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.

## Slice of (Math) Life

Way back in September, I had read about this neat activity from Marilyn Burns called “The Door Project“and had decided to use it to start my school year.  On day one I always like to take the students for a walk around the building.  If anyone is new, or even if they are just coming to my end of the school for the first time, I want to make sure they have a chance to orient themselves, find the washroom and drinking fountain – that sort of thing. On the first day of school, I combined that with some math.  It was our first provocation, if you will.

When we got back to class, I asked, “Did you notice how many different types of doors we have in our school?”  We took a look around the class, and started thinking of ways to sort the doors in our school. Some have windows, some don’t. Some are metal, and some are wood.  Some go to the outside, and some into closets.  I gave everyone paper, asked them to think of 2 or 3 categories to compare, and away we went.  (I’ve condensed it here – we actually spent a whole class period on this!)

It was a disaster. I just looked back to link you to my post, and found I didn’t write about it at all!  That’s how bad it was.  As I recall, we were having a lot of trouble managing our data.  The categories were all mixed up, the tallies were not organized, and nobody could do anything with the information we collected. I had intended to graph our data, but, alas, it was not meant to be.

Today we tried again.

I reminded everyone about this activity, and some sort of remembered it.  We quickly reviewed our door types.  I gave everyone a choice of paper – plain, lined, or graph.  They grabbed clipboards and pencils, and lined up like pros!

We made it all the way around the school, gathering all of our data, in very little time.  Nobody had to shut their door when we stopped to count!  When we got back to class, everyone was able to count their tally marks by 5’s and find their totals in record time!

I reminded them how far we had come.  I reminded them that in September this activity had been really hard, but now it was barely a challenge.  Everyone collected the information independently, found their totals, and is now ready (and able!) to graph it tomorrow.  Now I am sorry I didn’t keep our first disastrous attempt so they could see how far they’ve come! (Who am I kidding…I probably do have it and will find it on the last day of school when I am finishing my clean up!)

What a difference a year makes!