Adding and Subtracting to Solve Problems

5 min

Teacher Prep
Setup
Students in groups of 2. 30 seconds of quiet think time, then signal when they have an answer and a strategy for the first question. Discuss with a partner. Whole class discussion of the first question. Repeat with the second question. Then give students 30 seconds of quiet think time and ask them to give a signal when they have an answer for the second question. Then have them discuss their reasoning with a partner.

Narrative

In this Warm-up, students reason about the sign of the solution to an equation which has positive and negative rational numbers. They also find expressions that can be used to solve the given equation.

Launch

Arrange students in groups of 2. Give students 30 seconds of quiet think time, and ask them to give a signal when they have an answer and a strategy for the first question. Then have them discuss their reasoning with a partner. Ask for an explanation, and then ask if everyone agrees with that reasoning.

Then give students 30 seconds of quiet think time, and ask them to give a signal when they have an answer for the second question. Then have them discuss their reasoning with a partner.

Student Task

Complete the following problems without computing:

  1. Is the solution to -2.7+x=-3.5\text-2.7 + x = \text- 3.5 positive or negative?

  2. Select all the expressions that are solutions to -2.7+x=-3.5\text-2.7 + x = \text- 3.5.

    1. -3.5+2.7\text-3.5 + 2.7
    2. 3.5−2.73.5 - 2.7
    3. -3.5−(-2.7)\text-3.5 - (\text-2.7)
    4. -3.5−2.7\text-3.5 - 2.7

Sample Response

  1. negative
  2. -3.5+2.7\text-3.5 + 2.7, -3.5−(-2.7)\text-3.5 - (\text-2.7)
Activity Synthesis (Teacher Notes)

Poll the class for which expressions they chose for the second question. Discuss until everyone is in agreement about the answer to the second question.

Standards
Building On
  • 7.NS.1·Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
  • 7.NS.A.1·Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Building Toward
  • 7.EE.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
  • 7.EE.B.4·Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

10 min

15 min