The IQ Guide to
Teaching Functional Mathematics
Contents
Introduction
3
Developing functional skills
5
Functional Skills Summary Mathematics Entry 1
6
Functional Skills Summary Mathematics Entry 2
7
Functional Skills Summary Mathematics Entry 3
8
Functional Skills Summary Mathematics Level 1
10
Functional Skills Summary Mathematics Level 2
14
Functional skills Mathematics: Useful terms and their meanings
18
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 2
Introduction
The IQ Guide to Teaching Functional Mathematics has been produced to support the teaching of Mathematics Functional Skills qualifications. Other guides in
the series are:
• IQ Guide to Teaching Functional English
• IQ Guide to Assessing Functional English Speaking Listening and Communication (SLC)
• IQ Guide to Assessing Functional English Writing
• IQ Guide to Assessing Functional ICT
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 3
How to use this Guide
Introduction
Functional Skills mathematics standards
Coverage and range
The IQ Guide to Teaching Functional Mathematics
has been produced by IQ so that tutors can develop
teaching programmes that will prepare learners for
applying the skills in life and work and ensuring that
learners are successful in functional skills
assessment. The Guide should be read in
conjunction with the IQ Guide to Assessing
Functional Mathematics. Make sure you go to the
section you require.
Start with understanding the mathematics
standards. These are the ‘high level’ overarching
criteria that the tutor should understand and apply
in their teaching. They should be used to prepare
schemes of work (SOW). All of the standards,
coverage and range in mathematics will be
assessed and so make sure that your SOW or
support programme addresses all of these.
The coverage and range are just that. All the
things that the learner will need to know to be
successful in their course of study.
What does this mean?
The coverage and range are ‘amplified’ so that you
can see the detail of what learners must be taught
in order to be successful. The standard, coverage
Make sure you are confident in the differences in and range may use unfamiliar language. Use the
the criteria at each of the levels before you start to glossary to help your understanding of how to
deliver the skills to your learners.
deliver to learners; one level builds onto the next.
Examples
Included are examples of where learners can
practice mathematics skills. The examples are
only mean to be a guide. There will be others that
are suitable for your learners.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 4
Developing functional skills
The aim of the functional skills standards is to develop and recognise the ability of learners to apply and transfer skills to solve mathematical problems in ways
that are appropriate to their situation. The process skills apply at all levels. These are:
Representing
(Selecting the mathematics and
information to model a situation).
30%-40%
Analysing
(Processing and using
mathematics
30%-40%
Interpreting
(Explaining/justifying the answer)
30%-40%
•
•
•
•
•
•
•
•
•
•
•
•
Learners understands that a situation has aspects that can be represented by mathematics
Learners uses a suitable way to represent
Learners decide the methods, operations and tools to use in the situation
Learners select the mathematical information to use in the situation
Learners use appropriate mathematical procedure
Learners examine patterns and relationships
Learners change values and assumption to model answers
Learners find results and solutions
Learners interpret results and solutions
Learners draw conclusions
Learners consider the appropriateness and accuracy of results and conclusions
Learners choose appropriate language and forms to communicate results
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 5
Functional Skills Summary Mathematics Entry 1
Skill standards
Representing
1. Understand simple
mathematical
information in familiar
contexts and situations.
Coverage and range
What does this mean?
Examples
a
Understand and use numbers with
one significant figure in practical
contexts
Count up to 10. Add and subtract
numbers up to 10.
Add money and items up to 10 e.g. the cost
of lunch.
Work out the shortfall in numbers, e.g. eggs
for a recipe, plants to fill a display tray, cups
to serve visitors, volunteers for a jumble sale.
b
Analysing
2. Use mathematics to
obtain answers to simple
given practical problems
c
that are clear and
routine.
Describe the properties of size and
measure, including length, width,
height and weight, and make
simple comparisons
Compare small to large, wide to
narrow.
Understand full, empty, heavier and
lighter.
Select the lighter of two suitcases.
Recognise something is too small e.g. child’s
height for a ride at a theme park
Describe position
Be able to say that something is next
to, below, and above. Left or right.
Between, inside and near to.
Follow directions e.g. take a lift to the top
floor.
