KS2 Mathematics: Remainders in Context and Rounding Decimals

A division is only half of a word problem. The other half is deciding what the answer means: 260 pupils in coaches of 48 needs 6 coaches, not 5.4, while 850 g of flour in 60 g portions makes only 14 cakes. The Year 6 national curriculum asks pupils to interpret remainders as whole number remainders, as fractions, or by rounding, as appropriate for the context, and to solve problems that need answers rounded to a specified degree of accuracy. These decisions are tested again and again on the reasoning papers of the Key Stage 2 mathematics tests.

The twelve quiz questions practise exactly these decisions: a coach problem where you round up, a baking problem and a ribbon problem where you round down, a sharing problem where the remainder becomes a fraction, a bill shared by eight friends where the remainder becomes a decimal and is rounded to the nearest penny, and a long division with a remainder. Four questions practise rounding on its own: a decimal to the nearest whole number, to one decimal place, money to the nearest penny, and a six-digit number to the nearest 10 000. The last questions use factors and multiples: writing 60 as a product of prime factors, and finding when two flashing lights next flash together using the lowest common multiple.

The flashcards summarise when to round up and when to round down in a context, how to write a remainder as a fraction, the rounding rule, what decimal places are, and the words prime number, prime factor, composite number, common factor and common multiple.

The printable written work has eight problems to set out on paper: minibuses and their total cost, full boxes of eggs, a remainder written as a fraction and as a decimal, filling bottles from a jug, a long division with a decimal answer, rounding one number in several ways, the prime factors and highest common factor of two numbers, and two bus timetables that meet again. Each one asks you to say why you rounded the way you did, because a correct division with the wrong rounding does not answer the question.

In the oral exam an examiner gives you one short context at a time and asks you to explain what the remainder means there.

The material is aimed at Year 6 pupils preparing for the end of Key Stage 2 tests. A good habit to take from it: after every division in a word problem, read the question again and ask whether the answer must be a whole number, and if so, whether you need one more or one fewer.

• Decide whether to round up or down after a division, according to the context
• Write remainders as whole number remainders, fractions or decimals
• Use long division and check the answer with multiplication
• Round decimals to the nearest whole number, one or two decimal places, and money to the nearest penny
• Round large whole numbers to a required degree of accuracy
• Use prime factors, common factors and common multiples to solve problems

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): number (long division interpreting remainders according to the context; rounding; common factors, common multiples and prime numbers) and fractions, decimals and percentages (rounding to specified degrees of accuracy).