math, Number Sense & Numeration, Number Talks

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!

 

slice-of-life_individual
Just about every Tuesday I blog for the Slice of Life challenge over at Two Writing Teachers. You can read more posts on that blog.
math, Number Sense & Numeration

Math at Home

My son, who is in grade 1, has really good number sense.  He has a lot of mental math strategies that he uses efficiently and flexibly.  He adds on, he counts back, he finds landmark numbers, he even splits numbers!  And no, this is not because we spend a bunch of time every day drilling math.  It’s because we play lots of games and have math conversations that pop up throughout our day.

As I watched him play “Sorry” I was surprised that he was having some counting trouble.  He has been able to count in sequential order with one-to-one tagging for quite some time. He can count a variety of object by ones, more than 100, and when he makes a mistake he notices it on his own and fixes it.  He subitizes, and I feel like this what he is doing  while he counts and that his how he notices his own mistakes.  But that’s a tangent I won’t go on right now.

What surprised me as we were playing “Sorry” this week was the trouble he was having  moving his pawn the correct number of spaces on the board.  He recognizes every number in this game, and connects the number symbol with the amount. He’s done this with other games many times, such as when we play other games and he has to compare which of two numbers is larger. (I had a hard time writing that sentence because I kept thinking about how we haven’t played War in a long time!)  When he drew 5, for example, I know he knows that is 1, 2, 3, 4, 5.

When he would draw a number he would count to that number as he bounced his pawn around the board, but invariably any time he had a number higher than 3 he would bounce a different number of spaces.  Sometimes he would go fewer than he was allowed, and sometimes he would go farther than he was allowed.  If you draw a 4 in this game, you have to go backward, and he did OK with that but he would count slower than usual, so I built that into my intervention. I told him about the problem.  “Just like when you are counting things, your pawn has to touch each square when you count it.” I started by putting his hand in mine, and making sure that every bounce had his pawn landing in just one box without skipping any boxes.  After several rounds of this, he started doing it on his own.  He would slow down his counting and he’d land in the right spot.

The next day we played again, and the problem resurfaced.  This time I explained the problem to  him, then instead of holding his hand I put a finger on the square as he counted.  If he got ahead of me, or skipped a square, he would recognize this on his own and correct himself (and sometimes his big sister had to butt in and point out his mistake, but that’s a different post altogether!)

The third time we played the game, he needed a verbal reminder, but that was it.  And the fourth time he needed the verbal reminder.  And if we have time to play it again tomorrow, which I hope we will, I expect he’ll need the reminder again, but I’ll wait and see.

This whole thing has surprised me some, mainly because as I said before he knows how to count with one-to-one tagging and has for a while.  So why was he having trouble? This is what I think: there was a little pressure on him this time that isn’t normally there. First, he loves to win and he knew that winning in this game requires getting around the board quickly.  That was a distraction and a stressor when he was trying to count. Second, besides just counting, there was some other thinking that had to happen.  If you land on a square with a triangle you get to slide, and if you land on a square that already has a pawn on it then you say “Sorry!” and bump that pawn back to start, and sometimes I could see that he was making a move with one pawn while also thinking about how maybe he should actually be moving a different pawn to get a better outcome. He’d be in the middle of a move, suddenly stop, put the pawn back where it was and move a different one instead.  Third, …I don’t actually have a third.  I think those two things are enough to explain why he was having some trouble. I did double check to make sure he was wearing his glasses the first time I noticed it, and he was, so we can’t blame the vision.  And his coordination is such that moving a pawn around the board is not a physical difficulty for him.

Counting is such an interesting thing, isn’t it? I feel like I have some new insight into him as a mathematician.  I have since noticed that he also needs reminders to slow down when he is doing calculations.  He also does a better job when it is just me and him and he doesn’t have to worry about his sister butting in with answers. (Are you noticing a theme here?  It’s hard to be the little brother!) Finally, he does a much better job and enjoys the whole thing more when he can do single step problems. I feel like that last part is developmental and will work itself out over time.

