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
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.
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
We can say that two objects are similar if they look alike. In layman’s words, objects with the same shape, whether they have the same size or not are usually called similar. In mathematics, it is quite different. In this post, we are going to learn the three mathematical meanings of similarity.
In mathematics, two objects are similar when either one of the following three conditions is true.
1. When one figure is reduced or enlarged, it will become congruent with the other
The first meaning is based on the definition of congruence. That is, when two figures are similar, if one figure is enlarged or reduced, then they will become congruent with the other. This definition is better illustrated graphically, using a drawing or an applet just as the one shown below. Continue reading
For iPhone users, the long wait is over. In case you missed it (I missed it actually), GeoGebra has released the GeoGebra Graphing Calculator for iPhones last December. I have only personally used the app for a week and I’m really satisfied with its performance and speed on my old iPhone 5.
image via GeoGebra blog
For those who have not tried GeoGebra, it is a free and open-source software for teaching mathematics. We have a lot of tutorials about it here which I’m going to update to the current version of GeoGebra this year.
GeoGebra is available for desktop computers, tablets, and Android phones. It comes on multiple platforms including Windows, Mac, and Linux. You can also install it in the Google Chrome app.