A student came to me with a geometry worksheet, excerpt in photo above. Extemporaneously I created cut out sides of a triangle to help make the concept of lengths of sides of a triangle more concrete.

The concept is that the shorter 2 sides must be longer than the 3rd side or you cannot get a triangle. The worksheet is very abstract and very inaccessible. (Actually there is more to this topic but I am keeping it simple to allow lay people to focus on the instructional strategy and not the “mathy” stuff.)

Making math meaningful and maybe interesting is a challenge. The photo above refers to a real life application for triangles and trigonometry (see photo below) that is found in a news story about Russian jets and a US destroyer. The jet was flying at an altitude of 100 yards and within 200 yards of the destroyer. Topics that could be addressed:

Altitude (and perpendicular)

Pythogorean Theorem

Trigonometry: e.g. find angle of elevation or depression

Vectors (include velocities)

A relevant, real life application is a method to make information meaningful. When talking about the altitude of a triangle (the up and down part shown in the photo below) the vocabulary term of altitude becomes more meaningful both in terms of context and with the visual below.

Here is the agenda I would follow to use this application as an activity.

I would show the video (show on the webpage linked at bottom of handout) and explain what a destroyer and the jets are.

Discuss the situation with Russia (age appropriate discussion)

Show the picture and ask the students to draw a sketch.

Review the sketch and refer to the parts of the triangle in real life terms, e.g. altitude.

Task the students with a problem related to this problem – create your own, e.g. find the angle of elevation or use Pythagorean Theorem to find length of missing side.

Students have trouble with irregular shapes largely because they cannot visualize or determine the measures the dimensions of the individual parts. The photos below show a hands on activity to help students with these challenges. The students are cut out the individual shapes and write in the dimensions. This method allows them to see the individual parts and the respective dimensions. (The second has calculation errors.) This activity is followed by a handout in which students can shade in the different parts which is a step towards more abstraction – CRA.