Bed time has become more difficult for the 6-year-old since school has started. I think it has to do with adjusting to first grade. It’s a big transition year, and he’s got a lot of concerns that come up just as I’m about to turn out the lights. He’s no dummy. He knows how to stretch out bedtime…
The other night as I was tucking him in, he came up with a series of questions that I couldn’t resist. He is aware that I’ve just started a temporary medication that steps down…5 pills the first day, then 4 on the second day, and so on. I had asked him earlier in the day how many pills total I’ll have taken when I’m finished. We wrote them down and added them up to get 15, and that was that.
Or so I thought.
“Mom, what is 5 plus 4 plus 3 plus 2 plus 1?”
“Same as it was earlier today.”
“What is it?”
So, I took the bait and dove right in…
“Actually, kiddo, adding all the numbers in decreasing consecutive order like that is special in math. It’s called a factorial** (Whoops. A factorial is actually the product of these numbers, not the the sum. See my note at the end of the post.) And it’s written with an exclamation point. 5! And all it means is what you just said. 5 plus 4 plus 3 plus 2 plus 1.”
“What is it?”
Right. The answer. That’s what he’s shooting for here. Earlier in the day, we added 1 + 2+ 3 to quickly get 6. Then we noticed that 6 + 4 is one of those number bonds that combines to give 10. From there 10 + 5 was straightforward. 15. Time to show him another way…
“Check this out.” I held up 5 fingers to represent the numbers 1 through 5. “This is 1, 2, 3, 4, and 5,” I said as I point to my pinky, ring, middle, pointer, and thumb in order. “If I add 5 and 1 together, what do I get?” I pointed to my pinky and my thumb.
“Okay. If I add 4 and 2 together, what do I get?” I stepped in one finger on each side.
“Sure. And 6 and 6 together is…”
“Now just add the number that was left in the middle…3.”
“Cool, huh? Okay, go to bed.”
“Wait! What if you did it with 10 and all the numbers down to 1? What would happen?”
“Well. Add the first number to the last number. What is is 10 plus 1?”
“Yes, okay. Now add the next number up from 1 and the next number down from 10. 2 plus 9.”
Then I held up both my hands to indicate the numbers 1 through 10 and I paired them off: 1 with 10, 2 with 9, 3 with 8, 4 with 7, and 5 with 6.
“There are 5 pairs. Each pair adds to the same thing, eleven. So that’s 5 groups of 11. Or that’s 5 times 11.” The 6-year-old doesn’t yet do multiplication, so I verbalized it differently for him. “11 plus 11 is 22. Plus 11 is 33. Plus 11 is 44. Plus 11 is 55. That’s 5 elevens.”
I thought for sure he’d be asleep by now. But he wasn’t.
“Let’s do it with ONE HUNDRED!”
How could I resist??
“100 plus 1 is…”
“And 99 plus 2 is…”
“Okay. There will be 50 pairs that add to 101 because 50 is one half of 100. So 50 groups of 101 is…”
“5,050. Now go to bed.”
As I turned out the light, this is when he finally began to bring up the concerns of his day at school. So, I rubbed his back in the dark and listened. I asked a couple questions. Then I told him how glad I am that he tells me what is happening at school, and if he wants me to, I will talk to his teacher or help him find the words to do it himself. Sometimes he asks me to promise not to, and other times he is eager for help.
And then I go to bed…exhausted but also glad for our moments together, mathy and otherwise.
**Correction: A factorial represents the PRODUCT of consecutively decreasing integers, not the SUM, as I represent here. Thanks to Jennifer for pointing this out to me. Rather than edit this post to fully correct that error, I am noting it here instead. It is important for kids to know that parents, teachers, and everyone make mistakes. We correct ourselves, learn from it, and move on. (At the high school level, I didn’t mind my students working in pen because it necessarily preserved their mistakes…which were an important part of their problem solving process.)
(Mathematically…it may be a good strategy to talk about math at bedtime. Your child’s reluctance to discuss math may fold to his stronger reluctance to go to sleep! The discussion above was just another way to build mathematical fluency and flexibility while also reinforcing it’s daily application. The next morning, I drew a diagram —see below, and note again my incorrect use of the factorial notation in green at the top— of our calculation for my son, so he had also had a visual of it. It’s not so important that your child ever knows what a factorial is, but it is important that she learns that she can manipulate and move numbers around in some calculations. Kids will officially learn this as the “commutative property” at school, and it is incredibly handy. These at-home interactions are hands-on practice that reinforce the learning.)
I thought 10! represented multiplication not addition. Isn’t 10! = 10x9x8x7x6x5x4x3x2x1? Asking as I continue to prep for GREs…and don’t remember EVER learning about factorials decades ago…
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Yes, Jennifer, you are correct! I’ve edited the post to note my mistake. Thanks so much for quickly commenting so that didn’t hang out there for too long!