Data Management

## Venn Diagrams and Carroll Diagrams

I do not have time to write, but here I am anyway!

Yesterday we started working with Venn diagrams. I layed two hoola hoops on the ground and we sorted ourselves into them according to the headings. The first two were “brother/has only one sibling”. We also did “blond hair/male” and “female/born in October, November, December”. I do not have any children with other gender identities, but you may need to adjust accordingly. For the final two sorts, I wanted to sort them in a way that might be meaningful to someone so they would see a possible real-world application. I told them that I have seen a lot of people serving oranges to children at halftime in soccer games so I wondered if children who like soccer always like oranges. That was our next sort: likes soccer/likes oranges. It turned out to be more true than not, so we concluded it would be safe for me to plan to serve oranges at a soccer game, or to take orange juice.

Next, I said that schools are always thinking about how children who are tired have a harder time concentrating in school so it would be helpful to know why some children come to school tired. I have a theory, I told them, that some children are more tired than others because they have to get up earlier so they can catch the bus. Our sorting categories were “rode the bus to school/woke up before 7:00 a.m.” There was a nearly perfect correlation – bus riders get up earlier than those who walk or get dropped off. We talked about how this might be solved, and concluded that if we had a few more busses people wouldn’t need to be picked up as early, but agreed that a few more busses is easier said than done.

Today we used this digital Venn diagram tool: https://nrich.maths.org/6290

I let everyone come to the board and write a number in the correct circle so basically I am now the best teacher ever because writing on the whiteboard is a very special treat!

New to the 2020 Ontario math curriculum is the Carroll Diagram. It was previously in the French curriculum in Ontario, but not English. Every year I’m trying to find some good Carroll diagrams to use and this year I decided to make some. We are going to use them tomorrow.

## Multiplication Worksheets

I think last time I posted I said I’d be posting more often, so I feel like I need to point out that once a month is “more often” than once a year. So if you were expecting to come here every week I’m a little bit sorry to have disappointed you.

One of the reasons I wanted to learn how to make math resources for myself is because I never quite like the things that are available to me on the Internet. I mean, they’re okay I guess, but I usually end up feeling like they could have been more interesting. One of the first things I learned how to make are these “cut and paste” activities. They don’t take too long and I can customize them pretty quickly now that I have a template made. In addition, I like that it gives my class some practice cutting. The thing I had not anticipated, but love, is that they have learned how important it is to organize their answers before they start to glue them down. The first time we did one of these they were gluing too soon and regretting their choices. Now, however, they place the strips where they are pretty sure they belong, then double check everything before gluing them down. I love listening to the conversations they have when two people who sit beside each other aren’t sure if they have something right.

The next thing I learned how to make are these fun mazes. I have plastic covers that the papers slip into. I printed five of each maze style, then we passed them around all week for morning work. You’ll see some commonalities, so nobody was exactly sure which maze they were getting. They couldn’t fake their way through it! They had a great time doing them. They love using the dry erase markers to colour so this seemed fun to them. I have set these aside so that we can do them again in a few weeks for a review. Here is a picture of what it looks like when one is complete:

Speaking of reviews, the last thing I am posting today is a scavenger hunt. I think I mentioned in the money post that we LOVE LOVE LOVE scavenger hunts. I made this one as a review of all the things we have learned so far. It’s much more fun that doing worksheets for sure. Every child gets a recording sheet, copied front to back, and they wander around the room with clip boards looking for the equations they need to solve. I’ll definitely be making more of these reviews because it was so much fun. I was able to sit by one or two questions and observe every child as they came to that question. I have great notes! Most of them worked in self-selected pairs and they had great conversations about their strategies. I was initially thinking that 40 questions would be a lot and that we’d spend multiple days on this. I was prepared to shut it down if it was too much. However, they loved it. When I could see that some of them were more than 75% finished and others were less than 50%, I started observing them more closely. There were some students who were struggling with things we had left behind while working on multiplication. They had it while we were focused on it, but lost it when we moved on. That let me know that addition and subtraction need to be on constant repeat in our Number Talks, or in our morning work. This has definitely helped them.

We are moving on to division when we return after the holiday break, so I am already working on making my division worksheets, then it’s on to fractions.

## 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.

math

## Mid-year Assessment

A few weeks ago I wrote about creating my mid-year assessment for math. (You can read it here.)

