Glossary

2-D, 3-D

two-dimensional, three-dimensional. Having two or three dimensions respectively.

A

analogue clock

an analogue clock usually has 12 equal divisions around the perimeter/circumference, labelled 1 to 12 to represent hours. It has two hands that rotate about the centre. The hour hand completes one revolution in 12 hours, and the minute hand completes one revolution in one hour.

angle

a configuration of two line segments meeting at a point. The term is often used for the measure of rotation from one of the line segments to the other. In this sense, a right angle measures 90°, an acute angle is less than 90°, an obtuse angle is greater than 90° but less than 180°, and a reflex angle is greater than 180°.

approximation

a result that is not exact but sufficiently close to be useful in a practical context. Verb: approximate. Adverb: approximately.

area

a measure of a surface. Measured in squares, e.g. square centimetres (cm²), square metres (m²).

average

sometimes used synonymously with arithmetic 'mean'. More widely, measures of average include mean, median and mode.

B

bar chart

a particular form of representation of data. Frequencies are represented by bars of equal width where the lengths are proportional to the frequencies. The bars may be presented vertically or horizontally.

block graph

a particular form of representation of grouped data. In its simplest form, where the class intervals are equal and rectangles have bases of the same size, the block graph can be considered as a bar chart, and the length of each rectangle represents the total in each class.

C

calculate efficiently

use knowledge of number systems and operations, e.g. use multiplication rather than repeated addition. In the context of using tools, to use available operations and functions, e.g. memory and constant functions on a calculator, sum formula in a spreadsheet for a range of cells, rather than addition of individual cells.

capacity

volume, i.e. a measure in three-dimensional space, applied to liquids, materials that can be poured, or containers. Units include cubic centimetres (cm³), cubic metres (m³). Note - a litre is 1000 cm³ (the volume of 1 kg of water).

cardinal number

a counting number. Example: one, two, three, etc.

circumference

sometimes used for the boundary of a circle but more usually the length of the boundary. If the radius of a circle is r units, and the diameter d units, then the circumference is 2πr, or πd units.

combined events

a set of independent events with a single outcome. An independent event does not influence a subsequent event: for example, one throw of a die does not influence a second throw. Two throws of a die is a combined event with 36 possible outcomes (6 × 6). The probability of throwing two sixes is ¹/₃₆.

common

an adjective used to describe units, instruments, measures, date formats, etc. that are widely used in everyday life in non-specialist contexts.

common fraction

a fraction where the numerator and denominator are both integers. Also known as a simple or vulgar fraction.

commutative

an operation * is commutative if a * b = b * a. Addition and multiplication are commutative where 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2. Subtraction and division are not commutative.

composite shape

an irregular shape which can be partitioned into two or more regular or simple shapes, e.g. an L-shape made up of two rectangles.

continuous data

data resulting from measurement, e.g. length, temperature. Continuous data can take any value between two values, and can only be measured approximately to a certain degree of accuracy. Continuous data are usually represented by a line.

cuboid

a three-dimensional figure with six rectangular faces. Adjoining edges and faces are at right angles. (One pair of opposite faces may be square.)

D

data

information of a quantitative nature consisting of counts or measurements: where they refer to items or events that are separate and can be counted, the data are discrete; where they refer to quantities such as length or capacity that are measured, the data are continuous. Singular: datum.

decimal

relating to base ten. Most commonly used synonymously with decimal fraction, where the number of tenths, hundredths, thousandths, etc. are represented as digits following a decimal point. The decimal point is placed at the right of the units column. Each column after the decimal point is a decimal place: for example, the decimal fraction 0.275 is said to have three decimal places. The system of recording with a decimal point is decimal notation.

digit

one of the symbols of a number system, most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The number 29 is a two-digit number, for example, but there are three digits in 2.95. The position of the digits conveys place value.

digital clock

a digital clock is usually a 24-hour clock. It displays the time as hours and minutes past midnight: for example, four-thirty in the afternoon is displayed as 16:30. A 12-hour digital clock displays hours past midnight and midday and uses a.m. and p.m. to differentiate.

direct proportion

two quantities or variables are in direct proportion when they increase or decrease in the same ratio: for example, if 5 oranges cost £1, and 10 cost £2, then cost is in direct proportion to quantity - they both double, or both halve; expressed mathematically as y = kx where k is constant.

discrete data

data resulting from a count of separate items or events, e.g. number of people.

distribution

in recording data, the way in which values in the set of observations are arranged.

distributive

one operation Δ is distributive over another * if a Δ (b * c) = (a Δ b) * (a Δ c). Example: Multiplication is distributive over addition where 4 × (50 + 6) = (4 × 50) + (4 × 6). Multiplication is distributive over subtraction where 4 × (50 - 2) = (4 × 50) - (4 × 2). Division is not distributive over other operations.

