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Proportional Reasoning / Linear Patterning Real World Math Problem
This 3 Act Math Task focuses on the rate of change for proportional reasoning / linear patterning / direct variation linear relations problem.
Act 1 – Introducing the Task
Getting Ready To Gas Up
In the first act, students watch a 30 second video that shows someone pre-paying for gas, selecting the grade of fuel and start pumping. You’ll notice in the video that the cost per litre (rate of change) is blanked out on the pump.
Students will then be asked:
What is the price of gas?
Here are a few images in the case you don’t want to load a video / have a slow connection:
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- Pump Prices Covered
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- Gas Price Hidden
Act 2 – Revealing Some Information
Watch The Fuel Pump Metre As We Fuel Up
We then watch the gas being pumped in fast-forward and then at about the $20 mark, we see an image showing the price for a specific amount of fuel in Litres.
Students can then use the given information to determine the cost of fuel.
At this point, you can also ask the students to determine:
How much will it cost to pump _____ litres of fuel into the tank?
In this video, the total number of litres is 38.264 L. Suggesting they find the cost for exactly 38 L might lead to a good discussion about why the video doesn’t stop at exactly 38 L to fill the tank, etc.
Act 3 – Watching The Solution
Students See The Gas Price
This video shows both the cost of gas on the pump and on the Petro Canada sign.
The video also show how much gas was pumped into my 2011 Dodge Grand Caravan.
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- Pump Prices Showing
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- Gas Price Showing
Extension Questions:
- Did the 38.264 L fill the tank from empty? If not, what fraction or percent of the tank did it fill?
- Is this scenario a direct or partial variation? How do you know?
- Will you ever encounter a partial variation when filling up your vehicle like we viewed in this video?
- What other 2-variable relationship could we explore in this situation other than Volume of Gas and Time?
Resources:
Grab them all here or, individually below:
Act 1 [VIDEO]
Act 2 [VIDEO]
Act 3 [VIDEO]
Presentation [KEYNOTE SLIDE DECK]
Here’s a quick look at what the slide deck looks like:
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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.
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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]
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Practice [MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]
Statistics & Probability [S-ID.6, S-MD.4]