MPM1D1 - Day 38 Equations of Lines From Two Points

Hoping to continue our work from yesterday on finding equations of lines we started with this pattern.(with students working in groups up at the board):

Most students are so good at these patterns. I really like their strategy of finding the y-intercept by seeing how much they are off by when the substitute a step number into their equation. I don't want them to lose that intuition but at some point the numbers will become challenging enough that it may be easier to use an equation. I had one group that really struggled with this question but eventually they sorted it out.

When they were done they moved onto the next bunch of questions.

The last question was full of fractions. Many groups seemed fine to keep working with fractions which made me happy. One of the groups kept wanting to change their fractions into decimals and proceed that way. They got a little upset at me for insisting their work be done using fractions (everybody's favourite F-word).

Once they were finished I told them to plot the points and equations for the last two questions in Desmos to see if they got the right answer. Many groups realized that they made a mistake since their line didn't go through the points. They traced back through their algebra to find their errors (often a wrong sign).

Once they were finished I sent groups back to their seats to work on his handout so that they could practice.

I really think that finding the equation of a line that passes through two points is probably the most difficult topic in the course. However, I believe that spiralling the course has really helped. My students have looked at finding equations from tables since the first week of school. We didn't call the parts of the equation the slope and the y-intercept at the beginning of the semester. We had an entire table rather than just two points.  But, I really feel like my students have a good understanding of these parts of equations and are now able to hang the proper terminology on their understanding. Students who are still struggling with this concept will have an opportunity to revisit it was we move forward.

MPM1D1 - Day 37 Exponents & Equations of Lines

With Halloween approaching I thought today would be a good day to look at a candy corn estimate. As a side note, I'm not sure that Canadian teens are as fond of candy corn as American teens are. It seems that every year half of my class says that they hate this stuff. Perhaps a more formal study will be necessary.

My students had a three day weekend so I thought I should remind them of some of the exponent work we did last Thursday. We quickly recapped some of the rules and went through some of the challenging homework questions. We also spent some time talking about what it means to have a fraction raised to an exponent. The overwhelming majority of my students wanted to convert the fraction to a decimal then use their calculators. I pushed them to stay with the fractions and write the power as a multiplication statement. Most were able to do that, but again wanted to convert to a decimal and multiply. We got to the point where we had an answer as a fraction, but I think we need to work a little more with fractions so that students are as comfortable working with fractions as they are with decimals.

I also gave this problem:

I figured students would be able to come up with an answer but I asked them to also come up with an answer that involved using exponents. There were some great discussion, and arguments, around the room.

Next, we moved onto writing equations of lines. We've done this before, but there was always a context. I wanted to move away from the context to make this a little more abstract. The goal was to find the equation of a line given two points. We reviewed what the equation of a line looks like and how to find slope. Then we talked about how we could use a point, along with the slope, to find the y-intercept. We worked through an example and then I let them try it. Here's the handout we started with.They didn't have much time so we'll continue with this tomorrow.

MPM1D1 - Day 36 Surface Area, Exponents & Compound Interest

We did the extensions to the Big Nickel today (interior angles, exterior angles, cost to resurface, etc.). This provided some great review on topics already covered to date. It was interesting to watch them struggle with surface area. Right away they jumped to their formula sheets and started looking at formulas for triangular prisms. The trouble was that many of them couldn't make sense of the variables on the page. Now to be fair we haven't done any work with surface area. I stopped the class and asked what surface area means. They knew exactly what it was. I asked them to show me which parts of the nickel we had to find the area of. They nailed it, so I set them to work to find the area of all the pieces. No formula required. I can't believe I thought we'd get the entire task done in a day.

Once we finished with the nickel it was time to head into exponents. I threw this question up on the board and asked them to come up with an answer individually.

It was great to see where everyone was starting from. One student said "This is easy! I just have to multiply 3 by 3 by 3..." and off he went. Others used the exponent button but got caught up on  the order of operations. Many students found the value of the numerator, then found the value of the denominator, wrote both of them down then did the division. A handful of students were able to use the exponent laws to quickly realize that the entire expression was equal to 1. After getting all of the errors corrected a student who knew the rules wanted to share, so she told us how to do it.  It was such any easy transition into what is often a boring list of rules.

As we discussed the rules one boy asked why we needed exponents. He understood that the rules were helpful in evaluating the expression above but wondered when in his life would he ever come across exponents. This sidetracked me as we discussed one of my favourite mathematical topics: compound interest.

