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.

math

OAME (part 2)

I’ve been interested lately in the whole idea of spiralling curriculum.  I attended the first of two workshops about this today and it was great!

Spiralling in elementary, I think, will look quite different to secondary.  I feel like I have naturally been looping back to topics we’ve covered.  I will say I’ve been pretty haphazard about it, and that is one of the things that I recognize as a problem that I want to solve.

In the workshop the presenter (Jennifer Thiessen) showed us how she had cut apart all the math expectations and then sorted them herself into common themes.  This was how she created her units so she was integrating strands.  I am going to do this!  She found Rich Math Tasks from a variety of sources, then used a matrix to plot which areas of the entire math curriculum were covered with the task. She found those that could be taught during other parts of the day and moved them there so she could spend more time on Number Sense.  For example, I don’t teach my class about temperature during math.  Instead, all winter long, we check the Weather Channel website to see if we are going to be able to go outside or not and that short (mostly daily) conversation covers all the expectations in the document. But again, I have been more “Oh look!  A connection!” about the whole thing and I want to have it more planned.

She also showed us how she went through with different colour highlighters and picked out expectations that were brand new material and would require a fair bit of teaching time and those that were building on knowledge that kid already had and could maybe be taught in a Number Routine or Number Talk setting. For example I don’t need to do lesson in grade 2 about counting, but we had to practice counting a lot – especially skip counting – so I can practice that 150 different ways during 4-5 minute counting routines at the end of a lesson. But I will have to spend a fair bit of time doing actual lessons about adding double-digit numbers because that is going to be challenging new learning for most of the class.

I’m really excited about this, which I know is a bit weird, but I’m looking forward to spending some time analyzing the curriculum and sorting through tasks.

math

OAME 2019 (part 1)

I am attending my first ever Ontario Association of Math Educators conference.  Yesterday was the first day.  I told my children I was going to school to be a student and learn more about teaching math, and that is exactly what happened.  I signed up for a variety of workshops, and have not been disappointed in any.

The very first session I attended was called “Where Fractions, Area and Volume Come to Play” and was presented by Kawartha Pine Ridge DSB teachers Brandi Hollinger and Laurie Moher. It was great!  They shared an action research project teachers in their board had been involved with.  They studied and learned how to support students with learning difficulties in the math classroom.  They shared a really great document, available on Edugains called “Supporting Students with Learning Disabilities in Math“.  I already spent some time with this document last night, but will need to really digest it when I don’t have a brain that already feels stuffed (with more to come today!) I was so excited about it I put it out on Twitter, and someone else recommended that I take a look at “The Waterfall” document produced by York.  HOLY COW!  It’s a document full of information that is specific to math and learning disabilities and I feel like I am going to use to be a GENIUS IEP writer/implementor.

I also attended a workshop put on by the amazing Aviva Dunsiger. She teaches math all day long in her Early Learning Kindergarten classroom.  ALL. DAY.  And it’s integrated into the children’s play.  So what does this have to do with me, a not-kindergarten teacher? I’m thinking a lot about how I could be doing little bits of math throughout the day.  My friend, also at OAME with me, did a class with ideas for math DPA. So I’m thinking a lot about that, and how I could be doing math in little tiny snippets all day.

Day 2:
I am now in my 3rd workshop of the day and haven’t had time to even finish the first post.  This conference has cost me some money (though my board is supporting me with PD funds for most of it) and has cost me some time. But it is seriously so worth it.  I’m thinking about what I might teach next year. I’m thinking about what I am going to teach in June this year.  I’m thinking about improving assessment and note keeping (Oh the note keeping!!)

Slice of Life: Multiply the Money

I wrote yesterday about a Number Talk I had worked on with my class.

Today I extended that activity by making an array using money.  I used the Mathies money tool to display an array made of nickels, then I asked, “What do you see?”

We built this display of our thinking a bit at a time, so I am sure it made more sense to us than it might to you!  Someone saw 45 cents.  Then someone else saw 15 cents (3x5cents) and then 3 groups of 15 = 45.  Some saw the array 3 x 3 = 9 nickels all together. I pointed out 3 x 15 and 9 x 5.  Thanks to our work with fact families, a few realized 45 “shared by” 3 people means they get 15 cents each.  Seriously!  They didn’t just point out that 3×15=45 so 45 divided by 3 = 15.  They actually explained what was happening! (Full disclosure: not all of them.)

After this conversation, I cleared the board and made an array using toonies. Now, you might have been expecting me to use dimes, but I thought the \$2 coin was better considering that we haven’t talked about multiplying by 10 and my grade 2s would get a lot more out of the conversation if we were thinking about multiples of 2 rather than 10. I will probably give 10s a try tomorrow on their own.  After our success today it seems like a good way to get everyone to start thinking about multiples of 10. I’m looking forward to it!

What you see isn’t what I see

For Number Talks this past week I made some arrays on Smart Notebook and projected them on the board. We spent time each day talking about what we noticed and thought. Early on the fact families emerged. I’m glad because we’ve just finished up some multiplication and division learning and I was glad to see this being put into practice.

On Friday I displayed the picture below:

As you can see there were multiple ways to see this picture. Immediately people saw the array of 4 rows with 3 bikes in each.

One child kept insisting it was 2 groups of 6. It took a minute for him to convince his peers, and I had to help by circling the 2 groups. I’m glad we took the time to let him explain! He was clearly showing some beginning “partial products” thinking and I wouldn’t have known this if I hadn’t probed for an explanation.

Finally someone started talking about the bike tires. I don’t have a photo of that annotation, but it was interesting to see how the students went in to figure out that 12 groups of 2 = 12+12 = 24. Of course they were able to complete the fact family. At this point very few were counting by one’s. I was quite happy about that for sure!

It took me very little time to use the tools in Smart Notebook to make these arrays. I’ve definitely used Mathies for this as well, but the pictures in Smart Notebook led to a deeper conversation. This week I need to find some cars with 4 wheels to expand on our conversation.

This work also builds on the “Eyes on Math” number talks and picture-based number talks we’ve been doing all year. Tomorrow we are going on an array hunt around the school with our iPads. That activity has been preempted a few times but I think it will end up being a better activity now that we’ve discussed the picture arrays a few times.