Real World Mathematics Using Proportional Reasoning, Linear Equations & Measurement
In the Mowing the Lawn task, students will have an opportunity to utilize skills related to proportional reasoning, linear equations, and measurement after watching the information Mr. Pearce collected while mowing his lawn. This activity is geared for his grade 9 applied class, however it can be modified to suit many other levels.
Math Topics Related To This Activity:
- Proportional reasoning
- Linear equations
- Finding the area of composite figures.
Act 1: Introducing the Task
Some images to assist:
Problem To Be Solved:
How long will it take Mr. Pearce to mow his lawn?
Some prompts for students:
- What could we do to find low long it will take to Mow the Lawn?
- What information will be necessary to help us decide?
Act 2 – Providing the Details
Brand New Task Template File (PDF):
Click the image below or click here:
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- A view from the street…
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- Dimensions of the Yard from above.
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- Width of the Lawn Mower
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- Putting it all together…
Act 3 – Watch for the Solution
Consolidation & Discussion
I really like this problem because there really is no way for all students to come to the same answer. There are so many variables that affect the solution (how fast I’m walking, turns, objects in the way, etc.) that we can only expect students to come to reasonable answers. This is great because it helps students learn that math is about the process rather than the final answer.
For additional consolidation and practice, you could run this custom gameshow I created to complement this task:
Other Useful Resources:
Lisa Bejarano shared this Google Slides presentation that you can use right from your web-browser! Thanks, Lisa!
Mr. Connally (@MrConnallysMath) shared a PearDeck for this task. Thanks, Mr. Connally!
Silent Solution, Student Work, and Exemplars
I recently created a silent solution primarily to help teachers who are hoping to use the task, but aren’t exactly sure where the task can go. Here is a 1 minute silent solution video to assist with this:
Clayton Edwards shared some of his student work with the #MTbos:
ST dissertation 2/4 pgs on mowing.Needed lang. degree 2 decipher but was great http://t.co/DmVY4oobKD @MathletePearce pic.twitter.com/YCZF3rRHxn
— Dr. Clayton Edwards (@Doctor_Math) November 21, 2014
@MathletePearce Total time was 8 min 30 sec (it's there somewhere). Would have been closer w/ more time for turns… pic.twitter.com/plquJPdk7B
— Dr. Clayton Edwards (@Doctor_Math) November 21, 2014
Try out the problem and let me know how you like it below in the comment section!
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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]
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MCV4U [Derivatives and Their Applications - DA2]
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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]
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Help! I love the problem and would like to try it but I can’t figure out how the length of the unknown side is determined.
Hi Dawn! Glad you find the problem useful! In order to find the length of the unknown side, we can use the 39 foot and 15 foot sections that are parallel to the unknown side and then use pythagorean theorem to find the unknown portion.
(see image below)
If Pythagorean Theorem isn’t an expectation for your course, then you might want to give students the full length of the missing side (65.6 ft).
If you’re curious to learn more about pythagorean theorem, you can check out this series of posts that makes visualizing pythagorean theorem much easier:
https://tapintoteenminds.com/2014/06/28/pythagorean-theorem-part1/
Let me know how it goes!
I see that this is aligned to your 9th grade class. Do you have any suggestions for how to modify this for a 7th grade math class?
I think you could definitely use this in grade 7. Maybe consider scaffolding a bit more and give a few more measurements around the perimeter of the yard.
Thank you for the awesome task! I made it into google slides, if anyone else finds it helpful: https://docs.google.com/presentation/d/1qBAyn7TKPUdYMnjMjed-wKBeJDGDUB4jasn5R8Ebvso/edit?usp=sharing
Hi Lisa! Thanks so much for the comment. So glad you found the task useful.
Thanks for sharing the Google Slides presentation. I’ll add it to the post content so folks can find it easily! 🙂
Hi Lisa,
Any suggestions for using this with 6th grade students after doing it with 7th grade students? Thanks!
Hi Kyle,
Love this activity but I’m unable to view your knowledge hook game to go with it. Do you have to have the paid version to view it?
Thanks for sharing your awesome resources!