I developed a method of starting to teach algebra a number of years ago – getting the boys to invent it themselves since any mention of the word ‘algebra’ got an instant and negative “I can’t do that” reaction.
I start with ‘Spud the Airport Manager’ problem (yes, he was a real person in that job):
- Bring in a bunch of large and small envelopes and boxes in a bag and dump them on the floor and get the boys to sort and record (one boy to do this on the board) them as Spud would have to do WITHOUT knowing what is in them. Then I dump another load ‘at the airport’ to be sorted. The boys rapidly get tired of writing ‘4 large envelopes and 6 small envelopes’ and abbreviate to 4L and 6S. The idea of adding 4L + 5L etc, is the idea of the boys. So they invent the idea of using letters and having to add only like terms / letters.
The next step (a few lessons later) is to have food in each type, so they learn that 9L can be done as 9 x 3 jelly beans = 27 jelly beans which means they can substitute numbers for letters.
Once the boys are comfortable with this and proficient at doing it, we go on to solving equations:
- To have them work out a basic method, I bring in a ‘present’ for their girlfriend or mother as well as the wrapping material. A boy writes down (as others tell him) the steps to wrap the package – tissue paper, in box, close box, wrap, tape, make bow (whatever they say). Then we list the way for their girlfriend to ‘find out what is in the box’, i.e. find the ‘unknown’. When we write out the steps, the order to find the unknown is the exact reverse of wrapping it up. And you must do the exact opposite operation – untie rather than tie a bow. The boys have already been taught BEDMAS (order of operations, sometimes BODMAS or other variations). So we swap it around to SAMDEB instead to solve an equation.
This gives the boys a basic method of attack in 2 simple rules – SAMDEB is the order, and ‘do the opposite operation’.
The boys start with simple equations and can rapidly work up to 3x/2 -15 = 28
NOTE: I do NOT give them whole number answers in most cases or they just tend to guess. Some people teach a ‘back track’ method, but I find the boys do not learn to write out simple, clear steps downward and instead do a ‘run on sentence’ type of maths or get stuck if there is an x on both sides of an equation. I’ve taught ‘bottom band’ maths classes this way, and even the least able and most scared can manage.
Now that I just do day relief teaching, I find even classes above Year 9 level have a problem with algebra and do a basic lesson on this, often to, “Why did no one tell us this before? That makes it much easier.”
Some boys need a more ‘physical’ method, and I have resorted to using numbers on sticky labels on a board, where the boys actually pick up and move the sticky labels/numbers to solve an equation.
Rearranging equations such as F=mgh or a= (vel 2 – vel 1)/t just use the same rules. You are just moving the letters rather than a number.
The main thing students must do is practice on lots of problems of assorted variations.