These last weeks of school can be a bit hectic. Today was College and Career Fair in our district, some classes were disrupted, so I thought this oldie but goodie was an appropriate way to end our week.
Its a data collection activity shared by Donna Farmer around 2002. I’ve used it many, many times and just assume like most other stuff I do, it has been used by everyone else as well. But I’m reminded once again, we should all share – you never know when it may kindle someone else’s development of an idea.
You can scroll to page 10 of this file to find a rough copy, like I said, this is from several years ago! In past years, I provided students with various articles sharing stories of fallen balconies as a lead to the lesson. But today, we watched this clip from Inside Edition. There are several options for clips you could use as an intro.
We read the intro paragraph on the handout, pick up some pennies, rulers and find a flat surface, start stacking and crashing. Everyone is engaged on these days.
Collect data, scatterplot, analyze, create a model, use your model to make predictions.
The last two questions actually ask students to find the extension length for a given number of pennies. Three things happen: 1) they incorrectly use the pennies as their exponent, 2) they graph the number of pennies and look for the intersection point, or 3) they estimate from their data what the length will be and verify it, then adjust accordingly.
I’ll be honest, I am most proud of the 3rd…thinking on their own. Seeing how this data point relates to their collected data.
One thing I’ve noticed this week as we worked with writing exponential models, students were beginning to use some reasoning to adjust their exponents up or down rather than strictly guess and check. A couple of discussions with decay – if we need the predicted value to go down, the exponent would go up, vice versa.
Many students were comfortable using decimal exponents. In years past, I remember students wanting exponents to be whole numbers. The fact that it doesn’t seem odd to them to have decimal exponents makes me feel like I’m moving in a good direction with them.
I want to create better follow up questions, what if scenarios that could be used as an assessment in a different context possibly.
Anyway, hopefully someone can use / tweak the task and use it for their classroom!
Side note: I’m wondering how many other tasks I could use pennies for in math class. Past ideas:
Sample of pennies for a 5-Number Summary of the dates; Rolls of pennies and weigh use to create a sampling distribution in stats, I use pennies as the weights in spaghetti bridges, I need to take another look at the pennies in a circle task on desmos, what’s the average height of free standing stacks in a class? Other suggestions are welcomed!