I'm always surprised that students aren't aware that they are paid interest by their banks. In any case we talked about compound interest and how if you set aside money every month for the majority of your live you can become quite wealthy. When I was in high school my classes received these types of lessons from Bob Gunter. I had Bob as a teacher for four out of seven math courses. To me these lessons were the most memorable parts of any course. It was clearly something he was passionate about and he was able to share and spread that passion to his students. So Monday (tomorrow is a professional activity day) we'll look at some financial scenarios (at least a little bit).

I handed out some exponents practice and bid the class a happy and productive weekend.

MPM1D1 - Day 35 Quadratic Pattern & More Volume

Before we started today we talked about the definition of a prism. It was interesting to hear what students thought the definition was. Eventually we settled on a definition (that came from one of the students). We then talked about how we could find the volume of any prism.

We branched out a bit today and tried this visual pattern:

Groups began right away and created a table immediately. They found the first differences and realized that the pattern was not linear. Some groups showed that the second differences were the same. Others noticed it but didn't include a column for the second differences. Once groups realized that the pattern wasn't linear, they didn't know how to proceed. They realized that finding the slope wasn't an option. One group did find the y-intercept. After giving some time to struggle I stopped the class and told them that they needed to find another method. I told them that they should look at how the length and width grow from one step to the next. This was enough to get the groups to come up with an expression for both the length and width. They knew that to find the number of helmets they would need to multiply the length by the width but they struggled with how to multiply two algebraic expressions. That makes sense given that we haven't really done that yet. As a class we put the pieces together and came up with a possible solution.

Without saying, the warm-up took quite some time but I think it was time well spent. Once we were done we went back to the Big Nickel. We looked at the question of what happens to the volume if you double the height. We then explored, as a class, what happens if you double the width as well. What if we double all three dimensions? It seemed to make sense to them. I was hoping to get to the rest of the extensions of the nickel task but I also wanted to compare the volume of a cone to a cylinder. I held up the cylinder and cone and asked how many cones would fit into the cylinder (the areas of the bases are the same).

After taking some guesses I filled the cone with water then dumped it into the cylinder. I asked if anyone wanted to change their guess and a few students did. I added another one and asked if anyone wanted to change their guess. As I dumped the third one in many students were convinced that it wouldn't all fit but sure enough it did. We talked about how this relates to the formula. It seemed like lots of light bulbs went on at that point. I gave them a couple of pages to practice (here and here) and the period was over.

MPM1D1 - Day 34 The Big Nickel

We started with two volume questions as a warm-up. I wanted to see how groups did with questions that didn't have any diagrams.

Overall, they did quite well. All groups found the volume of the cone and the sphere. A couple of groups forgot to divide the volume of the sphere by two by as I asked them to explain what they did, they all got it straightened out.

I was expecting most of the groups to get tripped up with the slant height in Problem 2 but only about half did. Again, a bit of prodding on my part led to students realizing that they needed to use the Pythagorean Theorem to find the height.

We moved onto the Big Nickel. We started by finding the volume of the big nickel. I was surprised at how long this took. Many students were desparate for a formula for the volume of a dodecagon. When I told them they didn't need it, many seemed quite stumped. After pondering the problem and comparing to their list of formulas many realized that they could break the nickle into twelve triangular prisms. One group chose square based pyramids at first but when I asked if they could show me a square based pyramid they realized that they were on the wrong track.

Once the groups calculated the volume of the big nickel they found the volume of an actual nickel and determined how many nickels would fit inside the big nickel. Some students moved on from there to find out how much that would cost. We were pretty much out of time so I gave them this handout to practice. It has a bit of surface area on it, which we haven't done, but I think they will be able to figure it out.

I was a little shocked at how long things seemed to take today. I'm not sure why things took so long. I was a little under the weather so I wonder if my lack of energy led to a lack of energy for my students. We'll see how it goes tomorrow.

Through the work that we did today I have come to the conclusion that many students don't seem to know the definition of a prism. I'll have to address this tomorrow.

MPM1D1 - Day 33 Volume & Hot Coffee

The focus today was on volume. I started with this brilliant.org problem.

