## Sparking Curiosity

Students will extend their use of patterning to connect different representations of linear relations. More specifically, students will be exposed to rates of change, calculating the slope of a linear relation, building linear equations, and solving linear equations.The purpose of this Task is:

- to help students develop an understanding of how various representations of linear relations are connected;
- create a linear equation given two points; and,
- solve linear equations.

## Intentionality

As is true for **any task**, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit.

The mathematical ideas we are trying to elicit when we use this task are connect various representations of linear relations, build linear equations from two or more points, and solve linear equations.

This will be achieved by first having students watch how the cost of renting a scooter is related to the time rented. You can learn more about the actual scooters and the pricing structure at lyft.com.

## Spark Curiosity

WARNING!!! Be sure to share with your students the importance of wearing Bike Helmets while riding; we certainly should have. We realize that you may not want to do this activity with your students as a result of our poor judgement.

Show students this video:

Ask students to engage in a **notice and wonder** protocol. ANYTHING and EVERYTHING that comes to mind is fair game.

Here’s some of the “everything and anything” students noticed and wondered on chart paper:

- I noticed that they were riding scooters;
- I noticed that they weren’t wearing helmets;
- I noticed the map;
- I noticed that the cost changes;
- I wonder where that was?
- I wonder how much the scooters cost?
- I wonder what the range means?

Now you can focus in on the big question of the task.

How much does it cost to ride the scooter the entire length of the outlined route?

We can now ask students to make a prediction using their estimation skills. Ensure you use the Too high and too low strategy. Ask them what is a wrong answer? How much would be too high? How much would be too low?

Students will also be uncomfortable here because the length of time of the trip or how the scooter charges customers has not been revealed yet. We encourage you to hold off on revealing these answers because it will build anticipation. Anticipation is what students need so they can start formulating a plan.

At this point, we want to give students the opportunity to improve their predictions by engaging in developing a problem solving strategy.

Ask them: If we are going to improve our predictions what information will we need? Have students share with an elbow partner before sharing this information with the entire class.

As students voice the information they wish to see.

Ask them: “And what would you do with that information if I gave it to you?”

Listen in very closely here. Their responses will give you allow you to assess their prior knowledge and also their thinking into solving this problem.

## Slowly Reveal More Information

Once students have asked for information reveal the information that you do have.

**Reveal a key fact:**

The cost of renting a scooter depends on the time the scooter has been rented for (You may want to reveal depending on your students’ prior knowledge that there is a flat fee to get on the scooter).

**Reveal** three snapshots showing the cost at different points in the trip. We include three here so that we can verify that the relationship between the cost and the time is linear.

**Reveal** the total cost of the entire trip.

With this information students can start to develop strategies to determine how much it will cost for a 15 minute and 9 second trip.

## Fuel Sense Making:

After consolidating the learning using student generated solution strategies and by extending their thinking intentionally, we can share what the actual cost of the trip was: