Here’s a common word problem used for linear functions and equations (y=mx+b):

There are 6 inches of snow on the ground. Snow is falling at a rate of 2 inches per hour. Write a linear equation showing total snow as a function of time (in hours). The equation would be y=2x + 6.

Often the word problems like this are presented on a sheet of paper in isolation as an attempt to make the math relevant and to develop conceptual understanding. For students who have trouble with conceptual understanding, words on paper are likely too abstract or symbolic to allow applications like the one above to be meaningful.

The real life application is useful if presented more effectively. Here’s an approach to use the same scenario but in a more relevant and meaningful presentation. The photo above shows the current amount of snow – call it 6 inches. Students can be shown the photo to allow for a discussion about accumulation and for their estimates of the amount of snow shown. The photo below shows an excerpt from a storm warning. Showing this warning and a snow fall video can allow for a discussion about rate of snow fall and the purpose for storm warnings. Combined, this approach can lead into the above word problem.

Once the application is presented students can be asked to compute snow levels after 1 hour, 2 hours etc. Then they can be asked to determine how long it would take for the accumulation to reach 18 inches (the prediction for the day this post was composed). After computing the answers WITHOUT the equation the students can be shown how to use the equation – the “mathy way.”

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.