In working with students, parents and IEP teams, I find that there is an assumption that math at some point, possibly beyond arithmetic, is simply a science fiction movie that is minimally related to real life. I hear from students as well as adults, statements like, “algebra, when are we ever going to use it?” My response is, ALL THE TIME!
The math we often present in school is a “mathy” version of the math we encounter in life. For example, the top photo below shows a pizza menu and a situation that is realistic. The calculator screen shot below the menu shows how we likely would solve the problem using a calculator on our phone.
Below is the same type of problem, but solved using “mathy” math. How many of us (besides me) are doing this at the pizzeria?
The point is, we engage in algebra but maybe do not use all the symbols and vocabulary of algebra, e.g. when we typed in 2.25 repeatedly in our calculator, we were working with the math term “slope.”
This has implications for secondary students whose post-secondary plans do not include college. If the math class is teaching “mathy” math but you want your student to learn math as it is used in real life, then an alternative math course is needed. This could be addressed through the IEP.
Saw the following price tags, shown in the two photos, at an office supply store. $4 for 4 batteries or $9 for 8 batteries. To compare we can double the smaller pack to see that 2 packs would cost $8 for 8 batteries for a better deal.
Another method is to use unit rates. Rates are a measure of one quantity, with units, per 1 unit of another quantity, e.g. you make $10 per hour. To compute
Below is an example of instruction for unit rates to help a student conceptually understand (pretend that gas price shown on this pump is $2 per gallon). Say you pumped 3 gallons and it cost $6. Show the 3 1-gallon gas cans together and the 6 $1 bills together. Separate them to you have equal groups to get $ per 1 gallon. You can use actual gas cans (unused) or cutouts from Google Images.
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.
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.