(Tangent: Has anyone yet tried to prompt GPT3 to generate "deep" word problems?)
10-3 / 2 = 3.5 candies for Bob.
You may think that's a strange solution, but it's the only one that matches the problem statement. What was your solution?
Considering the problem as follows: "Bob and Alice have 10 candies in total, and Bob has 2 more candies than Alice. How many candies do Bob and Alice each have?"
My own solution would be to just define the variables as follows: Bob = Alice + 2; Bob + Alice = 10; 2xAlice + 2 = 10; Alice = (has) 4 candies; Bob = (has) 6 candies.
Adjusting the problem with an odd difference instead of an even number we have: "Bob and Alice have 10 candies in total, and Bob has 3 more candies than Alice. How many candies do Bob and Alice each have?" Bob = Alice + 3; 2xAlice + 3 = 10; Alice = (has) 3.5 candies; Bob = (has) 6.5 candies.
I find my solution to be easier to understand and somehow more logical than "let's add/substract this and that and divide by two". Probably my main issue was explaining to a kid how having 3.5 and 6.5 candies works seeing candies I known all my life are basically unbreakable (unless you have a kid's teeths which is known to be able to devour metal).
As an anecdote I recently dated a lady who has a teenage daughter and she showed me the math exams her youngling has been taking. Having never been one to withdraw from a challenge, even mildly implied, I printed the things and started working on them only to be horrified how much I've forgotten in terms of elementary mathematics. I genuinely felt shame even though I scored a decent number (but nothing to write home about).
I feel we're failing our children in how we're pumping them with information but without always teaching them how to learn and that makes me really sad :(
Bob and Alice have 10 candies in total, and Bob has 2 more candies than Alice. How many candies do Bob and Alice each have?
TAL's solution: this is called addition-subtraction problem. Add the two numbers and divide the sum by two, you get the bigger value for Bob. Subtract the difference from the total and then divide the result by two, and you get the smaller value for Alice. No mention of why. No mention of underlying intuition. No mention of any mathematical concepts. This is the most abhorrent teaching I've ever seen.