Piling Up Systems of Linear Equations

How much does each weigh?


No Expectations/Standards Selected
Ontario Alignment By Grade
Ontario Alignment By Overall Expectation
CCSS Alignment By Grade
CCSS Alignment By Standard

Contextual Tasks for Practicing Solving Systems of Linear Equations

There has been a lot of requests for more contextual and/or 3 act math tasks related to solving systems of linear equations when I work with teachers. A big realization I’ve come to this past year is that making students curious with contextual tasks doesn’t necessarily have to involve a relevant question. Dan Meyer has discussed it multiple times (like here and here), but it still takes a lot of reflection to start identifying what is important when trying to hook your students in.

Continuing the series of Tech Weight and the Tech Weight Sequel, we take the same context of weighing random items to give us some additional practice. You’ll quickly notice that these tasks are definitely contrived, but I still find tasks like these useful if introduced as a challenge to my students. Even though they REALLY don’t care how much each item weighs, they DO enjoy the challenge of solving the problem. The media and 3 act format gives them an easy entry into the task. After allowing students to intuitively solve simple systems of linear equations like in the Counting Candy Sequel or the Tech Weight Sequel, you can use these tasks as a way to practice substitution and/or elimination as a way to solve algebraically.

Task 1: Sticky Situation

Act 1 – Introduce the Task

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 – Reveal Some Information

Show students scene 1.

Alternatively, you can show students the following images:

The Weight of 4 bottles of glue and 5 glue sticks

The weight of 4 bottles of glue and 5 glue sticks is 679 grams.

Sticky Situation - Act 2 - screenshot1

The Weight of 3 bottles of glue and 12 glue sticks

The Weight of 3 bottles of glue and 12 glue sticks is 680 grams.

Sticky Situation - Act 2 - screenshot2

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

Act 3 – Reveal Solution

Show students the solution video.

Alternatively, you can show students these images:

The weight of one glue bottle is 145 grams:

Sticky Situation - Act 3 - weight of glue bottle

The weight of one glue stick is 21 grams:

Sticky Situation - Act 3 - weight of glue stick

At this point, your students should notice that their answers are close to these weights, but not exact.

Why might that be?

What extraneous variables could influence the results?


Task 2: Write N’ Erase

Act 1 – Introduce The Problem

Show students this video.

They will already know the question, so move on to Act 2…

Act 2 – Reveal Some Information

Show students scene 1.

Alternatively, you can show students the following images:

The weight of 13 pens and 5 packs of correction tape

The weight of 13 pens and 5 packs of correction tape is 166 grams:

Write N Erase - Act 2 - equation 1

The weight of 6 pens and 3 packs of correction tape

The weight of 6 pens and 3 packs of correction tape is 88 grams:

Write N Erase - Act 2 - equation 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:

The weight of one pen is 4 grams:

Write N Erase - Act 3 - Pen Weight

The weight of one package of correction tape is 20 grams:

Write N Erase - Act 3 - Correction Tape Weight

Again, the actual weight may differ from what students found algebraically.


Task 3: Paper Weights

Act 1 – Introduce The Problem

I find that sequel tasks like these often don’t require the “hook” as we’ve already engaged the learners to come towards the math. This task is simply additional practice prior to moving on to more traditional word problems and/or abstract problems. Thus, there is no act 1 video for this extension task.

Act 2 – Reveal Some Information

Show students scene 1.

Alternatively, you can show students the following images:

The weight of 5 large notepads and 7 small notepads

The weight of 5 large notepads and 7 small notepads is 882 grams:

Paper Weights - Act 2 - equation 1

The weight of 3 large notepads and 5 small notepads

The weight of 3 large notepads and 5 small notepads is 563 grams:

Paper Weights - Act 2 - equation 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:

The weight of one large notepad is 116 grams:

Paper Weights - Act 3 - large pad

The weight of one small notepad is 43 grams:

Paper Weights - Act 3 - small pad

Again, the actual weight may differ from what students found algebraically.


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





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




Search More 3 Act Math Tasks

Grade 1 [Number Sense and Numeration - NS1, Number Sense and Numeration - NS3]

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

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

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

Grade 5 [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 - 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]

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 - 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 - QR3]

MHF4U [Exponential and Logarithmic Functions - EL2, Exponential and Logarithmic Functions - EL3]

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

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

Subscribe