The Math Hatter: Estimation 180 & Statistics

I am late to the party here, but the website estimation180.com is amazing.
I have just this year finally started using it during class.

For those not familiar with the site, math teacher Andrew Stadal created some great problems and hooks that require students to use estimation and reasoning skills. Some very important skills that are getting lost in the standards driven era of school.

For example, this is the first and second problem I had my students think about.

#1) How many almonds in the 1/4 cup?

#2) How many almonds in the large container?

The website is called estimation 180 because they recommend one of these problems a day. I do not use it that way. I do two problems at a time, once a week. I use these problems a lot with 7th graders. In MN many of the standards in 7th grade deal with proportional reasoning.

So I have them do the first question shown above and ask the students for 3 numbers.

1. What number is too high?

2. What number is too low?

3 What is your best estimation? (your "bestimation")

Then I when they have those three numbers, I reveal the answer, drawing the moment out until they are begging for the answer. After I reveal the answer I immediately throw up the second image as well. Now I add a question to the mix...

1. What number is too high?

2. What number is too low?

3 What is your best estimation? (your "bestimation")

4. Explain your reasoning (more than "I guessed")

The more we do these the better the students are getting at thinking with proportionality. If they know how many almonds are in the 1/4 cup, they use that number to make a good estimation for the large container.

We are on about our 5th week of this. The answers I am getting are starting to get better and the reasoning more sound. When I give them feedback on their answers, I focus solely on the reasoning aspect.

We started our statistics learning target about a week ago. This entails measures of center and measures of variability. So when we did our weekly estimation problem last week, I had them submit their answers and reasoning using a google form.

The estimation problem was about the large pumpkin below.

Knowing the weight of the small pumpkin, they had to estimate the large pumpkin's weight.

Then this week I created a quick PDF with their best estimations sorted by class. Today their job was to analyze the data (find the mean, median, mode, range quartiles and IQR) for each class.

Then after they worked to find the answers to those, they took 5-10 minutes to discuss which class had the "best estimations." I left this vague on purpose. This led to some great conversations among the students. It also let me reteach where the meaning of the numbers was missing. For example some students tried to argue that a class's IQR was close to 14 (weight of large pumpkin), so they were the best. So it was good to catch those misconceptions early.

It was really nice that it worked out that one class had the closest mean, another had the closest median, and the other class had the closest mode. That was a little magical bonus I got with no planning whatsoever.

The 3 data sets are here if you would like to look at them.