Students were told that, when they multiply two numbers together, the product is 30 less than one of the multipliers. Off they went to random groups to explore the problem!
Some groups needed more nudges, but others spotted some patterns right away. It kept them busy and engaged for about 20-25 minutes before we moved on to CYU questions.
First day back from Spring Break! We created a list of twelve of our favourite ice cream flavours, and then students were asked to find the total possible number of combinations of 2 scoop cones. Two scoops of the same flavour were allowed, and each combination counted once (ex/ 1 chocolate topped by 1 vanilla was considered the same as 1 vanilla topped by 1 chocolate).
There were lots of different answers at first (ranging from 68 to 144) with lots of great reasoning given. I encouraged groups to use manipulatives. Some groups were asked to start exploring 3 cone combos too!
We had some extra time, so we looked at different ways of solving 3.75 ÷ 0.75 that weren’t the algorithm. A few different approaches were shared – yay!
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.
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.
Our professional development committee met about the upcoming Pro-D day – the one in one week (yikes! September is so busy!) With so little time restricting our options, I offered to host a workshop on Building Thinking Classrooms. I figured it would be good practice for me, since I need to prepare one for the Northwest Mathematics Conference in October. I convinced a few other committee members to share the awesome stuff they are doing in their rooms too.
I’m glad I did this, because I wasn’t too sure how to plan for a workshop. I assume it’s a lot like teaching – have a big idea in mind, know your stuff, be prepared to pivot depending on need. I ended up making my husband listen to me for a while, which helped me figure out what I wanted to say and in what order.
Preparation
The day before the presentation I peeked into the band room. There were two whiteboards, and one with stuff written on it. I wanted to avoid erasing the writing, since I’m not sure if the classroom teacher was hoping to save that for Monday. That’s okay, perfect opportunity to show off alternative sources of vertical non-permanent surfaces! I counted the number of accessible windows and borrowed two rolling easels from my neighbour. I spotted a rolling chart paper stand in the band room with a ledge for holding pens, so I propped up one of my shower board white boards on that. I tacked up two Wipebook pages onto the bulletin board, one with the white board facing out, one with the graph side out.
The next morning, I taped up large sheets of tissue paper to the outside of the windows for better visibility of writing, taped up playing cards to all the stations and set up my white board markers and erasers. A few years ago, my husband bought our kiddo a pack of size 6 socks, thinking the 6 meant age, not size – waaaaay to big for her. They make perfect marker holders and whiteboard erasers! I set one at each station. I prepared 12 stations, having no idea how many people would show.
The Presentation
9:15 am rolled around and I had 9 people. I guess 12 stations was a bit excessive – ha! Luckily, as people gathered around me for the start of the first task, six more people showed up. I love that the numbers worked out to only have groups of three! I picked The Answers Are as a task because I remember experiencing it at a workshop and loved the challenge.
My colleagues were fantastic at giving me opportunity to model and talk about teacher moves. I overheard one of the participants say, “You have to start with division for this one. You can’t use division for a lot of these.” It gave me a chance to walk around to other groups and give hints that increase ability (“Hey, I overheard this strategy. What do you think of that?“). As some groups started to solve the first problem, it gave me a chance to practice giving hints that decrease challenge (“What if I told you that this one (9-1) is correct?“). I stopped them after 15 minutes, and, as one always hopes for, they were not all pleased to leave the task. My presenter heart was also very happy to watch the taking pictures of the task or copying down the numbers.
I had decided to present BTC by breaking down ideas into toolkits. After exploring toolkit 1, I asked teachers to write down questions they had or takeaways. Two of takeaways included the socks and taping white tissue paper to the outside of the windows – teachers, we’re always practical!
