The Dancing Triangle and Its Applications

In the figure below, lines l and m are parallel lines. What can you say about the areas of triangle ABC and triangle ADC?

The distance between two parallel lines is equal at any point, so the two triangles have the same altitude (can you see why?). Further, the two triangles have a common base, therefore, their base lengths are equal. So, the areas of the two triangles are equal. In fact, you can choose any point P on line l and the areas of the triangle ACP will always equal to the areas of triangles ABC and ADC. We like to call this triangle the dancing triangle because using an applet, you can dance it by moving P without changing the area. In the applet below, move points B and D to dance the triangle.  Continue reading…


Online Peer Review with Canvas

I’ve been really busy in the past months due to my studies. In this post, I am going to share to you one platform that I have learned in one of my courses.

One of the platforms that we used in one of my courses this trimester that might interest teachers is Canvas. Canvas is an online platform that can be used for peer review. Using Canvas, students can comment on other students’ homework such as term papers and essays. Here’s how Canvas works:

1.) Teacher and students create their Canvas accounts.
2.) Teacher creates a course/classroom.
3.) The students join the course/classroom
4.) Students submit work in Canvas.
5.) Students comment and give marks to other students work.

One of the interesting thing about Canvas is that the teacher can set the comments anonymously. Aside from the comments, students can also give marks based on the rubric created by the teacher.

I have not explored the full capability of Canvas yet, but I think it is a very good tool for peer review.

It’s FREE, so you should try it.


An Alternative Algorithm for Subtraction

In the previous posts, I have shared to you an alternative algorithm for multiplication and division. In this post, I am going to share with you a different algorithm for performing subtraction. This algorithm does not involve “borrowing” from a higher place value but subtracts individual digits. To illustrate this algorithm, let’s consider some examples.

Example 1: 847 – 728

First, we separate the digits of the numbers as shown below.

Second, we subtract the corresponding digits.   Continue reading…

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