math

Summer Math: Canadian Tire Money

My children have been collecting Canadian Tire money this summer. It started one day in July when I received two 10 cent bills there.  I gave them each one, and the collections were born.  The grown-ups in our family aren’t serious about it, so they have found it lying around, in drawers, on their dad’s dresser, and used as book marks.

We need to go to go out this morning for some errands and my daughter just said, ” Can we go to Canadian Tire today?”  I asked her why and she replied, “You know I’m filthy rich with Canadian Tire money!”

I sent her to count out her money. We’ve done this a few times now this summer.  I am convinced that counting money is the only way kids learn how to count money.  No amount of classroom instruction or worksheets will truly help.  They need their hands on the money!  We had a lemonade stand and they counted up that money.  Claire is saving her money to buy her own tablet, so we’ve counted up that money over and over and over. And of course the Canadian Tire money.  She has no plan for what she can buy today.

Here are the skills we have practiced:  sorting the money, grouping the money to count it, rolling the money in to coin wrappers, adding on by 5s, 10s, 25s and dollars.  We are getting pretty good at it.

math

Summer Math: Vacation

I handed my 8 year old this packet off magnets and, “Half for you, half for your brother.”

 

“Wait…so we get 4?” I wasn’t sure how she’d decided on 4 as half of the package. As I tried to formulate my probing question, she said, “Wait. (Long pause). 1, 2, 3, ….we each get 5. Wait…5 is half of 10? Yeah. We get 5 each.” She wasn’t in the mood to explain her thinking though, so now we’ll never know what was going on in her head! One interesting thing I’m noticing often is that she says an answer quickly, then continues to work on the problem in her head nearly always catching her own errors and correcting then unprompted. I’m going to have to talk to her about why she gives the answer so quickly, before she’s sure she has the right one. And I need to get her to do some stuff in writing to see if this is only happening with mental math calculations.

This past week we spent a few days in Toronto. We had an Air BNB in the building where my brother in law lives. We found it when were visiting the CN Tower.

Tall, right? We were on the 6th floor. To get to his condo, we had to ride the elevator to the 15th floor, exit, wait for the other elevator, then go up to the 34th floor. Here are the things we practiced: counting backward, figuring out how many floors until we would reach our destination, how long we’d been waiting for the elevator, counting forward, paying attention to the pattern of button pushing so we’d know whose turn it was to push buttons. These questions have come up in other elevators, but there was renewed interest since my children have never been in such a tall building. The CN Tower elevator doesn’t have numbered buttons or a countdown display, so that was a bummer. The elevator was pretty slow most of the time, but slow enough for us to have time to work out “how many floors until…” Maybe I should ask the kids to figure that our now!  I feel like these conversations were all about developing number sense. Thirty-four isn’t a very big number, but it really high up in the air when one is in a skyscraper.  Fifteen also isn’t very big, but looking over the pool railing from the fifteenth floor makes 15 seem really high!

We also had lots of conversation about the size of the pool and how it compared to other pools we’ve used this summer. It’s deeper than 2 of them, shallower than 1. It is longer than 2, but shorter than 1. It is a rectangle (clear in this picture but not as clear to kids standing right beside it) but we were in 2 square pools earlier in the summer.

math, Number Sense & Numeration

Summer Math: Math Before Bed

We love doing “Math Before Bed” as part of our “read at bedtime” routine.  We get out of the habit sometimes though because we also love to play card games (UNO, Go Fish, Old Maid, Memory) before bed. Last night I pulled up this picture:

I quickly counted them:  10 per column, 4 in each row. 40.

My 8 year old started counting by ones.  She said, “I think there are 38.”  Knowing she was not correct, I asked, “Besides counting by ones, how else could you find the answer?”  At the same time, I started counting the far right column. Only 9.  Hmmm. I counted again.  Yup.  I had assumed all 4 columns had 10.  We chatted about this.  We talked about how we could use my original answer of 40 to find the answer.  “There are 2 missing from the last row!  How can we use that?”  She had a bit of trouble figuring this out.  She kept saying, “10, 20, 30, 40.” over and over. I said, “Well, 40 but two are missing.  Maybe someone ate them!”  She counted backward to 38 and we were done.

