## Monday, 14 November 2016

### Median, Altitude, Perpendicular Bisector Warm-Up

My grade 10 academic students have spent the last couple of classes working on finding the equations of medians, altitudes and perpendicular bisectors. Some did a lot of work and some, well, let's just say that some did less. As we move into looking at properties of quadrilaterals, I wanted to ensure that everyone has at least a basic level of comfort with the prior work. So, I came up with a warm-up that I thought I would share.

It incorporates collaboration and finding mistakes (there is no way that all groups will do this correctly on the first try). I suspect some will struggle finding the group with the same question as them, but they will learn to follow instructions better (hopefully).

Here are the questions, linked here, that I will cut into strips for them.

I have 28 students, so 14 pairs which means that I needed 7 questions in order for each question to be repeated. Two groups will eventually find the centroid (via equations of medians), two will find an orthocentre and three will find a circumcentre.

If you can think of ways of improving this, please let me know in the comments!

## Wednesday, 9 November 2016

### Centroid of a Triangle

Yesterday, my grade 10 classes learned about triangle centres. They each had a triangle awaiting them on their desk as they walked in (I copy them onto thicker-than-normal paper).

I gave instructions along these lines:
- cut out the triangle
- figure out how to balance it on your pencil
- make note of the balance point
- figure out how the balance point relates to the coordinates of the vertices of the triangle
- when you think you know, create your own coordinates for a triangle ABC, write them on the board along with their balance point

That last part was new. Its inspiration is Joel Bezaire's Variable Analysis Game which you can learn more about here. It helped some students see the pattern (especially the last line that I added to make it a little more obvious) and kept those who had found it early engaged as they were checking that other student's coordinates and balance points worked.

It was a fun way to start the class so I thought I would share... Thanks, Joel!