3. Generate results that
make sense for a
specified task.
d
Recognise and select coins and
notes
Notes £5.00 and £10.00
Coins 1, 2, 5, 10 pence
Recognise the coins that would be used to
buy lunch or pay for a bus fare.
e
Recognise and name common 2D
and 3D shapes
Round, square, rectangle, triangle
Name the shapes round, square, cubes,
rectangle, triangle
f
Sort and classify objects
practically using a single criterion
Sort using a single feature: colour,
shape, gender
Sort bottles into different coloured glass for
the bottle bank
Interpreting
4. Provide solutions to
simple given practical
problems in familiar
contexts and situations.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 6
Functional Skills Summary Mathematics Entry 2
Skill standards
Representing
1. Understand simple
practical problems in
familiar contexts and
situations.
Coverage and range
What does this mean?
Example
a
Understand and use whole
numbers with up to two significant
figures
Numbers up to 100
You can stack boxes on a shelf 5 across and
6 high. How many boxes fit on the shelf
b
Understand and use
addition/subtraction in practical
situations
Add and subtract whole numbers up to
100
Add the number of new and old pens to find a
total number.
c
Use doubling and halving in
practical situations
Double and half whole numbers and
money. Understand the term half and
half price
Work out the cost of a meal two are paying
an equal share
Work out the cost of prices in a half-price sale
Analysing
3. Use basic
mathematics to obtain
answers to simple given
practical problems that
are clear and routine.
d
Recognise and use familiar
measures, including time and
money
Use a digital and analogue clock
Know the months of the year
Understand measurement on clothes
Recognise hour, quarter past, half past
and quarter to.
Pay for items using coins and notes
Reading from a clock or timetable knowing
the next train time.
Count out £1.63 using coins available for a
pint of milk and .loaf of bread.
Write appointment in diary
4. Generate results to a
given level of accuracy.
5. Use given checking
procedures.
e
Recognise sequences of numbers, Recognise missing numbers in a
including odd and even numbers
sequence two’s, fives, ten’s.
Know what side of the road a door is using
odd and even numbers.
f
Use simple scales and measure to
the nearest labelled division
Read meter and a speedometer
Read a temperature
Read temperature on thermometer or read
weight of vegetables on scales.
Interpreting
6. Describe solutions to
simple given practical
problems in familiar
contexts and situations.
g
Know properties of simple 2D and
3D shapes
Understand the sides, edges, corners,
Know the names of 3D shapes e.g.
pyramid, cylinder
What is the shape of a box?
How many sides do you walk around
rectangle shape field?
h
Extract information from simple
lists.
Lists of numbers, words, tables,
compare temperatures in holiday
destinations, e.g. menu
Find the cheapest or most expensive item on
the menu
Highest temperature in the week
2. Select basic
mathematics to obtain
answers.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 7
Functional Skills Summary Mathematics Entry 3
Skill standards
Representing
1.Understand practical
problems in familiar
contexts and situations
2. Begin to develop own
strategies for problem
solving problems.
3.Select mathematics to
obtain answers to simple
practical problems that
are clear and routine
Analysing
4.Apply mathematics to
obtain answers to simple
given practical problems
that are clear and routine
5.Use simple checking
procedures
Interpreting
Coverage and range
What does this mean?
Example
a
Add and subtract using Use column addition and subtraction or A customer has £175 worth of vouchers. She wants
three-digit numbers
partitioning to add and subtract whole to use them to buy garden furniture. The furniture is
numbers less than 1000.
£200. How much money will the customer need to
add to the vouchers to buy the furniture?
b
Solve practical problems
involving multiplication
and division by 2, 3, 4, 5
and 10
c
Round to the nearest 10 Understand place value for units, tens and
or 100
hundreds.
Round numbers less than 1000 to the
nearest 10 and 100.
Estimate answers to calculations using
rounding.
d
Understand and
simple fractions
Whilst calculators are allowed for the tasks, You need £1 worth of 10p coins in your till at the
strategies should be understood e.g. to beginning of the day. How many 10p coins is this?
multiply by 10 move the digits one place to
the left, to multiply by 5, first multiply by 10
and then halve.
use Read and write common fractions, for
example halves, quarters, thirds, tenths.
Understand that the top number is the
number of equal parts there are and the
bottom number is the number of parts
something has been divided into.
Understand that equivalent fractions look
different but have the same value.
You need to buy 35 glasses for a party. The glasses
are sold in packs of 10. How many will you need to
buy to have enough?
A clothes shop reports its sales to head office to the
nearest 10 items. One week the shop sells 234
items. What number would this be reported as?
