math, Number Sense & Numeration, Number Talks, Problem Solving

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.

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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:

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Sorry about the cropping – I have written the initials of the person who contributed the idea and don’t want to publish them. Also, SO THAT’S WHERE MY ERASER AND RED MARKERS HAVE BEEN ALL DAY!

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!

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This friend needed help putting in the + sign, and also knowing where to put the $ sign.

 

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This friend needed help knowing that she’d arrived at the answer. Annotating our thinking continues to be a skill we need to practice.

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.

math, Number Talks

Collaboration

We’ve taken a little break from partner work in our class.  Increasingly our struggles with problem solving were getting all tangled up.  Instead of feeling frustrated because working with partners is hard, I felt too many of the students were starting to blame math for the problem and I didn’t want that feeling to perpetuate.  We took some time to do some worksheets *GASP* alone – mostly because I needed a bit more data to feel confident about assigning letter grades on report cards.  Geometry has been the focus of these.  We also took some time to loop back to patterning because this seems to be an area where lots of people hadn’t made a connection between patterning and using an open number line to add numbers.  I think we are there now!

Before we dive into our next unit (Trades, Jumps and Stops from the Context for Learning kits by Cathy Fosnot), I’m going to take some time next week to do some work on the collaboration part.  I have been assigning partners all year.  We’ve talked a lot about why I am choosing those particular partners for everyone.  Now it is time for them to make some choices of their own and I will also be asking them to justify those choices and articulate what makes a good partners.

Once partnerships are established, partnerships last for a month.  They stick together for every part of our day when they might need a partner – writing, reading, science, math and anything else. We will be working on building our collaboration skills all day long.  Specifically in math, I am going to ask everyone to do a “turn and talk” with their partner during each Number Talk.  Usually we do what I think most people do:  I put up a problem, kids work them out alone, then we discuss them together.  I think the turn and talk time will help them practice actually talking to their partner about how to solve the problems.  They will be empty handed, so they can focus on talking about the math instead of arguing about who will be using the marker to write it down.

The second thing I am going to do is create some problems for everyone to solve.  Today we are going to do an activity from The Super Source where partners work together on some describing and listening skills.  One builds a design using no more than pattern blocks. The second partner is not allowed to see this.  The first partner describes the design that was built so the second partner can recreate it.  It’s a tricky exercise for 7 year olds, believe it or not.  Positional language,  attributes of geometric shapes, and expanding on one’s own words are all practiced.  I find that the person describing often reverts to giving directions such as “get a triangle and put it on top of the square…no that way…no that way…no down…YES!”    The other problems are going to involve some addition, maybe some subtraction and will be put in a context they can work with.

The final thing I really need to work on is how to respectfully disagree, and how to accept that “No, I don’t think so” isn’t the same as “I hate your guts and will never speak to you again!”  It’s a hard one, but necessary.

I had initially planned for next week to be the start of my next unit.  But I’m feeling better about this plan of action.  It’s going to help us have a smoother run through the unit, and it is going too help me set up the Math Workshop groups we’ll need during the unit.