There was some discussion today on my FB feed, on the following math homework question, given to 9-10 year old kids here in some school (or perhaps it is part of the official book for that grade - don't know).
View attachment 684122
The question tells you that a student rolled the dice 5 times, getting the numbers 2,6,4,6,3, and that he will roll the dice two times more. And asks what numbers he should get in the two final rolls if the average value of all rolls is to be a natural number.
Personally (I took some part in the discussion) I am of the view that it is good that such questions are asked so early - ok, not all the kids will get the answer, but some may actually find the search captivating and develop a love of math.
I expect that the method expected to be used would be along the lines of: the 5 rolls he already got give a total of 21, with the 2 final rolls it will be 7 rolls, the average of the value of all rolls is (21+A+B)/7 => if the average is a natural number (or even an integer...) 21+A+B should be perfectly divisible by 7, but since 21 is already perfectly divisible by it, it follows that A+B should also be perfectly divisible by 7 => a,b (order interchangeable) are 1,6 or 2,5 or 3,4.
Some in the thread argued that it is just too hard on the majority of the kids, who may feel nervous. I agree. But imo there's also a lot to gain for those who will feel attracted to math so early on, so I like it was a question in class