MPM1D1 - Day 25 Graphing Stories & Collecting Like Terms

As part of Global Math Week I thought I'd start today with the International Math Salute. I had students stand up, put their arms out from, cross their right arm over their left, put their palms together then untwist.

The look on their faces as their hands ended in a twisted mess was priceless. I did it a couple of times. Some students said that they had figured it out but they couldn't seem to reproduce it. There were some great conversations going on.

Next, I handed out individual whiteboards so that students could sketch graphs of some Graphing Stories. We did the first two stories. The first one was a bit of a challenge given that students were graphing time vs. time. They struggled with this idea but after the first few seconds of the video they figured out what was going on. I let them create a graph then we reiterated some of the terminology. We talked about continuous vs. discrete data, partial vs. direct variation, interpolation vs. extrapolation, slope. These were all terms that we've seen before but based on last week's test many students still need practice with the terminology. We'll do a few more of these at some point.

The goal for today's lesson was to look at adding and subtracting like terms. We started by watching this video:

I was kind of surprised at how entertaining they found the video. After watching the video I asked if there would have been an easier way to place the order? Someone suggested that we group all of the similar items together and add them up. What a great idea!

We talked a little about some terminology: terms, polynomials, monomials, binomials, like terms. We took a note on adding and subtracting like terms then I gave them a handout for some practice.  I think the 'you can't add a burger and a Coke together' idea really helped some of them understand the idea of only adding (and subtracting) like terms.

MPM1D1 Day 24 Water Line & Distance-Time Graphs

Today we started our second cycle. For the warm-up we looked at a non-linear pattern for the first time (Visual Pattern #1).

The goal was to find out how many square were in the forty-third step and to come up with a general equation for the number of squares in the nth step. It was interesting to see the approach given that we've done so many linear patterns. Most groups created a table of values and found the pattern. They realized that the values weren't going up by the same amount. They were so accustomed to finding the first difference (though we haven't called it that yet), using that as the multiplier in the equation then finding the initial value. Some groups abandoned the idea of using the differences and instead starting looking at how the pattern actually grows from step to step (using the dimensions of the squares). Most groups that did this had no trouble finding an equation. For those that finished early I asked them to determine a rule for the number of toothpicks in each step. For the groups that didn't look at the dimension of the squares, things started to get difficult. They knew that they needed to add two more to what they added in the previous step but they couldn't figure out a way to do that in an equation. We'll do a few more of the quadratic patterns and I'm sure they will get better at them.

Once the warm-up was complete I meant to talk about distance-time graphs with motion sensors but I forgot. Instead I moved right into Water Line.

It's a great activity that allows students to graph the height of water in a glass over time. Immediate feedback is built right in as students click the play button to see if their graph matches the real life situation. The activity couldn't have gone any better. Students were working hard and some expressed how much fun they were having. Imagine, having fun in a math class! The best part seemed to be making their own glasses and trying to create a graph for their classmates' glasses.

After the Water Line activity we moved onto discussing distance-time graphs. What does it look like when you move towards a sensor, away from it, at a constant rate, speeding up, slowing down, etc. Then they practiced with this handout.

MPM1D1 - Day 23 Test Day

We wrote our first test on Friday. Many students seemed quite nervous as they started. I get excited on test days. I'm excited for students to show me what they have learned. If you're looking for a sports analogy, test day is like game day. We've spent all this time practicing and improving and I'm looking forward to seeing how much my students have improved.

As the test progressed I had questions such as "What does this mean?" and "How do I do this?". I told students to try their best. We had talked before the test about how it was important to write something down for every question. I was happy that for the most part they did. Some students need to work a little on presenting our solutions in a manner that's easy to follow.

I think that by the end of the test students had a good idea of what they needed work on before the next test. I'm hopeful that this will provide them with some focus for our upcoming work.

MPM1D1 Day 22 Review

Today was a day for students to work through a review package to prepare for their test tomorrow. Before they started I answered a bunch of questions about the test, such as "How long is it?" to which I gave my standard response "11 inches". I could have told them it was 8.5 inches wide but they didn't seem interested.

The room was just buzzing the entire period. Everyone was working on different things in different ways. Some students put their headphones on and worked on their own, others worked on problems but checked with a group member if they got stuck and a few worked on questions as a group. Some students started on the first question and worked through the questions in order while others focused on the content they felt least confident about. There were some great discussions and some excellent peer teaching. I'm hoping for good things tomorrow.

I offered to run an online tutorial tonight through Adobe Connect. As it turns out I didn't have anybody show up. I wonder if that's because they forgot, didn't need it or had technical difficulties. I was unable to login on my Windows machine but had no issues on my Mac or iPad. I guess I'll find out tomorrow.

MPM1D1 - Day 21 Mowing the Lawn

Today's warm-up was an Estimation 180 problem. Students had to estimate what percent of the pie was missing as well as the angle formed by the missing piece.

There was a lot of good discussion. It was interesting to see most students talking about fractions first (half, a quarter, etc) then converting those fractions to percents mentally. The percent estimates were pretty good, the degrees were not as good.

The main event for today was Mowing the Lawn. We've done a lot of group work this semester (which has been great) but as we approach the test I want to ensure that students are able to think, work and communicate on their own. I want them to take on more responsibility for their learning. So I asked them to work through this one on their own at their desks. They got to work right away. There were a number of different approaches being used it was a busy period. There were some great conversations about different approaches. I was hoping they would all finish during the period (and many did) but we were interrupted by a fire drill. Those that finished started working on the review for the test. The rest will (hopefully) finish up for homework.

Our test is Friday and I feel that some students aren't going to be ready. I've had very few come to see me for extra help at lunch. In the past I've run some evening online tutorials but they have been mostly with senior students. I thought I'd give it a try with this group and see what the response is like. More details to come.

MPM1D1 - Day 20 Percents & Footprint Data Collection

We started with a visual pattern today.

All groups came up with the equation and the number of stars in the 43rd step pretty quickly. I sent them back to their seats and had them write up a solution. I explained that I didn't just want an answer, I wanted an explanation of how they got the solution. I collected their work and had a look at it. Some did an amazing job with their explanations, others could use some work.

We did a quick note summarizing percents (converting to and from decimals and fraction, finding percentages, etc.) and I asked them to finish up the handout I gave out yesterday for homework (for those that hadn't finished already).

Next up was collecting data and working on graphs for the Footprint Assignment. Most groups were very quick to get their measurements and getting started. For whatever reason some students seem to feel like they don't need to do any work if they're holding a metre stick. Odd.

MPM1D1 - Day 19 Sunflowers

We started with this problem:

I was surprised to see the approaches that students took for this one. I had expected most to convert the fractions to decimals or percents. One of the groups did that. The rest of the groups created equivalent fractions with common denominators and compared that way. It's nice to see the different approaches.

Once the warm-up was complete we looked at some trouble spots from last week's assessment (everyone finally wrote it).

We then moved onto the Sunflower Task. A few people weren't really sure where to start and some didn't really want to start. Eventually, everyone got going. The goal here was to make connections between the table, the graph and the descriptions of relationships.

For those that finished early I gave out some percent practice. Tomorrow we'll go over percents to ensure that everyone has a good grasp.