After presenting the second toolkit, I launched another task – the Unusual Baker. In advance, I had enlarged and photocopied the task from Peter’s Building Thinking Classrooms in Mathematics book. I had strips of prompts – #1-5 on one strip, #6-10 on another. I had thought to walk around cutting off the questions one at a time, but due to time constraints, I just handed the strips out at need. To launch the task, I told a story of how I used to bribe my kiddo to leave daycare by going to the bakery across the street (true), and how one of her favourite people was one of the staff members, Heidi, who ended up being called, “Baker Baker” (also true). Then I explained that Baker Baker gets bored and loves to cut up her square $10 cakes in different ways every day (not true, I think…) I drew the first two cakes and asked participants how much each slice costs.
Off they went. I was able to model teacher moves about incorporating fractions and ways of thinking about them (“Oh. So this is half the cake? And this is a quarter? So, is a quarter of a cake half of a half?”). One group ended up trying to anticipate the questions, and started dividing their cakes in unusual ways, like thirds. It gave me a chance to talk about differentiation, and how we can do that by giving different hints and extensions (in their case, I asked them what Baker Baker should charge to avoid having to ask for $3.33 a slice). We consolidated again, which made it easier to anchor talking about the next toolkit.
I did a brief talk on toolkit 4, as I decided to follow Peter’s wise advice about not talking about assessment on the first date. “Come chat with me when you’re ready,” I invited them.
It ended and I felt good. Lots of lovely feedback about how engaging it was, and of course, some of my amazing colleagues stayed to help me take down the whiteboards and gather markers. Several shared that they plan on trying to some these things on Monday, which is so amazing. YES!
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?
Honest moment: last year, I attempted interleaving my curriculum. The students were exposed to everything I needed to teach, but I still don’t call the first attempt a win. There are definitely elements that I need to tweak and one was note-taking. Note-taking was not a featured thing, and because we moved from topic to topic, it should have been a super key part.
I put together a simple note-taking template and copies galore. The plan is start with one per section in our math binder (numeracy, fractions and proportions, patterns and algebra, probability and data analysis, geometry and measurement). As we spiral through content, we can always add to our notes (and, likely, more and more templates).
I knew that I needed to launch carefully to help students take good notes. It’s not a easy skill! Elementary students don’t have a lot of experience taking notes, and it usually consists of students frantically writing down whatever the teacher writes, word for word. “Wait!” they’d cry in past years, “I’m not done yet!”
I handed out the organizer and explained that I wanted students to work in groups to fill in the sections based on the addition strategies we’ve been looking at – but on the whiteboards. Playing cards were distributed, students went off to their groups, and off they went.
As they started, I noticed them writing things like, “Counting on fingers”, “Using manipulatives”, “Lining up numbers” and was baffled. What? Where did this come from? They were so off topic! Didn’t I say that this was supposed to be about the strategies we explored?
I called them back in, clarified and ended with “If I gave you a quiz about addition strategies that we looked at, would these notes be any use?” After a resounding “NO!” I urged them to make changes so that they were useful.
They obligingly went back to their boards and added a lot more. We did a quick consolidation and then I asked students to write down notes on their own sheets of paper, urging them to borrow anything they thought was helpful from any board – and adding more if they felt it was necessary.
The bell rang, and the students left for recess. I slumped down in my chair, feeling defeated. How were they so off base? Were my explanations that bad? (It should be added that I had not had a good night’s sleep the night before, combined with slight blahs from the rainy day, likely contributing to my despair.)
Wait!
When I sent the students to their visibly random groups (VRGs), they started trying to think of anything about addition they could recall. They were trying to create more content than I had given them. They were thinking! AND… I could see that they weren’t getting at what I hoped for because they were writing on vertical surfaces. One slow turn around the room was enough for me to catch that. I would have completely missed it if they were working on horizontal surfaces, especially if I had asked them to start taking notes on their own!
So maybe this wasn’t a misstep. This wasn’t a waste of time. This was their first attempt at note-taking in a building classroom. And yeah, building our note-taking is going to take a while, but we’ll get there. We have to go slow to go fast.
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.