Then she asked, “Can I make my own picture like this tomorrow?”  So that is what we have just finished.  She decided to use plasticine.  I was recruited to mix colours together and help her make tiny balls.  She decided she needed 60 of them. She also decided she wanted to do rows of three because 2’s and 5’s are too easy and she likes a challenge. (HOORAY!!!)  After counting over and over by 3’s, making a few mistakes along the way, I prompted her to notice that there were 10 in a column.  “10, 20, 30.  Oh.  Halfway there.”  🙂

In the end, we had more than we needed. She put those into groups of 5 (and one group of 4) to figure out how many were left. “5, 10, 14,” she said.  It’s so interesting to me that she can skip count, but often counts by ones.  She says this is because “ones is more easier.” She only switches to larger numbers and skip counting when she has a lot of things to count. I suppose this makes sense.

 

 

Geometry, math

Summer Math: Maps

There’s some mapping skills in the Geometry and Spatial Sense section of our curriculum, so that’s the connection I’m writing about today. One of the Grade 1 big ideas is: “describe the relative locations of objects using positional language.”  For Grade 2 students, one of the specific expectations is: “describe the relative locations (e.g., beside, two steps to the right of ) and the movements of objects on a map (e.g.,“The path shows that he walked around the desk, down the aisle, and over to the window.”) 

The girls at our church go on a camping trip every summer for a few days.  The girls have to be between the ages of 11 and 18 to go, but of course there are adult leaders.  I’m been about a million times and I love it!  We go to a place on Highway 144, north of Sudbury.  It’s in the town of Levack, and just past Onaping Falls. This year I only needed to go for one night, so I had my two children with me.  It was such a beautiful day that I decided we’d leave a bit earlier than necessary and stop at the Onaping Falls Lookout.  A.Y. Jackson painted a painting called “Spring on the Onaping River” here.

Thinking I remembered the way, we set off on a trail.  We got to here, but it was a dead end.

Back to the map we went!

 

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Sidenote: This graphic was beside the map, and my daughter said, “Wait. Is that the painting he’s famous for?”  I told her it wasn’t. (The visitors centre was closed so I couldn’t show her the actual paintings.)  Her reply was, “Oh good.  Cause I was like…that’s not that great!” LOL

Turns out we had followed the trail to the Handicap Lookout Area (it was wheelchair accessible.)  We used the triangle to orient ourselves, then re-parked the car in the “picnic and parking area” closer to the trail-head.  I wish I had a picture of the rocks we had to climb to get down into the river valley!  It was a lot of work and I didn’t have time to take photos on account of trying not to fall and break my neck – or allow my children to do the same.  At the bottom we enjoyed some time by the river.

After looking at the map, both children wanted to walk all the way to the lookout bridge, which we could easily see in the distance.  However, after this short hike, we all agreed that the bridge would need to wait for another time.  I think the trail would have been much easier after our descent, but I was already thinking about going back up the hill.

Car trips…or van trips…are a great time to practice lots of practical math skills.  For a while we played a “game” of finding numbers higher or lower than 50 on the road. The speed limit was 90Kp/h, we had to go 400 m to the next turn, there were 17 km until we got to Sudbury, etc. We then challenged ourselves to figure out how far away from 50 each number would be.  We mainly did this with the single- and double-digit numbers.  I feel like this is all part of gaining spatial sense.  By the end of the trip they were saying, “500 meters isn’t that far, right?” or “250 KM!  That will take forever!”

We’re headed off on another road trip today – this time going south. Both of my children are weirdly obsessed with taking surveys.  I’m going to challenge them to come up with some data they can gather while we are driving.

Finally, how beautiful is this: img_6432

math

Summer math: money and even& odd

What does 50 + boat + beaver = ?

