## Show Me The Money!

I’ve been super busy.

That’s the only thing I can say. I’ve neglected the math blog once again. I think of it often, but never quite find the time to update.

I’ve got some spare time right now, so here it is. The update.

I’m teaching grade 3. I love it. Having a straight grade is so nice.

Now, on to other things. This summer I took a quick webinar about how to make my own math worksheets. (more info here) It was a lot of fun and now I am making them all the time! I’m going to start posting some here. The webinar was intended to teach people how to get started making and selling resources on Teacher’s Pay Teachers. I can’t be bothered with that. I have a lot of issues with that website and prefer to give away resources. I am adding a copyright, however, because I don’t want to find out someday that someone is selling my stuff on TPT.

We did this activity for the first time today. I put piles of fake money out (bills only today) around the room. I had a number label for each pile. Every child had a recording sheet. They went around the room finding the piles, counting the money and recording their total. I let them choose if they would work alone or with partners, and they did a little bit of both. Some people started with one partner then moved to another. I spent a lot of time watching and taking notes. We’ve done a number of these scavenger hunt activities at this point and they love them! I like to watch them help each other out, correct each other’s mistakes, and show each other the strategies they use. Today everyone was able to count the money without difficulty, and there were a few different strategies they shared. Sometimes they started by sorting the money into groups (e.g. put all the fives into piles of \$10). Sometimes they had to count more than once to be sure.

On Monday, we are going to review the values of the coins, then we’ll repeat this with piles of coins. On Tuesday we’ll have mixed piles of coins and bills. (That’s assuming everything on Monday goes okay!) Finally, probably on Friday, we’ll have some more complicated piles with larger amounts. On that day I’ll most likely ask them to choose ten piles to count because sixteen will probably be too many. We’ll see!

I’ll be back soon with more of the things I’ve created. I like them and they’re working well.

You can download the recording sheet and labels for the piles here. I’ve also posted some cut and paste activities for counting coins. We haven’t used paste EVER in my class and I don’t think it’s even sold in stores anymore, but “paste continues to be what “cut and paste” remains in our lexicon so there you have it! Finally, I’m posting some word problems were’ going to work on in group using vertical nonpermanent surfaces, which you can read more about here.

## Money (or “Learn to get along with your classmates!”)

This week we learned more about money.  We started “Trades, Jumps and Stops”, a Context for Learning unit and the first thing students do in that unit is count some money.  On the first day, I did a Number Talk, which was definitely not a Number String! I had 50 cents in my pocket and I told the class about the 50 cents.  Then I asked, “Can you tell me which coins I have?” We wrote down 5 or 6 different combinations of coins that are equal to 50 cents.  Then I told them I had 4 coins and they immediately knew which of the options they’d given was correct.  But by “them” and “they” I mean it was only about 3 or 4 students.  Granted, we had a lot of students away due to illness but it was clear that we needed some practice with counting money and making amounts in different ways, so we took a pause from the unit and did that for a couple of days.  By Friday we were using the piggy bank cards, which we need later in the unit, to count out coins, adding up two different amounts to get a total, and comparing them to our partner. This is a detour from the original content of the unit, but I didn’t feel like we could go forward successfully without solidifying this skill. Or set of skills I guess.

I am happy to report that everyone was counting by 5s and 10s, and many were adding up quarters too!  This is because we have progressed as mathematicians!  It is also because I only gave each group 5 pennies so they didn’t have the option of counting out a very big amount by ones.

This week I am also reflecting on how well we are collaborating when we need to.  For the last several years I have done a lot of work with intentional learning partners.  I assign my students to a triad and those people are their partners for the entire month whenever they need partners. In the beginning, I assign them to a partner, or I use a random system for matching students.  As the months go by, I start to ask for their input and ask them to do some self-assessment of their ability to be a good partner.  By the 5th month of school I would not be doing random assignments anymore.

