> You're right, but the tricky part is, how do you explain that to a group of children who is just being introduced to the concept of adding fractions, without leading them off track? That's hard!
She's already introduced bottles of water and pencils. So one interesting question is, "If you take three bottles of water, and add three pencils, do you now have all of the bottles of water?"
This is interesting. I wonder if kids can then take that and transfer it over. Bottles and Pencils are obviously different but kids at table A and kids at table B are both kids. Even more problematically, the equation appears to work. I suspect there'll be some amount of dissatisfaction here and the kids won't understand.
Not sure if this is at the level of comprehension of these kids, but I'd explain it this way: "kids at table A" and "kids at table B" are both "kids", but different amount of kids. You can treat them as the same only if you have a conversion factor. So, if you know that there are 12 kids at table A, and 20 kids at table B, you can multiply your variables by these amounts, and now both expressions have the unit "kids", and you can add them together. But if you don't know the conversion factor, they're like Bottles and Pencils.
Since numbers are usually introduced to children in terms of quantities of things (e.g. 3 apples), I think it might suffice to stress the importance of keeping these things always attached to those numbers. In general, numbers very rarely go alone.
She's already introduced bottles of water and pencils. So one interesting question is, "If you take three bottles of water, and add three pencils, do you now have all of the bottles of water?"