The Detention Buy-Out

Which administrator should each student buy-out from?

Ontario Grade Levels:
Common Core Grade Levels:

Shared By:
Kyle Pearce

Math Topic:
Model and solve problems involving the intersection of two straight lines.

Ontario Curriculum Alignment:

Common Core State Standard Alignment:

The Detention Buy-Out 3 Act Math Task Resources

Grab all the videos/images by clicking download below:

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Solving Linear Systems of Equations Real World Math Problem

Explore Solving Linear Relationships | Direct Partial Variation

Learning Goals:

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.

Act 1 – Introducing the Problem

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

Act 2 – Revealing More Information / Working It Out

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?

The Detention Buy-Out - Which administrator should they 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.

Desmos Activity Builder Activity

I recently created a Desmos Activity Builder Activity that you can use with this task. Try it out and/or use it in your class by clicking below:

Desmos Activity

Act 3 – Consolidating the Task

Solving Systems of Linear Equations Graphically Once 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 4 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.

Additional Versions of The Detention Buy-Out

Some teachers have taken this problem into their own hands by creating their own version of the detention buy-out. If you have your own version you’d like to add to this post, please let me know via the contact button. Here’s one that was shared by Sabrina Crawford:

Another shared by Shelley Deering (@DeeringWMS):

Here’s a resource page created by Jon Orr and the peeps from Lambton-Kent District School Board:

Whatcha Thinking? - Detention Buy-Out Resources

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