)3, which is equal to 1012 before this pattern is generalized in a following activity.
Invite previously identified students to share their strategies for computing the volume. If not brought up in students’ explanations, show students the strategy of re-writing 10,000 as a power of 10 and raising 104 to the power of 3. Ask students what patterns they notice between (104)3 and 1012. If students mention the strategy of counting zeros to multiply powers of 10, emphasize that the exponent describes the number of factors that are multiplied together and not necessarily the number of zeros.