Re-recap

I can’t believe how quickly I run out of times to do things, and how many weeks go by without finding time to blog. Phew!

Some stand-out things:

• I got my hands on Math Games with Bad Drawings by Ben Orlin. HIGHLY recommend. I’ve only made it fraction of the way in, but there is such a lovely mix of humour, information and great games already. I also started reading it just in time. We had a few days of interrupted classes, where I may have had anywhere from a rotating door of 3-18 students in my room at any given time. We’ve tried Dots and Boxes, Spouts and Dandelions. I’ve spotted several students playing when they’ve had a free moment, and really enjoyed listening to them discuss strategies, odds, and modifications to change gameplay. So fantastic!
• I asked students to look over my recording instrument to see what three learning outcomes they wanted to show me. These may be things we’ve done, but I hadn’t recorded evidence of, or stuff we hadn’t done yet, but they felt they knew. I took their requests and created a personalized quiz for each student based on their choses learning outcomes and levels (basic, intermediate, advanced). For this particular quiz, students completed their work on their own. I then photocopied the quizzes and gave the photocopies back the next day. They could then use their notes, ask me questions or work with their peers to add more to their work – I just asked that they do that in a colour other than black pen, so I could easily see what was added. All of this was then added to my recording instrument.
• I need to rename things. Recording instrument needs an easier name. Quizzes need to sound less ominous, especially since they aren’t quite quizzes. Maybe Montre-moi? (Show me)
• We’re exploring percentages, and I’m about to launch a task where they have to decide what they want to buy with $75 imaginary dollars from a store of their choice, depending on the kind of coupon they might get (35% off one item or 15% off the entire purchase).

What we did

I’m a big fan of checking out Aleda Klassen’s Twitter posts about what her #mth1w class is doing. I’m going to try to capture ours in a similar way here. Maybe I’ll be more consistent?

We started out reviewing addition of integers by trying these Kakuro puzzles. Lots of engagement!

We followed this up by me modeling Multiplication of integers using a combo of Nat Banting’s bucket of zero and hot/cold cubes activities. Students seemed to really connect with content. Why have I never started with models for this before? Oh, because models are often less familiar to me. Must keep working to fix!

We had a few more minutes, during which students added notes to their future forgetful selves.

A little bit of catch up

How do people maintain blogs? They must have far better time management than I do. Once I no longer had a student teacher, any semblance of time to plan, prepare for lessons and assess just seemed to vanish. Report cards loomed. I missed two separate weeks with my students, so when it came time to start writing those, I felt like we hadn’t done much at all!

Our schedule changed slightly too – we lost a PE block (we were sharing with another class before, and dropped down to two blocks a week to reduce contacts with other classes). While I feel like that should have meant that I would have MORE time, somehow, I had less. I’m not sure how I fit everything in before… although a colleague pointed out that my math blocks are likely longer than previous years. Yeah, that story checks out.

So what have we been doing?

Bimonthly quizzes (twice a month, not every two months, in case you – like me – weren’t sure). I’ve been working with the students to try to explain that I don’t count points or average marks in math. These quizzes are opportunities for students to show me more of what they know. I wonder if I need to rebrand these? We’ve had a few different formats:

• Individual quizzes (you know, standard format)
• Individual quiz, followed by me frantically running to the photocopier. Once copied, I handed out the photocopies, randomly assigned students to groups to try and check their answers/add more in a colour of pen that stands out from the photocopies. This allowed me to see what they could do on their own, what they could do together, and give them another chance to review the material
• Collaborative quiz followed by individual quiz

Since we’ve been spiraling through units, I’ve been adding one or two questions per strand, to allow for more review. I’ve also been toying with the idea of giving the students a physical copy of my assessment grid so that they can choose an “I can” statement that they feel like I need to add. I suppose I’ll have to make up a question bank – but would love to leave an option for students to make up their own question too!

Spiraled units – I feel like I’m doing a better job of spiraling this school year. The loose plan I laid out has helped guide me. I’ve been able to explore MathUp a bit lately, and they also have some suggested year plans. I may try following one of those next year. I’ve also realized that I can address more than one thing at a time, like reviewing algebra while also talking about strategies for multiplying and dividing decimals. I know that sound silly, but it’s good for me to remember that I don’t have to do the two as separate lessons.

Thin slicing and problem strings – I’ve been experimenting with ways of doing problem strings and creating my own thin sliced activities. We had a great one with algebra which kept me moving around the room from group to group. Music to my ears? When I got to one group and a student confessed, “Oh, we did that question already. We, uh, copied the question from another group while we were waiting.” I definitely celebrated that outwardly, so hopefully that group knows they have my full support in doing that again! I also loved celebrating with students once they were able to answer something that took a while to get there. So. much. fun!