I decided that we needed a few more non-curricular tasks before launching into the curricular stuff. I launched The Answers Are task and the students were raring to go. In my verbal descriptions, I did forget a few details, but the students were quick to clarify and off they went!
Most groups made it through 2-3 different sets of answers. It was a great time for me to practice different kinds of hints – the type that increased ability (“Hey, what possible operations can we use to get 21?”) and the type that decreased challenge (“Hm. What if I told you that this one is 9-1?”). I pulled the kids away to write a journal entry. Not literally, but I definitely had to work to get some students away from the questions!
They were given two choices of prompts:
I did not block off enough time for this, so some kids wrote during silent reading instead of reading. Like I said, I need to block off longer math periods! I’m working on it.
That night, I went through the journals and took pictures to highlight different things. “Look!” I said, “Some people like to represent using visuals!”
And LOOK at the strategy talk here! I showed the students how the journal entries helped me see the thinking process that happened.
After seeing some of the journals, I sent the kids off to random groups to continue whatever The Answers Are problem was written on the board ended up at. Some kids skipped ahead to a new problem, some saw answers they had found equations for the day prior. No biggie! We kept going on.
Again, I stopped them to write a journal entry. This time, I asked them to tell me what went better OR what didn’t work.
Look at this entry!
“It’s okay to be stuck! Our brains will think of more options that we can do” and “I love the activities we have done this week. Each challenge was difficult, unique and new. I can’t wait until tomorrow.” Well, that made my teacher heart dance!
After our first hour of school, math for the rest of the week consisted of non-curricular tasks and videos from YouCubed’s week of inspirational math for middle school.
Rundown:
After a brief pause (you know, weekends and such!), we resumed our week of inspirational math. I had a student teacher observing this week, so I really wanted to make it good!
Reflections on this week
One of the highlights was this comment – “The math hurts my brain, but it was fun. I like it.” Yes! I am most definitely going to do name tents in future years. What a great way to connect with the kids and see how they are feeling about what is going on!
After watching “Speed is Not Important”, one of the students asked, “If speed isn’t important, why do teachers give timed tests?” It really reminded me of Peter Liljedahl talking about evaluation being a double-edged sword. We evaluate what is important to us, and we can say some things until our faces are blue, if our actions don’t match our words, our students aren’t going to believe us. I’m not sure how well I conveyed that in my answer back in the tiny box, but hopefully, he’ll see that for me, speed in math is NOT a thing.
Other thoughts
After poring through Building Thinking Classrooms in Mathematics by Peter Liljedahl (multiple times), taking part in a class with him, and following along with the Building Thinking Classrooms Facebook site, I was ready for day 1 with my new class.
The plan – I was going to launch the Tax Collector task right away. Like, “Hi, welcome to the class, I’m your teacher and… go!” I talked through this with a colleague, who pointed out that maybe just jumping in like that might be tough on students who might have more math anxiety (or, really, any anxiety about school). I have an advantage in that my students join me in their second year in Late French immersion, so they usually know each other pretty well. I’m the only new factor.
That said, she was right. I needed to think a little more.
I started with a softball question on the board – what emotion do you feel most strongly right now? I put up titles of “Tired”, “Happy”, “Excited”, “Nervous and “Other”. I had magnets with student names on them, and they placed their magnet under the category that made the most sense for them. Instant attendance – YAY!
Next, I passed out playing cards and helped students find the corresponding vertical whiteboards. In their random groups, I had them make guesses to questions about me (Am I a cat person or a dog person? How many years have I been teaching? What’s my favourite colour?). This way, their first task was low stakes – even though there was a right answer, how were they expected to know?
After this activity, I launched the Tax Collector task. There was a great buzz in the room! I eventually had to stop them to ask them to write in their name tents, an idea I got from Sara Van Der Werf.
After they left (what an hour!) I went from name tent to name tent reading their comments. I was excited to see the positive statements. Yes – day 1 was a success!
Notes for my future forgetful self 