## 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.

## Synchronicity

We’ve been working on multiplication and we’ve been having a good time doing it. It has taken about two weeks longer than anticipated, but I’m going to mostly blame snow days for that.

About a week ago I walked into the library and the book above was on display. It’s been in our library for a long time, judging by the state of it, but it’s a new to me title. I love these Math Start titles, and was so happy to discover that this book was going to help us move on to finding area.

In the book, the children are arguing over who has the bigger bedroom. They solve their fight using math. To measure their bedroom windows, their mom suggests using sheets of paper, and to measure the whole room they use sheets of newspaper. One child’s window takes two rows of paper with six in each row. The other child’s window is four rows of paper with three in each row. That lead to a fun discussion.

Then I set them up. We have several different kinds of tables in our classroom and I asked them to help me figure out which kind of table has the bigger top. We brainstormed a list of tools, and “sheets of paper” was added as a measuring tool. They also wanted sticky notes, but I only have tiny sticky notes so we decided to pass on trying those.

Next, everyone got to work.

Everyone used their favourite tools to measure, but only one team used the sheets of paper. On the second day, we used the photos I took to have a “mid problem” math congress. I focused on the snap cubes and the sheets of paper, so on the second day when we took up the measuring again, more groups used those two tools.

One group was really finding the area, as opposed to other groups that got sidetracked with finding the length and width. It’s okay and we’ll work it out, but I really wanted to focus on the concept of area so we talked about this one a lot. We have several rectangular tables like this. As you can see, it takes two rows of paper with six sheets in each to cover the top. We did get them lined up pretty exactly, even though this picture doesn’t show that well. But we had a problem…

…it was really hard to lay out the paper on the trapezoid shaped tables. They arranged and rearranged but couldn’t quite get it. They then started to try measuring the leftover bits with other tools and we were finally saved by the bell and they had all night to figure out what to do.

The next day, this group was at it again. They tried several different layouts but couldn’t figure out what to do about the gaps. I stepped in to help. I put down a piece of paper so half was on the table and half was off. Then I took a pair of scissors and cut it. “There,” I said. “So we know it is ten pieces, plus at least two halves, so we’ve used eleven pieces so far.” This was met with silence, then they got to work. They needed a bit of help with some of the wee corners, but in all, we finally figured that it took thirteen pieces of paper to cover the top, and we would need a bit more so clearly this brown table has the larger surface area.

Unbeknownst to me, one of our kindergarten teaching teams has been hoping to get a different table into their class. On the second day of this investigation, my colleague posted a request asking if anyone had a smaller table they would be willing to trade. I showed this to the class and told them that I asked if by “smaller” she meant shorter or smaller area on top. She meant shorter, but also needed the table to fit in a certain spot, so the surface area needs to be just right too. They then set out to measure the height of all our tables, especially the one with the smallest surface area, so we could see if it would be a good trade. Not wanting to disturb the kindergarten class, I took just two of my students to measure her table so we could compare.

Are you dying to know the results?? Well, I think we’ll need to trade her for one of our adjustable tables. Her table and our adjustable tables have the same surface area, and the table we have that has a smaller surface area is the same height! I’m going to try to have the children present their results to the kindergarten teaching team one day this week so they can decide. It will be a good chance for my students to practice communicating.

There were so many good things that happened: we got to talk about using the snap cubes in groups of 5 so they are easier to count; we had reminders about centimeters and meters; we did some mathematical modelling; we had conversations about why the centimeter cubes need to be in a straight line (see how it curves in one of those pictures?); we had lots of opportunity to practice communicating our thinking and solutions.

This week we will spend more time talking about area specifically. We will also be talking about why it takes fewer snap cubes than pieces of paper to cover a table, and why it takes so many centimeter cubes compared to snap cubes.

Measurement

## Time…

This week we had to pivot to online learning. There are a few topics I have figured out that are really good for online learning. One of those topics is telling time. The curriculum expectations for time are:

I think this is a good topic for at-home learning because there are some very active things we can do instead of staring at the computer all day. It’s also easy to find meaningful worksheets that those who are not meeting with us online can finish at home with their parents.

