Writing Equivalent Equations

5 min

Teacher Prep
Setup
Display the problem for all to see and give 1 minute of quiet think time. Ask students to give a signal when they have noticed or wondered about something. Follow with whole-class discussion.

Narrative

In this activity, students create equivalent expressions to given expressions. Students are encouraged to be creative in their answers, but should ensure that the new expressions are equivalent to the original. This work prepares students for writing equivalent equations in later activities.

Launch

Arrange students in groups of 2. 

Display for all to see: 100,1001,98+1+1,20031100, 100 \boldcdot 1, 98+1+1, \frac{200}{3-1}. Ask students what they notice. Move to the task when students notice that all the expressions are equivalent to 100. 

For the task, encourage students to be creative, but check with their partner that their expressions are still equivalent to the original. Tell students to try to give examples that they think nobody else in the class has written.

Student Task

Write as many equivalent expressions for each as you have time.

  1. 10
  2. 2x2x

Sample Response

Sample responses:

  1. 9+1,10+0,122,302+1,44329+1, 10+0, 12-2, \frac{30}{2+1}, 4\boldcdot 4 - 3 \boldcdot 2
  2. x2,10x8x,x+x,3+2x3,4020xx \boldcdot 2, 10x - 8x, x+ x, 3 + 2x - 3, \frac{40}{20}x
Activity Synthesis (Teacher Notes)

Invite 3–5 students to share examples that they have written for each expression. After each example, ask if other students can explain how it is equivalent to the original.

Standards
Building On
  • 8.EE.7·Solve linear equations in one variable.
  • 8.EE.C.7·Solve linear equations in one variable.
Addressing
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
  • 7.EE.A·Use properties of operations to generate equivalent expressions.

15 min

15 min