## Thursday, 28 February 2019

Tomorrow is test day so today we did review stations. But first, I took up a question from homework that many were doing incorrectly.

A number of students had not put the 5x + 7 in brackets so we talked about how that was not optional. The other brackets you see above were added after when a student asked if you could do that.

Then I explained how review stations work. There were brightly coloured sheets around the room with questions from an old test on them. Students would be randomly paired up (using cards) and each pair would pick up an answer sheet. They would work on the big whiteboards, transfer their answer to the answer sheet, and bring that to me to see whether they were correct. If so, they got a sticker, if not they got to try again. If they were incorrect a second time, then I went over the question with them.

They were so keen! There were a lot of errors but no complaining. They just got back to work and figured things out. Lots of perseverance. There were high fives and hugs. Crazy good.

Given that tomorrow is then end of unit 1, this is the end of my blog posts. I'll still post when I do things that I think are worth sharing, but I think it's clear that I don't do that every day! Thanks for reading :)

## Wednesday, 27 February 2019

We started with this warm up:

This was a challenge for many, but at least as many got the correct answer on the first try. The biggest issue seemed to be that if they did not simplify the fractions before multiplying, the numbers got big fast. And then it was too overwhelming to continue. We spent some more time going over this concept. Hopefully it sticks.

I had noticed some issues with certain homework questions so we tackled those next.

They continued to work on the practice test while I circulated and gave one-on-one help. I had planned on taking it up with them, but time did not allow. I have posted the solutions and hope that they will check their work tonight. We did work on one question together as many students were struggling to start it.

I found it really interesting that using letters actually made the question more approachable for many students. There were simply too many numbers for them to parse through, but once they replaced the bases with x and y, they were able to complete the question.

I also handed out "I can" statements. These are statements written in fairly friendly language that let students self-assess what they know. I'm sorry that the picture below isn't very clear.

Tomorrow we will do review stations!

## Tuesday, 26 February 2019

The sun is shining, the power is on and we had lots of math to do today. We started with this warm up. The intent was to highlight the power of simplifying before multiplying fractions.

I had made an agenda for the day, mostly to keep myself on track, and still managed to go out of order right from the start (sigh).

We jumped into the practice test. I am hoping that seeing the format of a test (3 page booklet) and the types of questions from this past test will help ease some of their anxiety on Friday (test day). I asked them to quietly work on it for 30 minutes. Some skipped questions that they didn't know how to do, while others zipped through it. I did not expect them to complete the test in this time, but wanted to break up the time to allow some conversation and learning to occur. At the end of the 30 minutes, they chose cards to organize themselves into random groups, and went to the big whiteboards to compare answers. There were some really good conversations going on and many misconceptions came to light. Some of the questions could have multiple correct answers so it was great to see them checking each other's work. During this time I circulated and made sure the mathematics was correct and answered questions.

I saved the last 10 minutes of class to talk about vocabulary. I had made a handout for them which we took up.

I think we are making progress. They are willing to talk about their mistakes with classmates and ask questions when things are clear. With a couple more days of review work I hope things will go well on Friday.

## Monday, 25 February 2019

Amid power outages due to ridiculously strong winds, we tried to put the material from this unit all together today. We started with the warm up from Friday's group work:

The discussion around this was really interesting and many struggled to correct the work so that the answer was correct.

They spent the next ~30 minutes working through this handout individually. I told them the goal was for each of them to figure out what they still need to work on. We spent the rest of the class working through each of the examples. Other than the vocabulary, we finished it all!

## Friday, 22 February 2019

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.

## Thursday, 21 February 2019

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...

## Wednesday, 20 February 2019

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.

## Tuesday, 19 February 2019

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!".

## Friday, 15 February 2019

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.