This is a problem I got from illustrative mathematics and it involves constant speed. They learned about constant speed in a previous lesson. I’m bringing it back for 2 reasons. First, it is a review of a concept already learned and second, when the students start working on their road trip I will be having them calculate their speed and how long it will take them to get to their destination.
The students will be looking at scale ratios and reading them to get a better understanding of their meaning. For example: 1:2 means for every 1 unit in the model is 2 units for the actual. Students need to know that in a scale ratio it is always set up model to actual.
This will be quick, but I wanted students to continue using their ratio language and apply it more specifically to scale drawings. I will be having the students write out how they say it in their notes to use as a resource, if needed, later.
In this section, there are several scale drawing problems that the students will be solving. I’m going to ask them if there is a model we can use to show our work? (ratio table). We are going to use the ratio table to help up set up and solve these types of problems (SMP 4)
Students typically struggle with where to put the numbers. As I model the problems, I alwasy write M over A (like a fraction) off to the side. I express to students that this will help them to figure out where the numbers go. Information about the model goes on top and information about the actual goes on the bottom. Labeling is key when using ratios (SMP 6)
The students will be creating their own road trip. They need to stop at 3 different places before their final destination. Additionally, they will be calculating how long it will take them to get to each destination given their travelling speed. Students will get a copy of the US map, scale, ruler, and speeds to each of their locations.
This project exemplifies MP1 because students will need to find their own entry point and push to find their own solution.
For students that are struggling, they can be given less destinations.
This activity had high student interest. They really enjoyed finding places to go, finding how many miles and finding how long it would take them.
A few pointers for this activity:
1. If using the map I included, use 4cm = 500 miles as the scale. It's too difficult to use exact measurements.
2. Students used ratio table to set up and solve and this worked out beautifully
3. When calculating the time it will take, I let the students use an approximate time. For example, if they were calculating how long it would take to while travelling 55mph, then their miles needed to be less than 55 miles from their actual distance. If they were travelling 60 mph, then they would need to be less than 60 miles from their actual distance.
We had a really great discussion on why this needed to be the way. We talked about the fact that we had the constant speed (unit rate) and it could be used to make our time calculations more precise.
I’m going to have students do a connect 3: Ratios, Constant Speed, Scale Drawings. For each line they need to make a connection and in the middle they need to complete a short summary of these 3 concepts and how they are related.