What I really like about this problem is that there are no numbers. I sent groups to work on it at the board. Some groups struggled at first not knowing how to go about the problem without any numbers. One group just wanted to give a verbal explanation. Another group explained exactly what they had to do and told me they couldn't start because they didn't have any numbers. I asked if it mattered what 'the numbers' were. They realized it didn't and carried on. Some groups quickly realized that it didn't matter what the dimensions were so they picked a number. For whatever reason four seemed to be a common dimension for the length of the cube. When I asked groups why they chose four, some said because there were four balls across in image C. Another group said that they thought four might be easy to work with since the perimeter of a square of length four was the same as the area of a square of length four. I'm not sure what this had to do with this problem, but I was happy to hear someone recalling a discussion we had as a class earlier in the semester. I'm guessing that some groups had a peek at the work of others and used their numbers (though nobody gave that as a reason).

This problem took a long time to get through, partly because of the lack of numbers and possibly partly because it was a Monday. Some groups had a hard time focusing. Eventually all groups were working effectively and came up with a solution.

Next we moved onto Hot Coffee. I had students complete the first part of the problem solving framework that we use on their own (state the problem, give an estimate, what do you know, what do you need). I asked what information they needed and gave it to them then I sent them up to the boards to do the work in groups. They started finding the volume (in cubic feet), then converted to gallons, then used some information about the flow rate to determine how long the process would take. The problem was good in that it involved some volume, some proportional reasoning and also dealt with rates. I often forget to do Act 3 of these problems. I tend to have faith in the work students have done and I'm happy with that. What I forget is how much pride students get from seeing that their answer was correct. I showed Act 3 and there were some pretty happy faces.

Once they finished at the board I sent them to their seats to get everything on paper so I can see how they're doing. I then collected their work so that I can provide some feedback.

I was hoping at this point to do the Big Nickel but we only had about ten minutes left so I handed out a page of volume questions they could practice. We'll save the Big Nickel for tomorrow.

MPM1D1 - Day 32 Not So Visual Patterns & Success Criteria

We began the day with a couple of patterns, but this time without the visual element. These came from @MrHoggsClass and they provided some great discussions. Thanks Mr. Hogg. I sent groups to the board and just let them go.

Most groups started this one by creating a table, then filling in the missing values. With the missing values in place they were able to determine the rate. A couple of groups figured out how much they were off by if they multiplied the rate by the step number. This was their y-intercept. A couple of groups worked back to step zero to find the y-intercept. I was very pleased with the conversations and how well groups were able to attack this slightly more abstract problem.

Next we moved onto this one.

The idea with this one is that filling in the gaps in the table is tedious. Some students were able to find a solution by inspection, which was cool. I pushed them to be specific about how they arrived at their answer and to explain in a way their group could understand. Most groups made a table again. Some were able to find the slope from the table, others struggled a bit but with a bit of guidance were able to make sense of finding the slope. It was nice to see some groups getting help from other grous. Groups found the y-intercept the same way they did previously.

For this final pattern I wanted to make it more difficult to find the y-intercept. I was hoping it would be too tedious for students to work back to step zero. I was hopeful that students might start looking for a tool (an equation) to help them. As it turns out not a single group wrote down an equation. Most solved the equation mentally. They took one of the step numbers, multiplied it by the slope then figured out how much they were off by. This number had to be the y-intercept. They checked their equation with the other point and it all worked out. I have mixed feelings about this approach. On the one hand the rigid, rule following math teacher side of me would love to see students substituting a point and the slope into the equation of a line and then solving for the y-intercept. On the other hand I was so excited to see students using the tools that they have at their disposal to solve the problem. They clearly understand the process they used and they own it. More and more I'm thinking this is more important than simply following some abstract procedure that they don't really understand yet.

The best part about this warm-up was that students who have been struggling seem to be getting the ideas. The girl who's convinced she is going to fail the class was contributing to the group discussions. In fact, I would say she led her group today. When I asked her to explain one of her group's answers she did so very well. When I prodded the group to explain in more detail she was the one who stepped up and dug deeper. When she finished explaining I had a huge smile on my face. I was so proud of her. She too had a smile on her face. I think her confidence may be starting to improve.

Once the warm-up was finished I handed out the Bicycle Assignment. I shared the success criteria that groups created yesterday plus some of the criteria that I thought should be there. I really don't know what I'm doing with this but here is the criteria that I shared. I explained the assignment and went over the success criteria and still many students seemed to have no idea what to do. Somehow some of them had no idea that they needed to write a report. If you have any suggestions about how I could improve my use of success criteria, I'd love to hear them. They had the rest of the period to work on the assignment. I will collect them on Monday.