During our second week of online learning I scheduled some 1:1 time with all the children who were working with me virtually. I had created the assessment as a series of PowerPoint slides, so it was easy for me to share my screen and ask the questions. This week we have been back in class, but two of those days were inclement weather days and I only had a few students. That made both days great days to sit with those in attendance. Out of nineteen students I only have six left to sit with. I could have had them done this week if I had given up my preparation time to work with the students, and that was my original plan. Alas, other tasks took priority and I will now have to finish next week.

The first two students I met with did exactly what I expected them to do. The first did surprise me by using very inefficient strategies. But when I prompted them to try some of the other strategies we have talked about they were used without trouble. At times that child even tried to use some strategies that were not going to work at all, but they still wanted to try. Every time they eventually landed on a strategy that worked beautifully. The next student completely surprised me by using several strategies very efficiently, and then by describing the strategy clearly and concisely. When asked how many beads were on the left of the math rack (picture below), the child said, “One hundred. That’s my estimate but I’m going to check…10, 20, 30, 40, 50, 60, 70, 80, 90, 100!! My estimate was right! I said to myself ‘It’s probably 100’ and I was right!” Time and time again the students surprised me either because they were able to solve a problem I wasn’t sure they’d be able to get, or because they were so articulate in describing their strategies.

It’s been a really rough year and there have been many times when I have thought my time has been completely wasted. Maybe not all of it, but I certainly haven’t felt 100% effective with my math teaching in particular. Completing these interviews has helped me see that we have made a lot of progress. If I compare the results to the interviews I completed in September, I can see so much growth in so many of my students. I also see exactly what we need to work on.

Today I am working on report cards. I am using the data I collected in the interviews, as well as other information, to report on everyone’s math progress. I’m also going to do some tracking so I can see what trends exist. Then I’ll really know exactly what to focus on next. It’s all a giant mess in my “virtual learning notebook” right now because organizing my own work continues to be my personal most frequent next step.

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?

math

## I’ve done it again…

…I planned to blog every week about math in my class, and I have not followed through.

In my defence, I have been really, really tired. Exhausted, in fact. And after spending time planning and organizing my day I didn’t have it in me to properly reflect on how things have been going. December is ROUGH.

Alas, a two week break has been really good for me. I have a few days until our return to school, and have started to think about what that will look like. January is the end of term, so I need to do some math assessments for everyone. I have blogged before about doing math interviews. I do love them, but have decided to create my own set of questions for this mid-year assessment. I know what we did, I know where the curriculum says we need to be in June, and I want to figure out exactly where we go next. I can do that best if I create my own assessment.

Up until yesterday I was pretty sure we would be doing some online school in January, so when I was thinking about the problems I wanted to pose I made them into slides. I’ll still use these when we are working in person.

More than any other year, my students have such a wide range of skills. They are definitely not divided into “grade 2” and “grade 3”. We’ve had to spend quite a bit of time on counting, especially skip counting. I decided to use Toy Theater to make some images. I anticipate that some of my people will still count by ones. But I think most people will at least count by 5s and 10s, and at least one will count by 20s. (These are just 3 of the 8 images I am including.)

I’m also asking some problems that ask them to work with single digit numbers and double digit numbers, and I have a multiplication question. That is where I know we need to go soon, so I want to see what happens. I predict a few will count by ones, a few will skip count by 4s and three will say, “4×4=16.”

We’ve done some geometry and money as well, so I will have coins and shapes in front of us that everyone can manipulate.

Two summers ago I updated my spiralled math map to reflect the new curriculum. I am pretty much on track with that, although we are a bit off track. By the end of first term in previous years my grade 3s would have been working with three-digit numbers and we haven’t done that yet. All my 2s would be working with double digit numbers, and we aren’t quite there yet. But we will have half the year to go so I am not worried about it.

I am also really interested to see where everyone is in their communication skills. That was definitely a “need to work on” area for lots of and I think we’ve done a pretty good job so far.

Finally, I want to know how they all feel about math.

The interviews will take a while. I predict I’ll be spending at least 10 minutes with each child, and I have 20 in my class. But the information I gather will help guide us in the right direction for the next few months so I know it will be time well spent. I have a total of 18 slides. Some students won’t need all of them at the end, and some can start in the middle. I’ll try them out on my son before school starts. They’ll be too easy for him, but it will help me work out any trouble spots.

## 98…99…100!

We started keeping track of our own acts of kindness about 2 weeks ago. We needed to know of what it really means to be kind, and conscious of when we were actually doing it.