Telling time, however, is a topic that I often wonder about. Is it really useful to today’s children? When I asked them to tell me the time, every kid could do it. They looked at their computer screen and that was that. The digital clock is right there.

The grade 2 expectations make a lot of sense to me. Kids do need to develop a sense of the time it takes to do something. I had them talk about some things that might take an hour, or a minute, or a second, or longer to complete. We timed ourselves to see how long it would take to touch the front door, the back door. We talked about relative time when I asked them to touch a bedroom pillow. That wasn’t long for some who are working in their bedrooms but it was longer for those working at the kitchen table.

The grade 2 expectations are a little more challenging. Digital clocks are no problem at all, although some aren’t quite sure how to say the time when they see it. 9:00 is “nine o’clock” but some want to call it “nine zero zero”. It’s easy to clarify that for them. 9:15 could be nine fifteen, or quarter after nine, or fifteen after nine. Again, it doesn’t take long to get everyone to start saying this the right way, and we will have many practical opportunities to practice at home and at school. The analog clock is quite a bit more challenging, but after a few days all those who are working online with me are doing okay.

It does have me wondering if being able to read an analog clock is a skill that will become obsolete in the not-to distant future. I wear a watch, but it is digital and it’s really there tracking my movement through the day. If I need to know the time I always have my phone with me. Will there every come a time when analog clocks disappear?

## It’s sinking in

I had intended to spend the whole week measuring. But guess what? They’re really pretty good at it! It’s the second time this year we’ve visited measuring and I’m pleased to see the spiralling is paying off. I had an activity planned that involved us measuring which of my many mini cars could go furthest after one push, but decided that is better suited to a science investigation we’ll do later. I

t was pre-Halloween week and I wasn’t sure we could handle that much excitement.

Instead we worked on an unplugged coding activity. (Find it here) It went so well! I’m feeling hopeful that we have rounded a corner. I finished gathering all the math assessment data so I feel better able to meet the range of needs (because I know what the needs are!) This week we’re tackling addition. I’ve done a few addition number talks but this will be our first real jump into the fire. Then in two weeks we’ll circle back to coding.

## Week 1: Done

This week we did many of the same activities I used last September for the first week of school. Namely we measured things that are a meter apart. Once again I was hoping that all I had to do to keep everyone a meter apart is show them how big a meter is. Don’t you love my optimism? Once again, we finished the week still needing practice.

As I sit here today working on my plans for the coming week I’m reflecting on how quickly everyone did fall back into some of the Number Talk routines that are common in my school. I typically have a class mostly inherited from one teacher, but this year it is a mixed group. I’m at a dual-track French/English school and I have more transfer students from French Immersion than I’ve ever had at once. I wasn’t sure how many of them may have used a “thumbs up” for Number Talks, or how many may have discontinued this during online school in the spring.

Last week we did a lot of counting for our Number Talks. I know I originally got this activity from Graham Fletchy, but I cannot find it! Basically I had a plastic cup (noisy) and I dropped small stones into it while making sure they could not see the objects falling. The class had to count as I dropped and then tell how many were in the cup based on what they heard. It’s a great activity that helped us talk about listening closely while also establishing our Number Talk routine. I’m definitely doing the “popping balloons” activity (from Graham Fletchy) this week, and few others I’ll report on next week. I didn’t expect to need to spend time on counting (grade 2 and 3!) but we need it anyway. Many students went right to rote counting and reciting and I want to make sure everyone remembers (and is able) to match a number to a “plunk” in the cup, or to an object they touch or see. I suspect we just need to get back into the groove of school, but one can never tell in September!

This week I will also be plopping everyone online for a few minutes. I want to make sure everyone can sign in and knows where to find our class page. I hope we don’t ever end up back online again, but I need to make sure everyone is ready…just in case!

