By the time they get to Algebra 1 I think kids have done scatter plots before so it's important to move off of just making them and telling what kind of correlation there is. I did a ton more this year looking into doing linear regressions, interpreting the correlation coefficients and then using the equation for the line of best fit when there's a strong correlation.
In the past I've done an activity where the kids measure their wingspan and height, graph it and identify the correlation. It's always a crowd pleaser. But in hindsight I was mis
sing a good chance to take it further. For starters height and wingspan are pretty close so I was nervous that kids thought that correlation meant equal.
This activity mainly arose from a day where I was getting blank stares and no one was focusing on a word out of my mouth. We were working on linear regressions using their calculators and I had printed out various tables of data with the intention of having them practice using the calculator to find lines of best fit and then tell me what the r value implied about the data. But they weren't having it so I needed something to get them up and awake because I just didn't feel like fighting with them to make them work.
I pulled out my Ikea measuring tapes (last time I was there a bunch of them may have made their way home with me) and gave my kids the task of measuring each other's height, wingspan, hand size, foot size and then one kid asked if we could add in their waist to floor measurement. The goal was going to be to see which one was the best predictor of a person's height. To be completely honest, I had NO idea if this was going to work.
As they started measuring, I typed up a quick google form and when kids were done they used their phones to enter their measurements. I had the chart projected on the board so they could see the measurements as they came in which was actually a happy accident because that led into a conversation about the accuracy of data. A couple measurements were really far off from the others and didn't make sense so they'd make a kid go remeasure something and typically it turned out that they had made a mistake the first time or maybe typed a number wrong.
When everyone was done, I printed out the table and they did 4 linear regressions:
- hand size vs. height
- foot length vs. height
- wingspan vs. height
- waist to floor vs. height
A kid pointed out that I didn't get measured which ended up working perfectly.
With the help of a kid, I measured my hand, foot, wingspan and waist to floor measurements (not my height). They had to then use each equation to predict my height. It was pretty interesting how close they got. After they had the 4 predictions we talked about which prediction was probably the best (one with the highest r value) and only then did I measure my height.
In one of my smaller classes they were really into the idea of measuring random kids in the hall so I told them that they had to decide what measurement to choose (that period ended up being wingspan). So we set up a "measuring station" in the hallway and grabbed people that walked by. The kids would measure their wingspan then use their equation to predict what their height would be. Then they measured the height to see how close they got. I have to say I was pleasantly surprised with how close they got. They got a really big kick out of it too when they were right or really close. The thing that I liked was that we moved beyond the idea that positive correlation means your height and wingspan are the same. They never actually used that logic..they used their equation to make the prediction.
Since this whole thing was really done on a whim I have no pictures, no handouts, nothing at all. It is one that I plan to keep around for next year though and hopefully fine tune a bit. So I'd love to hear any ideas or suggestions you've got!