Triangles in Scratch

The video below is a follow up to the one I made here. This one is not that much different. Instead of drawing a square I show how to draw an equilateral triangle. To me the interesting part of the tutorial is having students play around in scratch to see if they can create an isosceles or scalene triangle. I haven't had a chance to do this in a class yet, but I'm hoping that there will be a lot of trial and error and eventually some students will get close enough. Close enough that they will be able to answer the questions "What is the sum of the angles in any triangle?".

The second challenge is to have students draw a regular pentagon, hexagon, etc. In order to do this they will have to determine the sum of the angles in each of these figures. We've done enough visual patterns that I hope this will be easy for them. I'm hoping this will be a fun way to cover some of the geometry in the grade nine math courses.

Give it a try.

Playing With Rectangles

I'm currently teaching my grade 9 students about linear relationships. We create scatter plots, draw lines of best fit, use the information to make predictions and so on. As we came to the end of the unit I felt as though we hadn't done enough. I felt that somehow it would be far more interesting if we could connect this section of the course to another section. The measurement unit seemed like a simple connection.

I gave students 12 straws and asked them to find the rectangle that would give the largest area. They messed around with the straws, made tables and graphs and determined from their graphs what the largest possible area was. Next I gave the 12 linking cubes and asked them to create the rectangle with the smallest perimeter. Again they played, created tables and a graphs but the solution wasn't as obvious.

None of this work is ground breaking or much different from what I have done in the past. The only differences were that I cross pollinated (some might say spiralled) the units. I think this helps show students that mathematics is interconnected, that it's possible for units to have a common thread. The other difference was that I physically gave them objects to manipulate, which is different from how I taught this before. In the past I would have them draw out rectangles. I think something gets lost here. It was very obvious to students what was going on when they were manipulating the physical objects.

Although neither of the graphs were linear it was useful to create them and to discuss what type of correlations there were and read information off the graph. We will revisit this concept again in the measurement unit. I look forward to seeing how well they retain the information.

As a side note, the graph of the maximum area was a parabola as expected. Without thinking too much about it, I expected the perimeter to do the same. As I saw students' graphs I wondered why they were the shape they were. I did the algebra and recalled that the resulting function was a rational function. Looks like a good problem for the grade 12 students. Tomorrow: Determine the function that minimizes the perimeter of a rectangle.

Let's Start Coding

The second week in December is Computer Science Education Week (CSEd Week). I get really excited about this because more teachers start talking about coding. The trouble with this event is that it often seems to be a one off event. Teachers give up an hour of their curriculum time to participate and once the hour is done they tend to move on. It's great that they participate but it could easily become part of any teacher's curriculum. I realize that it's "one more thing" to do but it can be very engaging for students and I believe that it really helps develop skills that are useful in many disciplines both in and out of the class.

Why are teachers not extending coding into their regular routines? I think for many of them it's about comfort. The Hour of Code tutorials are great. They are well laid out and could be coordinated by anyone. If you're going to start building coding into your classes, however,  you need to understand the tools a bit and you also have to find a way to weave in some curriculum expectations. No small task.

Brian Aspinall is a teacher who has not only embraced coding in his class but has taken it upon himself to help other teachers see how their students can code and meet curriculum expectations at the same time. He uses Scratch, which is really easy to use. You can find his videos here.

Brian's work had inspired me to play around more with Scratch and to find more ways to work it into the curriculum. I've decided to create videos that introduce some coding ideas but also create a challenge for teachers (or students) to work through. Hopefully, some teachers out there will decide to follow up on the challenges. If not, at the very least I will have thought more about how coding can be woven into my courses.

If you're interested in integrating computer science into your curriculum check out the #CSk8 hashtag.

Here's my first video. 

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!