144, 18, 8

I was a bit silly over math last week.
I was at a meeting for a new homeschooling co-op.
The new co-op meets for 18 weeks a year.
Over the course of the year the kids memorize a 144 point timeline.

The question came up, how many timeline cards do the kids memorize each meeting?

I didn't do the math. Sigh. The numbers didn't automatically line up for me, and I didn't want to plug and chug.

So, at first I decided to just flip to a page in the manual and count the number of timeline cards for that week. Eight cards. Flip to another week. Eight cards. Okay, it's eight cards per week. At least usually.

But that didn't feel right, because another co-op meets for 24 weeks per year, memorizes a 160 point timeline, and does eight cards per week.

So I got out the calculator and did the math. 144 cards divided by 18 weeks equals 8 cards per week. Okay, so now I trusted the result. Plus, I remembered that the other co-op doesn't take all 24 weeks to memorize the 160 point timeline.

However, the numbers matched up so nicely that I was irked that I didn't figure out out mentally.

I did remember that 144 is 12 squared. But that was where I stopped. I should have worked it out further. After all, Sparkle and I had just done the Sieve of Eratosthenes for her math lesson. (I created a bunch of pattern templates for multiplication and we had fun using them, culminating with the sieve!) Thinking about prime factorization should have come naturally.

Anyway, here goes my ultimate thought process.

144 = 12 squared
144 = 12 x 12
144 = (4 x 3) x (4 x 3)
144 = two 4's and two 3's

18 = 9 x 2
Ah, ha, the two 3's from the 144 match up with the 9 in the 18.
I can split one of the 4's in the 144 to get a 2 to match with the 2 in 18.
That leaves the other 4 and the leftover 2 in the 144, and they make 8. So, 8 cards per week.

144 cards = 3 x 3 x 4 x 4 cards
18 weeks = 9 x 2 weeks

144 cards = 9 x 2 x 2 x 4 cards
18 weeks = 9 x 2 weeks

144 cards = 9 x 2 x 8 cards
18 weeks = 9 x 2 weeks

So, 144 cards in 18 weeks means 8 cards each week.

It also works if you think of it this way.
144 = two 4's and two 3's
18 = 3 x 6

The 3 in 18 matches with one of the 3's in 144.
The 6 in 18 matches with the other 3 and a 2 from one of the 4's in 144.
That leaves 2 x 4 in the 144, which is 8.

I suppose my way of thinking through was rather cumbersome and inefficient.
I mostly did it because when I saw that nice round number 8 confirmed, I just knew that the numbers had to fit together elegantly. I wanted to make sense of it. So, I went through my convoluted thought process that my math smart brothers would probably find ridiculous.

I'm satisfied.

Oh, and I signed up for the co-op.
The timeline cards are *gorgeous*!