Teaching algebra using some visual and cultural features

Teaching algebra using some visual and cultural features

8 = 6 - 2(t - 3)

CM (indigenous helper who is studying to become a teacher) was having trouble solving this equation. So, I thought of a different way to teach it which incorporated some conventional elements with some new ideas. The conventional element was a seesaw. This was mentioned in the text but only in passing. The way to use the seesaw is that one side needs to balance the other side. As we move items around from one side of the equation to the other the seesaw is not allowed to become unbalanced in the process, both sides have to remain equal.

                               8                      6 - 2(t - 3)

CM's difficulty was figuring out which things to move to the other side first. So I suggested that the brackets represented a nest and the t stood for a turtle inside the nest. Since there was a 2 times outside the bracket that meant there were two nests. The nest was hard to get at so it was best to move those items outside the nest first. That meant move the 6 first. How do you get rid of +6? The opposite is -6. So subtract 6 from the right hand side (RHS). But that unbalances the seesaw, so you have to subtract 6 from the left hand side (LHS) too.

                                 8 - 6                 6 - 6 - 2(t - 3)

                                   2                    - 2(t - 3)

The turtle nest is multiplied by -2. To get inside the nest we have to deal with that issue next. How do we get rid of a multiplication by -2? By doing the opposite which is dividing by -2. But this will unbalance the seesaw so we have to divide both sides by -2.
                                 2 / -2                     - 2(t - 3)/ -2

                                 -1                         t - 3

Now at last we can get inside the turtle nest. Just finish up by adding 3 to both sides in order to get rid of the -3 on the right hand side.

                               -1 + 3                         t - 3+ 3

                                  2                             t

t = 2