If you are Canadian, you may have known that it equals 65 cents. “The one with the boat” is what my 6 year old often calls a dime, and of course the nickel is the beaver coin. Not sure why the names of these coins elude him. He has no trouble remembering the value and I suppose that’s what matters now.

This conversation came up because we saw yard sale signs. Last summer we started letting the kids do their own yard sale shopping. It really helped them start to understand the value of money. I don’t mean the actual value of the coins and bills, but the whole concept of working hard to earn (or find!) the cash and then having to decide if the desired item was worth that amount. Of course they have to count it themselves, and they are both getting pretty good at it. I’m getting pretty good at making them think it was their idea to not buy the junkiest item on the table.

Money came up again today at Canadian Tire. I received 40 cents in Canadian Tire money after my transaction (I haven’t embraced the electronic version of this.) The self-checkout (which I only used because the boy was not getting a new bike helmet like his sister and needed a job to distract him from the injustice of it all) gave us eight 5 cent CT dollars. These had to be equally shared. There was a “some for you, some for me exchange”, some negotiation and finally each was convinced they had an equal amount. It fit nicely into an ongoing conversation we are having about even and odd numbers as well.

Speaking of even and odd, did you know that 13 is odd? 6+6=12, so if you have one more than that it’s not even because there is one extra. (Explanation courtesy of the 8 year old!)

math, Number Sense & Numeration

Summer Math:Counting and Subitizing

I’ve been in a “blogging about math” funk for a few months.  One of my summer goals is to write more, so I thought I’d start a series of blog posts about the math that I am doing with my children at home this summer.  To be clear, this is not a series that is planned.  Instead, I am going to try to be very mindful of the times we do math together formally or informally.  My children, who just finished grade 1 and 2, are probably involved in informal math conversations about the same as many children of teachers. Both of them are pretty good mathematicians, and by that I mean they use flexible strategies to do mental math calculations, they notice math in the world around them, and come up with strategies for solving math problems that naturally occur around them.  I’m a firm believer that this happened because I am intentional about helping them mathematize their world, just as I am intentional about making sure they learned to read by reading to them at least every night before bed (and usually more often!)

Earlier in the week I received an e-mail about the latest Mathies resources.  This morning we finally had time to sit down and explore a bit.  I picked a game for my 6 year old called “Representation Match” and if it wasn’t for his Minecraft addiction I think we’d still be playing it (he only gets to play on Saturdays and when he sneaks my phone into his closet unnoticed so it’s tough competition!)

I chose the numbers 0-20 for him, and I chose all the representations of those numbers.  He had to find matches – two ways to make 14, or 19, or 17, or any number between 0-20. These are all the choices available.

Screen Shot 2019-06-29 at 10.13.03 AM He had to work at this!  He was not able to subitize all the numbers so we had a few conversations about how to figure out the number represented.  For example,  there were 3 dice, two showing 6 and one showing 5. I prompted him to think about 6+6 which he knows is 12.  Then I pointed to the 5. He counted on by 1’s to get to 17, then chose the numeral 17 as it’s match. Sometimes he had to match two picture representations.

When he played again, he chose 2 or 3 representations for himself, always a different combination.  My daughter did the same.  She played with the 0-20 cards, even though she is in grade 2.  She likes to get answers fast, so this appealed to her. She was also playing with the cards hidden, more like a traditional memory game and said she had a lot to keep track of in her mind if she was playing with the higher numbers.

We use Dreambox a lot at school.  I love it!  But I also like to have students doing some targeted math activities that keep them immersed in a specific skill for a while.  Dream box allows them to pause a game and move on to something else, which is fine, but also lets them give up too easily sometimes.  I think this Mathies game would make a great supplemental activity for us during the first month or more of school when we are talking about counting strategies, as well as for practice throughout the year.  Did I tell you I’m scheduled to teach a grade 1, 2, 3 split next year? I haven’t taught grade 1 before so I am anticipating how that will look.  The “Representation Match” game will let me set them up to match numbers 0-5, 0-10, 0-20 and 20-50, I think it will be good for the whole class.

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.