I had a number of students who hadn't submitted the last assignment so I kept them in at lunch today to get it done. I kept them for up to 30 minutes. If they weren't finished they were to do the rest at home and hand it in on Monday.

MPM1D1 - Day 31 Truck and Bike Task

We started with this Two Truths and a Lie:

The slope of the following relations is 2.



I sent them to the boards to work in their groups. There was a ton of great discussion and arguments. There were lots of questions between group members. At one point a couple of groups had gathered around the board to listen in as the peer tutor provided some explanation. 

All groups were able to figure out the correct answer. I really liked how this activity made connections to the different representations. I think my students are starting to make some headway in terms of connecting these representations.

 After the warm-up I handed out Bike and Truck Task. I gave very little in the way of instruction to see what they would do. Some students started working away dilligently. Others seemed to be filling out the handout without really reading (or perhaps understanding) what the questions were asking. I let them work for about fifteen minutes then interrupted them. Now that they were familiar with the task I wanted them to work in groups at  the board to create some success criteria for it. I've never created success criteria and I've never had students do it but I thought I'd give it a shot. I was surprised at how quickly things were appearing on the boards. As I looked around I noticed there were lots of great suggestion.

But as you can see very few of the suggestions have anything to do with the task. I was surprised at the lack of connection to the actual work we were doing. I commented to the class about their great list of criteria and asked if they could also add items that were specific to the task. A couple of groups added some, but the success criteria seemed to be lacking detail.

Tonight I'll make a list of their criteria along with my criteria and share it with them tomorrow. I'll do this because tomorrow they will get an assignment that is similar that they need to complete and submit.I'm not convinced that having the students come up with the success criteria was very useful, but maybe they we will get better at it over time.

With success criteria on the boards it was time to move on. We did took up the mastery test on slopes and equations of lines that they wrote yesterday and then they wrote it again.



For homework I asked them to finish the Truck and Bike task by adding to it to meet their success criteria.

MPM1D1 - Day 30 Calculating Rates From Graphs

I was away today so here's what I'm hoping the class did today. I left the following Estimation 180 tasks to start:

After the estimating they were to move onto a couple of graphing stories (here and here). After those two videos they were to have a look at Kyle Pearce's Walk Out task. It's the same idea as the others but the graph was ideal for looking at calculating rates from a graph.

Once they were done watching the videos they watched a video of me explaining how to calculate a rate from a graph. The graph at the end of the video is ideally setup because each square did not represent one unit, which makes it easier to subtract the coordinates to find the change in distance and the change in time. The idea was to connect the abstract work we did with slope yesterday to a context in order to reinforce the connection. I left a bit of practice for them as well.

MPM1D1 - Day 29 Interior & Exterior Angles

I started by having groups up at the board working on this Would You Rather problem.

This was the first time we've worked at the board in a little while. There were a number of people who were quite off task. Others got to work right away but the group dynamics were not what they should have been. Once they were done the activity I sent them back to their seats and we talked about contributing effectively to a group and how it benefits everyone in the group.

The main event for today was some geometry, specifically interior and exterior angles of polygons. I put the image below up on the board and asked students to work at the whiteboards to see how they would do without any instruction. 

The group work was much better this time around and all groups were able to answer all of the questions. A few groups needed some reminders about supplementary angles and a couple asked about opposite angles. They were doing great.

I brought them back together as a group and we summarized the different types of triangles, supplementary angles, opposite angles and began exploring the sum of interior angles. Everyone knew that the interior angles in a triangle sum to 180° so we began looking at other polygons. We did this by looking at the number of triangles in each polygon:

From this they were able to determine the sum of the interior angles. Next I had them fill out the table below to come up with an equation.

We've done enough visual patterns that to many this process came easily. They had no trouble finding the rate but had to think a bit about the initial value.  I had a couple of different results which was neat. The most common was that the sum of the interior angles = 180n-360 and the other was that the sum of the interior angles = 180(n - 2). It was exciting to see these different results.

We had just enough time to look at exterior angles. To do so I showed this video:

 We had a few minutes left which was enough time for me to handout the work for the day.

MPM1D1 - Day 28 WODB, Tables of Values & Equations of Lines

We started with this Which One Doesn't Belong:

I figured that this would be a bit of a challenge. I knew that students would be able to look at the equations and pick some characteristics out (which they did). I also knew that my students see these four equations differently than I do. When I see these equations I picture the graphs. My students can't do that yet. We've done a lot of graphing of equations but most of that graphing was with scenarios that are concrete and have some meaning. These equations are very abstract.

