### Using Linear Relations to Model a Car Commute

The following lesson resource material provides **Real World Math Problems** that were created with the Grade 9 Ontario Mathematics Curriculum in mind. A video and series of screenshots from a smartphone were taken by a passenger as we attempted to best capture **The Drive to Work**. On this particular day, we were running late and thought we might be able to inspire some deep thinking with the questions that could be posed to our grade 9 students.

### Math Topics Related To This Activity:

# Act 1 – Introduce The Problem

Students will watch a 1-minute real world math video **The Drive to Work**. In the video, students view a section of the drive to work from the perspective of passengers in the car.

**Watch the Video Below:**

Question that will likely come up through class discussion:

How fast is the car going?

In Dan Meyer “3 Act” fashion, a great start to the discussion might be to have students make predictions:

- What is a number that is too low?
- What is a number that is too high?
- What number do you feel best represents the speed?

Discussion about whether the car is going at a consistent speed, what road we are travelling on and other interesting pieces of information may be asked. For the record, cruise control was used where possible and the road was County Road 42 outside of Windsor, Ontario, Canada.

# Act 2 – Reveal Some Information

After students have made their predictions, the teacher can then begin to reveal more information about the trip.

Students can now analyse this photo and have a discussion with their table group to see what questions they have and what information they will need to answer their question(s):

Some questions students may have:

- Where did the car start?
- Was the car travelling at a consistent speed?
- What is the speed limit of that section of road?

Other questions are also possible.

In this particular situation, cruise control was being used at the starting point on the map to the end point.

**Reveal More Information:**

Assuming students determine that the time and distance travelled at the start and end point of the map are important, you can reveal the following:

In my classroom, I have students use their own method to find the distance travelled at the end point on the map. Since we have a paperless iPad classroom, I have students use Google Maps or similar to find the distance travelled at the end point.

**Scaffolding:**

If your students are having trouble getting started, or if you want to promote the use of finding a linear equation using two points, then you may want to offer the following visual as a starting point. In my classroom, students are able to use any method they see fit and we then share out over the Apple TV via AirPlay on our iPads to compare solutions and attempt to find the most convenient solution for our bag of math tricks.

Something else students might not consider is the fact that the timer shows minutes and seconds travelled. This could provide for a great teachable moment when student answers differ and may provide for a great classroom discussion about units and conversion.

### Consolidation:

Students may then work together to form their solution to the problem.

In some cases, if students have had experience working with different representations of linear equations, you can ask them to show their solution in multiple ways such as the following:

# Act 3 – Share the Solution

### Download a PDF Worksheet to Help Guide Your Lesson:

##### Suitable for the Following Ontario Mathematics Curriculum Courses:

- Grade 6 Mathematics
- Grade 7 Mathematics
- Grade 8 Mathematics
- Grade 9 Mathematics
- MAT1L – Locally Developed Mathematics, 9
- MFM1P – Foundations of Mathematics, 9
- MPM1D – Principles of Mathematics, 9

## 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.

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