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?