A pizza has been divided in 8 pieces. If 4 of the
pieces have been eaten, what fraction of the pizza
is left?
Understand fractions used in sales or special offers,
e.g. 1/3 off
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 8
6.Interpreting and
communicate solutions
to practical problems in
familiar contexts and
situation
e
Understand, estimate, Read scales on measuring instruments. Find the coldest day from a set of temperatures for
measure and compare Know common units and which to use when. an identified place or country. (not negative
length, capacity, weight
temperatures)
and temperature
f
Understand decimals to Understand that the decimal point separates Given some heights, work out who can go on a
two decimal places in pounds and pence, m and cm.
theme park ride where the minimum height allowed
practical contexts
is 1.5m.
Understand prices on a menu in a restaurant, hotel
or café.
g
Recognise and describe Recognise patterns with repeated addition or Solve a delivery problem with house numbers
number patterns
multiplication such as doubling.
where the even house numbers are on one side of
Recognise odd and even numbers by looking the road and the odd ones are on the other side.
at the unit value.
h
Complete
simple Work with money amounts in pounds and
calculations
involving pence and measures with both whole
money and measures
numbers and numbers including one decimal
place.
i
Recognise and name Recognise 2D shapes: circle, rectangle (not Recognise the shape of different everyday objects
simple 2D and 3D oblong), square, triangle. 3D shapes: cube, e.g. box, phone, ball, money, road signs, health and
shapes
and
their cuboid, sphere, cylinder, cone
safety signs.
properties
j
Use metric units
everyday situations
k
Extract,
use
and
compare
information
from lists, tables, simple
charts and simple graphs
in Know that length is measured in millimetres,
centimetres, metres and kilometres; weight in
milligrams, grams and kilograms and
capacity in millilitres and litres.
You spend £2.95 on a bus fare, how much change
should you get from a £5 note.
You get paid £7.50 per hour and work 6 hours a day
how much do you get a day?
Calculate how much flour will be left in a 1kg bag
after baking a batch of cupcakes that need 300g
flour.
Measure milk for use in a recipe.
Read information from bar charts, Use a price list to work out how much a 25kg bag
pictograms, simple pie charts and tables.
of sand costs.
Understand the importance of titles, labels Transfer data from a tally chart into a table.
and keys.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 9
Functional Skills Summary Mathematics Level 1
Skill standards
Representing
Coverage and range
a
1.Understand practical
problems in familiar
contexts and situations,
some of which are nonroutine
2.Indentify and obtain
the necessary
information to tackle the
problem
4. Apply mathematics in
an organised way to find
solutions to
straightforward practical
problems for different
purposes.
Example
Read, write, order and compare numbers,
including large numbers.
Be able to read meters with large numbers (up to 7
digits) such as gas and electricity meters.
Recognise negative numbers in the context
of temperature.
Understand the storage temperature on frozen
food packets..
Work to the given level of accuracy, for
example nearest whole number or nearest
ten.
Work out how much tip to give a hair stylist if you
want to include a 10% tip. Round the answer to
the nearest pound.
b
Add, subtract, multiply
and divide whole
numbers using a range
of strategies
Use a range of calculation strategies,
including mental methods, formal and
informal written methods and use of a
calculator.
Calculate the daily takings in a shop, given the
receipts for that day.
c
Understand and use
equivalences between
common fractions,
decimals and
percentages
Read, write, order and compare common
fractions, including mixed numbers,
decimals with up to two decimal places and
percentages.
Be able to calculate 50% of the cost of an order by
knowing that 50% is equal to a half and 25% being
equal to a quarter
Add and subtract
decimals up to two
decimal places
Add and subtract monetary amounts.
Check a bill is correct when the amount involve
both pounds and pence.
3.Select mathematics in
an organised way to find
solutions
Analysing
Understand and use
whole numbers and
understand negative
numbers in practical
contexts
What does this mean?
d
Add and subtract with metric units for
example length.
Know which is more - 25% off or a 1/3rd off the
price.
Work out wages from an hourly rate.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 10
5.Use appropriate
checking procedures at
each stage
e
Solve simple problems
involving ratio, where
one number is a
multiple of the other
Interpreting
6.Interpreting and
communicate solutions
to practical problems
drawing simple
conclusions and giving
explanations
Understand simple ratio as the number of
parts, for example three parts to one part.
Understand direct proportion as the same
rate of increase or decrease, for example
double, half etc.
