# How long is an hour and forty minutes?

My son and I had this exchange earlier in the day when we were negotiating about whether or not we would watch an afternoon movie.

Me: “Okay, so the movie is 90 minutes long. That’s an hour and a half.”

My son: “How did you know that?”

Me: “An hour is 60 minutes, so I just took 60 minutes away from 90 to get 30 minutes left over, which is half of an hour.”

My son: “So what if the movie was 100 minutes long? No, don’t help me! Let me figure it out… Uh… an hour and forty minutes.”

Me: “What if the movie was 110 minutes long?”

My son: “That’s easy. It’s just 10 minutes different. So instead of 100 take-away 60, it would be 100 take-away 50. Uh… That’s 50 minutes! So the movie would be an hour and 50 minutes long.”

Easier question: What’s the biggest success here?
Harder question: How does this kind of number sense develop in children?

# What’s 9 plus 9?

My six year old son and I were working on cutting out snowflakes (more on this later, it’s a fun project in itself) and at one point we wanted to count the number of symmetries our snowflake was going to have, which we worked out would be 9 + 9. My son said aloud, “Okay. 8 + 8 is 16. 9 + 9 is… uh… 18! Because 8 + 9 is 17!”

How often do you see students use counting as a strategy for finding a sum of two numbers? Is this common? How do we encourage this type of reasoning?