Lesson 3

Reasoning about Equations with Tape Diagrams

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Problem 1

Draw a tape diagram to match each equation.

  1. \(5(x+1)=20\)

  2. \(5x+1=20\)

Solution

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Problem 2

Select all the equations that match the tape diagram.

Tape diagram, 1 part labeled 8, 6 parts labeled x, total 35.
A:

\(35=8+x+x+x+x+x+x\)

B:

\(35=8+6x\)

C:

\(6+8x=35\)

D:

\(6x+8=35\)

E:

\(6x+8x=35x\)

F:

\(35-8=6x\)

Solution

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Problem 3

Point \(B\) has coordinates \((\text-2,\text-5)\). After a translation 4 units down, a reflection across the \(y\)-axis, and a translation 6 units up, what are the coordinates of the image?

Solution

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(From Unit 1, Lesson 5.)

Problem 4

Figure 2 is a scaled copy of Figure 1.

Two 4-sided figures in a coordinate plane labeled Figure 1 and Figure 2.
  1. Identify the points in Figure 2 that correspond to the points \(A\) and \(C\) in Figure 1. Label them \(P\) and \(R\). What is the distance between \(P\) and \(R\)?
  2. Identify the points in Figure 1 that correspond to the points \(Q\) and \(S\) in Figure 2. Label them \(B\) and \(D\). What is the distance between \(B\) and \(D\)?
  3. What is the scale factor that takes Figure 1 to Figure 2?
  4. \(G\) and \(H\) are two points on Figure 1, but they are not shown. The distance between \(G\) and \(H\) is 1. What is the distance between the corresponding points on Figure 2?

Solution

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(From Unit 2, Lesson 3.)