Grade 9 Academic - Day 12

I turned yesterday's quiz question into today's warm up. They worked in random groups on the whiteboards. I reminded them to introduce themselves as not everyone has worked with everyone else yet.  To avoid repetition for those who completed the question on the quiz, I had each group draw the simplified expression for each of their questions.

Here are a couple of samples of their work:

I have saved this one as the warm up for Monday - a little error analysis.

I love hearing their conversations while they work. "Two Nice Things" was overheard at some point, which means that they are listening to the words they choose and realize that they matter.

I returned their quizzes and circulated for the remainder of the period answering questions as they worked through a handout. Several students are also planning on coming in at lunch for a little extra help. I love that they are starting to get comfortable asking questions and want to improve their understanding.

Grade 9 Academic - Day 11

Today's recall was more work with fractions so I thought it would be fun to do a warm up from Fraction Talks. I asked them to show multiple ways of finding the answer.

I was pleased that they seemed comfortable working with these fractions and showed flexibility when looking at how to regroup the shaded parts.

We worked on multiplying and dividing fractions next. Though I tried to channel my inner Fawn Nguyen, I sucked. Oh my, it did not go well. I did a lousy job when answering questions. My explanations were not good. I need to work on all of this... But this is what we did:

I know that I have the luxury of being able to just move on. My students already have tools for working with fractions,. Many of those tools are memorized, not understood, and I was trying to work on that. Sigh...

We also did a few more examples with distributive property and exponent laws. They groaned when they saw the second one, but did a good job nonetheless.

Despite knowing that it wasn't a good idea to give the quiz I had planned with only 15 minutes remaining, I did (why do I not listen to myself sometimes???). Many students continued the quiz into lunch which I appreciated. I think I will start tomorrow with the last question from the quiz, in random groups at the big whiteboards. Here it is: 

"Martha simplified an exponent rule question and ended up with the answer -2x²y. What could the question have been? Determine 3 possible questions with this answer that demonstrate each of the exponent rules."


I am hoping to see a lot of creative answers that push their collective skills forward. And I will work on my lack of skills teaching fraction multiplication & division...

Grade 9 Academic - Day 10

Today started with another WODB? In my haste to hit publish yesterday (it was a very long day), I didn't talk about how I run WODB in my classroom. I ask for 60 seconds of absolute silence for everyone to think about what they see. This is hard for them. I then have them share their reasons in their table groups before we consolidate as a whole class. Each group gets to share one reason then we get extra reasons once each of the 6 groups has had a turn. In this case the 1/20 was blank until the end. They came up with a couple of ideas and then someone impressed the class by using something they had just seen. Taking the reciprocal (that had come up with 20/25) turned 1/20 into a whole number. Along the way we talked about vocabulary and made connections (i.e. numerator > denominator is the same as improper fraction).

After the warm up we returned to yesterday's work. We did one more addition/subtraction of fractions question before reviewing how to turn a mixed fraction into an improper fraction.

They, as expected, came out with the trick where you multiply the denominator by the whole part and add the numerator. I used that on the next example and got -13/5. We decided that my answer didn't make sense and talked about how to convert a negative mixed fraction into an improper fraction.

After our review work with fractions, we finally circled back to exponent laws.

I think it's really important to make sure that everyone understands what the outside exponent means in a question like the one below. We wrote the power in expanded form first and used the product of powers law and then used the power of a power law to do the same question in a different way.

We did another one two ways. There were a lot of questions that arose along the way. Cubing one-third was a challenge!

I circulated and gave out stickers as they worked through the next example. I saw that some students got a coefficient of 686. They explained to me what they had done but I'm still a little lost. I think we cleared up how to do it correctly...

The last one combined a lot of skills. 

We spent the rest of the class taking up yesterday's quiz. I only give feedback on quizzes (no mark/grade) so I asked them to spend a couple of minutes correcting the first question with the help of their notes/neighbours. It was all about terms - type of polynomial, state the coefficients, state the constant, state the degree of the polynomial). We then corrected it together. The big error that I saw was a number of students who changed every x^2 into 2x. We talked about the difference between the two.

Have I mentioned recently that I really love this class? In a happy, exhausted kind of way.

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.