Know how to use a simple scale to estimate
distance on a road map.
Make up a drink of juice in the ratio of 1:5 juice and
water. How many litres of drink will you make from
2 litres of juice?
Scale up amounts of food for three times the
number of people, put items in piles with twice as
many items in one pile as in the other.
Calculate how far it is between two towns given a
copy of a road map and the scale of the map.
f
Use simple formulae
expressed in words for
one- or two-step
operations
Solve a problem that is given in words that
includes a rule. N.B. There is no need to be
able to generate an algebraic formula.
A joint of meat takes 40 minutes per kilogram to
cook plus an extra 20 minutes. How long will it take
to cook a 4kg joint of meat?
g
Solve problems
requiring calculation
with common
measures, including
money, time, length,
weight, capacity and
temperature
Add, subtract, multiply, divide and record
sums of money.
Complete an expenses sheet including mileage
costs, meal costs and parking.
Read, measure and record time using both
the 12-hour and 24-hour clock and add and
subtract times in hours and minutes.
Calculate how long a gym is open for by using the
opening and closing times displayed on a sign.
Read timetables correctly.
Use a bus timetable to work out which bus you
need to catch to arrive at in interview by 11am.
Read, estimate, measure, compare and
calculate length, distance, weight, capacity,
and temperature.
Calculate the amount of wallpaper needed to
wallpaper a room given the room dimensions and
the size of a roll of wallpaper.
Understand and use a mileage chart.
Work out the shortest distance for a delivery driver
when given the distances between each town in a
mileage chart.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 11
h
i
Convert units of
measure in the same
system
Understand the metric system and be able
to convert between metric units for length,
weight and capacity.
Work out areas and
perimeters in practical
situations
Know that the perimeter is the boundary of a Calculate the amount of fencing needed to go
around a play area.
shape and is measured in units of length.
Know that area is a measure of 2D space,
measured in square units and that the area
of a rectangle = length × width.
Know that measurements must be in the
same units before calculating.
Convert someone’s height in centimetres to metres
for an application form.
Convert grams to kilograms for building materials.
Calculate the amount of turf needed for a football
pitch.
Calculate the area of a door when the height is
given in metres but the width is given in
centimetres.
Work out how many smaller boxes can fit in a
larger box for delivery.
j
Construct geometric
diagrams, models and
shapes
k
Extract and interpret
information from
tables, diagrams,
charts and graphs
Construct models, draw shapes.
Draw the net of a packaging box.
.
Understand that title, labels, and key provide
information and know how to read a scale
on an axis.
Know how to use a simple scale such as
1cm to 1m, 20mm to 1m. 1cm to 1km
Get information from tables such as a
timetable or pricelist, and charts such as a
pictogram, simple pie chart or bar chart,
single line graphs.
Given a graph of sales, write a comment as to
whether the sales have increased or decreased.
Be able to plan furniture for a room given room
dimensions and furniture sizes.
Work out the attendance at a series of sports event
by reading the information from a bar chart.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 12
l
Collect and record
discrete data and
organise and represent
information in different
ways
Collect (including by making accurate
observations) and record discrete data in a
tally chart.
Organise discrete data in a table.
Represent discrete data in pictograms, bar
charts and line graphs.
Draw a table to record the lunch order in an office.
Draw a correctly labelled graph to show your head
office weekly takings.
Identify that more staff are needed to handle
enquiries between 12:30 and 1:30pm because a
graph shows that this is the busiest time.
Know how to choose a sensible scale and to
label charts, graphs and diagrams.
Represent the results of calculations to
show the purpose of the task.
m
n
Find mean and range
Use data to assess the
likelihood of an
outcome
Calculate the mean average by summing all
the values then dividing by the number of
items.
200 people donate some money to a charity. The
total raised is £470, what the mean average
donation?
Understand that the range measures the
spread of a set of data and is calculated by
finding the difference between the largest
and smallest value.
Identify the most consistent runner given a table
with some runners and their last four lap times.
Understand that some events are
impossible, some events are unlikely to
occur, some events are likely to occur and
some events are certain.
Know that if a shop is closed on a Sunday, it is
impossible that someone can buy a meal on a
Sunday in that shop.
Know that the chance, or probability, of
something happening can be calculated but
understand that having two outcomes does
not mean each are equally likely.
