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# What are they doing?! Common misconceptions

How can you recognise when children are suffering from important mathematical misconceptions? How can you preempt or teach away from these? What shortcuts should you avoid now so as not to have to unpick misconceptions later? What is the key vocabulary that will help children stay on track?

• You teach your Year 1s addition by counting on. You mark some practice sheets and one child’s answers are all 1 too small. What’s going on? Well, it’s very likely that the child has included the first number in the count, e.g. for 6 + 3, saying six, seven eight, instead of seven, eight nine.
• You ask your Year 3s to list pairs with a total of 100. One child’s pairs of numbers are all 10 too big. What are they doing?! The child has probably thought of numbers where both the 10s digits and the 1s digits add to 10, e.g. 68 + 42.

These aren’t simple arithmetical errors, but important common misconceptions which need unpicking. If you’ve been teaching these year groups for a while, you may already recognise these misconceptions but what if you are new to a year group or new to teaching? And, to be honest, we can all use a reminder of the many ways that understanding can be derailed.

To help, our new maths blocks have a common misconceptions document for each unit, so you can look out for what might go wrong. If you are aware of these, you can adapt your teaching to try and pre-empt them.

We’ve also included a ‘Resist the temptation to…’ section. Let’s be honest, we’ve all said something in our teaching and then regretted it! ‘When you multiply by 10, you add a zero’. Oops, the children add a zero when multiplying decimals (10 x 4.5 = 4.50). How many of us have used the word ‘borrow’ when teaching column subtraction? A child with a heightened sense of justice asks, ‘When will give it back?’ Perhaps not a helpful word to use here! (The word ‘borrow’ dates back to an old method of subtraction, but that’s another story.)

You will also see a section of key words and phrases that are useful for the unit, and a few key questions to tease out if the children have got the key understanding and skills being taught.

So, in our new flexible and short blocks, click on the Common Misconceptions download button in the 'Teaching and Activities' box if you want to be en guard for misconceptions.

Explore Hamilton's flexible blocks: Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6

Explore Hamilton's short blocks: Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6