Grade 9 Academic - Day 9

Today started with a quiz which I have yet to look at. I wanted to get a sense of where they are with the material we have worked on thus far. I have not had a moment to look it yet.

We finished Friday's work on distributive property. It was pretty interesting to work through - there's still a lot of learning to be done. We went over what like terms were again and how to multiply variables together. I worked on my wait time and on trying to find the good in all their answers while still moving them forward.

Today's warm up was their very first Which One Doesn't Belong? We practiced on the logo to ensure that they all knew how this worked - there is at least one reason for each member of the set to not belong.

Then we did today's actual warm up. I loved their answers, but even more, I loved their attitude. They actually clapped when an interesting answer was given. Twice. It was so lovely. And one of my quieter students volunteered to share an answer, which was also a great moment.

Our "Recall" for today was adding and subtracting fractions. Well, we didn't even finish all of that, let alone look at exponents again! Here's what we did:

I distributed graph paper to those who did not have any. I made them stop talking about common denominators and think about a visual model. There were all kinds of models - circles and rectangles and squares. It was a mess. There were a few really good ones too, and they helped us get to this:

They shared a number of strategies for finding the lowest common denominator and I shared mine with them.

And that's when the bell rang. Understanding fractions is huge so I think it's worth spending a little time to ensure that they get the basics. We'll continue with more tomorrow, and maybe we'll even get back to those exponents!

Along the way today, one of my students said to me "Have you ever talked to a mathematician about infinity?" We finished the joke in unison: "They could go on forever!".

Grade 9 Academic - Day 8

Today's warm up was challenging. As I circulated, I did not see the same answer twice. But as they talked and compared work, they fixed errors and did a really good job of this. I told them how happy it made me that not a single person did 15 - 2. We then consolidated together.

Next they worked the remainder of yesterday's questions. They did the first two on whiteboards in random groups.

It was interesting to see the strategies used and the different answers. Once they had attempted both questions, I had all the groups rotate clockwise and give feedback. I asked them to check for mathematical correctness and communication. They wrote notes on the whiteboard then rotated back to their original solutions to see the feedback. We then consolidated together. What's in green for example 2, below, is what they told me had to be true about all the solutions.

Then we finished off the rest of yesterday's handout. Most students were okay working through this on their own, though we did take it up together.

We did a little refresher lesson on distributive property. 

We had enough time left to practice a little bit. We talked about what happens when you multiply x by x and what happens when you multiply x by y.

I had a few more questions that I wanted to do with them, but I think it's far more important that my students understand what we have done and feel confident moving forward than just rushing through the work. We'll pick up where we left off on Tuesday.

Grade 9 Academic - Day 7

We had a special guest visiting our class today - Ann Arden, who works at the board office, wanted to see my class in action. (She was also supposed to come yesterday but the snow storm changed that plan in a hurry!)

We started with this warm up:

I went back and forth on whether I wanted them to work through this individually or in groups at the whiteboards. I eventually focused on the fact that if they are working on the big whiteboards in random groups, it's to learn something new. This warm up was applying skills that they have already learned so my goal was to see where they are individually which made my decision clear. They each worked on their small whiteboard. I love how they compare work and try to find errors when their answers don't match. We took it up together once they had all had a chance to correct their work.

Next I introduced them to Desmos. I showed them Suzanne von Oy's beautiful graph and I showed them a Mathogram (since it's Valentine's Day) before explaining how to get into today's activity. I also went over the rules of borrowing Chromebooks. The activity focused on like terms. It was created by Andrew Stadel and edited by me - I took off a couple of screens and added one that I really liked from a different activity by Cathy Yenca (thanks Andrew & Cathy!). Here is the link. They worked through this activity in pairs and had good conversations along the way. The best was when one student said "Can we do more? This is actually fun!".

As I looked through the dashboard I saw a lot of different answers for a couple of screens so I hit Pause and we talked about them. Here is one:

I also had grabbed some snapshots of the last screen and we talked about the interesting, different approaches that were used.

They were really good at putting the Chromebooks back in the correct bins and did so pretty quickly. I gave each student a handout for the next part of the class.

We went over vocabulary, some of which we have talked about previously, but needed something a little more formal.

We then returned to adding and subtracting polynomials. Well, we really just combined like terms because that's all we had time for. We will continue with that tomorrow.

I also had them fill in a "Just checking in..." form. I like to give them the opportunity to tell me if things are not going well in my class or at school or in life. 

After the Storm

This morning, as I shoveled the vast quantities of snow that fell last evening and overnight, I could not help but think about TMC. I tweeted this out as it seemed like where we are.

The storm has passed but there is a mess left behind. We can see where we’ve come from and there’s a path ahead yet to be forged.

