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 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 15 Desmos Intro & First Assessment

We started the class by revisiting Hula Hoop Relay. I had a set of Chromebooks and we made our way to Desmos. This would be our first use of Desmos. We had a few password hiccups and a couple of network issues but they were fairly easily sorted out.

I demonstrated how to create a table, adjust the scale and find the equation of the line of best fit. I used a group's set of data to demonstrate. As it turns out the slope and y-intercept had the same absolute value. What an unfortunate and potentially confusing coincidence. The potential was there to dive into expanding and factoring binomials, but it wouldn't serve the purpose for today's lesson so I let it go. We talked about how we could find how long it would take for 43 people to do the challenge. We discussed how we could use the graph to extrapolate and how we could use the equation. It was a nice link between the graph, the equation and what was really going on. We did it both ways and some students seemed surprised that everything matched up.

As a result of our Desmos introduction I felt as though some students would be able to do it on their own while many would need a little more practice. There will be plenty of opportunity for more practice.

We put the computers away and did the mid-cycle assessment (using the term mid very loosely). A couple of students seemed really worried about how they were going to do. I told them to do their best as it would give them a sense of what they needed to work on for the test at the end of the cycle. This is our first real assessment and I intend for it to be formative. I'm hoping it will provide students with some feedback on what they need to work on. It will also give me a chance to see if there is any particular topic that we need to revisit.

Trigonometric Regressions with Desmos

I decided that this year I was going to make trigonometric modelling a little easier for my students. I've used Kate Noak's Moon Safari in the past but I found that something was lost using a graphing calculator. The process of entering the data is time consuming and causes some students to get turned off the activity before they managed to get to the good stuff. This year I decided to give Desmos a try.

I entered the data into a Google spreadsheet that I made public. I gave students Chromebooks and had them open the spreadsheet. They copied the data from the spreadsheet, then pasted it into Desmos (yup just two steps) and then got to work trying to determine the equation that best modelled the situation. I really liked that they could see the graph as they modified the equation and see the coefficient of determination to help them determine if one equation was better than another. When they were done they could get Desmos to do the regression to see how close they were.

This was so much simpler than using a graphing calculator. It seems like Desmos gets better every time I use it. Thanks Team Desmos!