This past week at OAME, I was pretty focused on spiralling the math curriculum and on finding more problem solving tasks to use with my class.  I find that a lot of the tasks are a bit beyond our reach, which is frustrating.

One of the things I was introduced to was Graham Fletchy’s 3 Act Math Tasks. I so appreciate when a person is willing to create a resource like this and then share it with the wide world!  While planning my week, I picked out a few in particular that I thought would engage my students, while also spiralling us back to some Big Ideas we haven’t worked with for a while.

Today we did this task, called Snack Machine.  We have had a lot of practice working with each other.  We have had a lot of practice thinking about a strategy to use to solve a problem.  But this task, and others on the site, really allow for a lot of divergent thinking.   There are multiple entry points, and multiple paths to a solution.  It’s great!

In the Snack Machine, a video shows a girl buying something from a vending machine.  We watched, then talked about it, then watched again, then talked again.

At this point, the children didn’t know what the problem would be.  They were simply looking at the video and mathematizing it. The discussion started off with someone suggesting that the girl in the video looked at her change and was disappointed.  That definitely had people thinking about why.  I got a kick (as my grandma would say) out of one of them suggesting that the machine scammed her.

After the second viewing, we had things to add.  We heard 4 coins fall, so which coins might they have been?  That lead to a long conversation, mainly because 4 toonies would make that sound, but would be an awful lot of money for a bag of chips, but 4 nickels wouldn’t really make sense either.  In act 2, there is a picture of the vending machine showing us that the chips actually cost 60 cents. Then another video shows the machine counting up the money.  We added that to our board:

After this, I sent them off to figure out the coins she must have used.  Amazing things happened!  After everyone had a pretty good shot at solving the problem, I showed the final video.  In that video we see that the change was 2 dimes.  They used this to confirm that 80 cents had gone in, 20 cents had come out + 60 cents worth of chips, so it all made sense. No scam!

The money used was American money, and of course a little bag of chips would cost more than 60 cents in a Canadian vending machine. But I told them the two coins we saw were dimes, and that was good enough for them.

Yesterday we worked on Sliced Up, which had us estimating, thinking backward from oranges cut into wedges to whole oranges, and finally multiplying (5 whole oranges, 4 wedges from each orange so how many wedges in all?) For tomorrow, I am debating between It All Adds Up which is a nice money connection to Snack Machine, and The Whopper Jar   which is a nice follow up to the estimating we did in Sliced Up.  Whichever problem doesn’t make the cut tomorrow will our Monday task.  I’m learning toward the money problem because I have a bunch of activities we could do as Number Talks to stretch that learning all week.

It’s EQAO week at our school and I like having some fun, confidence building task for my students to work on.

## Estimation

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.