[#TMWYK] Logic & Equivalence

Some logic and equivalence #tmwyk* this morning:

8yo (trying to get me to do something for her): Please plus please!
Me: What does that mean?
8yo: It means yes.
Me: So, what does a thank you + thank you mean?
8yo: That means yes, too.
Me: How about a no thank you plus a thank you?
8yo: No.
Me: And a no thank you plus a no thank you?
8yo: Maybe.
Me: How does that work?
8yo: Because there are two no's and two thank you's.
Me: You mean there's an equal number of both?
8yo: Yeah.

A little later, about our cats Max and Lucy:

8yo: Max + Lucy = Trouble
Me: That's for sure.
8yo: Actually, cat + cat = Trouble.
Me: So, Max + Lucy = Cat + Cat = Trouble!
8yo: NO!
Me: Why not? If cat + cat is trouble, and so are Max + Lucy, then don't Max + Lucy = cat + cat? They both equal trouble...

She had reached her limit with my questions by then, but I found the whole series of ideas rather fascinating.  First because this was the first time I've had this particular kind of conversation with her. It seems Christopher Danielson's Talking Math with Your Kids is really having a positive influence on my conversational abilities! Second because the whole idea of equivalence in equation form seems to flummox kids. The equal sign often seems to mean "an answer" and not a relationship. It was fun to test/push her a little on this idea and see how it would play out in conversation.

*#tmywk is the hashtag for Talking Math with Your Kids on Twitter. You can also go to Talking Math with Your Kids.  You'll be glad you did!!

How Are We the Same?

At my daughter's school, middle of the morning, to pick her up for a dentist appointment.  Ran into the restroom before I went to get her.

In the restroom I inadvertently opened a stall door with a little person inside. Apologizing, I moved on to the next stall.  A darling conversation ensued along the lines that the latches weren't that tricky, but were very tricky if you were a five-year-old child. And then the delightful conversation continued when I noticed that we had both opened our respective doors at exactly the same time...

Me: "Hey look! We left at the same time!  ... And now we're washing our hands at the same time..."

Child: "And we're both using soap at the same time."

Me: "And now we're both rinsing..."

Child: "Do you like to do things at the same time?"

Me: "I don't know, do you?"

Child: "Maybe."

Me: "... and now we're both drying our hands at the same time."

Child (walking toward the closet door): "Oh, I thought that was the door..."

Me: "They do look the same, don't they?  Hey, I know, let's go out the restroom door together at the same time!"

And out we go, into the hall, and on with our respective days. 

At the same time. She is little, I am big.  She is young and I am ... not young.  She was at one sink, I the other.  And yet, we did the same actions at the same moment.  And in that moment we were the same.  And we knew it.  And that was fun!