In any case, I put this up to see what would happen. Right away one student asked for graph paper. Others then started asking if they had to graph it. I told them that they didn't have to. Many said "Wait! What? I don't know how to graph that." I gave them a bit of time to think this one through. I helped a few students who really wanted to be able to graph. We took it up and had some great discussions. I had some superficial type answers (the first one doesn't have a number added or subtracted). I thought I would be disappointed with these types of answers but I really wasn't because each of them led to some talk (led by other students) about what those parts of the equation are, what that means about the relationship and what it means about the graph. The discussions were fantastic. Some of the students were having a hard time connecting all the pieces but it's a conversation we can revisit throughout the semester.

This seemed to be a good time to discuss how we can graph a relationship using a table of values. This was a bit of a leap for some students, which surprised me given the number of visual patterns that we've done and the number of times we've graphed those patterns. I think had I told them that each equation came from a certain pattern, and given the pattern, they would have been fine. We took a step up the ladder of abstraction and talked about how we can create a table of values and plot those point. We did this, together, for the equation in the upper left and then they worked on the one in the bottom right. Did I mention this was just the warm-up? #longestWarmUpEver?

With the warm-up behind us we could move onto connecting slopes, y-intercepts and equations of lines. As it turns out we already had some equations, tables and graphs on the board. We talked about how to find the slope and y-intercept from the graph, from the table and finally they told me how to find them from the equation. My favourite comment of the day: "You mean we can just look at the equation and get slope and y-intercept? We don't have to graph it or make a table?" I think there was some incentive to understand y=mx+b.

I gave them the first two pages of  this handout (thanks @MrHoggsClass). Once that was done I handed out some practice on creating tables of values and equations of lines.

MPM1D1-Day 27 Desmos Linear Activities

The goal for today was to talk about slope. We started with the Polygraph: Lines activity from Desmos. The idea is that they get paired up with another student in the class. One of them chooses a line from a list, the other asks questions that can be answered with a yes or no to help pick which graph their partner chose. It's basically Guess Who with lines. I wanted to start with this to see if students would use some of the vocabulary we've talked about.

They started right away and got right into it. I saw the use of lots of terminology but not much about what we've talked about. I heard comments about corners rather than quadrants. I heard some reference to the origin. And more than once I saw "Is your line straight?". This one drove me crazy! When I asked "Isn't every line straight?" these students would reply with something along the lines of "Yes, but I mean like this", indicating that they were talking about a vertical or horizontal line. We'll keep plugging away at the terminology.

  I let them play a round or two then brought them back together as a class. I asked which types of questions they found helpful. I then reminded them of some terminology (slope (positive and negative), quadrants) then introduced some new terms for some (x and y-intercepts). They played again and their questions were much better. There were a couple of math fights about wrong answers to questions such as "You said it had a negative slope. That slope is positive."

Once we'd had a bit of experience with the activity we moved onto Polygraph: Lines Part 2. They worked through the activity, hopefully improving their vocabulary and understanding of lines. Some students we motoring through the work, others needed a little encouragaement.

The last activity for the day was Put the Point on the Line, where students have to determine where a third point needs to go in order to be on a line with the other two. The best part about these activities is the teacher dashboard that allows me to see all the work my students have done, even after the fact. I can look the work over and see where the gaps are and then look at providing some assistance in those areas and I have a record that will allow me to see a student's growth over time.

There are lots of other Desmos activities involving linear relations here.

Once they were done the activities we talked about finding the slope between two point on a graph. We've done this before but this was a good reminder. Then we moved into finding the slope without a graph. I gave them this handout to practice with.

MPM1D1 - Day 26 Solving One & Two Step Equations

I was away today so here's what I hope happened.

As a lead-in to solving equations students were to work through some Solve Me Mobiles as a class. I left about 10 of them to try. I really like using these because the principles are the same as those used to solve equations but students see them as non-threatening puzzles. I guess part of the reason for this could be that the puzzles are very visual and there can be some trial and error. I guess they're not quite as abstract as an equation with letters as unknowns.

After the warm-up students watched a video of me working through some examples of solving one and two step equations. After seeing the examples they had some equations to solve. I imagine that a good number of students were done early. If they finished early I'm hoping that they tried more Solve Me Mobiles on their phones.

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.