Algebra's Reasoning with Equations and Inequalities

By Tara Mason on Apr 24, 2017

Student will learn about how we graph equations with two variables in order to compare which real life problem will work better.


In this lesson, student will compare two equations using a hypothetical bake sale. This lesson will help reinforce algebra lessons for students working in high school math courses. It will help TVIs practice using spreadsheets to reinforce math concepts and solving problems involving inequalities and reasoning using mathematics. 

1. Questions to get started:

  • What will work better, selling products at a bake sale at a lower price or higher price?
  • What are the factors to consider when developing a scenario for each possibility?
  • What would be the most effective route for your bake sale if you are hoping to raise $500, and why?

2. Using two spreadsheets, layout the problem in both ways, i.e., selling many items at lower price to reach $500 or selling higher priced items to reach $500. Have your student write a narrative for both sides and way the pros and cons for each scenario.

3. Ask your student what equation he/she could use to compare the two scenarios? What would be a quick way to explain this problem mathematically? Have your student set up the equation to represent both potential scenarios as if he/she was explaining it to someone much younger.

  • For example, if the bake sale was stocked with 20 cakes, x= price per piece and 30 bags of cookies at y=price per bag, the equation would be: 20(x)+30(y)=500. If your student wanted to see how to make their goal faster or how it would be effected by price or quantity of baked goods, he/she could adjust numbers of the above equation to come up with scenarios. This would be a mathematical way to plan supplies and fundraising using a bake sale.

4. Have your student graph two different scenarios using their spreadsheet and tactile graph paper.