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:

Grade 2 is in yellow and grade 3 is in blue.

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.

math, Mathematical Processes, Social Emotional Learning

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.

Guided Math, math, Math Workshop

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.

You can get a copy of the game boards I created here.

Coding, math, Measurement

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.

math

Teaching is Hard!

This past week was a challenging one. We’re struggling with the return to school – struggle I thought would be long past by now. It’s been hard to move forward in math (and everything else) but move forward we must! So how, I wonder, can I meet everybody’s social-emotional needs, physical needs, and academic needs?

We’ve worked for two weeks on making patterns with math manipulatives. I don’t remember ever needing to teach this before. Usually everyone arrives with this basic math skill. This year they are even struggling with chanting the skip counting patterns. We aren’t anywhere near being able to talk deeply about number patterns.

So I gave everyone an academic break on Friday and we made beaded bracelets. This type of activity is fun, and it really motivates everyone to do some social emotional work. They had to make a pattern, politely ask a neighbour (or me) for certain beads, string them all on the elastic cord (which can be tricky & requires perseverance), and deal with the frustration of dropping beads. It was fun, and taught them a lot. Communication and resilience are two really important math skills.

This week I’m moving forward. We’ll do some counting routines every day for Number Talks, but our focus is going to shift to measuring. We really need to start moving toward understanding number lines, so I want them all using rulers and measuring tape this week.

Coding, Executive Skills, Geometry, Number Talks, Patterning & Algebra

Making Progress!

We had some interesting conversations about shapes last week.  I was still working on getting my math interviews done so I needed everyone to be independently busy while also learning.  You might think that by the time someone is 7 or 8 years old they know what they need to know about shapes and using blocks, but it’s just not so.  I think wooden blocks aren’t as popular as they once were, so kids don’t necessarily have them to use at home (where they have spent a lot of time in the last 2 year) and I also think it’s because when kids are playing for fun, they don’t have metacognitive conversations with themselves about what they are learning – they just have fun. After they had all rotated through the different types of blocks, I started asking questions and they didn’t have much to say.  But after I asked questions, let them play again and then asked the questions again, there was a lot to be said – two chart paper pages full in fact! 

One child pointed out that we can build castles and other stuff by stacking.  At first everyone thought that spheres and pyramids can’t stack, but after some consideration they realized that pyramids can be on the top of a stack, just not the bottom and spheres can go on top of things, but they need other things to keep them in place, like a cube to lean on. Some students noticed tat some shapes were not represented in the box. They then figured out they could make the missing shapes: two squares make a rectangle, two triangles make a rhombus, etc.

We also talked about the difference between 2D and 3D shapes. We need do some more work here. This week we’ll be talking in casual conversation about how 3D shapes are made of 2D shapes. We’re also going to try to get back on track with the curriculum map I made for myself. I need to get some patterning done so we’ll continue to use the shapes and now start to use them as pattern blocks, along with the colour tiles and lots of other manipulatives from my classroom. We need some community building too, so we are going to make our own bracelets using pony beads and elastic string. I have a collection of beads that’s been hanging around far too long so I want to use them up. AND I need to get going on all the Number Talks that will help us review basic addition/subtraction strategies for numbers up to 20. I completely skipped the fun unplugged coding activities I wanted to do in September, so I will be doing those during our gym time.  I’m excited about trying this out in the big space which we were not allowed to use last year. 

Whew!  I’m tired thinking about it. But also energized. My math interviews are complete and sitting on my desk waiting to be brought home, so I’ll sort through them this week (instead of today like I originally planned!) and find the trends and strengths/needs in number sense. I’m so glad they are done for many reasons, not the least of which is that I can be part of the explorations this week and can MAYBE start taking some anecdotal notes so I can make some informed decisions about what to write on progress reports. 

Guided Math, math, Social Emotional Learning

Repeat

All that stuff I planned for last week went differently than expected. I thought I could interview 4 students per day and finish the whole class. Instead I missed a day because my son was sick and another day because of our Terry Fox walk. Also, I could only interview two students each day because that’s all the time the rest of the class could stay busy.

Despite not reaching my goal I do feel good about the work we did. I’m repeating the plan for the week, just switching out the colour tiles for 3D shapes. Everyone will have a chance to play with those, the pattern blocks, iPads and my new giant “pop it” game board where they practice addition facts. After I interview two friends each day we’ll be talking about attributes of 2D and 3D shapes.

Reflecting on my week really is helpful. I feel like I’m climbing up hill all week and seeing little progress because I can’t meet any of my goals. Taking the time to reflect helps me see that we really are doing good things. Returning to school has been challenging. But not everyone is asking me when they can go home every ten minutes like they were two weeks ago, so I’m taking that as a sign that we’re settling in.

math

Games

We played a fun game this past week called “Cover up”. I learned it from the book “What to Look For” by Alex Lawson.

Each pair of students got 20 tiles. One partner closes their eyes while the other covers or removes some tiles. Then the first child figure out how many are covered up.

It didn’t take long for all the groups to realize organized arrays are better than disorganized piles. The array allows a child to count empty spaces.

I enjoyed watching them use lots of other strategies to figure out how many were missing: counting what was left then counting up to 20, counting backward from 20, noticing a whole row was missing, subitizing the number left. I had one group work with only 10 tiles on the first day, but by day 2 they also had 20. Even the kids who had trouble at first soon, with the support of their partner, figured out what to do. It was a great task! I’ll be adding it to our repertoire of games for Guided Math.