Solutions to Linear Equations

5 min

Teacher Prep
Setup
Ensure students know what is meant by the shaded region. Display figures. 1 minute of quiet think time, followed by a whole-class discussion.

Narrative

The purpose of this activity is to activate student thinking around expressions and equations with two variables by considering the cost of different combinations of 2 fruits. This will be useful later when students interpret the meaning of variables in context and reason about systems of linear equations.

Launch

Begin by asking students to share their favorite fruits. If possible, record student responses for all to see. If necessary, explain that sometimes fruit is priced by weight and sometimes it is priced based on the number of items. 

Give students 2 minutes of quiet work time followed by a partner then whole-class discussion.

Student Task

At the market, avocados cost $1 each and pineapples cost $2 each. Find the cost of:

  1. ​6 avocados and 3 pineapples
  2. 4 avocados and 4 pineapples
  3. 5 avocados and 4 pineapples
  4. 8 avocados and 2 pineapples

Sample Response

  1. $12

  2. $12

  3. $13

  4. $12

Activity Synthesis (Teacher Notes)

The goal of this discussion is to make sure students have a strategy for calculating the cost of different combinations of fruit. Begin by inviting students to share their strategies and record them for all to see. Consider asking:

  • “What do all of these methods have in common?”

  • “What do you notice about the combinations of fruit that all cost the same total amount?”

  • “What do you notice about the one combination of fruit that cost a different amount than the others?”

Standards
Building On
  • 6.G.1·Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • 6.G.A.1·Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

10 min

20 min