Passing from One Square to Another

After our work with the cubing part 1 and part 2, I figured it was probably time to officially present "Passing From One Square to Another" since he'd already done the allegedly harder work of "Passing From One Cube to Another" (just subsequent passings at this point - not jumping two sizes).

rebuilding the square of pythagoras from primary
YES, this comes in a LOT in elementary
in particular using the bead bars! 

First he wanted to stack the squares to make a flat pyramid.
Then he turned them a bit to make them "fancy"
(think of all the art ideas a child could do with this work alone!)

Backwards order - he passed from square of 6 to 7;
then he passed from square of 5 to 8.
Hm. Looks like the binomial cube he said.
Then quickly added: but DIFFERENT colors!
(see previous posts on cubing to get the joke)

Displaying the originals with the finals. 

When we were done, we verbalized what we had done. We also noted that pattern on each side - for example, the square of 7 IS the square of 6 plus the square of 1, but with two rectangles add of 1 taken 6 times. The square of 8 IS the square of 5 plus the square of 3 plus 2 rectangles of 5 taken 3 times.

Now let's look at the values: the square of 7 (49) is the square of 6 (36) plus the square of 1 (1) plus those two 6x1 rectangles (12). It adds up!

Repeat with the second square. It still works!



Yep. We did the work out of order - some things are entirely ok to change up! This was all strong interest-driven and the main pre-requisites were in place - that's ALL that matters! We have plenty of time to review the concepts again and again to be sure of thorough understanding. (and see my previous posts this past week on that aha! moment when a child verbalizes something his actions have shown he's known for YEARS) ;)

Yes, scope and sequences are great - they get us organized - but feel free to diverge from it! Cover pre-reqs (could be informally) - that's all that matters!