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6-8 Accelerated 7 Unit 7 Lesson 7

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14

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IM K-5 Math
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Unit 7, Lesson 7

Combining Bases

Accelerated 7

Practice

Problem 1

Select all the true statements:

\(2^8 \boldcdot 2^9 = 2^{17}\)
\(8^2 \boldcdot 9^2 = 72^2\)
\(8^2 \boldcdot 9^2 = 72^4\)
\(2^8 \boldcdot 2^9 = 4^{17}\)
\(72^3 \boldcdot 72^2 = 72^5\)

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Lesson 7 Resources

Student Materials

Problem 2

Select all the expressions that have the same value as \(12^4\).

\((2 \boldcdot 6)^4\)
\(6^4 \boldcdot 2^4\)
\(3^2 \boldcdot 4^2\)
\(12^3 \boldcdot 12\)
\(4^4 \boldcdot 3^4\)

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Problem 3

Elena and Diego are evaluating \((3 \boldcdot 2)^3\).

Diego begins by evaluating \(3 \boldcdot 2\), which is 6. His next step is to find \(6^3\). Does Diego’s method work? Explain your reasoning.
Elena starts by writing \((3 \boldcdot 2)^3 = 3^3 \boldcdot 2^3\). Her next step is to multiply \(3^3\) by \(2^3\). Does Elena’s method work? Explain your reasoning.

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Problem 4

ForLesson 7: Linear Functions and Models

The cost of cheese at three stores is a function of the weight of the cheese. The cheese is not prepackaged, so a customer can buy any amount of cheese.

Store A sells the cheese for \(a\) dollars per pound.
Store B sells the same cheese for \(b\) dollars per pound, and a customer has a coupon for \$5 off the total purchase at that store.
Store C is an online store, selling the same cheese at \(c\) dollars per pound, but with a \$10 delivery fee.

This graph shows the total cost functions for stores A, B, and C after discounts are applied.

Coordinate plane, horizontal, weight of cheese in pounds, 0 to 12 by 2, vertical, cost in dollars.

Match Stores A, B, and C with Graphs \(j\), \(k\), and \(\ell\).
What is the price per pound for cheese at each store?
How many pounds of cheese does the coupon for Store B pay for?
At which store will the customer pay the lowest amount for a half a pound of cheese?
A customer wants to buy 5 pounds of cheese for a party. Which store has the lowest total purchase price for 5 pounds of cheese?
How many pounds would a customer need to order to make Store C a good option?

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