NCEA Numeracy key terms

The value a digit has because of its position in a number. In 4,082 the 4 means four thousands, the 0 means zero hundreds, the 8 means eight tens and the 2 means two ones.

A whole number written in the usual way with digits only, without words or expanded parts. For example 3,506 rather than three thousand five hundred and six or 3000 + 500 + 6.

A number broken into the value of each digit, often using powers of ten. For example 2,704 is written as 2000 + 700 + 4, or as 2 × 10³ + 7 × 10² + 4.

Replacing a number with a nearby number of a chosen accuracy. Look at the next digit: 4 or less rounds down, 5 or more rounds up. 3,847 rounded to the nearest hundred is 3,800.

Finding an approximate answer by rounding or simplifying numbers before calculating, then judging whether the result is sensible. Useful for checking that a calculator answer is reasonable in a real situation.

A position to the right of the decimal point showing tenths, hundredths, thousandths and so on. In 6.482 the 8 is in the second decimal place, so it represents eight hundredths.

The digits of a number that carry meaningful information about its accuracy, starting from the first non-zero digit. 0.00456 has three significant figures; 4.56 rounded to two is 4.6.

A way of showing part of a whole, written as one number over another. The bottom number says how many equal parts the whole is split into; the top says how many parts are taken.

In a fraction, the numerator is the top number counting the parts taken; the denominator is the bottom number showing the total number of equal parts. In 3/8, 3 is the numerator and 8 the denominator.

Different fractions that describe the same amount, made by multiplying or dividing the top and bottom by the same number. For example 1/2 equals 2/4 and 5/10.

Writing a fraction with the smallest possible whole numbers by dividing the top and bottom by a common factor. For example 12/18 simplifies to 2/3 because both parts divide by 6.

A fraction expressed out of one hundred, shown with the % sign. 45% means 45 out of every 100, which is the fraction 45/100 or the decimal 0.45.

A number written using a decimal point to show parts of a whole, such as 2.75. The digits after the point stand for tenths, hundredths and so on, so 2.75 equals 2 and 3/4.

A comparison of two or more quantities by their sizes, written with a colon. A drink mixed 2 parts cordial to 5 parts water has a cordial-to-water ratio of 2:5.

A statement that two ratios or fractions are equal, used to solve sharing and scaling problems. If 3 pens cost $6, proportion gives that 5 pens cost $10.

A ratio that compares quantities with different units, such as kilometres per hour, dollars per kilogram or pay per hour. A rate lets you work out a total from a quantity and a per-unit amount.

A way of solving rate and proportion problems by first finding the value of one unit. If 4 kg costs $12, one kilogram costs $3, so 7 kg costs $21.

A change in an amount expressed as a percentage of the original amount. Increase $80 by 15% by finding 15% of 80 ($12) and adding it, giving $92.

Goods and services tax, a tax added to the price of most goods and services in New Zealand. It is currently 15%, so a GST-exclusive price is multiplied by 1.15 to find the total price.

A reduction in price, often given as a percentage or fraction of the original price. A 20% discount on $65 saves $13, so the customer pays $52.

The agreed order for calculating expressions with several operations: work out brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

A mathematical phrase combining numbers, variables and operations but with no equals sign. For example 3x + 5 or 2(a − 4) are expressions that can be simplified or evaluated.

A letter or symbol standing for a number that may change or is not yet known. In the formula C = 4n, the variable n is the number of items and C is the total cost.

A mathematical statement that two expressions are equal, containing an equals sign. Solving an equation means finding the value of the variable that makes the statement true.

An equation in which the variable appears only to the first power, so its graph is a straight line. For example 5x − 7 = 18 is solved by adding 7 then dividing by 5 to get x = 5.

A rule written with symbols that shows how one quantity is calculated from others. For example the area of a rectangle is A = l × w, where l is length and w is width.

Replacing variables in an expression or formula with given numbers and calculating the result. Substituting r = 3 into A = πr² gives A = π × 9, about 28.3.

A measure of how steep a line is, found by dividing the vertical change by the horizontal change between two points. A positive gradient rises to the right; a negative one falls.

A whole number that divides exactly into two or more given numbers. The common factors of 12 and 18 are 1, 2, 3 and 6, and the highest is 6.

Perimeter is the distance around the outside of a shape; area is the amount of flat surface it covers, measured in square units such as cm². Both are needed for fencing and flooring jobs.

The amount of space a three-dimensional object occupies, measured in cubic units such as cm³ or m³. A box 2 m by 3 m by 4 m has volume 24 m³.

How much a container can hold, usually measured in litres or millilitres. One litre equals 1000 millilitres, and 1 cm³ holds 1 millilitre.

Changing a measurement from one unit to another using a known factor. For example 1 kilometre equals 1000 metres, so 2.5 km becomes 2500 m by multiplying by 1000.

The decimal measuring system used in New Zealand, based on metres, grams and litres with prefixes such as milli-, centi- and kilo-. Moving between prefixes means multiplying or dividing by powers of ten.

A diagram that shows a real object smaller or larger in a fixed proportion. A scale of 1:200 means 1 cm on the drawing stands for 200 cm, or 2 m, in real life.

The number by which every length of a shape is multiplied to make an enlarged or reduced copy. A scale factor of 3 triples each length, and the area becomes nine times as large.

Shapes with the same angles whose matching sides are in the same ratio. One shape is an enlarged or reduced copy of the other, so corresponding lengths share a common scale factor.

For a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides, written a² + b² = c². It finds a missing side length.

The average found by adding all the values and dividing by how many there are. The mean of 4, 7, 9 and 12 is 32 ÷ 4 = 8.

The middle value when the data are put in order. With an even number of values it is the mean of the two middle ones. In 3, 5, 8, 10 the median is 6.5.

The value that appears most often in a data set. A set can have one mode, several modes, or no mode if every value occurs the same number of times.

A simple measure of spread found by subtracting the smallest value from the largest. For the data 4, 7, 9 and 12 the range is 12 − 4 = 8.

The spread of the middle half of the data, found by subtracting the lower quartile from the upper quartile. It ignores extreme values, so it is more robust than the range.

A graph showing the lowest value, lower quartile, median, upper quartile and highest value of a data set. It displays the spread and centre of the data at a glance.

A graph for numerical data grouped into equal intervals, with bars that touch. The height of each bar shows the frequency of values in that interval, revealing the shape of the distribution.

The number of times a value or category occurs in a data set. Frequencies are often shown in tables or graphs and add up to the total number of observations.

The frequency of a value divided by the total number of observations, giving a proportion or percentage. It estimates how likely that value is to occur in a similar situation.

A table that sorts data by two categories at once, with totals for each row and column. It helps compare groups and work out probabilities from real data.

A number from 0 to 1 measuring how likely an event is, where 0 means impossible and 1 means certain. It can be found from equally likely outcomes or estimated from data.

The complete list or set of all possible outcomes of a probability experiment. For one roll of a fair six-sided die the sample space is 1, 2, 3, 4, 5, 6.

Two events that together cover every possible outcome, so their probabilities add to 1. If the chance of rain is 0.3, the chance of no rain is 0.7.

Judging whether an answer makes sense in the context of the problem, including its size, units and money amounts. Checking reasonableness catches errors such as a misplaced decimal point.

The option that gives the lowest cost for each unit of what is being bought. Comparing price per 100 g or per litre shows which pack is better value than comparing total prices.

A plan that lists expected income and expenses over a period so spending can be managed. Totals are compared to check whether income covers costs or savings are needed.