HSC Minimum Standard Numeracy key terms

The value a digit has because of its position in a number. In 4,072 the 4 means four thousands, the 0 means zero hundreds, and the 7 means seven tens.

Any one of the ten number symbols 0 to 9 used to build numerals. A numeral such as 358 is made of three digits placed in different positions.

A written symbol or group of symbols that stands for a number, such as 27, 3.5 or 1/2. The numeral is the written form; the number is the amount itself.

A number written with a decimal point to show whole units and parts of a unit. The digits after the point show tenths, hundredths and so on, as in 2.75.

A way of writing part of a whole as one number over another, such as 3/4. The bottom number shows how many equal parts the whole is cut into.

Different fractions that name the same amount, such as 1/2, 2/4 and 5/10. Multiplying or dividing the top and bottom by the same number keeps the value unchanged.

To rewrite a fraction or expression in its shortest form by dividing out common factors. For example, 6/8 simplifies to 3/4 because both parts divide by 2.

A fraction expressed out of one hundred, written with the % sign. Fifty per cent means 50 out of every 100, which is the same as one half.

Replacing a number with a nearby simpler value of about the same size. You look at the next digit: 4 or less rounds down, 5 or more rounds up.

A sensible approximate answer found by rounding or using easy numbers. Estimating first helps you check whether a calculated answer is reasonable in size.

A whole number that divides another number exactly with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.

The result of multiplying a number by a whole number. The multiples of 5 are 5, 10, 15, 20 and so on, continuing without end.

The smallest number that is a multiple of two or more given numbers. For 4 and 6 it is 12, which is useful when adding fractions with different denominators.

The top number in a fraction. It tells how many equal parts are being counted, so in 3/5 the numerator 3 means three parts are taken.

The bottom number in a fraction. It names the size of each part by showing how many equal parts make one whole, as in 3/5 where the denominator is 5.

A comparison of two or more amounts showing how much of one there is for each of another. A ratio of 2:3 means two parts to three parts.

A comparison of two amounts measured in different units, such as kilometres per hour or dollars per kilogram. Rates let you work out one amount from another.

A statement that two ratios or fractions are equal, or a share of a total worked out using a ratio. Scaling a recipe up or down relies on proportion.

The cost of one item or one unit of measure, found by dividing total cost by quantity. Comparing unit prices shows which package is better value.

The option that gives the most goods for the least money. Working out the unit price of each option is the usual way to find it.

The total distance around the outside edge of a flat shape. For a rectangle you add the two lengths and two widths, or use 2 times length plus width.

The amount of flat surface a shape covers, measured in square units such as square metres. A rectangle's area is its length multiplied by its width.

The amount of space a solid object takes up, measured in cubic units such as cubic centimetres. For a box it is length times width times height.

How much a container can hold, usually measured in litres or millilitres. Capacity describes the inside space of a container rather than the material it is made from.

A unit from the measuring system based on powers of ten, such as metre, gram and litre. Converting between them means multiplying or dividing by 10, 100 or 1000.

Changing a measurement from one unit to another without changing the actual amount. For example, 1.5 metres becomes 150 centimetres by multiplying by 100.

The relationship between a drawn size and the real size, often written as a ratio such as 1:100. Maps and plans use scale to show large distances on a small page.

A single value used to summarise a set of numbers, most often the mean. You find the mean by adding all the values and dividing by how many there are.

The result of adding all the values in a data set and dividing by the number of values. The mean of 4, 6 and 8 is 6.

The middle value when a set of numbers is arranged in order. If there is an even number of values, the median is the mean of the two middle ones.

A drawing that shows numerical information visually, using bars, lines, points or slices. A well-labelled graph makes patterns and comparisons easier to see quickly.

One of the two numbered lines that a graph is drawn against. The horizontal axis usually shows categories or time, and the vertical axis usually shows amounts.

Information arranged in rows and columns so that values can be compared. Headings at the top and side tell you what each row and column contains.

Facts, numbers or observations collected for a purpose, such as survey answers or sales figures. Data becomes useful information once it is organised and interpreted.

A measure from 0 to 1 of how likely an event is. A probability of 0 means impossible, 1 means certain, and 0.5 means an even chance.

The everyday word for how likely something is to happen. Statements such as likely, unlikely or even chance describe chance in words rather than numbers.

Working out an answer using arithmetic operations such as addition, subtraction, multiplication or division. Showing your working helps you check the result for errors.

The agreed sequence for doing mixed calculations: brackets first, then powers, then multiplication and division, then addition and subtraction, working left to right.

A conclusion you reach by combining clues in a text with what you already know. The answer is not stated directly, so you must read between the lines.

The most important point a paragraph or text is making about its topic. It is often stated in a topic sentence but can also be implied by the details.

A sentence, usually near the start of a paragraph, that states what the paragraph is about. The remaining sentences support or explain it.

Details, facts or quotations from a text that support an answer or opinion. Good answers point to specific words in the text rather than guessing.

Information in the surrounding words or sentences that helps you work out the meaning of an unfamiliar word. Definitions, examples and contrasts are common kinds of clue.

The reason a writer produces a text, such as to inform, persuade, entertain or instruct. Recognising purpose helps you judge how to read and trust the text.

The group of people a text is written for. Writers choose vocabulary, detail and layout to suit that group, whether it is children, customers or experts.

The attitude a writer shows through word choice, such as friendly, serious or critical. Tone affects how a message is received by the reader.

A group of sentences about one idea, separated from other groups by a line break. Paragraphs help readers follow the structure of a longer piece of writing.

A group of words that expresses a complete thought and contains a subject and a verb. It begins with a capital letter and ends with a full stop, question mark or exclamation mark.

Marks such as full stops, commas, question marks and apostrophes that clarify meaning and show how a sentence should be read. Correct punctuation prevents confusion.

The rules that govern how words are arranged and changed to form clear sentences. Following them makes writing easier for a reader to understand.

Writing words with the correct letters in the correct order. Checking spelling matters in formal writing because errors can distract or confuse the reader.

The set of words a person knows and can use. Choosing precise words helps writing convey exactly what the writer means to the audience.

Reading a finished piece of writing carefully to find and fix errors in spelling, grammar and punctuation. It is best done after a short break.

An early version of a piece of writing that is improved through editing and revising. Most writing goes through several drafts before it is finished.