For our regular lessons, we’ll do some more measuring. Looking at our class numbers I’m predicting some reorganization AND I want to stick with a gentle start to the year. Everyone in grade 2 seems to like measuring.

## Detour to Measuring

This week we took a slight detour on to some measuring.  We spent the week talking about making sure the measuring tool goes from end to end when measuring length.  We talked about the difference between length and width.  We talked about why we need to use standardized measurement tools.  (Most of my class are in grade 3, and that is the year students move from non-standard to standard measurements.)

One of the activities we did comes from the Effective Guide to Instruction (Page 99 of this document).  Last week I wrote about how I wanted my students to make more intentional decisions about which tools they choose for their math.  The day before we measured the paper snakes, we had measured our shoes. As always, the two most popular tools were the connecting cubes and the “special stones”.  Before starting with the snakes, we had a talk about why they like these, and which one is actually better for measuring.  I was excited at the end when most of them were talking about using the connecting cubes because you can take them apart and put them back together in different shapes.  One student told us they can be used to go around the perimeter of things.  Several of them talked about how the special stones, the colour tiles and the pattern blocks slip and move around, but the connecting cubes stay put which makes them easier.

On to the activity:

Two children also tried to use rulers and measuring tape.  Discussing their experience was a great way to wrap up the lesson because even though these are specifically measuring tools they weren’t the best tools for this job.

We had a really good conversation about which method was actually going to give us the real length of the snakes.  Everyone agreed by the end that we have to measure every part of the snake’s length, and many of them wanted them put the cubes into connected towers.  I was sorry that none of them thought to do groups of 5 to help make the counting more efficient.  That’s something we clearly need to work more on. We recorded everything on a chart and that’s where we started on Friday.  We talked about why everyone had different answers, and why it was important to have the same answers which we get when we agree on the units.  I told them about the king’s foot and how this wasn’t even that standard, and that even though a lot of grown-ups still talk about inches for certain measurements, we are going to focus on the metric system and I think they’ll agree that it’s a lot more efficient.  I had them wander around finding things that were the same size as a 1cm cube.  Then we used the rulers and the measuring tapes to find things that are 10 cm.

I think it’s so important for them to have these many points of reference.  It helps them to estimate measurements.  They all now know that their fingernail is about 1cm and they will always have that fingernail to help them measure.  We even talked about how for me it’s only my pinkie finger because I have grown over time.

Next week it’s on to addition and subtraction.  But we’ll be coming back to measuring on a regular basis. This is actually the second week we’ve spent measuring this year, so now I feel confident that everyone has a pretty good idea of how to do it, and we can focus on practicing.  We are also going to do a fair bit of our measuring during art and science, especially when we move on to capacity and weight.

## First 2 Weeks: Frog Jumping

I have made a commitment to myself to work through the Edugains document that spirals the math curriculum this year. I’ve put a fair bit of time into creating a long range plan that follows the document. But one thing I’m worried about is that it will effect my flexibility. Will I be able to follow our interests on a tangent? Will I be able to speed up or slow down as we want to? I suspect I’ll be able to, but I’m still wondering about it.

The activity we’ve been working on this week is an example. I’d intended to spend one day on it, but tomorrow will be day 3 and I am sure I’ll have to/want to come back to it. We’ve had such a good time and have used so many math skills at once, not to mention some science and literacy skills. I want to keep doing that! I also want to reap the benefits of spiralling our learning.

I bought a bunch of plastic frogs from Amazon. I wanted us to measure whose could jump furthest.

Day 1:

They came up with fun ways to get the frogs to go farther. They had them jumping from chair to chair, and across a gap between tables.

They even got interested in how high the frogs could jump!

Getting the frogs to jump took some fine motor skills I hadn’t anticipated, which is the main reason this 1 day activity needed a second day…or so I thought!

