Representing Subtraction

5 min

Teacher Prep
Setup
1 minute of quiet work time followed by a whole-class discussion.

Narrative

In this Warm-up, students make use of the relationship between addition and subtraction to write related equations (MP7). 

Monitor for any students who create a number line diagram to help them generate equations that express the same relationship in a different way.

Launch

Give students 1 minute of quiet work time. Remind students that each new equation must include only the numbers in the original equation.

Student Task

Consider the equation 2+3=52+3=5. Here are some more equations that express the same relationship in a different way:

3+2=53 + 2 = 5

5−3=25 - 3 = 2

5−2=35 - 2 = 3

For each equation, write two more equations that use the same numbers and express the same relationship in a different way.

  1. 9+(-1)=89+ (\text- 1)= 8
  2. -11+x=7\text- 11+ x= 7

Sample Response

Sample response:

  1. For 9+(-1)=89+ (\text- 1)= 8:
    • -1+9=8\text- 1 + 9 = 8
    • 8−9= -18 - 9 = \text- 1
    • 8− (-1)=98 - (\text- 1) = 9
  2. For -11+x=7\text- 11+ x= 7:
    • x+(-11)=7x + (\text- 11) = 7
    • 7−x= -117 - x = \text- 11
    • 7−(-11)=x7 - (\text- 11) = x
Activity Synthesis (Teacher Notes)

The purpose of this discussion is for students to share their responses and reasoning. Invite students to share their additional equations for each given equation. Display any number lines created by students for all to see. Use the number line to facilitate connections between addition equations and related subtraction equations.

The key ideas for students are that every addition equation has related subtraction equations and every subtraction equation has related addition equations. 

Anticipated Misconceptions

If students struggle to come up with other equations, encourage them to represent the relationship using a number line diagram and then think about other operations they can use to show the same relationship with the same numbers.

Standards
Building On
  • 1.OA.4·Understand subtraction as an unknown-addend problem. <em>For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.</em>
  • 1.OA.B.4·Understand subtraction as an unknown-addend problem. <span>For example, subtract <span class="math">\(10 - 8\)</span> by finding the number that makes 10 when added to 8.</span>
Building Toward
  • 7.NS.1.c·Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
  • 7.NS.A.1.c·Understand subtraction of rational numbers as adding the additive inverse, <span class="math">\(p - q = p + (-q)\)</span>. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

15 min

15 min