What grade level of math would you consider this question?
If you have 11 cookies and you split them evenly among 2 kids how many would each kid get and how many would be left over?
I would say that conceptually it's about a 1st grade level. In terms of formulating it as a formal math operation (i.e. understanding it as 11 ÷ 2 = 5 R 1) it's more like 3rd grade, but any kid with the number sense to know that two 5's makes ten (i.e. I have five fingers on each hand and ten fingers altogether), and that eleven is one more than 10, would be able to work this out much much earlier than 3rd grade.
At school.....my girls are doing this in their first grade in a regular classroom math program (whole group instruction), both mentally and as an illustrated problem solving activity. Not as formal division.
In a home setting, informally (as in setting the table or distributing things in the house) age 3.5 or so. For example my DDs would see 5 stuffed animals to play with and verbally say- we each get two and there will be one left over we will give it to mom! They do this a lot since there are two of them and they want it to be 'fair'. They also have 'divided' items between the four of us for years (they are 6) when helping pack picnics, getting dinner (muffins or rolls or pizza slices), or other things.
Could they solve 11/2 R x or do the long division work. No- but they can solve it informally.
Same with multiplication- they could not do higher level 'paper/pencil' multiplication, but they have known " If we (two people) each have 3 cookies then we have 6 altogether. And that developed about the same as the informal division.
In class they do informal multiplication as well- mostly doubles and times ten. (ten dimes is 100 cents) in the 1st grade classroom.
Yes, I'd say first grade for this particular problem too. If it were dealing with large enough numbers where manipulatives would be difficult to use I'd say 3rd grade but splitting 10 with 1 left over is something we saw as part of the standard, non-differentiated curriculum in 1st grade.