Had a fascinating experience with a number talk last week. Question was:
After 3 hours, your phone battery is at 93%. How long do you expect it will last before it dies?
I was fascinated and concerned by the students answers:
A small but significant number of students used estimation or proportional reasoning strategies to arrive at an answer.
A large number of students didn’t calculate — they said that the initial situation was unreasonable, and the battery would be much lower. They all made estimates based on their own experiences, separate from the question asked.
The final group, which was the largest, told me — with complete confidence — it will last 31 hours, because 93 / 3 = 31.
I shouldn’t have been surprised, but I was — in particular by their confidence. It’s a huge problem in number sense — the belief that every question with two numbers is either addition, subtraction, multiplication or division. And given that belief, what they did makes sense — the other three operations clearly give answers that are unreasonable, and 31 hours isn’t too far off.
Still, I’m adding it to my list of things I want to fix through number talks and number sense activities this year.