E

equivalent fraction

fraction with the same value as another, e.g. ⁶/₁₂ = ³/6 = ¹/₂; these fractions are equivalent.

estimate

to arrive at a rough answer by calculating with suitable approximations for numbers or, in measurement, by using previous experience.

evaluate
(an expression)

to work out the value of an expression when numbers have been substituted for variables.

event

used in probability to describe the outcome of an action or happening.

everyday

an adjective used to describe numbers, measures, units, instruments, etc. that fall within the daily lived experience of most people in non-specialist contexts.

expression

a mathematical statement involving variables written in words or symbols, e.g. length × width, a × b (or ab).

F

factor

when an integer can be expressed as the product or two or more other integers, these are factors of the first. Example: 24 = 6 × 4, so 6 and 4 are factors of 24. A prime factor is a factor that is a prime number.

familiar

describes contexts, situations, numbers, measures, instruments, etc. of which the learner has some prior knowledge or experience.

formula

any identity, general rule or mathematical law. Plural: formulae.

frequency table

a table for a set of observations showing how frequently each event or quantity occurs.

G

grouped data

observed data arising from counts and grouped into non-overlapping intervals, e.g. number of people in different age-groups with intervals 0-9, 10-19, 20-29, 30-39, 40-49, etc.

H

I

imperial unit

a unit of measurement historically used in the United Kingdom and other English-speaking countries. Units include inch, foot, yard, mile, acre, ounce, pound, stone, ton, pint, quart and gallon. Now largely replaced by metric units.

integer

any of the positive or negative whole numbers including zero, e.g. -2, -1, 0, 1, 2.

inverse operations

operations that, when they are combined, leave the entity on which they operate unchanged: for example, addition and subtraction are inverse operations, e.g. 5 + 6 - 6 = 5; multiplication and division are inverse operations, e.g. 6 × 10 ÷ 10 = 6.

J

K

L

line graph

a diagram showing a relationship between two variables.

line symmetry

also reflective symmetry. The property of a shape where one half is a reflection of the other; the 'mirror line' is the axis of symmetry or line of symmetry.

M

mass

a fundamental characteristic of a body, relating to the amount of matter within it. Mass differs from weight, the force with which a body is attracted towards the earth's centre. Under certain conditions a body can become weightless, whereas mass is constant.

mean

a type of average. The arithmetic mean is the sum of quantities divided by the number of them: for example, the arithmetic mean of 5, 6, 14, 15 and 45 is (5 + 6 + 14 + 15 + 45) ÷ 5 = 17.

median

a type of average. The median is the middle number or value when all are arranged in ascending order: for example, the median of 5, 6, 14, 15 and 45 is 14. Where there is an even number of values, the arithmetic mean of the two middle values is calculated: for example, the median of 5, 6, 7, 8, 14 and 45 is (7 + 8) ÷ 2 = 7.5.

metric

relating to the decimal system of measurement based on the metre, kilogram and second.

metric unit

unit of measurement in the decimal system. Metric units include metre, centimetre, millimetre, kilometre, gram and kilogram.

mixed fraction

a whole number and a fractional part expressed as a common fraction, e.g. ¹²/₃ is a mixed fraction; also known as a mixed number.

mixed number

a whole number and a fractional part expressed as a common fraction, e.g. ¹²/₃ is a mixed number; also known as a mixed fraction.

mode

a measure of average - the most frequently occurring in a set of data.

multiple

any number that has a given number as a factor is called a multiple of that factor.
Example: 14 = 7 × 2, 49 = 7 × 7 and 70 = 7 × 10. So 14, 49 and 70 are all multiples of 7.

N

negative number

a number less than 0.

non-standard unit

unit of measure which is not fixed or widely agreed, e.g. pace, cup.

number bond

a pair of numbers with a particular total, e.g. number bonds to ten, all pairs of numbers with the total 10.

numeral

a symbol used to denote a number. The Roman numerals I, V, X, L, C, D and M represent the numbers one, five, ten, fifty, one hundred, five hundred and one thousand. The Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used in the Hindu-Arabic system giving numbers in the form that is widely used today.

O

operation

a means of combining numbers, sets or other elements. Addition, subtraction, multiplication and division are four operations on numbers.

ordinal number

a term that describes a position within an order, e.g. first, second, third, fourth...twentieth, etc.

