Maths misconceptions: multiplying by 10

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Editor’s note: This is an updated version of a blog post published on April 29, 2017.

If you’ve ever said ‘just add a zero’ when teaching how to multiply by 10, your learners could be missing out. Avoid this common maths misconception and give learners a deeper understanding of the base-ten system.

One particularly prevalent maths misconception that often gets taught is adding zeros when multiplying by a power of 10. Teachers don’t deliberately set out to teach this misconception but many have inherited it from when they were in school, innocently reproducing this flawed maths in their own practice.

“Just Add A Zero”

While being taught, learners often hear this misconception: “when multiplying by 10 just add a zero”.This approach is limited in its usefulness and can be damaging. It’s almost taught as some sort of ‘recipe’ instruction but ‘adding a zero’ is like cooking the books, it’s maths fraud!

Blind acceptance of this method for multiplying by 10 means pupils apply this rule incorrectly because they don’t appreciate the underlying mathematics at work. The ‘adding zeros’ trick can work when multiplying whole numbers by powers of 10, for example, 678 x 10 = 6780, 213 x 100 = 21300, 34 x 1000 = 34000, but this method completely falls down and is totally unsuitable when multiplying a decimal value by a power of 10. In this example, 9.5 x 10 isn’t 9.50 because simply inserting a zero on the end gives exactly the same value.

Try this one with your class:
10 x 10 =
10.0 x 10 =

It’s possible that you’ll get 100 and 10.00 as responses.

The ‘adding a zero’ trick is commonly taught as a helpful rule when multiplying by 10 but it prevents learners from developing a deeper understanding of the base-ten system.

Imagine ‘adding the zero’ when multiplying 0.05 by 10. Pupils who have learned this rule might answer 0.050, or they could decide to add the zero elsewhere such as 00.05 because they are unfamiliar with decimals.

What’s The Point?

What pupils need to grasp from the outset is that when you multiply by 10, 100, 1000 and so on, each digit shifts to the left on a place value table, because they’re adding another place to the number.

They should remember that the decimal point never moves (it’s another piece of faulty maths advice is to say that it does). Think of the decimal point like a concrete post — it exists to separate whole number places from decimal fraction places. It’s an immovable dot.

Imagine that 0.25 is divided by 100. If we say that ‘you move the decimal point two places to the left’, we have a problem. Here there’s only one number to the left and this will confuse some children who can easily forget which direction to move.

A Tricky Business

Teaching maths shortcuts can upend pupils further down the line. Discovering that you’ve been doing something wrong all along can upset pupils. After all, they’ve only followed what they’ve been taught. This means they have to unlearn, start again and trust someone else to teach them the correct method.

Pupils trust teachers and will seldom challenge what they’re being taught. So it can come as a nasty surprise to find that they’ve been given wrong information. Finding out a maths teacher was wrong can be hard to take. How will they trust the next teacher to teach them what’s what and what’s not? Perpetuating the same ill-advised methods to the next generation dents learning, affects maths confidence and can twist understanding out of shape.

Some might argue that shortcuts are really only helpful to pupils after they have mastered a concept. To this I’d say that there is value in showing a shortcut but only to expose it as a maths misconception alongside examples where the trick doesn’t work.

If you come across the ‘just add a zero’ rule in your teaching it may take a fair bit of clearing up. On the other hand, it can be used as a powerful learning opportunity to set the record straight. Understanding place value, what multiplication is, and concepts of quantity have to come first.

Teaching maths really is a tricky business but let’s leave the tricks out of the equation and teach for full understanding. If you see or hear the ‘just add a zero’ rule when multiplying by 10, challenge it! Because this is one misconception that can easily grow, solidify and undermine pupils’ confidence if left uncontested.

References

Swan, M. (2006) Collaborative Learning In Mathematics (London:NRDC)

is an Education Consultant and Author who specialises in primary maths, and a blogger on Pedagogy.

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