At a family Thanksgiving this past Thursday there was the usual mix of adults and kids. The adults were mostly catching up with each other. Exchanging old war stories of mayhem at the office and other parts of life.

The kids were rambunctious. First it started out with the usual running around and the trying to score dessert in advance. Then, it turned into indoor dodgeball, a game that typically ends in tears. As a kid, I’d play indoor tackle football. That ended in blood and tears. So indoor dodgeball felt tame. Although a different risk existed — namely that priceless vase …

Anyway, eventually in this dodgeball game, I almost became collateral damage as a nerf-ish ball whizzed by my head. The second time around I was more prepared and I got hold of the ball. Grabbing the ball meant that I somehow became a participant of the game and so a second ball came flying my way. This one was deflected back to the kids and like a good recursive process, that ball came right back at me. After a few of these harmless one-sided volleys, I decided that enough was enough. I got up and motioned that I too would return fire. The kids ran.

The power of adults.

Ah, but the ingenuity of kids. They returned, taunting / threatening with a Captain America shield.

They wanted their balls back.

Do not fire the arrow that will return against you. — Ancient Proverb

Playground antics are an introduction to battlefield strategy.

So as the pleading continued, I let them try to grab it out of my hand. You know, a show of strength. The power of adults.

When their braun was no match, I engaged them in conversation. How old are you? The older one said she was seven and the younger one (boy) was six. She also quipped that her age difference meant that she was one year older.

One year older! Sounds like math to me!

So I made them a deal, if they could answer a math question, they could get their ball back. One correct answer, one ball back. They agreed. But before I could ask them a math question, they had to tell me what math they knew. The younger one blurted out, $$5 + 6 = 11$$ and the older one said she could do bigger addition like $$12 + 12 = 24$$

so I asked them what \(12 + 19\) was. The older one did some counting and came back with \(31\). Ball returned. Now the other ball would be given to the younger one, but he had to answer. So I gave him a softball, $$12 + 8$$ and he responded with \(20\). Second ball returned.

And they ran off in triumph.

Now I was on guard because I had just handed back the weaponry. And sure enough a minute later, they returned. Trying to be sneaky behind the wall, but I noticed. They ran out from behind the wall and darted straight towards me with balls in hand. But to my surprise, rather than throw the balls at me, they handed them to me and yelled, “Give us another problem!”

Holy moly! Ok! Well, I’m the guy to go to for more math problems.

So I asked them what $$1000 + 1000$$ was. The older one responded immediately with \(2000\). Done! Ball returned.

Then I asked if they were ready for a team challenge. They agreed. And I asked, “What is $$1001 + 1001$$?”

They looked comically at the ceiling, in deep thought. Without conferring with each other, the younger one blurted out first,

“4000!”
“Nope.”

The older one chimed in,
“2000!”
“Nope! That’s what you said \(1000 + 1000\) was!”
“Oh yeah!” <lots of giggling>

Then they thought for a little longer and a new guess came in

“2001!”
“Nope!”

Another adult interjected as he was intrigued that the kids were this excited about adding. He reasked the question, “What is one thousand ONE plus one thousand ONE”. As he emphasized the units place, the wheels turned in the little ones’ heads. And out came

“2002!”
“Yup! Here ya go!” And the ball was returned.

Maybe they just guessed again on 2002. Regardless, they knew they got the right answer because the ball had been returned. And off they ran.

How the heck did the little guy come up with \(4000\)? Oh right, it’s the same way that some kids get \(34 + 12 = 10\) when written as a stacked addition problem. Except here, he also knew that we had a four-digit number. Thus, the answer must have been a four digit answer and since \(1 + 1 + 1 + 1 = 4\), what other answer could it be other than \(4000\)?

Interesting!

They came back. “More math!” Rinse and repeat.

So I thought to myself, what the hey, let’s try some Algebra.

What number do you have to add to 12 to get 26?

First they processed the question. I don’t think they had ever heard that type of question before. So I repeated the question.

Out came the fingers and they came up with 14. Bingo! Not bad, a seven and six-year old doing some Algebra.

“Great! How can you solve this without counting on your fingers? Let’s try a really tricky problem!”

And I asked, “What number do you have to add to 16 to get to 54?” They puzzled over this one. It was too high to count with fingers. They ran off and came back with 38. I gave them their ball back.

But they could not tell a lie.

“We asked our mom! She told us!”

We all laughed and conveniently it was turkey time.

The educational takeaways here are huge.

• Math can be fun.
• Math is fun.
• The little kiddos can do a lot more than what standards say.
• The little kiddos also have a developing sense of a mathematical system. In fact, they will make up their own system because likely at some deep cognitive level, they too crave for logic. Or at the very least, they crave to make sense of the world. The answer of \(4000\) has some great logic in it.
• The little kiddos will eventually resort to guessing because they want to be right. So maybe we should stop telling them that they are always wrong and steer them with sound reasoning.
• Not everything has to be formal and rigorous to have educational value. Just have fun and who cares if there’s some sloppiness at the outset. There are plenty of ways to right the ship and they don’t all require formal, summative assessment. I know when they’re guessing, I know when they’re getting solutions from other sources, etc. There’s nothing wrong with letting it slide from time to time so long as we keep the focus on learning and circle back to the areas where they are just guessing so that they can be right.
• The ball being given back was feedback. It was also the reward. Make the reward of learning, the feedback. Make the feedback meaningful and fun, rather than a form of classification (and an instrument of shame).