# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# Finding your distance traveled with speeds

My last post was about how I named my blog. In this post I’ll include the assignment that I give my class regarding accumulating a rate(my title) and talk about my new plans regarding this lesson.

For the past 5 years or so I have given this project to my class:

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The idea is that they drive somewhere they think is fun like Starbucks, Burgermaster, or Target(???) They usually choose a food location which isn’t too surprising… they are 16-18. I ask them to have 3-4 people in their group so that they can have a driver, a recorder, a timer, and a speedometer reader. Their job is to record the speed they are going every 5, 10, 15, or 20 seconds during the drive. I let them choose their time interval and they could even choose every23 seconds if they wanted. (But, honestly, who in the world would want to do that?) The groups create graphs with the time on the x-axis and speed on the y-axis. Then they create rectangles using the data points and find the area of all the rectangles. I have them do a Left Riemann Sum and a Right Riemann Sum, but if they start and stop at 0 mph the end up being the same. It has provided some good discussion in class about why the two sums are the same. Each group has to have a group name and some pictures of their trip which they put on a poster with their graphs to display on the wall. Their answers are the distance they traveled which is checked to their odometer and with google maps.

I refer back to these projects often when we are talking about accumulating a rate. We would have an equation that gives the rate of something; for example: The rate of cars going through an intersection or number of people coming into a park. The goal is to figure out how many cars came through the intersection between 7 and 9am or how many people came into the park while it was open that day from 8am to 11pm.

There have been some questions on the AP test just like this over the past few years. There are not any questions like this in my book that I could find, so I’ve made some that I like for students to practice:

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View this document on Scribd

View this document on Scribd

View this document on Scribd

View this document on Scribd

View this document on Scribd

This last year, I had been checking out the blogs on math and came across Dan Meyer and his pictures and videos in 3 acts to  demonstrate/ask a problem. I then got an idea about do a video that would accomplish the same thing as the project with way less coordination on the student’s part. The idea was to video my speedometer and tell them where I started. Then ask or let them ask, “Where did I go?” It seems like the obvious question. I did a video for it the other day and the only thing I don’t like is that I didn’t cover up the odometer and you can see it a couple times in the video. I may go back and video it again. It’s hard to hold my ipad and drive at the same time. Don’t worry, I was really careful. I passed a cop once and he didn’t notice what I was doing, but I could just hear the conversation of me trying to explain what I was doing. I’m guessing it wouldn’t go over very well. As I was editing the videos, I was trying to decide if I would use this before the driving project, after it, or instead of it. What do you think? I would like to continue doing my project, but if students can get as much from something that takes less time I have to consider it.

Here are the two videos:

This is the video to play first that shows where I start and my speeds along the way.

This is the video to play second that shows the odometer and my final location.

The extra challenge with the videos is figuring out where I drove, not just the total distance traveled. As I write this I was thinking that students doing their projects could present their graphs and tell where they started and other groups could try to figure out where they went. Hmmm.

### 7 comments on “Finding your distance traveled with speeds”

1. Damon
August 25, 2012

This is a great idea for a project. Makes me wish I taught Calculus. I just need to figure out how to use it in Algebra 2.

2. kaleb40
August 25, 2012

Maybe with quadratics and projectile motion??

3. Megan Hayes-Golding
September 1, 2012

I love the original project — your videos could be used before the project to increase the excitement level. I totally wanted to know where you were driving (and even more so if it was in an area I knew about).

Welcome to the blogotwittersphere!

4. kaleb40
September 3, 2012

Thanks, I first thought to do the speedometer and then I thought that if I showed where I started there would be a reason to know how far I went. “Where is he now?” would be a natural question that I don’t think I would even have to ask.

5. Renee
February 7, 2015

Hey–Just found your blog today! Wondering if there is way to get these materials other than paying for a subscription to Scribd. I don’t mean to sound cheap but this is my first year teaching calculus and I’ve already spent way more money than I should have! Thanks!

• kaleb40
March 12, 2015

Sure, send me your email and I’ll send them to you.

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This entry was posted on August 25, 2012 by in Calculus.