Distance Between Two Points with Tacos & Zombies

I thought it was about time to dust off my blog. I am spiralling my two grade 10 academic classes this semester (I also have a section of grade 12 Advanced Functions). It is really nice to have last year's plan and homework sets to work from and tweak. I recently saw what Nathan Kraft did to a cool Desmos Activity Builder activity created by Andrew Stadel and knew that I wanted to adapt it for my class. Their activity focused on horizontal and vertical distances between two points. I needed to include the distance between any two points. Due to the size of the activity (so many images!) Desmos struggled to keep up with my changes and I ended up having to hard code the points I used rather than having them referenced with variables. Using variables would have made it easy to move the points, but I will have to save that for another time. I think I'm getting ahead of myself here though. I should back up for a minute and start at the beginning of today's class. We started with Dan Meyer's Taco Cart 3-Act found here. 

After setting the scene with the Act 1 video, I asked what information they needed to know. They requested distances and speeds so they got this:

Next, they worked on big whiteboards in their table groups to determine whether Dan or Ben would get to the taco cart first. We talked a little about the Pythagorean theorem along the way.

Then, I played the Act 3 video to confirm their answers (all groups said that Dan would arrive at the taco cart first).

It was now time for the zombies! I used my Popsicle sticks to select random pairs and handed out Chromebooks. The link to the activity is here.

Despite the activity not running as smoothly as I would have liked (points were not showing up for some students and overall it was very slow), students seemed to learn what I wanted them to. After working out the distance between four sets of points on this screen, they understood the process and were ready to generalize. (Screen 13 was planned as an extension - I really wanted to ensure that everyone completed screen 8.)

We consolidated to close the lesson and did one quick practice question.

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.