Not really ready for fractions

Talking Math with Your Kids week continues.

I worry about how much fraction work we do in early elementary grades, before lots of kids are really ready.

Some evidence…

Griffin (seven) has been doing his second-grade math homework, which is to find of 4, and then  of 8, and then  of 20, etc. After several of these, he is to fill in the blanks:  of ___ is ___. He begins with  of 4 is 1.

Me: You already did that one; it was the first problem. You have to do a new one.

Griffin (seven years old): But I don’t know what else to do.

Me: Any other number that you haven’t already done is fine.

G: Hmmph.

Me: What about doing 2?

G: I already did that, it’s 8.

Me: No, no. What about doing 2 as the thing you find 1/4 of?

G: Dad, there is no 1/4 of 2. It’d be in the negatives!

I have to believe that some extended time thinking about sharing situations would be a much better use of Griffin’s homework time than expressing the results of this sharing abstractly as of a discrete quantity.

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Things that come in pairs

Talking Math with Your Kids week continues.

I was doing the dishes one morning while Tabitha (who was four, nearly five) drew in the other room. She came in for help.

Tabitha: Where are the scissors?

Me: I don’t know. How many pairs of scissors do we have anyway? We have a lot, but we can never find them. Why is that?

T: I just need one pair of scissors.

Me: Isn’t it weird that scissors come in pairs?

T: Yeah.

Me: What else comes in pairs?

T: Pants do. And shoes.

Me: Oooh. Good. What else?

T: Legs. And ears. And noses [giggles].

Me: Noses?!? Noses don’t come in pairs, silly!

T: Eyes do. And glasses.

Me: Nice! Eyes. You know, it’s not just people who have eyes that come in pairs. Fish do, too.

T: Of course!

Me: How many pairs of eyes are in our aquarium?

T: Seven.

Me: So how many eyes is that?

T: Nine?

[Griffin (who was seven years old) wandered in from the living room.]

Me: Griff, how many pairs of eyes are in our aquarium?

G: Seven.

Me: So how many eyes is that?

G: Fourteen.

Me: How did you know that so fast?

G: Seven plus seven is fourteen.

Me: Right. But that’s two sevens. Don’t we need seven twos?

G: Yeah, but it’s the same answer either way.

If kids are going to understand place value, they’ll need to be able to think about different units. Sometimes a unit is a thing (an eye); sometimes a unit is a group (a pair of eyes). Giving them practice counting groups and individual things supports their mathematical development. Helping them notice that some things usually do come in groups supports it too.

Correcting Tabitha when she added 7 and 2 to get 9? That wasn’t nearly so important.

But you’d better believe I talked with Griffin later about things that are commutative.

Can a number be bigger than anything you can count?

It’s Talking Math with Your Kids week here on OMT.

We’ll get started with a favorite topic: large numbers.

My son Griffin was thinking about large numbers in the car the other day. He was trying to figure out what good it is to have a number (here, googolplex, which for the record is ) that is larger than anything you can count.

Griffin: If you put all the things [in the world] together, would that make googolplex?

Me: No.

G: Even if it’s nanoinches?

Me: Nope. Still not googolplex.

G: Even if it’s half-nanoinches?

G: Even if it’s all of the seconds of the world being alive?

Me: Nope.

G: Even if all the seconds of the universe existing?

Me: No.

I love the developing proportional reasoning embedded in Griffin’s questions.

For each example, he scales it up when his first try doesn’t do it.

If nanoinches don’t work, surely half-nanoninches will! Plenty still to learn about orders of magnitude, I’m afraid.