10 mins to bell. I should probably do all the things.

Round up

I am NO GOOD at keeping up with these posts, now that I’m back to teaching full time!

In the past few weeks, we have:

• Had our first bi-weekly quiz. It was a great chance to explain how I gather data and record it, and reinforce that learning is an ongoing process. Students got 5 questions, covering topics we’ve addressed so far since we are interleaving material. To help me in this process, I decided to build a problem bank throughout the year by strands, so future me can put together appropriate quizzes without constantly having to reinvent questions.
• Explored integers and how to represent them (we used the Chef’s Hot and Cold Cubes to do so). The students really seemed to grasp the concepts. The only hesitation I had was that, for the activity, we used red counters for hot (positive numbers) and yellow for cold (negative numbers). Typically, I’ve used the opposite (you know, red for being in debt), so I had to be extra clear as to what I was doing on worked examples of VTC!
• Explored how to add integers using student examples to explore patterns. We used red and yellow counters and number lines. I took the students outside to create a human number line and had them move along it to represent different problems. They were really into it, but, as with many of our activities outdoors, the students got rather silly quickly. (It was also pretty cold!)
• Played with probability, discussing certain and impossible events and how to use a tree diagram (does it just translate to that in English?) to represent possibilities. At present, they are making their own probability games up and will share today.

Which tee-shirt company?

We started our math block with an Esti-Mystery. I had them write down their estimations in their journal as the clues came up. They loved it so much, they asked to do more (we didn’t have time, so I promised them we would do more another day).

I pulled all the students in to a board and asked them how much their grad hoodies cost. I reminded them that they were warned that they needed to submit their orders in time, because if they ordered late, they would have to pay a special fee for the company to set up the stencil again.

I explained the scenario. As a fundraiser, we want to do a tee-shirt order, but we had to pick a printing company. One company just charges per shirt – $15. The second company charges $50 to set up the printer, and then $10 per shirt. How do we know who to order from?

“No, we don’t know how many people will want to order shirts yet, sorry!”

Off they went. Interestingly, most groups jumped straight to 10 shirts being the same cost, writing this out with words. “Prove it to me!” I prompted.

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This is what they came up with. Sadly, I only noticed how one of the groups wrote out formulas as I was taking the photos. They students were crowded so close during the activity, I couldn’t see that part! I wish I had seen it. It would have been great for consolidation.

I had noticed that despite prompting, some kids had a hard time giving up the marker, so this time, I set my watch to time 2 minutes and established a rotation of job of writer. It definitely prompted some arguments amongst the students (“She SAID to switch the marker. Pass it over!”) but also some great check-ins (“Do you know why I told you to write this? Do you understand what’s happening?”)

I did have one group misunderstand and assume that one company would charge $60 per shirt, but they generated some great questions about it before I spotted it.

After consolidation, the students took notes and we did individual whiteboard practice to help us all see what they might need to add to their notes to their future forgetful selves. A common confusion was what to write for the coefficient or constant term when it’s not explicitly shown in the expression.

Factors, Divisibility and Measurement

Post-Halloween, we moved from using ratio tables for multiplication and division to looking at rules of divisibility. We did an Open Middle task, where students came up with some really great strategies. Then, I gave them a scenario, where one student claimed that 260 was divisible by 4 and 5, and therefore also divisible by 20. A different student chimed in an said that 148 was divisible by 2 and by 4, and therefore also divisible by 8.

Off they went to explore this in groups at the whiteboards. They all determined that the second student was wrong, but then needed to explain why. One of the groups did a great job of describing how to determine if a number is divisible by 4 or 8, which was exciting. Before seeing that, I was trying to figure out how to lead students to discovering it with less input from me. Well! Thanks to Group 6 for helping me out!

Next class, I had students write a journal entry about the factors of 120. Unfortunately, I was away and not able to present the task myself. I had some pretty neat strategies presented though!

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The following class was a complete change in direction. We did the 3 Act Math file cabinet activity from Andrew Stadel. The students launched into it. I had the chance to try the, “Oh, I forgot…” strategy shared by Fawn Nguyen, because I genuinely couldn’t remember if students should be trying to cover the top of the cabinet in addition to the four sides. Ha!

I was going to get the students to measure a random object with a non-standard measurement, but after having a chance to watch the first Re-Imagining Mathematics Education webinar over the weekend, I was inspired to make the activity more meaningful. Instead of measuring a random object, we were going to get outside! Students worked in pairs. One student closed their eyes and the other guided them to a tree. The student with their eyes closed explored the tree with their hands, trying to get a sense of the texture and unique features. After they were guided back to the starting point, their job was to find their tree. Once they did this, we only had time to try measuring some part of their trees with whatever they had on them. Some students used their bodies, some used sticks – one used a plastic wrapper they had on them! One student pointed out that she picked a leaf because she could wrap it around a branch to measure that way. Since we were rushed, we didn’t have time to share our measurements, but we were able to have a discussion about criteria we needed for precise measurement (measuring end-to-end, making sure to use consistent length, etc). Next, we’ll do a proper journal entry describing our tree and the non-standard measures we use.

