##### Ontario Alignment By Overall Expectation

## Introducing Systems of Equations With Context and Visuals

Recently, I’ve shared a few tasks related to linear relations with a push to explore multiple strategies including simple systems of equations. The intention of this post is to take students from working with partial variation linear relations to systems of linear equations.

While I’m excited to share the sequel to the Tech Weigh In task, I think it is important that you explore some of the following tasks prior to introducing systems of equations. Check these out with your students as suggested prerequisites prior to introducing the new tasks from this post:

- Stacking Paper – Proportional Reasoning / Direct Variation Linear Relations
- Stacking Paper Sequel – Partial Variation Linear Relation Given Slope and a Point
- Thick Stacks – Partial Variation Linear Relation Given Two Points
- Tech Weigh In – Direct Variation & Partial Variation Linear Relations
- Camera Case & Pads of Paper Weigh In – Partial Variation Linear Relation Given Two Points

# Act 1 – Introduce the Problem

Show students this video.

Ask students what they are wondering? What questions come to mind?

After discussing with a group, help direct the focus to the question:

How much does each weigh?

Students can make predictions and argue why they believe their guess is best.

# Act 2 – Give Some Information

## Act 2, Scene 1

Show students scene 1.

Alternatively, you can show students the following images:

### The Weight of 1 x laptop, 1 x iPad Mini, 1 x iPad 2

### The Weight of 1 x laptop, 1 x iPad Mini, 2 x iPad 2

### The Weight of 1 x laptop, 2 x iPad Mini, 1 x iPad 2

Now, students can try to solve this system intuitively, by graphing or algebraically with substitution or elimination.

# Act 3 – Show The Solution

Show students the solution video.

Alternatively, you can show students these images:

Try it out and let us know how it goes in the comments!

## DOWNLOAD THE COMPLETE GUIDE

Take the learning with you by **downloading the complete guide** that you can save and print to share with colleagues during your next **professional learning community** meeting or for your own independent learning!

## Share With Your Tribe:

## 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

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

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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 - 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 - 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 - 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.3, 3.OA.1, 3.OA.5, 3.OA.9]

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

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

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

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