Mathematical Tasks: Number of Solutions and Answers

Different types of mathematical tasks let us tests the various skills of students. Close ended tasks let us test students basic knowledge of facts and procedures, while open-ended tasks lets us elicit various solutions answers. In the book Mathematical Thinking, Isoda and Katagiri classified mathematical tasks into three types:

Type 1: one solution, one answer

Type 2: many solutions, one answer

Type 3: many solutions, many answers

Examples of such problems are shown below. The first task is a Type 1 task, or a task with one solution and one answer. Students who have already learned how to calculate the area of rectangles can just use the formula to calculate the area of the rectangle.  » Read more

4 GeoGebra 5 Updates Teachers Will Love

It’s been a while since I have written about GeoGebra, but I have started updating some of the tutorials to GeoGebra 5. For those who have not explored the Archives, I have written numerous GeoGebra tutorials ranging from basics to advanced.

GeoGebra is now version 5.0. New features were added and a lot of improvements had been made. The 3D is now stable and 4 new tools were added. The Insert Image tool now support SVG files. But aside from these, there are simple updates which I really like and I think teachers will also love them. Here are four of them.

1.) Automatic Color Change

Every time you graph a new function in the current version of GeoGebra, it automatically selects a different color. You don’t have to trouble yourself changing the color of the graph of the new functions.  » Read more

The Basics of Inverse Proportion

In the previous post, we have discussed the basic of direct proportions. Recall that when two quantities x and y change and if x changes n times, then y changes n times, then we can say that y is directly proportional to x. In this post, we are going to learn about inverse proportions.


A rectangle has area 24 square units. Find the possible areas if the length and width are both whole numbers.

Solution and Discussion

The table shows the pairs of length and width that has area 24 square units.  » Read more

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