I shoveled the snow, at times light and easy to move, other times hard and so icy that I was forced to work at it at an angle, not head on, for an hour and a half. When I came in my phone showed that I had been active for 7 minutes. This too reminds me of where we are with TMC. I feel like many have been drawn to the issues of the past week, but cannot see all the work that has been done to bring us to this point. I want to tell my phone that no, it wasn’t just 7 minutes. It was over 90 minutes. You can see that my shirt is soaked through and my cheeks are all rosy. But it feels like I’m making excuses. It feels like if I want to tell everyone what a profound effect TMC has had on so many educators, it will be seen as making excuses. I want everyone to thank those who have helped create and sustain TMC thus far, but do not want to be seen as going against those who have felt left out. I want to say that no one on team TMC ever wanted anyone to feel excluded, and that we are all in different places on our journey towards equity. It hurts me to know that some are being vilified because hurting more people doesn’t solve the problem. I am starting to understand white fragility but I think that 7 years of work making something remarkable and special should not be so easily dismissed. Team TMC has been fractured and dysfunctional for a while now and we each need to own our part in that. I should have done more. I am quiet by nature and tend to be happier helping in the background, but I should have tried harder and made time. I think we would all do things differently if we could go back, but we can’t so we must try to move forward. Publicly acknowledging your failures is hard, especially at a time when emotions are running high and responses are quick and harsh. I am flawed but I continue to try to be a better person. To learn from others who know more. To listen and to make meaning of what is being said so that I can do better the next time.

As I head back out into the snow, I can see my tracks. I see where I did a good job and where I should have tried harder. Ahead there is only fresh snow, and new paths waiting to be created.

Grade 9 Academic - Day 6

The plan for today was to get through exponent laws. Tomorrow will likely be a snow day so I wanted them to have the tools to be able to practice working with exponents and order of operations. We had not worked through the examples planned for yesterday so I photocopied the questions and let them work through them in their table groups instead of a warm up.

Lots of misconceptions arose and their understanding of both exponents and the order of operations seems to be improving. I decided on the weekend that order of operations is really the crucial foundation they need to build on. If that is not solid, the rest will fall apart.

Next, they worked on this question in groups:

The conversations were really interesting to listen to. Many groups took our calculators only to find that they weren't helpful as the question asked the expression to be simplified, not evaluated. I'm not sure how much this shows, but this is our consolidation.

I am being very intentional about saying "simplifies to 1" and not "cancels".

We broke things up a little to state each exponent law individually.

We had a little time left to try putting it all together before summarizing.

Though it seemed a bit rushed to me, we focused on understanding, not memorizing rules. Hopefully the practice they will get over the next couple of snowy days will serve them well.

Grade 9 Academic - Day 5

We started today's class by finishing the examples from Friday.

Then I had them do today's warm up in random groups on the white boards.

I asked them to sit down when they finished, but they wouldn't! They were busy comparing answers and trying to figure out who was right and fixing mistakes and it was fantastic! They did eventually all sit down and we talked about the order of operations.

Then we returned to the warm up which they each completed individually before we took it up together. Some were feeling much more confident this time around.

In light of the 40 cm of snow heading our way Tuesday night into Wednesday, I skipped today's visual pattern :(

Instead, we launched into exponents. I try to emphasize that an exponent affects only what is immediately in front of it and try to help them make sense of negative numbers raised to an exponent.

Somewhere along the way I returned their quizzed to be corrected tonight. Their quizzes were actually quite encouraging.

Grade 9 Academic - Day 4

After handing back feedback forms, I asked students to take out, but not hand in their homework (they normally hand it in at the beginning of each class, I check it somewhere along the way and return it before the end of class). I asked whether they knew that the answers were in the back of the book and this was news to many! So together we found the answers and I had them check their answers and place a check mark or x next to each question using a different coloured pen. Then they handed it in to me. This simplifies my job as it became very clear whether they struggled with any of the questions. Sometimes we forget the soft skills so I am trying to be deliberate in imparting them to my students.

Instead of a warm up today, I gave a quiz on integers. I realized last night (it was our school's open house so I was here until 8 pm) that I have no firm evidence that my students are understanding the material we have looked at thus far. I made sure to explain to them that they shouldn't be stressed about it, that it would help me know if we need to spend more time on integers or if we are ready to move on.

After the quiz we carried on where we left off yesterday - like terms.

The next question sounds like a Marian Small question so I will give her credit. My students did well with answering it, but we had to work hard to explain what everyone's answers would have in common.

Then we practiced combining like terms and dealing with the many misconceptions that came up along the way.

I loved the multiple ways of writing the solution to this next example.

We skipped today's visual pattern, in part because the teacher next door had borrowed my cards, and in part because I wanted to get everyone feeling a little more comfortable with the distributive property before the weekend. We worked through area models with numbers then added a variable. A big thank you to Sheri Walker for sharing this handout with me. Students who were unsure were encouraged to count the number of x tiles to get the area and then try to make sense of that answer in terms of length and width.

We continued to build up our area models and were careful about including brackets when writing out the length x width expressions.

A little summary and some more examples (I know this is not very exciting - I would change this to become work on whiteboards next time. Actually I can do some of that next class.)

We had a few more to do, but it was the end of the period so that's the end of the first week.