Realise that when crossing the road, you will either
get to the other side safely or not, but it is not
equally likely that both events occur.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 13
Functional Skills Summary Mathematics Level 2
Skill standards
Representing
1.Understand routine
and non-routine
problems in familiar
contexts and unfamiliar
contexts and situations
2.Indentify the situation
or problems and
identify the
mathematical methods
needed to solve them
3. Choose from a
range of mathematics
to find solutions
Analysing
Coverage and range
What does this mean?
Example
a
Understand and use
positive and negative
numbers of any size in
practical contexts
Read, write, order and compare positive and Find the lowest temperature from a chart where
negative numbers of any size.
some numbers are positive and some are
Understand the meaning of negative
negative (minus)
numbers in a practical context.
Use a bank statement to work out if you need to
ask for an overdraft or are in surplus.
b
Carry out calculations
with numbers of any
size in practical
contexts, to a given
number of decimal
places
Add, subtract, multiply and divide numbers
up to two decimal places. Use column
addition and subtraction.
Use short and long multiplication and
division and chunking.
Work out calculations mentally, with jottings,
and with a calculator. Interpret money and
time amounts on a calculator.
Estimate answers to calculations. Nearest
hundred, ten, unit, tenth hundredth, nearest
pound. Use estimation to work out distance
and time. Use the calculator to check
answers.
Work out the cost of holiday for four, with flights,
hotel, transfers. Compare with an alternative
holiday to find the cheapest.
Work out the cost of building an extension to a
house, given cost of items and the quantities.
Work out times and distances to compare types
of transport.
Work out the weekly budget of family. Estimate
the cost for a month and a year.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 14
4.Apply mathematics to
find solutions
c
5.Use appropriate
checking procedures
and evaluate their
effectiveness at each
stage
Understand, use and
calculate ratio and
proportion, including
problems involving
scale
Write a ratio in its simplest form. 6:4 = 3:2.
Recognise when a ratio is used.
Divide an amount into a given ratio.
Use scales in both maps and diagrams.
Scale quantities up or down
The total cost for a job is £200. If the ratio
between labour and materials is 5:3, how much
was the labour?
Calculate the distance of a journey from a map
Interpreting
6.Interpret and
communicate solutions
to multi-stage practical
problems in familiar
and unfamiliar contexts
and situations
7.Draw conclusions
and provide
mathematical
justifications
Work out materials in construction materials,
diluting liquid for hair preparations.
Work out the scale of a plan that is 1:20 e.g. if a
room is 9m by 7m, what are the dimensions, in
cm, on the plan?
Scale up (and scale down) recipes when cooking
e.g. if 200g of flour for 12 cakes, how much
would you need for 24?
d
Understand and use
equivalences between
fractions, decimals and
percentages
Simplify fractions. Simplify fractions to their
simplest form e.g. = .
Find fractions of a quantity.
Improper and mixed numbers.
Work out percentages of a quantity. Work
out percentage increase and decrease
Convert between fractions, decimals and
percentages.
e.g.37% as a fraction and a decimal?
Order fractions, decimals and percentages.
Write one number as a fraction of another.
Compare overtime rates
Find of a restaurant bill
Show as a mixed number. Write fractions of
an hour as decimals on a time sheet.
Work out the discount on goods for increased
quantities
Work out which is the better value 25% off or off? Calculate a percentage pay increase and
decrease.
Write mixed forms from smallest to largest
e.g.0.23, , 27%, , 0.029.
Work out what fraction of gym members are
males if there are 300 men and 550 are women.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 15
e
Understand and use
simple formulae and
equations involving
one- or two-step
operations
Substitute numbers into a formula and
derive a formula in words.
Understand the order of
operations.(BIDMAS)
Calculate the speed when a car travels 8 miles in
10 minutes using the formula
s=d÷t
Work out the cooking time for a joint of meat
which can be calculated as 35 minutes per 500g
plus an extra 35 minutes. Calculate how long a
2.2 kg joint would take.
3+4x5=?
Add brackets to make this calculation correct:
7 x 5 + 2 = 49
f
Recognise and use 2D
representations of 3D
objects
Sketch 3D solids and draw them accurately
on isometric grids.
Use of nets to calculate surface area.
Use plans, elevations.
Draw the net of a packaging box
Given a 3D representation of a house, draw the
front and top view
g
Find area, perimeter
Perimeter and area of triangles, trapezoids,
and volume of common and parallelograms and rectangles.
shapes
Calculate circumference and areas.