My diagnosis is that there is an executive functioning thing going on.  He is using his working memory to do multiple tasks each time he takes a turn, not the least of which is to manage his emotions around the fact that his big sister is always butting in.

I am, of course, thinking about how to help my son with this particular thing.  But what does this look like in a classroom?  I’m thinking it would be useful to sit down with a few of my students and play a round of “Sorry” or “Trouble” or even “Snakes and Ladders” and really play with them.  They do these sort of things sometimes during indoor recess, but if I were to set this as an activity during class it would be so a group of children would be busy while I work on the real math with other kids.

Time to rethink that practice.

math, Math Workshop, Number Sense & Numeration, Number Strings, Number Talks

Early Algebra

We started the “Trades, Jumps and Stops” Context for Learning unit quite some time ago. A variety of inclement weather days has interrupted us a lot, so we are behind where I thought we’d be at this point. That might be part of the issue I’m having with this unit.  I’ve not taught it before, so that has to take a bit of the blame as well.  And finally, I’m thinking I might have misjudged our general readiness for this unit.  But I talked to my down-the-hall neighbour who is also doing the unit and she concurred:  It seems that some kids are easily getting it, and some are really, really having to work hard to get it.  There’s not a lot of in-between here.

Day 4 of the unit begins with a mini-lesson that we needed quite a bit of time with.  I was to fill 2 separate bags with a certain amount of coins in each, plus a “mystery” coin.  We have had a bit of trouble adding up coins, so I decided to stretch this out a bit instead of trying to get through it in 15 minutes.  Instead of putting the bags out of reach, I gave the coins to kids.  I started by explaining, “X and Y have some coins.  They have an equal amount of money, but they have different coins.  I want to see if you can figure out which coins they have.” On the first day only one child had a “mystery” coin (a poker chip!), but on the second day both kids had one.  The children holding the coins were very excited to be given this job. It gave them practice identifying the coin by name and value.  Have you ever thought about how we interchangeable use “dime” & “10 cents” when talking about coins? Some of the kids are still calling this “The Boat”.

We unpacked the bags a bit at a time.  I don’t have pictures of the whole process, but this is how it looked in the end.  Obviously our mystery coin was worth 10 cents this time.  This is the beginning of the children learning about a variable, and I think they did OK!

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On the second day, we talked more about the signs < > and =.  We added up the coins in chunks, as suggested in the lesson, and then decided if we needed to have a < or a > or if we finally needed the =.  This time, instead of adding them up as a group, I had the students work with partners.  We knew that X had 40 cents, and Y had 5o cents, but how much would they have once they each got another quarter?  This partnership was trying to make a number line across the bottom end of this photo, without actually making the number line.  It’s a step in the right direction for them!

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They wanted to have the numbers in a long line, but couldn’t hold all those totals in their head. Writing them above helped them work on the math and compensated for the stress load on their working memory.

We had lots of people able to do this:

Finally we made it to the mystery coin.  We knew how much money everyone had in actual coins, but what was that mystery coin worth? This led to one of those really cool moments when I felt like (most) everyone was excited about the math.  You can see here where I recorded some of the different responses to the value of the mystery coin.

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I was even able to use a double number line to show two of the answers, and since that is the goal of this unit (developing an understanding of the double number line is in fact the very next lesson we will do!) I felt very good about that.

The next day I needed a Number Talk to reinforce the understanding of the variables.  I didn’t really NEED to do it, since this doesn’t come into the curriculum until a later grade, but they were excited about it, and it certainly can’t hurt them so we did it anyway. I found some images on Math Before Bed and use them for our Number Talk.  I feel like they really help to reinforce the student’s number sense because there is more than one way to make 10, or 12, or any number really.

