ACARA v9 CONTENT DESCRIPTION “recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents”
Builds on fractions and decimals, where a part of a whole is written as a fraction or a decimal. Year 5 adds a third way to describe a part: the percentage, which means out of one hundred. Recognising that one hundred per cent is the complete whole, using percentages to describe and compare relative size, and connecting familiar percentages to their fraction and decimal equivalents gives a flexible language for parts that appears everywhere, from shopping to statistics.
Per cent means out of one hundred
The word per cent means out of one hundred, and the symbol for it is the per cent sign. A percentage describes a part of a whole by imagining the whole divided into one hundred equal pieces and counting how many are taken. Twenty-five per cent means twenty-five out of one hundred, and seventy per cent means seventy out of one hundred. Thinking of a hundred-square, shading the matching number of cells shows a percentage as a picture. Because every percentage is measured against the same hundred, percentages are an easy way to describe and compare parts.
Per cent means out of one hundred
A percentage counts out of a hundred squares.
25% shades 25 of the hundred squares, so a percentage is a part out of a hundred.
One hundred per cent is the whole
One hundred per cent represents the complete whole, all of the amount with nothing left over. If every one of the hundred pieces is taken, that is one hundred out of one hundred, or one hundred per cent. This makes percentages a natural scale: zero per cent is none of the whole, fifty per cent is half, and one hundred per cent is all of it. A percentage larger than one hundred would be more than the whole, which is why ordinary parts of a single whole run from zero to one hundred per cent. Knowing that the whole is one hundred per cent anchors every other percentage.
One hundred per cent is the whole
100% is all of it; 0% is none of it.
100% fills the whole bar: all of the amount.
Percentages, fractions and decimals
Percentages, fractions and decimals are three ways of writing the same part, and familiar percentages connect neatly to the other two. Fifty per cent is fifty out of one hundred, which is the fraction one half and the decimal zero point five. Twenty-five per cent is one quarter, or zero point two five, and ten per cent is one tenth, or zero point one. Because a percentage is already a number out of one hundred, writing it as a decimal just means dividing by one hundred, and writing it as a fraction means simplifying that hundredth. Knowing these equivalents lets a part be moved between the three forms whenever one is more convenient.
Percentages, fractions and decimals
The same part, written three ways.
Write 50% as a fraction and a decimal.
Comparing relative size with percentages
Percentages make relative size easy to compare, because every percentage is measured against the same whole of one hundred. Forty per cent is a larger share than twenty-five per cent, simply because forty out of a hundred is more than twenty-five out of a hundred. This is the real advantage of percentages: two parts of different wholes, like a score on a short test and a score on a long one, can be compared fairly once both are written as percentages. Describing a result as a percentage turns it into a share of one hundred that can be lined up against any other.
Comparing relative size with percentages
Out of the same 100, the larger number wins.
Which percentage is the larger share?
Matching familiar percentages
A small set of familiar percentages is worth knowing by heart, because they appear again and again. One hundred per cent is the whole, fifty per cent is one half, twenty-five per cent is one quarter and seventy-five per cent is three quarters, ten per cent is one tenth, and one per cent is one hundredth. Matching each of these to its fraction and decimal makes everyday percentages quick to understand: a half-price sale is fifty per cent off, and a tenth of a class is ten per cent. Recognising familiar percentages instantly is what makes the idea genuinely useful.
Matching familiar percentages
Know the common ones by heart.
Match the percentage to its fraction or decimal.
Using percentages with confidence
Percentages come down to one simple idea: a part written as a number out of one hundred, with one hundred per cent as the whole. Reading a percentage as so many out of a hundred, connecting familiar percentages to their fraction and decimal equivalents, and comparing percentages as shares of the same whole are the key skills. With these habits a child can describe a part as a percentage, switch between percentages, fractions and decimals, and compare relative sizes, ready for finding percentages of quantities in later years.