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A guide for all staff and parents.
Introduction
“All teachers have responsibility for promoting the development of Numeracy.
With an increased emphasis upon Numeracy for all young people, teachers will
need to plan to revisit and consolidate Numeracy skills throughout schooling.”
Building the Curriculum 1
All schools, working with their partners, need to have strategies to ensure that all
children and young people develop high levels of Numeracy skills through their
learning across the curriculum. These strategies will be built upon a shared
understanding amongst staff of how children and young people progress in Numeracy.
Aims of this booklet:
To provide support to non-mathematicians when delivering Numeracy within
their subject.
To help pupils recognise more easily the transferable Numeracy skills required
for their life, learning and work and ensure consistency in their methods.*
*Due to guidelines from the examining body, some subject workings have to be
approached differently.
How to use this booklet:
It is envisaged that teachers and support staff will refer to this booklet in
advance of teaching Numeracy skills. This will ensure consistency of teaching
methods where appropriate.
Parents can also refer to this booklet when their child is having difficulty with
their homework. Again this will ensure workings are consistent with what they
are being taught in school.
The booklet also highlights key words that we are all encouraged to use when
delivering lessons so we do not confuse pupils.
The two main organisers for Numeracy are:
Number, Money and Measure
Information Handling
Within each organiser there are subdivisions.
This booklet will show helpful workings on the subdivisions (in bold) for developing
essential skills across the curriculum.
Number, Money and Measure Information Handling Estimation and Rounding Data and Analysis
Number and Number Processes
including: Addition
Subtraction Multiplication
Division
Negative Numbers
BODMAS (order of operations)
Ideas of chance and uncertainty
Fractions, Decimal Fractions and
Percentages including
Ratio and Proportion
Money
Time
Measurement
Each classroom has a chart showing a symbol for the two organisers to enable pupils
to recognise the numeracy skill they are doing in class that day. Staff will also refer
to any Numeracy skill being done.
Introduction to Curriculum for Excellence courses
Early Level – pre-school + P1 or later for some.
First Level – to end of P4 but earlier or later for some.
Second Level – to the end of P7 but earlier or later for some.
Third and Fourth Level – S1 to S3 but earlier for some.
The fourth level broadly equates to SCQF 4 (Credit).
Basic calculations – some common vocabulary
Addition (+)
sum of
more than
eg. what is 6 more than 10?
add
total
and
plus
increase
Multiplication (x)
multiply
times
product
lots of
sets of
of
eg ½ of 16
Equals (=)
is equal to
same as
makes
will be
means
answer is
Subtraction (-)
less than
eg. how many less than 12 is 7?
subtract
take away
(try to use subtract)
minus
(try to use subtract)
difference between
decrease
Divison (÷)
divide
share
split
groups of
Estimating and Rounding
At Second Level we expect pupils to:
estimate height and length in mm, cm, m and 12m
estimate small weights, small areas, small volumes
round 3 digit whole numbers to the nearest 10
round any number to the nearest whole number, 10 or 100.
At Third and Fourth Levels we expect pupils to:
estimate areas in square metres, lengths in mm cm and m
give an estimation for a calculation
round any number to 1 decimal place
round to any number of decimal places or significant figures.
When asked to round to a particular value we look at the digit immediately to the
right of that value i.e.
round to nearest 10 – we look at the units digit
round to the nearest 100 – we look at the tens digit
round to one decimal place – we look at the second decimal place digit.
If the digit to the right is a 5 or more (half way or more) ie 5, 6, 7, 8, or 9
we round up and if less than 5 (less then half) we round down or some may
see it as ‘chopping off’.
WORKED EXAMPLES
1) Rounding to nearest 10
74 70 as units digit is less than 5 we round back down to 70
since 74 is nearer 70 than 80.
2) Rounding to nearest 100
2350 2400 as tens digit is a 5 so round up to 2400
3) Rounding to 1 decimal place (to 1 d.p.)
5.31 5.3 (to 1 d.p.) as 2nd d.p. is less than 5 so round down to .3
11.97 12.0 (to 1 d.p.)
4) Give an estimate for 37 x 82
37 x 81
≈ 40 x 80
= 3200 So an approximate answer will be 3200.
WORKED EXAMPLES FOR SIGNIFICANT FIGURES
The significant figures of a number are those figures that express a size to a
specified degree of accuracy.
Zeros can be complicated – when do we count them? When do we not?
If zeros are used only to show where the position of the decimal point is
or the size of a number then they are NOT significant.
If zeros are trailing in a decimal they show accuracy and ARE significant.
The rules of rounding to significant figures is the same as for decimals – always round
up for 5 or more and round back for less than 5.
1. 607 has 3 s.f.
2. 60.7 has 3 s.f.