Understand the symbol for pi and know its
approximate value.
Volume of cuboids and cylinders.
Calculate the area of a compound shape made
up of rectangles and triangles for example, a plot
of land
Calculate how much edging strip would be
required for a circular pond with a diameter of
10m?
Calculate the volume of water in a pond that is
3m by 2m and 60cm deep.
h
Use, convert and
calculate using metric
and, where
appropriate, imperial
measures
Use a conversion graph to calculate how many
Euros you would get for £100
Calculate the total length of skirting board if you
have three strips which are 1.2m, 1.7m and 67cm
long.
You want to bake a cake which needs 8oz flour.
You have a 500g bag, will this be sufficient?
Conversion-graphs.
Convert between metric units and use mixed
units of measure within the same system, for
example m and cm, giving answer in m.
Convert between metric and imperial units.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 16
i
Collect and represent
discrete and
continuous data, using
ICT where appropriate
Collecting data in tally charts.
Represent data in Frequency tables, Pie
charts, Bar charts, Line graphs, Scatter
graphs.
Get relevant information from different sources or
first-hand by measuring or observing.
Understand how to use scales in diagrams,
charts and graphs.
Know how to choose a suitable format and scale
to fit the data and ensure all charts, graphs and
diagrams are labelled.
j
Use and interpret
statistical measures,
tables and diagrams,
for discrete and
continuous data, using
ICT where appropriate
Know how to extract discrete and
continuous data from tables, spread sheets,
bar charts, pie charts and line graphs.
Draw a conclusion from a scatter diagram,
Work out percentages for each part of pie chart,
Identify trends looking at graphs and charts.
k
Use statistical methods Comparison of two groups using measure of
to investigate situations average and range or by comparing
proportions in a pie chart.
Find the mean, median and mode and
understand that each average is useful for
different purposes and use the range to describe
the spread within a set of data, for example sales
results.
l
Use probability to
Calculate theoretical probabilities and
assess the likelihood of compare probabilities.
an outcome
Explain why the probability of choosing a red
card from a pack of cards is = a club =
and an ace = A bag of 10 balls contains six red balls. A spinner
divided into five equal sections has two red
sections. In which situation is red most likely?
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 17
Functional skills Mathematics: Useful terms and their meanings
Acute angle
An angle less than 90°.
Adjacent
Adjacent sides are next to each other and are joined by a common vertex.
Algebra
Algebra is the branch of mathematics where symbols or letters are used to represent numbers.
Angle
An angle is formed when two straight lines cross or meet each other at a point. The size of an angle is measured by the amount one line
has been turned in relation to the other.
Approximate
An approximate value is a value that is close to the actual value of a number.
Arc
Part of a circumference of a circle.
Area
The amount of space a shape takes up. E.g. the area of the lawn is 35 square metres.
Asymmetrical
A shape which has no lines of symmetry.
Average
A value to best represent a set of data. There are three type of average - the mean, the median and the mode.
Axis
An axis is one of the lines used to locate a point in a coordinate system.
Bearing
A three digit angle measured from north in a clockwise direction.
BIDMAS
A way of remembering the order in which operations are carried out. It stands for Brackets - Indices - Division - Multiplication - Addition Subtraction.
Bisect
To divide an angle or shape exactly in half.
Brackets
Used to determine the order in which operations are carried out. For example, 3 + 4 x 2 = 11 but (3 + 4) x 2 = 14.
Calculate
To work out the value of something. This does not have to mean you need a calculator!
Centilitre (cl)
A measure of volume. 100 centilitres = 1 litre (100 cl = 1 l). 1 centilitre = 10 millilitres (1 cl = 10 ml).
Centimetre (cm)
A measure of distance. 1 centimetre = 10 millimetres. (1 cm = 10 mm). 100 centimetres = 1 metre. (100 cm = 1 m).
Chord
A straight line drawn from one point on the edge of a circle to another.
Circumference
The perimeter of a circle.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 18
Coefficient
The number in front of an algebraic symbol. For example the coefficient of 5x is 5.
Congruent
If you can place a shape exactly on top of another then they are said to be congruent. You may rotate, reflex or translate the shape.
Constant
A letter or symbol whose value always stays the same. The constant Π is a common example.
Credit
To add money to a bank account. For example, I had £500 credited to my bank account.
Cross section
The end section created when you slice a 3D shape along its length.
