One of my favorite ways of presenting a problem is not presenting the problem at all but just letting learners observe first and then ask them to make questions about what they observe. Here’s an applet you can use to do that. It involves area of rectangles which is studied in Grade 4. This means you can use this from Grade 4 up to high school.
Before I give some teaching tips, try exploring the applet yourself. The figure is a rectangle with diagonal CD. Point E is a point on the diagonal.
Move E. What do you observe? What is changing and what is not changing? Write down questions/problems base on the figure below?
Sample questions learner could come up with.
- Which sides are equal?
- Which shapes are congruent?
- Which rectangle has a bigger area? the blue or the red?
- Which rectangle have a longer perimeter? the blue or the red?
Remember that learners need time to think of a question especially if they are not used to this kind of activity. It is however worth the wait since this is an important thinking habit: to ask questions based on what one observes.
Note that if you use this in the elementary, it would be best to supplement it with actual cutting activity so they can compare the congruent parts and measure the sides so they can compute for the area. High school learners should be able to justify it by reasoning.
Answer to Question #3 is found here.