The weather here is terrible today (Sunday) but I’m hopeful there will be plenty of actual school days this week when we can move forward with this unit.  I don’t want to lose our momentum!  Next time I do this unit, however, I am going to maybe wait a bit.  Of course, the thing that keeps getting me through is that I have to trust Cathy Fosnot! She says this will work, and she has seen it work with many, many children, so I am going to go ahead and finish the unit.  The students are mostly getting the ideas behind the math. Some of them are actually in need of more practice with adding up money.  I am going to make sure we have a day this week when we have some activities that require counting money and we’ll rotate through those to give everyone lots of practice. Often these blogs help me think through what has happened and what needs to happen next!  Time to stop writing and plan my money counting activities.

math, Number Sense & Numeration

Money, Money, Money

According to the TIPS4Math scope and sequence maps found at edugains, it was only going to take me 5 days to teach money.  I had 5 days before March Break, so it seemed a perfect match.  I mean, I thought it would take more than 5 days, but I had 5 days and wanted to believe that if I had enough faith I could finish all of the math stuff in those 5 days.

Then on Monday I found out we didn’t have to be at school on Friday.  (I pay really close attention to calendars, obviously.)  But that didn’t matter, because I had technically started doing some things with money the week before, so I was going to be OK.

Let me stop right here and say that if all I wanted to do was check the curriculum expectations off my list, then I would have been “finished” with all of the money stuff after 5 days.  I seriously would have.  But, I don’t know.  Money just seems like one of those things kids should not just do.  They need to understand money, even when they are 8 or 9, right?

Here’s what we did:

  • We dumped money out and identified coins/bills.
  • We made combinations of coins that were equal to a dollar, or $20 for grade 3 students.
  • We counted piles of coins & bills to find their total.
  • See…I’m practically done a day early!

If you haven’t ever seen The Pancake Menu, take a look here. Such a fun book and activity! We read that and talked about it, but I didn’t want to make pancakes again, so I told my grade 3’s to come up with their own cafe idea.  Then we ran out of time, so on Wednesday night after school I bought a bunch of stuff for ice cream sundae’s, plus root beer and dragged it all to school on Thursday.  I gave the grade 3s a blank menu and they figured out prices.  I told them each grade 2 would have $1, so they had to keep the prices low.  They did pretty well with this, double checking the addition with different combinations of toppings for the ice cream.

They gave each child a plastic Loonie, which I had to explain was a problem if they didn’t want to make all sorts of change.  So they counted out a dollar in different coin combinations for each of their grade 2 classmates.  Except some of the kids got more than $1 and some got less than $1.  Then the grade 2s came to the table to give their orders and everyone gave up on counting money because there was ICE CREAM within their line of sight and the grade 3s were in a panic that we’d run out before it got to them.  They were just taking all the money and the grade 2s were trying not to climb over tables to get their sundaes and thus did not care about receiving change. I was busy scooping out ice cream and training kids to use the whipped cream in a can (#VitalLifeSkill).  Then when everyone asked for seconds, I said, “Depends on how much money you have left.” and that’s when they realized they’d been ripped off by the ice cream sellers.  The entire class stared silently at me and my half-full bucket of ice cream, unsure if I was actually going to keep the rest for myself.  (I’m not going to lie – it crossed my mind. I had homemade hot fudge!)

Morals of the story:

  • You can cover all the money expectations in 5 days.
  • You will not have actually taught very many kids to use money.
  • You can’t assume children will have all had root beer floats. (#LifeChangingEvent)
  • You can assume someone will complain about not getting a third sundae, even though they have all received a second sundae for free.

When we get back from March Break, I am going to have everyone write out their orders for the grade 3 students, and they will figure out the actual totals, and then I will have them count out the right amount of money they would need to pay a cashier.  I will not be giving them more ice cream until at least June.

One day, not that long ago, my daughter, who is in grade 1, was convinced she had $21.  Can you see why?

She wanted to buy something that cost $21 and I told her she’d have to use her own allowance because it was something junky.   She names every coin, but she’s not unitizing the money yet, and doesn’t really get that each coin has a different value.  She can count by 5s and 10s, so she can count dimes and nickels if I am next to her walking her through it.  She’ll get there though!