P

parallel

always equidistant. Parallel lines never meet, however far they are produced. Parallel lines must lie in the same plane.

pattern

a systematic arrangement of numbers, shapes or other elements according to a rule.

percentage

a fraction expressed as the number of parts per hundred and recorded using the notation number%, e.g. one half can be expressed as 50%, the whole can be expressed as 100%.

perimeter

the length of the boundary of a closed figure.

pi (π)

the symbol used to denote the ratio of the circumference of a circle to its diameter. Approximately 3.142.

pictogram

a particular form of representation of data. Suitable pictures/symbols/icons are used to represent objects. For large numbers one symbol may represent a number of objects; a part symbol then represents a rough proportion of the number.

pie-chart

a particular form of presentation of data. A circle is divided into sectors. The frequency or amount of each quantity is proportional to the angle at the centre of the circle.

place value

the value of a digit that relates to its position or place in a number, e.g. in 1481 the digits represent thousands, hundreds, tens and units respectively. The value of the 1 on the left is one thousand while the value of the 1 on the right is one.

prime number

a prime number has exactly two factors, itself and 1. Examples: 2 (factors 2, 1), 3 (factors 3, 1); 51 is not prime (factors 51, 17, 3, 1), and 1 itself is not considered a prime number.

probability

the likelihood of an event happening; a measure of certainty. Probability is expressed on a scale from 0 to 1. Where an event cannot happen, its probability is 0 and, where it is certain, its probability is 1. The probability of scoring 1 with a fair die is ¹/₆.

product

the result of multiplication, e.g. the product of 2, 3 and 4 is 24 (2 × 3 × 4).

property

any attribute, e.g. one property of a square is that all sides are equal.

Q

quadrilateral

a polygon with four sides and four interior angles.

R

range

a measure of spread in statistics; the difference between the greatest and the least in a set of numerical data.

ratio

a comparison of quantities of the same kind, written a:b; for example, a mixture made up of two ingredients in the ratio 3:1 is 3 parts of the first ingredient to 1 part of the second; the first ingredient makes up ³/₄ of the total mixture, the second makes up ¹/₄ of the total.

rectangle

a quadrilateral (four-sided polygon) with four right angles. The pairs of opposite sides are equal. If all sides are equal the rectangle is a square. Adjective: rectangular.

regular

a polygon is a regular polygon if all the sides are equal and all the internal angles are equal, e.g. a regular quadrilateral is a square. When referring to a shape, the adjective regular refers to common 2-D or 3-D shapes whose areas can be found using a formula, e.g. a rectangle, circle, cylinder.

right angle

one quarter of a complete turn. An angle of 90 degrees. An acute angle is less than one right angle. An obtuse angle is greater than one right angle but less than two. A reflex angle is greater than two right angles.

round (verb)

to express a number or measurement to a required degree of accuracy, e.g. 543 rounded to the nearest 10 is 540.

S

scale

a measuring device usually consisting of points on a line with equal intervals.

sequence

a succession of terms formed according to a rule, in which there is a definite relation between one term and the next and between each term and its position in the sequence, e.g. 1, 4, 9, 16, 25, etc.

sign

a symbol used to denote an operation, e.g. addition sign +, subtraction sign -, multiplication sign ×, division sign ÷. In the case of directed numbers, the positive + or negative - sign indicates the direction in which the number is measured from the origin along the number line.

simple

an adjective applied to numbers, information, diagrams, charts, etc. that make limited demands on the learner, for example: small whole numbers; numbers that are easier to work with, e.g. multiples of 2, 5 10, 100; uncomplicated representations of limited amounts of data, etc.

square number

a number that can be expressed as the product of two equal numbers, e.g. 36 = 6 × 6, and so 36 is a square number.

standard unit

units that are agreed throughout a community, e.g. the metre is a standard unit of length. Non-standard units are not widely agreed.

straightforward

describes information, subjects and materials that learners often meet in their work, studies or other activities.

substantial activity

an activity that includes a number of related tasks, where the results of one task will affect the carrying out of the others.

substitute

to assign a value to a variable.

symbol

a letter, numeral or other mark that represents a number, an operation or another mathematical idea: for example, V is the Roman symbol for five, > is the symbol for 'is greater than'.

symmetry

a figure has symmetry if parts can be interchanged without changing the whole. A geometric figure may have reflective symmetry or rotational symmetry. Adjective: symmetrical.

system
(of measure)

an agreed system of measure in which units are defined and are in a fixed relationship to each other.

T

table

an orderly arrangement of information, numbers or letters, usually in rows and columns.

tally

to make marks to represent objects counted.

tessellation

a surface in a plane covered by the transformation (translation, reflection, rotation) of a single shape. Verb: tessellate.

U

unit

one. A standard used in measuring, e.g. a metre is a metric unit of length.

unit fraction

a fraction that has 1 as the numerator and whose denominator is a non-zero integer, e.g. ¹/₂, ¹/₃.

V

volume

a measure in three-dimensional space, measured in cubes, e.g. cubic centimetres (cm³), cubic metres (m³).

W

weight

the force with which a body is attracted towards the earth's centre. In non-scientific contexts, often used synonymously with mass (though technically different).

X

Y

Z