Goings on

It’s been a while, I know. Having a student teacher means I have less time with the students, so I haven’t gotten to do many of the things I want to do. That’s okay, there are trade-offs, for sure!

I presented Exploring Building Thinking Classrooms at the 60th Northwest Math Conference, which was so much fun.

Most recently with the students, we explored ratio tables and other multiplication and division strategies. I’m not sure I’ve convinced them that they are worth doing in lieu of the algorithm, but baby steps! To explore division, I showed students different strategies for the same problem (taken from the Math Strat Chat archives) and had them work in groups to explain how the strategy worked.

We also explored Desmos for the first time this year. I assigned them the Pumpkin Carving. Most students didn’t finish their pumpkins in the time allotted, so when I asked them to put their computers away, there were moans and groans. “Can I work on it at home?” Yes!

When class ended yestserday, I had 3 pumpkins complete. When I checked in this morning, there were 5 more. Aren’t they fun?

My Favourite Mistake

I heard about “My Favourite Mistake” being a teacher-move, but I never remembered to do it. When two students found the difference between two numbers, rather than finding the sum, I knew I wanted to use it.

Both students had opted to use a number line to model their thinking, so I drew that up on the board. I explained that it was my favourite mistake because it showed something awesome, even if it wasn’t what I had asked for. I sent the students off to random boards and off they went.

They quickly found that the calculations were correct. Yup, 58-39 = 19. Shoot. That’s not it.

Next, a number of students said that the mistake was that there were too many steps. The student could have gone over by 20 to get to 59, and then subtracted 1. That would be easier! “Is breaking something down into more steps wrong?” I asked. They begrudgingly admitted that it wasn’t wrong…

“I know!” exclaimed a student, “The dollar sign is the wrong spot!”

“Good spot!” I said, “But in French, that’s not wrong. What else could it be? What did I ask you to find in that journal question?” After asking a few groups that question, someone finally thought to check their journal. “OH! They subtracted!”

So, with a brief consolidation, we covered models for different subtraction strategies. I’m so pleased with how that worked out, I wonder if I should just use that mistake in future years, even if I don’t have a future student doesn’t produce it?

You have to go slow to go fast, part 1

To start out our exploration into curriculum in the BTC way, I decided to start with addition strategies. I’m still not sure if is the starting point I want to use in the future. One one hand, so many of my students approach math with algorithms and not number sense, so this is a great place to start. On the other hand, I wonder if my students feel like I’m lowering the difficult level by starting with something they think they are so familiar with.

I’m going to keep thinking on that.

Anyway, I used Addition Workout 1 from Pam Harris‘s Lesson and Activities for Building Powerful Numeracy. I drew out four strategies on the whiteboard and explained that four different students tried answering the same question the different ways. I asked them to explore the strategies in their random groups, trying to figure out what each student was thinking. We consolidated and gave the strategies names.

Fact: Maybe this is because French is my second language, but I find the translated French terms more cumbersome than the names in English. Over/Under – Aller trop loin. Adding a friendly number – Addition un nombre simple. Just not. the. same.

We pulled out our journals. I looked at the clock. 4 minutes until recess. “Keep them on your desks!” I said, “We’ll do our journals after recess during silent reading instead.” (I promise, I won’t keep doing this.)

I explained that Carl likes video games, and ended up buying a new one for $58 and a used one for $39 dollars. I asked them to try out one of the four strategies we explored to find the total and then explain why they picked the strategy they chose.

Most students opted to add by place value (which, again, is way wordier in French – additionner par valeur de position). It was, they explained, the strategy that aligned best with they way they thought. Some added that they didn’t like drawing number lines because it took too long, which is when I realized…

Oh. I somehow neglected to explain the difference between strategies and models. Oops. To be rectified after.

That said, I did have students who appreciated the other approaches too.

I had two students who ended up finding the difference between the two numbers, which led to a future lesson about my favourite mistake.

The next day, students tried some problem strings in their groups to explore the strategy of give and take (we later named it balancer). I had *thought* that I would have plenty of time to explore this and then launch note taking, but I was once again very wrong about how long we need for each activity. I briefly toyed with the idea of cramming an explanation of note-taking into 10 mins, when a responsible student saved us all from that pain by asking if the primary lunch monitors could leave to do their job.

Right. Let’s do agendas, students, and we’ll attempt note-taking tomorrow.