MPM2D - Day 16: Taco Cart --> Distance Between Two Points

Today's goal was to come up with a way of finding the distance between two points. I didn't know if we would actually get to the distance formula itself, but wanted to make sure my students had a solid understanding of how we find these distances. We started  with Dan Meyer's Taco Cart problem:

I showed the Act I video (the link above will get you to all the videos) and before I could even ask, a student said "But we don't know how fast they are going." Great! What else do we need to know? Distances. Here you go:

And they got to work. There were good conversations about rates and the Pythagorean theorem. I asked who was on team Dan and who was on team Ben and Dan won by a landslide! At this point one student was about to leave the room and said "I'll wait because I need to know how this turns out!" - how cool is that? This is where we ended up:

with a little detour to talk about the relationship between speed, distance and time:

And then I played the Act III video (I won't spoil it for you).

My next question for my students was "How can we find the distance between two points if we know the coordinates of the points?". We started with what I thought was a straightforward example:

A number of students had no idea what to do until I suggested plotting the points. I think this was the first time I had seen them just sitting there, not knowing what to do and not trying something. I am trying to think of what I could have asked them to help them get going without explicitly saying plot the points... Any ideas? Once they had the points on a grid, they quickly saw that they could make a right triangle and then use the Pythagorean theorem.

They worked through two more examples after which I asked them if they could figure out a way of getting the distance without drawing the triangle.

A student solved (b) and you can see that the side lengths had been labelled as 6^2, etc. so we addressed that along the way. I let them struggle for a while, trying to find a relationship between the points and the side lengths before we consolidated that piece.

We then began to generalize but didn't complete that part so I will pick it up there tomorrow. Here is today's homework. One of the benefits of doing lagging homework is that there are only 3 questions asking for the distance between two points. So even if they create a right triangle for each one, it should not take too long. I am being mindful to keep homework to one page and to ask meaningful questions, not the same one 20 times over.

I wanted to share the nice email that I received from the parent of one of the students in this class:

This is one reason that I wanted to spiral this course. I hope I can make math accessible to all my students and make them like it along the way.