I was recently invited by a class to work with them on collecting and analysing data. After brainstorming some ideas with the classroom teacher, we settled on collecting data from pull back cars. I checked out Fawn Nguyen's Vroom Vroom lesson and Simon Job's Car Racing lesson to get some ideas on how to organize this lesson. We started the lesson by sharing the first half of Simon's video of cars racing across the floor. We had the students do some notice and wonder about the action taking place in the video and then introduced activity.
We showed students the recording sheet that we would be using and how we would be taking measurements (A link to the record sheet Google Doc is here). Then we brainstormed some ways to make sure that we all collected good data and avoided errors: we would all use the same units (centimeters), all measure our distances the same way (from the front bumper), not use data if the car bumped into a wall or a desk, etc. We split up into racing teams of three students each. Each group got a measuring tape, a pull back car and a recording sheet on a clip board.
The classroom teacher and I circulated the room (and a bit of the hallway) to help students and answer questions. After students finished collecting their data and plotting their values we came back together as a class. We asked several groups to plot their data on the whiteboard at the front of the room. We then had a discussion about general trends as well as why each car had a slightly different graph. Cars might have different wind up springs, different tire grip, dusty floors, aerodynamics, etc.
We finished the class with a bit of excitement... the 150 Challenge. Each team had to use the data for their car to predict how much they would need to pull back to make the car travel as close to 150 cm as possible. Teams huddled to interpret their data and select a pull back distance. Each team brought their car to the front of the class to give it their best shot. There was lots of cheering and excitement as some teams got very close. The winning distance was only 2.5 cm! Much closer than I had expected. This activity could be easily extended for higher grade levels by incorporating linear relationships, linear equations and linear regression.
Nova Scotia Mathematics Curriculum Outcomes
Mathematics 6 SP01 - Students will be expected to create, label, and interpret line graphs to draw conclusions.
Mathematics 6 SP02 - Students will be expected to select, justify, and use appropriate methods of collecting data, including questionnaires, experiments, databases, and electronic media.
Mathematics 6 SP03 - Students will be expected to graph collected data and analyze the graph to solve problems.
Mathematics 9 PR02 - Students will be expected to graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.
Mathematics 10 RF07 - Determine the equation of a linear relation, given: a graph, a point and the slope, two points and a point and the equation of a parallel or perpendicular line to solve problems. (including RF07.06 Determine the equation of the line of best fit from a scatterplot using technology and determine the correlation)
Mathematics Extended 11 S01 - Analyze, interpret, and draw conclusions from one-variable data using numerical and graphical summaries.
I recently visited Memory Lane Heritage Village in Lake Charlotte. It is a living history museum depicting coastal rural life in Nova Scotia during the 1940s. My five year old son had a great time. He especially enjoyed sitting in the 1928 Ford Model A car and pretending to drive. On the way back home I was thinking about other living history museums in Nova Scotia and realized that, based on my experience, it appears that the further away from my home in Halifax that I drive, the farther back in time the museums depict. When I got home, I dug up some data. Sherbrooke Village depicts a typical Nova Scotian village from the 1860s and the Fortress of Louisbourg allows you to experience life in Louisbourg during the 1740s.
I used Google Maps to find the driving distance from my house to each of these locations and discovered a nearly perfect linear relationship. How perfect you ask? The correlation coefficient was 0.99906. I quickly created a scatter plot with a line of best fit to show my wife. Despite my exuberance, she appeared to remain unimpressed.
It is also interesting to see that the points on the scatter plot are almost exactly where the sites are on a map of Nova Scotia as well. Mind Blown.
A question that I still have is whether this apparent temporal relationship is based on distance or displacement. Perhaps I need to collect some additional data (or not intentionally disregard data that doesn't fit my hypothesis)? If I travel in the opposite direction, should a living history museum depict life in the past or in the future? I'd love to visit Yarmouth some day to experience what life will be like in rural Nova Scotia in the year 2213!