ALGEBRA: WHAT IS IT? WHY CAN IT BE DIFFICULT?
Algebra does us the favor of assigning numbers to cause-and-effect relationships.
For instance, we sense that exercise leads to weight loss.
Algebra answers that key question: "How much?"
Difficulties come in three forms: expressions that mix numbers with letters, minus signs, and fractions.
View equations as balance scales or "seesaws": (+)weights point down, (-)wts point up, with "=" as the pivot.
Vocalize equations like a "recipe": 2x-7 = 9 is "double the 'x' and remove '7' to make '9'."
Use "containers" instead of letters: "x" is a box and "y" is a bowl. What's in the box for "box +box -7 = 9?"
Move "minus" elements "to the other side." What's in the box for "box +box = 9 +7?"
Re-scale to get rid of denominators: x/2 - x/6 = 8/3 becomes (box +box +box) -box = 16 or 8 per box.