: I teach high school drafting. Many of my students have alot of
: trouble adding, subtracting, and dividing fractions. I have ways
: of doing it in my head and I try to explain it to them. They have
: learned it in math classes but I don’t remember how it is taught
: so I really can’t help them remember to much. Much of the problems
: they solve in their math classes don’t use common fractions of an
: inch so when they are required to divide 3-3/8” they stumble
: or to add 2-1/4” to 7/8”. I need some techniques to
: review these concepts at the begining of each new semester.Believe me, you aren’t alone. Your kids are like 90% of the students I’ve seen and heard of across the continent — maybe better, because they don’t sound resistant to working with numbers (Many of mine literally scream, cry, or turn their heads away and refuse to look as soon as a fraction appears.)They “learned” this stuff in elementary school, sort of, usually by teachers who disliked it as much as the kids did and rushed through the fractions chapter as quickly as possible; also with grading systems that attempt to be kind and helpful by dropping the kids’ lowest grade, so they know they can ignore one test, and guess which one.If you ask in depth, you’ll be shocked and disturbed. Get your students to draw a ruler and locate 3/8”, 2 3/4”, 11/16”, and 15/4” (Yes, that’s the improper fraction) on it. If they get more than half of those, your group is well above average.As a drafting teacher, you have a huge advantage; you’re *supposed* to be using concrete measures (math teachers find a high resistance to this, because everybody knows that math is verbal rules and drill from the book).Yes, you do need to go back to the old pie. Ask the students what the two numbers in the fraction mean; they may give you the names numerator and denominator, but few will know why those two numbers are there. Start with the pie and then the ruler and show them that the bottom number tells how many parts a single object is divided into and the top number tells how many to take. This will be original and exciting news to quite a few of them. Have them locate fractions on a ruler (magnified at first) using this rule; first proper fractions, then improper, then mixed numbers. Show the equivalence of mixed numbers to improper fractions on your ruler by counting them out. Stress that “equals” MEANS “exactly the same size” (another concept many of them have never heard). Then go to equivalent fractions — different names for exactly the same distance. Again, a new and exciting concept for many. Avoid for some time the verbal just multiply both the numbers rule — that’s the problem that has got them where there are, not the solution. Teach addition and subtraction first by measurement: draw a line exactly 2 1/2” long, and extend it another 1 3/4”; how long is the result? THEN, finally, you can show the usual common denominator addition as a process that makes some sense in the real world. Multiplication and division can be interesting too: How thick is a floor made of three 3/4” sheets of plywood? How many 1 1/2” studs can I stack in a box 12” high? (Draw it and look!)Advanced students: How many 4 1/4” square bathroom wall tiles to cover a wall 5 feet long to a line 4 feet high?With a few weeks’ work ten or twenty minutes a day, you can go a long way to helping those students out of the math depths and into a better educational future.