Exploring Linear Relationships – The Detention Buy-Out

Using iPads in Math as a Tool for Problem Solving

Explore Solving Linear Relationships | Direct Partial Variation

Success Criteria:

After our exploring linear relationships lesson, I will be able to:

  • analyse a real-world situation and make a connection to the prior knowledge I have learned throughout this math course,
  • deconstruct the problem and use prior knowledge to create a solution to the problem,
  • and, show adequate steps to clearly demonstrate my understanding.

Minds On:

Students will watch a video called The Detention Buy-Out. In the video, three administrators from Tecumseh Vista Academy K-12 School are interviewed and propose individual options for students to avoid serving detentions by paying the administrators according to their buy-out offers.

See the Exploring Linear Relationships – Detention Buy-Out video below:

Solve Linear Systems of Equations | Substitution & Elimination


Exploring Linear Relationships - The Detention Buy-Out

Click Image Above to Download PDF

Students will then be split into groups of 2 or 3, arranged by the teacher, to determine which administrator should each student buy-out from.

Encourage students to show their solution in any way they would like or you can assign certain methods to particular groups.

The exploring linear relationships problem can be solved in a number of ways, including:

  • Trial and error / guess and check (grades 6-10)
  • Table of values (grades 6-9)
  • Graphing to find point of intersection (grades 9-10)
  • Creating equations and substitute different values of x (grades 9-10)
  • Solving a system of equations using elimination (grade 10)
  • Solving the system of equations using substitution (grade 10)

Graphing Linear Relationships Equations | Solving Graphically

Students can solve the problem using iPads in neu.Annotate+ or GoodNotes – Notes & PDF.


Solving Systems of Linear Equations GraphicallyOnce groups have solved the problem, they will take screenshots of different parts of their solution in the PDF annotation app they used and import the photos into Explain Everything to create a video that allows the students to communicate their understanding. Once they have completed their video, they will share over Apple TV with the rest of the class.

Alternatively, students can share their solutions directly from an annotation app like neu.Annotate+ PDF or GoodNotes – Notes & PDF over the Apple TV.

If you do not have technology in the classroom, you can also have students solve the problems on chart paper and present them from the front of the room to explore the different methods of solving the problem.

Additionally, the teacher can give another problem involving linear relationships as a consolidation activity for students to complete in the last portion of class or on their own time.

Suitable for the Following Ontario Mathematics Curriculum Courses:


Download our Complete Guide to successfully implementing our Make Math Moments 3-Part Framework in your math class!
Make Math Moments 3-Part Framework Guidebook

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About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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