Lesson 3

Reasoning about Equations with Tape Diagrams

Let’s see how equations can describe tape diagrams.

Problem 1

Draw a tape diagram to match each equation.

  1. 5(x+1)=20

  2. 5x+1=20

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

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?

(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?
(From Unit 2, Lesson 3.)