Day 2:

Day 3:

Finally the contest! I thought, based on previous results, that a ruler would be long enough for everyone to measure the distance their frog jumped. Then I sat beside a friend who had a metre stick and made my frog jump 74 cm. We spent Friday discovering lots of could make the frogs jump farther than we thought. Having the contest going helped them focus on that one thing instead of continually experimenting. One group even showed us a great way to record the measurements:

We were interrupted as I was beginning to get to the group who was using this strategy, so I can’t explain what the S’s are for. We’ll take this up on Monday! my nicely organized measuring tool bucket looked like this as we rushed out the door for dismissal:

I learned a lot from this activity! I know that everyone knows about rulers and tape measures. I know that not everyone sees them as the best way to measure distance. I know some kids recognize the need to record their thinking so they can share later. I know who has some great strategies for working with partners and who sees math as a solitary venture. At least this math anyway.

I feel like I want to do more measuring. I also want to move forward with patterning because we clearly need that. According to The Plan, we are going to start with sorting and classifying objects.

But the whole point of spiralling is that I figure out how to measure AND pattern next week. I’m also documenting this work electronically so I don’t have to start fresh again next year! I’m also noticing, but probably won’t bother collecting data (maybe I should?), how often I mention “other” math. We weren’t talking about fractions but I found that discussion about 1/2 came up frequently. We weren’t talking about probability but we did talk about “average”. And we weren’t talking about data management, but we certainly did manage our data.

So there you have it! First 2 weeks: done!

## First 2 Weeks: Bulletin Board Borders

One of the things I love about the first 2 weeks of school and the last two weeks of school is the freedom I feel to do fun and interesting things without feeling pressure to stick to curriculum or assess and document what happens all the time. I can focus on relationship building and connecting with my students.

One of the activities I had planned for this week is something that many of the kindergarten classes in my school have done. It doesn’t represent a whole lot of creativity on my part, but I’m so glad we’ve done it!  We have been creating our own borders for the classroom bulletin boards!

A few more than half of my students are looping from grade 2 into grade 3 with me.  I love this!  Last year we completed a Context for Learning math unit called “Measuring for the Art Show.”  In that unit we use cash register tape to measure things and create number lines. For this activity, I gave each group a roll of the paper and asked them to use it to create their borders. I assigned each group one bulletin board to work with.  I asked them to measure properly, and decorate the paper with patterns.  Those are all of the instructions I gave.

Three of the four groups actually measured.  One group has decided to keep cutting pieces of paper, different lengths, and then piece them together like a puzzle.  I was happy today when a child in that group told me exactly where to put one piece of paper.  It fit exactly in a gap, and the child said she measured before she cut the paper to make sure it would fit.  So this is a bit of a “guess and check” strategy, but I feel like it’s evolving into measuring.  They still have a few big pieces to do, and I think they will use this strategy going forward to create bigger pieces.

Of the three groups that measured, two realized that they could measure the bottom, easy to reach edge and then cut two of that length.  They didn’t have to reach up to measure the top because the top and bottom are the same.  They also realized that the left and right are the same. The third group needed some prompting for this.  I think if they could have reached the top they would have simply measured 4 times.  Of the three groups that measured, only one used a tool (measuring tape) to measure instead of simply using the paper.

It has been very interesting to note that there has been very little actual patterning occurring.  Some of the groups have drawn on the paper.  We’ll have to work on that a bit. I want to make sure they understand the difference between patterns and designs.

There has been a lot of cooperative work happening.  There has been some arguing.  C’est la vie! That’s how a community of children often gets started in their work together.

I have already decided I will do this activity several more times throughout the year.  I want to see how it evolves.  I am going to keep the groups the same each time.  I can’t wait to see how their thinking and group-work skills grow.

As the end of Winter Break approaches, it’s time for me to sit down and do some planning for the coming weeks.  Reports cards are due at the end of the month and I need to get all of my assessments up to date and my comments organized.  The report card should reflect what the child is capable of at that time, not what they were doing 2 or 3 months ago. I last formally reported on everyone in November. I know there has been growth for everyone, some big and some small.

