KS2 Mathematics: Arithmetic with Fractions and Decimals

The arithmetic paper of the Key Stage 2 mathematics tests is a page of bare calculations to be worked out without a calculator, and a large share of them involve fractions and decimals. This material trains exactly those calculations from the Year 6 national curriculum programme of study: multiplying simple pairs of proper fractions and writing the answer in its simplest form, dividing a proper fraction by a whole number, adding and subtracting mixed numbers with different denominators, multiplying decimals by whole numbers, dividing decimals by a one-digit number, multiplying and dividing by 10, 100 and 1000, and finding fractions and percentages of amounts.

The quiz has twelve calculations, one of each kind. The wrong options are the answers pupils really write when they slip: adding the denominators instead of finding a common one, forgetting to simplify, putting the decimal point in the wrong place, or multiplying when the question asks for a division. Every explanation shows the working step by step, so a wrong answer tells you which step to look at again.

The flashcards collect the methods you need to remember: how to multiply fractions, how to divide a fraction by a whole number, how to turn a mixed number into an improper fraction, how to move digits when multiplying or dividing by 10 or 100, the decimal equivalents of common fractions, and quick ways to find 10%, 5% and 1% of an amount.

The printable written work has eight longer calculations to set out by hand, as you would on the test paper: fraction multiplication with simplifying, dividing fractions by whole numbers, subtracting and adding mixed numbers, long multiplication with decimals, short division with a decimal answer, percentages of amounts and a short problem about a bag of flour. Showing the working matters, because on the arithmetic paper a correct method can still earn a mark on the longer calculations even when the final answer is wrong.

In the oral exam an examiner asks you one calculation at a time and asks you to explain your method, which is a good way to find out whether you really understand why the methods work.

The material suits pupils in Year 6 preparing for the end of Key Stage 2 tests, and Year 5 pupils who want a challenge. Start with the quiz to see which kinds of calculation cause trouble, learn the methods on the flashcards, then practise setting out complete answers in the written work.

• Multiply simple pairs of proper fractions and give the answer in its simplest form
• Divide a proper fraction by a whole number
• Add and subtract mixed numbers with different denominators
• Multiply decimals by one-digit and two-digit whole numbers
• Divide decimals by a one-digit whole number and multiply or divide by 10, 100 and 1000
• Find fractions and percentages of amounts without a calculator

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): fractions (including decimals and percentages), and on the question types of the STA key stage 2 mathematics test framework (paper 1, arithmetic).