Read more about the purpose of the MAP Classroom Challenges

Modeling Situations With Linear Equations

Mathematical goals

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students:
  • Explore relationships between variables in everyday situations.
  • Find unknown values from known values.
  • Find relationships between pairs of unknowns, and express these as tables and graphs.
  • Find general relationships between several variables, and express these in different ways by rearranging formulae.



This activity links several aspects of algebra. A situation is presented, and relationships between the variables are explored in depth. Letters are used to represent unknowns, generalized numbers, and variables. The problem-solving context gives you a chance to assess how well students are able to combine and apply different aspects of their algebra knowledge and skills.

  • Before the lesson, students work individually on the assessment task The Guitar Class. You then review their work and create questions for students to answer at the end of the lesson, to help them to improve their solutions.
  • During the lesson, students translate between words, algebraic formulae, tables, and graphs in an interactive whole-class discussion. The intention is that you focus students on making sense of the context using algebra, rather than just the routine use of techniques and skills. Students then work in pairs to graph the relationship between two of the variables. In a final whole-class discussion, students identify general formulae showing the relationships between all the variables.
  • At the end of the lesson, students review and improve their individual work.

Materials required

  • Each student will need two copies of the assessment task The Guitar Class, either the lesson task sheet Making and Selling Candles, or the lesson task sheet Rescue Helicopter, depending on the outcome of the assessment task, a mini-whiteboard, a pen, and an eraser.
  • Each pair of students will need a sheet of graph paper.
  • There are some projector resources to support whole-class discussion.

Time needed

15 minutes before the lesson and a one-hour lesson. All timings are approximate. Exact timings will depend on the needs of the class.

Mathematical Practices

This lesson involves a range of mathematical practices from the standards, with emphasis on:

Mathematical Content

This lesson asks students to select and apply mathematical content from across the grades, including the content standards:


Lesson (complete)

Projector Resources

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP Classroom Challenges for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to

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