My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has appeared in the sample paper. I am not able to understand how i should explain it to her.
A square box is filled with two layers of identical square pieces of chocolate. Kirill has eaten all 20 pieces in the upper layer along the walls of the box. How many pieces of chocolate are left in the box?
I asked her to start by putting a piece of chocolate on each of the corners and go on adding a piece to each of them one by one till she finished $20$ pieces (by drawing a figure). The to combine four sides to get the complete square of $6\times6$ . Then she has to figure out $4\times4$ square on top layer and $6\times6$ at the second one.
Is there a better way of explaining this to her, as I am not convinced with my explanation(i dont think its clear enough). Thank for reading through the question.
Here's the thing, we don't know how many pieces we have "per edge" to start. So we have to figure this out, first. But we at least know the box is square.
Your idea of "starting at the corners" is good. That gives us $4$ pieces to start with. That leaves us with 4 sides of "in-between pieces". Let's say there are $k$ "in-between pieces" on each side:
$4 + 4k = 20$.
Taking $4$ from each side of this, we have:
$4k = 16$, so $k = 4$.
Note we could also add $1$ piece "in-between" (giving us $+4$ each time) until we hit $20$. That works, too. This way gives us: $8,12,16$ and finally $20$, on the $4$-th piece added to each side.
So, each edge consists of $4$ "in-between pieces" and $2$ "corner pieces". That's $6$ pieces per edge, so we have a $6 \times 6$ box, or $36$ pieces per layer.
$20$ pieces have been eaten off the top layer, leaving $36 - 20 = 16$. The second layer still has all $36$, so we have $36 + 16 = 52$ pieces left in the box.