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.
-
5(x+1)=20
-
5x+1=20
Problem 2
Select all the equations that match the tape diagram.
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?
Problem 4
Figure 2 is a scaled copy of Figure 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?
- 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?
- What is the scale factor that takes Figure 1 to Figure 2?
- 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?