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Tag Archives: mathemtics

Why some teachers say 5×3 does not mean 5+5+5

A child was marked as incorrect for translating “5×3” to “5+5+5” on a grade school math test.

Further discussion is at

According to Common Core: Represent and solve problems involving multiplication and division,  5×3 should be interpret as 5 groups of 3 objects each, which means 3+3+3+3+3.

I think this come from how every-day English express this kind of thing. Like 5 apples (apples appear 5 time), and 5 3’s is similar (3 appears 5 time). This also affect the definition of multiplicand and multiplier. Quote from Wikipedia Multiplication

When thinking of multiplication as repeated addition, the number to be multiplied is called the “multiplicand”, while the number of addends is called the “multiplier”.

In other world, 5×3 should be read as:

3 multiplied by 5

But for division, 5 ÷ 3 is read as:

5 divided by 3

IMHO, this is indeed confusing and inconvenient. If a teacher trying to teach multiplication using the word “multiplied” with blackboard and chalk, she need to

  1. Write 3 first, and say “three”
    Become:  3
  2. Write ×,  and say “multiplied by”
    Become: × 3
  3. Write 5, and say “five”
    Become: 5 × 3

Right to left writing, which is not a usual practice in English.

If the teacher  insists on left to right writing, she has to say “three” when she write “five”. 😛

Luckily, we have times to rescue. 5×3 should be read as:

5 times 3