Cube number
The product when an integer is multiplied by itself twice. For example 5 cubed = 5 x 5 x 5 = 125.
Cuboid
A 3D shape with all sides made from rectangles.
Cumulative
frequency
A running total of the frequencies, added up as you go along.
Day
A time period of 24 hours. There are 7 days in a week.
Debit
To take out money from a bank account. For example, £400 was debited from my account.
Decagon
A ten sided polygon.
Decimal
Not a whole number or integer. For example, 3.6 or 0.235.
Decrease
To make an amount smaller.
Denominator
The bottom part of a fraction.
Diameter
The distance across a circle which passes through the centre.
Difference
Subtract the smaller value from the larger value to find the difference between two numbers.
Distance
How far away an object is. For example, it is a distance of 3 miles to the city centre.
Distribution
How data is shared or spread out.
Equal
Used to show two quantities have the same value.
Equation
Two expressions which have the same value, separated by an '=' sign. E.g. 3y = 9 + y
Equilateral triangle A triangle with all sides and angles the same size.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 19
Estimate
To find an approximate answer to a more difficult problem. E.g. 31.2 x 5.94 is roughly equal to 30 x 6 = 180.
Even number
Any number which is a multiple of 2. Even numbers always end in 2, 4, 6, 8 or 0.
Expand
To multiply out brackets in an expression. For example, 2(3x + 7) = 6x + 14.
Expression
A collection of terms which can contain variables (letters) and numbers. E.g. 4pq - q + 7
Factor
A number that divides another number exactly. E.g. 4 is a factor of 12.
Figures
Another name for numbers. For example one thousand and fifty in figures is 1050.
Formula
An equation used to describe a relationship between two or more variables.
Frequency
How many times something happens. Another word for 'total'.
Frequency density The frequency divided by the class width.
Gradient
How steep a line is. Found by dividing the distance up by the distance across.
Gram (g)
A measure of mass. 1 gram = 1000 milligrams. (1 g = 1000 mg)
HCF
Stands for 'highest common factor'. It is the largest factor common to a set of numbers. E.g. The HCF of 16 and 24 is 8.
Heptagon
A seven sided polygon.
Hexagon
A six sided polygon.
Histogram
A diagram drawn with rectangles where the area is proportional to the frequency and the width is equal to the class interval.
Hypotenuse
The longest side on a right angled triangle.
Increase
To make an amount larger.
Indices
Another name for powers such as ² or ³.
Integer
A whole number.
Inter-quartile range
The difference between the upper and lower quartile.
(IQR)
Irrational
A decimal which is never ending. It must also not be a recurring decimal.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 20
Justify
Another word for 'explain'. Often crops up on your maths exam. E.g. 'Calculate the mean and range for each player. Who is the better
player Justify your answer.'
Kilogram (Kg)
A measure of mass. 1 kilogram = 1000 grams. (1 kg = 1000 g)
Kilometre (Km)
A measure of distance. 1 kilometre = 1000 metres. (1 km = 1000 m)
LCM
Stands for 'lowest common multiple'. It is the smallest multiple common to a set of numbers. E.g. The LCM of 3 and 4 is 12.
Litre (l)
A measure of volume. 1 litre = 100 centilitres (1 l = 100 cl). 1 litre = 1000 millilitres (1l = 1000 ml).
Lower range
The smallest value in a set of data.
Mean
A type of average found by adding up a list of numbers and dividing by how many numbers are in the list.
Median
The middle value when a list of numbers is put in order from smallest to largest. A type of average.
Metre (m)
A measure of distance. 1 metre = 100 centimetres. (1 m = 1000 cm).
Millilitre (ml)
A measure of volume. 10 millimetres = 1 centilitre (10 ml = 1 cl). 1000 millilitres = 1 litre (1000 ml = 1 l).
Millimetre (mm)
A measure of distance. 10 millimetres = 1 centimetre. (10 mm = 1 cm).
Modal
Another term for mode
Mode
The most common value in a list of numbers. If two values are tied then there is two modes. If more than two values are tied then there is
no mode. A type of average.
Month
A time period of either 28, 30 or 31 days. There are 12 months in a year.
Multiple
A number which is part of another number's times table. E.g. 35 is a multiple of 5.
Natural number
A positive integer
Negative
A value less than zero
Nonagon
A nine sided polygon.
Numerator
The top part of a fraction.
