##### Ontario Alignment By Overall Expectation

## Patterning, Identifying Linear and Non-Linear Relations

Here’s an extension to the Placing Toothpicks task I posted recently. While the previous task hit on quite a few learning goals from the Grade 9 Academic and Applied courses in Ontario, this task will focus on identifying linear and non-linear relations in those same courses. It should be noted that this task could also be used in grade 10 courses for learning goals related to Quadratics. On my radar right now would be the following grade 9 academic expectations:

- LR2.02 – I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).
- AG1.01 – I can determine, through investigation, the characteristics that distinguish the equation of a linear relation (straight line) from the equations of non-linear relations (curves).

## Act 1 – What’s the Question?

Show the students the video below:

Can’t see the video? Click here.

At this point, I’d be asking my students what questions they have. You can write these questions on the board or if the kids have devices, use something collaborative like a Google Doc or Padlet wall.

## Act 2 – Revealing More Information

After some questions are shared out, you can show students the following video:

Can’t see the video? Click here.

As we did in the original Placing Toothpicks task, the question(s) I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

I would likely have students figure this out on their own, using any strategy and then consolidate the task. The following math task template might be a good option to consolidate student thinking:

## Act 3 – Reveal the Solutions

You can now let students see their solution in action!

### Act 3, Scene 1 – Figure 6 Solution

Can’t see the video? Click here.

### Act 3, Scene 2 – Figure 11 Solution

Can’t see the video? Click here.

Have you tried this task? How can we make it better? Share your thoughts in the comments below!

## 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!

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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.

Access Other Real World Math Tasks

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Grade 2 [2.B1.1, 2.B1.3, 2.B2.1, 2.B2.2, 2.B2.3, 2.B2.4, Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3]

Grade 3 [3.B1.5, 3.B2.1, 3.B2.3, 3.B2.7, Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3]

Grade 4 [4.B2.1, 4.B2.4, 4.E2.5, 4.E2.6, Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 5 [5.B1.7, 5.B2.9, 5.D1.3, 5.D1.6, 5.E2.6, 5.F1.2, 5.F1.5, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 6 [6.B2.12, 6.B2.9, 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 [7.B1.3, 7.B1.4, 7.B1.7, 7.B2.2, 7.B2.3, 7.C1.1, 7.C1.2, 7.C1.3, 7.C1.4, 7.D1.6, 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 [8.B1.4, 8.B2.5, 8.C1.1, 8.C1.2, 8.C1.3, 8.C1.4, 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]

Grade 9 [9.B3.5, 9.C3.1, 9.C3.2, 9.C3.3]

Kindergarten [k.15.1, k.15.10, k.15.2]

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, 1.OA.6, 1.OA.A.1, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5, 1.OA.C.6]

Grade 2 [2.NBT.5, 2.NBT.B.5, 2.NBT.B.8, 2.NBT.B.9, 2.OA.2, 2.OA.A.1, 2.OA.B.2]

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

Grade 5 [5.B1.7, 5.D1.3, 5.D1.6, 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.NS.B.3, 6.NS.C.6, 6.NS.C.7, 6.NS.C.8, 6.RP.1, 6.RP.2, 6.RP.3, 6.RP.A.1, 6.RP.A.2, 6.RP.A.3, 6.RP.A.3.C]

Grade 7 [7.EE.3, 7.EE.4, 7.EE.A.1, 7.G.3, 7.G.4, 7.G.6, 7.NS.A.1, 7.NS.A.2, 7.RP.1, 7.RP.3, 7.RP.A.2.B, 7.RP.A.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]

Grade 9Kindergarten [K.CC.A.1, K.NBT.A.1, K.OA.A.1, K.OA.A.2, K.OA.A.3]

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

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