To help us out, I printed a sheet of 100 hearts. Our goal was achieved in only 6 school days!

Of course I found a way to add some math. There are ten hearts in each row. Initially I coloured in 5 hearts with one marker and the other 5 in another colour. We were counting by 5s and it was all going well until someone decided to put us on the fast track and do some covert colouring of hearts.

For the second attempt I switched to bingo daubers and counting by 10s. At first only one child was counting the hearts…both up and down. “We have 12, so 88 to go!” They’d say. Then more kids jumped in and every time I’d colour in a few (they always had many acts of kindness to report after recess) more and more kids would help with the running total, as well as the number remaining. They’ve been less than enthusiastic about lots of the math we’ve done, so I was excited that they got excited about this.

Of course we had to keep going. Today I added more hearts to our new chart. The filled chart was behind it. “How many do we have now?” I asked. They all agreed we had seven. “I disagree I said. They started to try to convince me I was wrong. It was good to see they are learning some math reasoning skills, but I was right. I pulled out our filled chart and put them side by side. “I think we have 107,” I said.

They had no choice but to agree with me.

I can’t wait to see where this goes tomorrow.

It also helped them become more aware of opportunities to help out. Someone dropped crayons one day and I made a big deal out of adding some hearts for the helper. I truly don’t know if they had ever considered helping a classmate out, especially for a chore like cleaning. I’m happy to report this type of thing has become more common for us.

## Fun and Games

It’s not really all fun and games, but I have found math games to be a life saver for us this year. All of the math that happens during a game seems to be secondary to the learning that comes from actually participating in a game with a group of ones peers: sharing, turning taking, good sportsmanship and gracious losing.

One of our favourite games as been played with dice and a giant pop-it board. I bought a few of these and we’ve definitely gotten my money’s worth.

The kids take turns rolling dice, adding up the totals and then popping that many pop-its. Nothing like jumping on a trend! They love this. I’m already seeing many more kids subitizing, counting on instead of counting every dot, and doing the addition from memory.

We have also played a card matching game. We removed the face cards and tens. The remaining cards are layed out in an array. Kids turn over two at a time and try to make a match. A match is any two cards that add up to ten. We still need some help with this game. Mostly we need help remembering what makes a match instead of just trying to find two of the same number.

Picture this:

Me: No. 4+4 isn’t a match. A match is two cards that add up to 10 and 4+4=8.

Them: But that’s hard!

Me: But it won’t stay hard if you keep practicing.

Them: *dramatic sigh*

We’ll keep working on this game.

This past week I introduced a new game. This game is all over the Internet and is typically called “Shut the Box”. I have no idea why it earns this name because the boxes are usually laid out in a straight line. It should be called something like “Fill the Line”. For now I’m calling it, “This cool new game I think you’ll like.” I’ve got until Monday to come up with a better name.

For this game they need a game board (one each) and a pair of dice. On their turn they roll the dice twice, then try to figure out which of the numbers on the game board can be covered with a counter of some sort. They can add or subtract the numbers on the dice. I made my own game boards and printed them on 8.5 x 11 paper.

This game was a big hit with everyone, especially the kids who got The Tricky Version.

I didn’t have enough ten-sided dice, so the groups playing this version used virtual dice on Toy Theater. They were especially excited to find that I’d made a mistake! In my haste to completed my planning and creating, I neglected to notice that the 10 sided dice here have the numbers 0-9, not 1-10 as I had assumed. On Monday I am going to have them help me figure out which numbers I need to add or take away on the game board.

I’ve also created a game board we didn’t use yet. It uses the “count by tens” dice on Toy Theater. I’ve decided the 00 side will count as 100.

One of the really interesting things about my class this year is that they have such a wide range of abilities. It’s a 2/3 split, but in math they are more like a k-4 split. Some of the students will stick with the first game board for a while, while others will be creating their own game boards using the fancy dice on Toy Theater. I’m glad for games that can be adapted to meet a wide range of needs. I’m also glad for games that can be played independently. We’ll be using this, the pop-it game and the card game all month while I am doing Guided Math. I’ve always talked myself out of Guided Math, but I can’t this year. There’s no other way to meet the needs of all the people in the room. I’m teaching two different Fosnot units (Double Decker Bus and The T-Shirt Factory) at the same time and I really need to be with everyone while they work. The group that is not with me can play a game or work on Dreambox.

## 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.