Obtuse angle
An angle between 90 and 180 .
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 21
Octagon
An eight sided polygon.
Odd number
A number that is not a multiple of 2. Odd numbers always end in 1, 3, 5, 7 or 9.
Operation
An action which when applied to one or more values gives an output value. The four most common operations are addition. subtraction,
multiplication and division.
Parallel
Two or more lines which are always the same distance apart.
Parallelogram
A quadrilateral with two pairs of parallel sides.
Pentagon
A five sided polygon.
Perimeter
The distance around a shape.
Perpendicular
Two or more lines which meet at right angles.
Pi (Π)
An irrational constant used when calculating the area and circumference of circles. It is approximately equal to 3.14.
Polygon
A shape made from straight lines.
Positive number
A number greater than zero.
Prime
A number which has exactly two factors. The number one and itself.
Prism
A 3D shape with the same cross section all along its length.
Probability
A measure of how likely an event is to occur.
Product
The answer when two values are multiplied together.
Quadratic equation An equation where the highest power is two. For example x² + 4x + 6 = 0 is a quadratic equation.
Quadrilateral
A four sided polygon.
Radius
The distance from the centre of a circle to its circumference. The plural of radius is radii.
Random sampling
A method of choosing people at random for a survey.
Range
The largest number take away the smallest value in a set of data.
Rational
A decimal number which ends or is recurring.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 22
Reciprocal
The reciprocal of any number is 1 divided by the number. E.g. the reciprocal of 3 is 1/3., the reciprocal of 3/4 is 4/3.
Recurring
A decimal which never ends but repeats all or parts of the sequence of numbers after the decimal point. E.g 0.333333 or 0.141414.
Reflex angle
An angle greater than 180 .
Regular
A shape with all sides and angles the same size.
Remainder
The amount left over when a number cannot be divided exactly. For example, 21 divided by 4 is 5 remainder 1.
Right angle
An angle of 90 .
Rotation
To turn a shape using an angle, direction and centre of rotation.
Round
To reduce the amount of significant figures or decimal places a number has. For example £178 rounded to the nearest £10 is £180.
Scale factor
How many times larger or smaller an enlarged shape will be.
Segment
An area of a circle enclosed by a chord.
Sequence
A list of numbers which follows a pattern. For example 6, 11, 16, 21, ...
Simplify
To write a sum, expression or ratio in its lowest terms. For example 4:10:6 can be simplified to 2:5:3.
Solid
A 3D shape.
Solve
To find the missing value in an equation.
Speed
How fast an object is moving. Average speed = Total distance divided by time taken.
Square number
The product when an integer is multiplied by itself. For example, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Sum
The answer when two or more values are added together.
Surface area
To total area of all sides on a 3D shape.
Symmetrical
A shape which has at least one line of symmetry.
Tally
A system of counting where every group of four vertical lines is followed by a horizontal line to easily count in steps of five.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 23
Tangent
A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the tangent.
Term
A number, variable or combination of both which forms part of an expression.
Transformation
The collective name for reflections, rotations, translations and enlargements.
Translation
To move a shape from one position to another by sliding in the x-axis followed by the y-axis.
Trapezium
A quadrilateral with one pair of parallel sides.
Tree diagram
A method of solving probability questions by listing all the outcomes of an event. Probabilities are calculated by multiplying down the
branches.
Triangle
A three sided polygon.
Triangular number A sequence of numbers generated by adding one more than was added to find the previous term. For example, 1, 3, 6, 10, 15, 21, ...
Units
A quantity used to describe a measurement. Examples are kilograms, metres and centilitres.
Upper range
The largest value in a set of data.
Value
A numerical amount or quantity.
Variable
A letter which we don't know the value of.
Volume
The amount an object can hold. E.g. a bottle of cola has a volume of 2 litres.
Week
A time period of 7 days.
Wide
Used to describe the width of something
Width
The distance from side to side. E.g. 'The swimming pool is 10 metres wide.'
X-Axis
The horizontal axis on a graph. The line going across the page.
Y-Axis
The vertical axis on a graph. The line going from top to bottom.
Y-Intercept
The value of the y-coordinate when a graph crosses the y-axis.
Year
A time period of 12 months or 365 days. (366 in a leap year.)
Z-Axis
Represents the depth of an object when working with 3D coordinates.
IQ Guide to Teaching Functional Skills Mathematics | August 2014 | 24