For math assessment, I am going to re-do the interview I used in September.  I know that for some children I can start in a different place because they have shown mastery in areas I previously assessed.  I will have to go beyond where I left off with them because they have shown growth toward the end of year goals. I also need to add in some geometry and data management questions so I can report accurately on that as well.  I have a lot of anecdotal notes to draw from, but I want to be really sure of what they can do now.

As I have been reflecting on this, I am struck once again with how hard it is to divide math into 5 strands.  I suppose it is easy in the Primary grades to do that with Geometry, Data Managment/Probability and Measurement.  But even at this point they are all starting to blend together. Everything we learn in Number Sense is related to everything we learn in Patterning and Algebra.  I can hardly decide how to mark everyone sometimes because I’m not always sure if the things they need to build understanding about exist in one strand of the curriculum document or another.  I have to consult it every time because in my mind it’s all mashed together into “math”. Everything we do in Number Sense is related to what we do in Measurement too, but it’s a little easier to seperate out the skills that will be reported on.  Same for Geometry and Data Management/Probablity.

Here is one example of this from the Grade 2 curriculum document (2005):

• identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1’s, 2’s, 5’s, 10’s, and 25’s on a number line and on a hundreds chart (e.g., the numbers 90, 80, 70, 60, 50, 40, 30, 20, 10 are
• count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5’s from 15; count by 25’s from 125);
• count backwards by 1’s from 50 and any number less than 50, and count backwards by 10’s from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.);

Two of those are from the Number Sense strand and one is from P/A.  But I teach them simultaneously. And if a child is having trouble with skip counting is it because s/he isn’t understanding the patterns associated with the skip counting, or is having trouble memorizing the order, and if they seem to not be having any trouble is there some rote counting, or is the child processing the numbers and thinking about the patterns?  It’s tricky to assess sometimes. And sometimes it isn’t. For instance, if a child can say, “2, 4, 6, 8, 10” but then stops and can’t figure out what comes next, I know the first 5 terms are acutally just counted by rote. Or if a child can count by 2’s even further, but then isn’t able to do this when there are actual things to be counted, I know there has been some memorizing. And if a child gets to ten, then pauses to work it out in his head, comes up with 12, then slowly with 14, and so on, I know there is some understanding.  It’s tricky to boil all of that down to a letter grade.

Someday when I open my own school and can make my own rules, I am not going to assign letter grades to Primary kids ever. The report cards at my school will be all about the comments.  And I will definitely not divide math up to strands!  But for now, I’ll sit down and go through my assessment and the curriculum documents, then I’ll sit down with everyone in the next 2 weeks or so and ask them the questions I’m wondering about.  And then I’ll sit down and give them all a grade that reflects what they can do.  Easy, right?

## Who is the tallest?

Every June I wish I had measured everyone’s height in September so we can see how much everyone has physically grown. Every September I forget. But not this year!

On the third day of school, we started talking about measuring things. Grade 2 is the first year students use standard units of measurement instead of investigating things like “how many markers tall are you?” I know the grade 1 teacher was working on this in May and June, so measurement seems like a good place for us to start. It’s a quick thing we can work on after spending some time each day setting up Number Talk routines.

It was really interesting to note that the grade 3 students in the class aren’t necessarily the tallest, and the tallest grade 2 is not the oldest grade 2.

After measuring our height, we brainstormed other things we can measure and compare – who has the longest feet, the biggest hands, longest hair, and biggest eyebrows? We don’t have answers to these questions yet, but we will by mid-week.

Changes in season make interesting times to measure temperature too. I’ve got my thermometer ready to go, and we’ll be tracking the temperature each day as we move from “It’s so hot we shouldn’t be keeping schools open” to “Sorry I was late. I had to scrape ice off my windshield.”

Grade 3 students study plants in science, and this is a great opportunity to integrate math into science, or science into math if you prefer. We’ll be planting some plants for our windowsill soon, and measuring their growth.

Most exciting of all is that when the final days of this year arrive, we’ll have both the skills and the data to determine exactly how many centimetres taller everyone has grown.