This year is different. On Thursday I pulled out our partner matching cards and I immediately thought, “Why am I still using these?  Why don’t I have partner assignments ready to go?”  Intentional learning partners are meant to match students who will be able to actually help each other out and collaborate together.  Peter Liljedahl does the opposite and has students work with different students every day.  But his work is mostly focused on older students.  I believe that in the primary grades the students need different social things than they do in the higher grades.  For example, practice putting up with each other’s oddities in order to learn some tolerance, practice noticing someone else’s preferred work style and then trying out some tips from that person, and of course they need to learn how to take turns.  They also need to be matched with someone who is close in ability.  Maybe not the exact same ability, but in a split grade class I can’t have my most accomplished grade 3 matched with a grade 2 who is really struggling.  Or worse, a struggling grade 3 matched with a grade 2 who is sailing along! I take all of this into consideration when making matches.

So, why not this year? Well, I think there are a few reasons.  First, we have an attendance problem.  I don’t want to say too much about that, but some kids are away a lot. Second, we have a few kids who are really struggling with being told what to do.  I’m quite concerned that I will assign them to a partner and they will make such a fuss that it will ruin the class period/day/week/month.  Or worse, they will want to be partnered up with someone I do not want them to be partnered up with and I will not partner them up with that person because I am the adult and IT WILL NOT END WELL!  It all seems like a better idea to say, “Sorry, not my fault.  Talk to Fate! She’s the one who picked your partner.” or, “The cards decided, not me.” (which is what I am most likely to say.) We’re a little behind in some of our executive functioning skills and random partnerships let us work on some of those areas while avoiding some of the more volatile ones.  And as I’m writing this I feel like maybe I’m taking the easy way out because I’m exhausted from all the emotional stuff that goes with teaching.

And now I’m going to spend the day thinking about maybe putting some more time into developing the executive skills that will allow everyone to manage frustration in a way that does not make Mrs. Corbett want to cry every day on the way home from school.

But we can all count money, so HOORAY!

math

## I need money for a taco truck

Sometimes I sit back at the end of a week and I can’t remember what even happened! That’s one of the reasons I’m enjoying my weekly reflections this year. It reminds me to sift through the feelings and find something positive. It’s easy to wallow in the discouragement of a busy week. I know I’m not the only educator who ends a week thinking, “That did not go as planned!” Or “I’m basically a failure and I’m wasting everyone’s time! Or “I wonder if it’s too late to trade this all in and buy a taco truck.” I mean, how many bad days can a taco truck operator actually have? I bet a taco truck driver never goes home feeling like a failure!

This week we talked about money. We finished the week being able to identify every Canadian coin and it’s value. We know why we need the cent sign and dollar sign. We even counted money quite successfully. We were not incredibly successful completing some math work sheets but everyone does understand that a horizontal math question and a stacked math question are asking us to figure out the same thing. That’s big learning for some kids. And we sang “Canada in My Pocket” a lot (though less than I would have liked.)

So yeah…clearly I was not a failure as a teacher. Nothing really exciting happened. Nothing made we want to rush home and blog. I don’t have any photos of our week. But we still had a successful week. Not a very exciting week, but, yeah, successful.

I’m thinking, however, that if I’m kind of bored with math (I didn’t even title my reflection last week!) then chances are other people are bored with it too.  This week we are moving on to some 2D and 3D geometry.  Or we might move on to area.  In the math long-range plan I am following shapes are up next, but I’m at a different place than I though I’d be at this point, so I might do area first.  Geometry fits nicely with the holidays because there are a lot of crafty projects we can do with our shapes.  Every day between December 1 and the last day before Winter Break gets harder and harder, and crafty math helps us get through. Plus we can talk about snowflakes a lot, and there is a lot of geometry in snow flakes.

Sounds like I’ve talked myself into area first.  Maybe we can figure out the area of the perfectly sized tortilla for my taco truck business.

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!)

## 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!

## 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.

## 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!

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!

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.

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.

## 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!