KS2 Mathematics: Arithmetic and Reasoning

Four of these ten questions are bare arithmetic, the way the arithmetic paper asks: a long multiplication, a long division, a subtraction of fractions with different denominators, and one calculation that turns entirely on doing the operations in the right order. The other six are the reasoning papers in miniature — short word problems where the numbers are easy and the difficulty is working out which sum the question is asking for.

Every wrong answer here is a real mistake rather than a random number. In the long multiplication, 2776 is what comes out when the second line is not moved one place to the left — you have multiplied by 2 instead of by 20, which is the slip that costs more marks than any other in this paper. In the fraction question, 1/8 comes from turning one half into two eighths instead of four, changing the denominator without scaling the numerator to match. Two of the word problems are two-step, and in each case one of the options is the answer you get by stopping after the first step: 75 apples instead of 40, 38 passengers instead of 46. In the percentage question, one of the options is the discount rather than the price you pay.

The explanations set the working out in short steps and then name the mistake behind the closest wrong answer, because at this age knowing which mistake you made is more useful than being told the right number.

Nothing here is taken from a past test paper. Worth knowing, though: past KS2 papers are Crown copyright, published free on gov.uk under the Open Government Licence, and they are the best supplement to any practice of this kind.

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• Multiply a three-digit number by a two-digit number, keeping the place value right in the second line
• Divide a three-digit number by a two-digit number using the formal method
• Subtract fractions by finding a common denominator, scaling the numerator to match
• Apply the order of operations rather than working left to right
• Finish a two-step word problem instead of stopping at the first step
• Find a percentage of an amount and give the price paid rather than the discount
• Calculate a perimeter, scale a recipe, and find a mean including a negative value

Calculate 347 multiplied by 26. — one of ten Year 6 questions written for this set, alongside long division, fractions, the order of operations, two two-step word problems, a percentage, a perimeter, a recipe scaled up and an average that includes a temperature below zero.