The ah ha moment when a 7 year old realizes she’s got a square quadratic and that she can put three x’s on the side and three more on the top and easily fill in the corner with 9. Thus the loudly spoken, “Oh, I get it!”. She then quickly figured out that it was easier to use three 3’s instead of 9 units to fill in the corner. While she was figuring all this out I sat back mouth closed hands on my lap because as she and I both agreed sometimes adults are just “a pain in the butt” because they try to do too much for the child rather than letting the child problem solve on their own. It took her some time to finish this, especially since she decided the dog and crocodile needed to have a little battle in between, but this was all her. The most awesome moment for me as a teacher was when she went to factor it and knew intuitively that she did not need to write both factors out but rather went right to using economy of symbol.
To rent my VOD lesson and learn how factor a positive coefficient quadratic polynomial with base ten blocks and see how it correlates to the symbols scroll down to the bottom of this page.