The primary maths SATs test can be tricky business, and there’s nothing worse than children making common maths mistakes on the big day. In 2019, Learning by Questions published a revolutionary set of [purposeful SATs preparation materials](https://www.lbq.org/search/mathematics/assessment?keywords=sats&hide=true) where children were given instant, constructive guidance if they gave an incorrect answer. After analysing the actual responses from tens of thousands of Year 6 children from across the UK, we’ve gathered together the most common maths mistakes that pupils made. ## The 5 most common primary maths mistakes on Learning by Questions Catch those pesky errors _before_ the test in May. ### 1. Place value ![The numbers 279843 are displayed with the question, use each digit card once to make the smallest possible even number.](/filestore/BlogImage/90e62719-ac8a-403b-ad89-56f1cbd186ba/8881a209-509e-4d98-bcb7-9a38dfc2e880Errortunities1.jpg "Place value") The most common mistake for this question was not realising that there were two instructions contained within one phrase that looks relatively simple (‘smallest possible even number’). Predictably, many children (20% of all responses) used the cards to make the smallest possible number - but they didn’t take into account the keyword **‘even’**. Regular practice of worded problems is essential - skim reading or focusing too heavily on digits will lead to these kinds of avoidable errors. Learning by Questions’ mastery sets all contain worded problems throughout, with a range of mathematical language used, especially in [multi-step problems](https://www.lbq.org/search/mathematics/place-value/reasoning-and-problem-solving/solve-multi-step-problems-place-value?keywords=multi%20step%20problems&openpreview=true). (Click on the link to sample this Question Set. Be sure to give some wrong answers to see the unique feedback that your pupils will receive on the LbQ platform.) ### 2. Scaling known facts ![2.7 divided by 30 = Correct answer: 0.09, percentage of all answers incorrect: 48% most common incorrect answer 0.9](/filestore/BlogImage/90e62719-ac8a-403b-ad89-56f1cbd186ba/edfd4342-5bfc-441b-94b7-7fc51de8f13cerrortunities2.3.jpg "Scaling known facts") A large number of children made scaling errors with this question. The incorrect answers of 9 or 0.9 show recognition of a link between 2.7 ÷ 30 and 27 ÷ 3, but incorrect adjustments were made. A key piece of understanding here is recognising that a larger divisor means a smaller quotient, not a larger quotient. LbQ’s [Division facts with problem solving](https://www.lbq.org/search/mathematics/multiplication-and-division/practice/practise-10-times-table-division-facts-with-problem-solving?keywords=division%20with%20problem%20solving&hide=true) sets contain many opportunities to practise this key skill. ### 3. Calculating with fractions ![1 1/4 x 20 = correct answer: 25, percentage of all answers incorrect: 42% most common incorrect answer: 100](/filestore/BlogImage/90e62719-ac8a-403b-ad89-56f1cbd186ba/d6eb02c4-369b-413c-b4c2-2d0f2134423berrortunities3.1.jpg "Calculating with fractions") This problem elicited a range of pupil mistakes, with most of these being a result of children choosing an inefficient way of calculating. The simplest way to get this answer is by partitioning 1 ¼, multiplying 1 by 20 then finding ¼ of 20 before adding together. Going down the possibly drilled route of always converting all mixed numbers to improper fractions before attempting any calculations can lead to several learning moments, or ‘errortunities’, in this question. A significant number of children put the mathematically equivalent answer of 100/4 in without simplifying. This indicates that these children have mastered a process of multiplying a mixed number by a whole number, but have not spotted the more efficient way of arriving at the simplest answer (25). The Learning by Questions set [Multiply Mixed Number Fractions by Whole Numbers](https://www.lbq.org/search/mathematics/fractions/multiplication/multiply-mixed-number-fractions-by-whole-numbers?years=1,2,3,4,5,6&hide=true&) can help pupils to see when using a partitioning strategy is more efficient. ### 4. Calculating with decimals ![10 - 7.3 = correct answer: 2.7 percentage of all answers incorrect: 38% most common incorrect answer 6.3](/filestore/BlogImage/90e62719-ac8a-403b-ad89-56f1cbd186ba/7bb4c6e3-d8b9-4ef8-8e0c-4cd19eb67b60errortunities4.jpg "Calculating with decimals") It perhaps isn’t immediately obvious why 6.3 is the most common incorrect answer for this question. To arrive at this mistaken answer, it’s likely children were trying to use a partitioning method: subtracting 3 tenths and 7 ones from 10. However, they have mistakenly subtracted 3 ones and 7 tenths instead. This second highest answer of 3.7 is more predictable. Children may have used a mental strategy like ‘jumping up’ using number bonds, not realising that the second jump should be from 8 to 10 instead of from 7 to 10. They may also have attempted a written method, but not taken into account the required exchange in the tenths column. LbQ has a range of mastery and practice [calculating with decimal](https://www.lbq.org/search/mathematics/addition-and-subtraction/decimals/b814c3b6c-6d5b-470f-be59-c84f628a59ac?years=5,6&keywords=decimal%20numbers&hide=true) sets with individual feedback, so children know to avoid common mistakes and are armed with clear strategies to solve such problems. ### 5. Inverse operations & understanding structures ![4,036 + space = 6,804, correct answer: 2,768, percentage of all answers incorrect: 32%, most common incorrect answer: 10,840](/filestore/BlogImage/90e62719-ac8a-403b-ad89-56f1cbd186ba/162e62dc-17f2-432e-8c4e-cb29756b8d5berrortunities5.jpg "Inverse operations & understaning structures") Lots of children made the mistake on this question of adding the two given numbers, showing that they don’t fully understand the role of the equals sign or additive mathematical structures. Learning by Questions recognises that this is a key skill for children, and the vast majority of our Question Sets include at least one problem that requires the use of an inverse operation. There are also dedicated sets focusing on inverse operations and mathematical structures. So there you have it: the most common primary maths mistakes from LbQ’s Maths SATs papers as answered by tens of thousands of Y6 children. Some predictable, some a bit less so. But consider each of them as an ‘errortunity’ for the children in your class to avoid the same pitfalls. Try these questions out with your class today by signing up for a [free LbQ trial](https://www.lbq.org/TryLbQ).