Like I already told you I was going to (here), I started talking about estimation in my class last week. We read a book called Great Estimations by Bruce Goldstone, tried out a few of the problems he posed, and then tried some of our own.
I had prepared some bags of stuff for us to estimate in advance. For each item, there were two bags: one had 10 of the thing in it, and the other had an unspecified number of the thing in it. Here you can see I used Mike ‘N Ike candy and mini marshmallows. I also had popcorn kernels, elbow macaroni, and Cheerios.
I gave a set to each table, and asked them to estimate. They also had a piece of paper they could record their thinking on. At the end, we shared our estimates. We did not get an actual count of the items. This was on purpose. I wanted them to feel like their estimate was good enough. Mostly their estimates were in close proximity of each other, and I complimented them on that.
The following day, I have them 2 bags and an item. They were to put 10 in one, and count as many as they wanted for the next. I gave them Lego, glass beads, counting chips and colour tiles. Most groups put around 30 in the bag. Just we had the day before, they traded bags with each other until they had an estimate for everything. Then, we shared our thinking, and confirmed the count for everyone.
One group thought it would be funny to put over 100 counting chips in their bag. They were each counting out 100, rather than working as a team, so we had a good conversation about that. When another group got that bag, they were sure it was impossible to estimate. Imagine their surprise when their estimate was within 5 of the actual number! That group was composed of grade 3 children who are still adjusting to the idea that they are the older students in the class now, so I think this was a good confidence booster for them.
This is what I discovered: they are mostly pretty good with recording their thinking so they can share it later. We do need to do some work on labelling. We also need to work on each person contributing to a group assignment or task. In each group there was a clear leader who railroaded, or attempted to railroad, the rest of the group.
This is what they discovered: they really were training their eyes (as it says in the book) and their estimates were closer to the actual counts as we went on. In some groups, they discovered the need to label. They had written a number, say 34, but didn’t label it as “colour tiles = 34”. When it was time to share it was tricky to share! I like that they discovered this on their own. I know I will need to talk about this again, but I’d say about half of them were able to identify this as an important thing to do going forward.
Using the website www.estimation180.com as inspiration, I am going to create some more provocations for my students to explore. I want to add this as an activity for them to complete during Guided Math. (Yes, I am still trying to figure that out!)
My hope is that these estimations activities, revisited throughout the year, will help my students develop a stronger sense of numbers. I think they will develop a better understanding of magnitude, and that the numerical reasoning skills will improve.
Finally, here is an article from Math Solutions that has had me thinking about all of these things.