##### Ontario Alignment By Overall Expectation

## Solving Linear Systems of Equations Real World Math Problem

#### 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:

## Act 2 – Revealing More Information / Working It Out

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
(grades 9-10)**x** - Solving a system of equations using elimination (grade 10)
- Solving the system of equations using substitution (grade 10)

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:

## Act 3 – Consolidating the Task

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.

## Download the Resources

You can download the:

- 3 Act Video
- Lesson Cheat Sheet
- Task Consolidation Template*

*Please note that I recommend allowing students to solve the problem through inquiry prior to using the task consolidation template. Let them inquire, tinker and struggle. When you’re ready to consolidate the task, then the template can be useful. Hopefully, students have come up with some of the models that are on the template!

## 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):

http://youtu.be/XawFxAzTl04

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

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

## Share With Your Learning Community:

## 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.

Access Other Real World Math Tasks

## Search More 3 Act Math Tasks

Grade 2 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3]

Grade 3 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3]

Grade 4 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 5 [Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 6 [Data Management and Probability - DP3, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 7 [Data Management and Probability - DP3, Geometry and Spatial Sense - GS1, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 8 [Data Management and Probability - DP1, Data Management and Probability - DP3, Geometry and Spatial Sense - GS2, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

MAP4C [Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

MAT1LMAT2LMBF3C [Data Management - DM1, Data Management - DM2, Geometry and Trigonometry - GT1, Geometry and Trigonometry - GT2, Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

MCF3M [Exponential Functions - EF2, Quadratic Functions - QF1, Quadratic Functions - QF2, Quadratic Functions - QF3, Trigonometric Functions - TF1, Trigonometric Functions - TF3]

MCR3U [Characteristics of Functions - CF1, Characteristics of Functions - CF2, Exponential Functions - EF2, Exponential Functions - EF3, Trigonometric Functions - TF3]

MCT4C [Exponential Functions - EF1, Trigonometric Functions - TF3]

MCV4U [Derivatives and Their Applications - DA2]

MDM4U [Counting and Probability - CP2, Organization of Data For Analysis - DA2, Probability Distributions - PD1, Statistical Analysis - SA1, Statistical Analysis - SA2]

MEL4EMFM1P [Linear Relations - LR1, Linear Relations - LR2, Linear Relations - LR3, Linear Relations - LR4, Measurement and Geometry - MG1, Measurement and Geometry - MG2, Measurement and Geometry - MG3, Number Sense and Algebra - NA1, Number Sense and Algebra - NA2]

MFM2P [Measurement and Trigonometry - MT1, Measurement and Trigonometry - MT2, Measurement and Trigonometry - MT3, Modelling Linear Relations - LR1, Modelling Linear Relations - LR2, Modelling Linear Relations - LR3, Quadratic Relations in y = ax^2 + bx + c Form - QR1, Quadratic Relations in y = ax^2 + bx + c Form - QR2, Quadratic Relations in y = ax^2 + bx + c Form - QR3]

MHF4U [Characteristics of Functions - CF3, Exponential and Logarithmic Functions - EL2, Exponential and Logarithmic Functions - EL3]

MPM1D [AG3, Analytic Geometry - AG1, Analytic Geometry - AG2, LR1, LR2, LR3, MG1, MG2, MG3, NA1, Number Sense and Algebra - NA2]

MPM2D [AG1, AG2, AG3, QR2, Quadratic Relations - QR3, Quadratic Relations - QR4, T2, T3]

Functions [F-BF.1, F-BF.3, F-IF.4, F-LE.1, F-LE.2, F-LE.3, F-TF.5]

Geometry [G-C.5, G-C.8, G-C.9, G-GMD.3, G-GMD.4, G-GPE.4, G-GPE.5, G-GPE.7, G-MG.1, G-MG.2, G-SRT.11]

Grade 1 [1.NBT.4, 1.OA.1]

Grade 2 [2.NBT.5, 2.OA.2]

Grade 3 [3.NBT.2, 3.NF.1, 3.NF.2, 3.NF.3, 3.OA.1, 3.OA.5, 3.OA.9]

Grade 4 [4-MD.3, 4.MD.1, 4.MD.2, 4.NBT.6, 4.NF.3, 4.NF.5, 4.NF.6, 4.OA.1]

Grade 5 [5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.NBT.2, 5.NBT.3, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.5, 5.OA.1, 5.OA.2, 5.OA.3]

Grade 6 [6.EE.1, 6.EE.2, 6.EE.5, 6.EE.6, 6.EE.7, 6.G.1, 6.G.2, 6.NS.1, 6.NS.3, 6.NS.6, 6.RP.1, 6.RP.2, 6.RP.3]

Grade 7 [7.EE.3, 7.EE.4, 7.G.3, 7.G.4, 7.G.6, 7.RP.1, 7.RP.3, 7.SP.2, 7.SP.5, 7.SP.6]

Grade 8 [8.EE.1, 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8, 8.F.2, 8.F.3, 8.F.4, 8.F.5, 8.G.5, 8.G.6, 8.G.7, 8.G.9, 8.SP.1]

Practice [MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]

Statistics & Probability [S-ID.6, S-MD.4]