As I wrote previously, shopping is dense with math tasks as are grocery stores. Here are some division situations that are sneaky challenging and require a student to know when and why to divide before even reaching for the calculator. I will use these to help illustrate the fact that life skills math is not simply counting money or using a calculator to add up prices. There is a great deal of problem solving and thinking skills that need to be developed.
For example, if a student has $60 to spend on gifts for her 3 teachers the student needs to understand that she can spend up to $20 per teacher (before even talking about taxes).
An entry point for division can involve a dividing situation the students intuitively understand, e.g., sharing food. Start with 2 friends sharing 8 Buffalo wings evenly (below).
This can lead into the 3 teachers sharing the $60 evenly (below). In turn, this can be followed by the online shopping shown above.
This approach can be used to develop an understanding of unit cost (cited in the shopping is dense post). Start with a pack of items to allow the students to see the cost for a single item before getting into unit cost by ounces, for example.
I have had success with teaching these division related concepts using sheer repetition as much of our learning is experiential learning. Using a Google Jamboard as shown in the photos allows for the repetition.
Very clever activity implemented by the teacher who runs the Life Skills program at our school. She created envelopes (below) for each teacher. The envelopes do not contain any content but are used for practice sorting mail for the students in the program. The students in the program sort and deliver them to our mailbox. We return them to this return bin for reuse.
Such experiences should be available to all of our students who are more severely impacted. Many will need YEARS of practice to develop skills which means a transition program from 18-21 years old may not be enough.
Math is often considered an esoteric set of information that is disjointed from the reality people face, aside perhaps from money. Sadly, in school, especially in older grade levels, math is indeed presented this way.
A situation as simple as riding an elevator provides opportunities to show and engage a student with math applied in authentic and common situations. For example, the elevator buttons address counting and cardinality (4 indicates a total of 4 floors – ignoring the R), comparison (if we are on floor 2 and need to go down, which floor do we go to?) and measurement (height above ground floor measured in floors). Such situations also provides opportunities for generalization into other settings – the important settings of every day life!
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.”
Found this (above) cool example of corresponding angles (see photo below for explanation). This window photo could be a nice introduction to this type of problem by printing it out on paper and having students match angles as the teacher shows the photo on the Smart Board or screen.
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)
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.
Real life applications in of themselves will not make a concept real for many if not most students with special needs. They likely need the concept broken down into more concrete form (CRA).
For this problem I would fudge the numbers and have 42 oz at $6 (7 oz per dollar) and a 5 oz at $1. I would have a photo of a “42” oz yogurt and cut it into 6 pieces and have 6 $1 bills and match each yogurt piece with a dollar bill to help students visualize the unit rate.
I took this photo tonight at Big Y and threw together this idea on the fly.