By your first definition above, both the definition of equal and equivalent define two things having the same *value.* the very technical details of this is that the student (who is a first grader) very thoroughly understood the core concepts of grouping and commutativity, exactly as he was taught. 3×5 is equivalent to 5×3. That’s why we use the equals sign. Math exists to express quantities of physical things. If I have 5 rows of 3 oranges, that’s 15 oranges. If I have 3 rows of 5 oranges, that’s 15 oranges. The quantities of both of the arrangements *are equal*.

Matrices are not integers. Those are apples.

Media hype misinterpreted as clever. It’s heartbreaking to see this little mind molded into thinking he must conceptualize things by the same template as everyone else.

Ask the teacher to use the grading logic to draw a picture of what 10 ÷ 3 is equal to using tick marks.