# ﻿Tape Diagrams and Equations

Warmup

Label the length of the diagram in the applet below.

Activity #1

`Draw a Tape Diagram to Represent an Equation.  `

A tape diagram is a pictorial model that represents a mathematical relationship. They are commonly used with word problems, but they can also be used to solve equations. In this activity, you are going to solve simple algebraic equation using tape diagrams.

• Study the following equations and draw tape diagrams to represent them. Click inside the box “Show Controls”, if you need help with the diagrams.

(i.) 4 + 3 = 7

(ii.) 4 · 3 = 12

(iii.) 18 = 3 + x

Find the value of the unknown that makes 18 = 3 + x true.

(iv.) 18 = 3 · y

Find the value of the unknown that makes 18 = 3 · y true.

Activity #2

` Draw a Tape Diagram to Represent an Equation.`

In this activity, you are going to solve more simple algebraic equations using tape diagrams. Continue to work on these exercises in order to master the concept.

• Study the following equations and use the applet provided to draw a tape diagrams representing each equation.

(1.) x + 4 = 17.

(i.) Which part of the diagram shows the quantity x? What about 4? What about 17?

(ii.) How does the diagram show that x + 4 has the same value as 17?

(2.) x + 9 = 16.

Find the unknown value of x + 9 = 16.

(3.) 4 · x = 28.

Find the unknown value of 4 · x = 28.

Activity #3

` Exercise Questions on Tape Diagram.`

In this activity you are going to match equations with tape diagrams. This is a demonstration of your understanding of tape diagrams and equations.

• Solve the following by matching the equations to the tape diagrams.

Study this tape diagram.

Study this is a tape diagram.

Study this is a tape diagram.

Study this is a tape diagram.

Challenge #1

Label the length of the diagram in the applet below.

Challenge #2

Diego is trying to find the value of x in 5 ∙ x = 35. He draws this diagram but is not certain how to proceed. Complete the tape diagram so it represents the equation 5 ∙ x = 35.

What is the value of ?

Challenge #3

Quiz Time