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:
\(358=6x\)
Problem 3
Point \(B\) has coordinates \((\text2,\text5)\). 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?