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6-8 Accelerated 7 Unit 3 Lesson 6

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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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Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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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 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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Accelerated 6
Accelerated 7

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Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
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Lesson 6
Lesson 7
Lesson 8
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Curriculum

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

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Unit 3, Lesson 6

Reasoning about Solving Equations (Part 1)

Accelerated 7

Practice

Problem 1

Explain how the parts of the balanced hanger diagram compare to the parts of the equation.

\(7=2x+3\)

Balanced hanger, left side, 7 blue squares, right side, 2 red circles, 3 blue squares.

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Lesson 6 Resources

Student Materials

Problem 2

For the hanger diagram shown:

Write an equation with the variable \(x\) to represent the relationship.
Draw more hanger diagrams or describe how you would change the given diagram to show each step you would take to find the value of \(x\). Explain your reasoning.
Write an equation to represent each hanger diagram you drew or each change you would make to the given diagram. Explain how each equation matches its diagram.

Balanced hanger, left side, 5 circles labeled x, 1 square labeled 2, right side, rectangle labeled 17.

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Problem 3

ForLesson 4: Reasoning about Equations and Tape Diagrams (Part 1)

Match each story to an equation.

A stack of nested paper cups is 8 inches tall. The first cup in the stack is 4 inches tall, and each of the other cups in the stack adds \(\frac14\) inch to the height of the stack.
A baker uses 4 cups of flour. She uses \(\frac14\) cup to flour the counters and the rest to make 8 identical muffins.
Elena has an 8-foot piece of ribbon. She cuts off a piece that is \(\frac14\) of a foot long and cuts the remainder into 4 pieces of equal length.

\(\frac14 + 4x=8\)
\(4+\frac14x=8\)
\(8x +\frac14=4\)

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Problem 4

from an earlier course

In each equation, the ? represents an operation. Which operation makes each equation true?

\(48 \text{ ? } (\text-8) = (\text-6)\)
\((\text-40) \text{ ? } 8 = (\text-5)\)
\(12 \text{ ? } (\text-2) = 14\)
\(18 \text{ ? } (\text-12) = 6\)
\(18 \text{ ? } (\text-20) = \text-2\)
\(22 \text{ ? } (\text-0.5) = \text-11\)

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Problem 5

ForLesson 12: Similarity

Describe a sequence of rotations, reflections, translations, and dilations that show one figure is similar to the other. Be sure to include the distance and direction of a translation, a line of reflection, the center and angle of a rotation, and the center and scale factor of a dilation.

polar coordinate plane with center at A. quadrilateral BCDE and quadrilateral QRST graphed.

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