Completing the square really is using square numbers, after doing some fairly complex math with ease last week this week we did simple things but still reinforced the concepts of squares and the symbols for square numbers and while we were at it we did the cubes too. So here you see him playing with blocks after completing the square and solving for x for this problem:
x2 +10x + 9 = 0
Getting a feel for the symbols that represent squares and cubes...it's important to give students experience with numbers and concepts in a fun non-threatening way. I am working with a group of teenage girls who have never seen the squares and cubes before being presented with lessons on exponents, much to their detriment. Because of me they will KNOW 1728 is the cube of 12, and when later lessons come up about cubic feet and cubic yards they will have some experience with these numbers. This will not be the last time he writes out squares and cubes. You may also note he is still working on mastering his times tables so this dove tailed perfectly into his work on that.