Under the interpretation of multiplication we are using, AxB always means A groups with B in each group, or alternatively stated, B things taken A times.
1. What is the basic conceptual interpretation of the product 3×5?
2. What is the basic conceptual interpretation of the product 5×3?
3. How are the interpretations for 3×5 and 5×3 different?
In each case, we are counting the same collection of objects, but we are grouping them different. Imagine that you have 15 marbles. You could use them to make 5 groups of 3 or 3 groups of 5. Each of these would correspond to a different one of 3x5 and 5x3.
Be super clear and thorough in explaining so that a elementary student would be able to understand the answer.