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6-8 Accelerated 6 Unit 4 Lesson 7

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•Accelerated 6 Accelerated 7

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 4, Lesson 7

Equal and Equivalent

Accelerated 6

Practice

Problem 1

Draw tape diagrams that represent \(x + 3\) and \(2x\) when \(x\) is 1.
Draw tape diagrams that represent \(x+3\) and \(2x\) when \(x\) is 2.
Draw tape diagrams that represent \(x+3\) and \(2x\) when \(x\) is 3.
Draw tape diagrams that represent \(x+3\) and \(2x\) when \(x\) is 4.
When are \(x+3\) and \(2x\) equal? When are they not equal? Use your diagrams to explain.

Lesson 7 Resources

Student Materials

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Problem 2

Do \(4x\) and \(15+x\) have the same value when \(x\) is 5?
Are \(4x\) and \(15+x\) equivalent expressions? Explain your reasoning.

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Problem 3

Show that \(2b + b\) and \(3b\) have the same value when \(b\) is 1, 2, and 3.
Do \(2b +b\) and \(3b\) have the same value for all values of \(b\)? Explain your reasoning.
Are \(2b+b\) and \(3b\) equivalent expressions?

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Problem 4

ForLesson 5: Represent Situations with Equations

80% of \(x\) is equal to 100.

Write an equation that shows the relationship of 80%, \(x\), and 100.
Use your equation to find the value of \(x\).

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Problem 5

ForLesson 5: Represent Situations with Equations

For each situation:

Choose an equation that represents it.
Solve the equation.
Explain what the variable and solution mean in the situation.

Jada’s dog was \(5\frac{1}{2}\) inches tall when it was a puppy. Now her dog is \(14\frac{1}{2}\) inches tall. How much did Jada’s dog grow?
- \(x+5\frac12= 14\frac12\)
- \(x=5\frac12+14\frac12\)
- \(5\frac12 \boldcdot x=14\frac12\)
Lin picked \(9 \frac{3}{4}\) pounds of apples, which was 3 times the weight of the apples Andre picked. How many pounds of apples did Andre pick?
- \(p+3= 9\frac34\)
- \(9\frac34=3p\)
- \(9\frac34 \boldcdot p=3\)

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Problem 6

ForLesson 17: Calculating Products of Decimals

Find the value of each product.

\((2.3) \boldcdot (1.4)\)
\((1.72) \boldcdot (2.6)\)
\((18.2) \boldcdot (0.2)\)
\(15 \boldcdot (1.2)\)

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Problem 7

ForLesson 20: Dividing a Decimal by a Decimal

Calculate \(141.75 \div 2.5\) using a method of your choice. Show or explain your reasoning.

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