# Making Connections

*Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.*

*Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.*

(National Curriculum in England Framework Document, September 2013, p9)

## Connections within Mathematics

### Making connections to this topic in adjacent year groups

#### Year 3

Statutory requirements:

- count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
- recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
- recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
- recognise and show, using diagrams, equivalent fractions with small denominators
- add and subtract fractions with the same denominator within one whole (e.g.
^{5}⁄_{7} + ^{1}⁄_{7} = ^{6}⁄_{7})
- compare and order fractions, and fractions with the same denominators
- solve problems that involve all of the above

Non-statutory guidance:

Pupils connect tenths to place value, decimal measures and to division by 10

They began to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, relating this to measure.

Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.

They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, or unit fractions as a division of a quantity.

Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.

#### Year 5

Statutory requirements:

- compare and order fractions whose denominators are all multiples of the same number
- identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
- recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g.
^{2}⁄_{5} + ^{4}⁄_{5} = ^{6}⁄_{5} = 1 ^{1}⁄_{5})
- add and subtract fractions with the same denominator and multiples of the same number
- multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
- read and write decimal numbers as fractions (e.g. 0.71 = 71/100)
- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
- round decimals with two decimal places to the nearest whole number and to one decimal place
- read, write order and compare numbers with up to three decimal places
- solve problems involving number up to three decimal places
- recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator hundred, and as a decimal fraction
- solve problems which require knowing percentage and decimal equivalents of ½, ¼,
^{1}⁄_{5}, ^{2}⁄_{5}, ^{4}⁄_{5} and those with a denominator of a multiple of 10 or 25.

Non-statutory guidance:

Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.

They extend their knowledge of fractions to thousandths and connect to decimals and measures.

Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.

Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.

Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.

Pupils continue to practise counting forwards and backwards in simple fractions.

Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.

Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line.

Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.

They mentally add and subtract tenths, and one-digit whole numbers and tenths.

They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1).

Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.

Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is ^{1}⁄_{100} , 50% is ^{50}⁄_{100} , 25% is ^{25}⁄_{100} ) and relate this to finding ‘fractions of’.

## Cross-curricular and real life connections

Learners will encounter fractions and decimals in many other aspects of mathematics:

Measurements – Children can be asked to find the position ^{1}⁄_{10} along a metre stick. Where would ¾ be? How many centimetres along the stick is that?

Reading scales – When using a tape measure, kitchen scales, a measuring jug. They may be asked to find ^{1}⁄_{10} of a metre, a kilogram, a litre.

Exploring fractions in everyday contexts – how many square pieces make half of this chocolate bar?

Data handling – which flavour crisps did ¼ of the children like best?

The National Gallery of Art website provides a wonderful resource based on Thiebaud’s ‘Cakes’ picture, and provides some wonderful starting points for fractions work in mathematics.