3. 0.607 has 3 s.f. since leading zero just showing position
4. 0.06070 has 4 s.f. since front zeros show position, trailing zero is for accuracy
5. 4386 to 1 s.f. 4000
6. 39264 to 3 s.f. 39300
7. 5.746 to 2 s.f. 5.7
8. 0.008317 to 2 s.f. 0.0083
EXAMPLES OF OTHER SUBJECTS WHO USE ESTIMATING AND ROUNDING:
PE - when measuring distance and heights.
Music – for rudiments of theory.
TECH – finding midpoints in practical craft.
Science – in most calculations.
History – population growth.
Geography – census material.
Number and Number Processes
Addition
From Second Level onwards we expect pupils to:
add and use carrying over method
use mental strategies where appropriate.
WORKED EXAMPLES
Carry over:
24
+ 37
61
1
Mental – breaking up number :
136 + 59
= 136 + 50 + 9
= 186 + 9
= 195
or 136 + 59
= 136 + 60 - 1
= 196 - 1
= 195
Subtraction
From Second Level onwards we expect pupils to:
subtract using decomposition i.e. exchanging one ten for 10 units or one
hundred for 10 tens etc when needed
use mental strategies where appropriate.
WORKED EXAMPLES
Decomposition, this is where we exchange:
2 7 1 4 0 0
- 3 8 - 7 4
723 3 73 2 6
Mental - counting on:
To solve 41 – 27, count on from 27 until you reach 41
27 30 41
3 + 11
= 14
Mental – breaking up the number:
41 – 27 or 41 – 30 + 3
= 41 – 20 – 7 = 11 + 3
= 21 – 7 = 14
= 14
PLEASE AVOID USING THE TERM ’borrow and pay back’
always talk about ‘exchanging’ instead.
1 6 3 1 9
1
Multiplication
From Second Level onwards we expect pupils to:
recall all the times tables to 10 then up to 12
connect tables together ie 4x is double 2x, 6x is double 3x etc….
use their fingers to help if struggling with the 9x
either do long multiplication sums or they can break up the multiplier
use mental strategies where appropriate.
WORKED EXAMPLES
Connecting tables:
6 x 8 or 6 x 8
= 48 = double 3 x 8
= double 24
= 48
Fingers for 9x:
Place hands out in front of you
9x1 – put 1st digit down, left with a space then 9 together = 09 or just 9
so 9 x 1 = 9
9x2 – put 2nd digit down, left with 1 digit, a space then 8 together = 18
so 9 x 2 = 18
9 x 5 = 45 9 x 7 = 63 9 x 10 = 90
Long multiplication:
23 x 56
23
X56
138 x 6
+1150 x 50, put in 0 then x 5
1288
Break up multiplier:
47 x 25
47 47 then add answers 940
x20 x5 +235
940 235 1175
Mental strategies:
74 x 20
Double 74 = 148
148 x 10 = 1480
PLEASE TRY AND AVOID USING REPEATED ADDITION
ENCOURAGE PUPILS TO USE MULTIPLYING STRATEGIES
1
1
1 3
Division
From Second Level onwards we expect pupils to:
recall all the times tables to 10 then up to 12
connect tables together i.e. ÷4 is half then half again etc….
do long division sums in Third and Fourth Level
use mental strategies where appropriate.
WORKED EXAMPLES
Division sum:
0 2 6
4 48 7 1 18 42
Connecting tables:
48 ÷ 4
=48 ÷ 2 ÷ 2
=24 ÷ 2
=12
Long division sum by carrying over method:
0 2 5 6 ie 4352 ÷ 17 = 256
17 4 43 95 102
Long division by subtraction:
2 5 6
17 4 3 5 2
3 4 17 x 2 = 34 so subtract 34 from 43 to get 9, then bring down 5
0 9 5
8 5 17 x 5 = 85 so subtract 85 from 95 to get 10, then bring down 2
1 0 2
1 0 2 17 x 6 = 102 so subtract 102 from 102 to get 0.
0 0 0
12
4 ÷ 4 is
1 exactly,
so put 1
above
8 ÷ 4 is
2 exactly, so
put 2 above
1 ÷ 7 is 0
then carry
the 1 that
hasn’t
been used over
18 ÷ 7 is 2
then carry
the 4 that
is left over
42 ÷ 7 is
6 exactly
Negative Numbers
At Second Level pupils we expect to:
use a number line (vertical or horizontal) to work with numbers less than zero
recognise where easy negative numbers are used in real-life e.g. temperature.
At Third Level and Fourth Level pupils are expected to:
use the four operations on negative numbers
recognise where negative numbers are used in real-life e.g. bank accounts.
WORKED EXAMPLES
If the temperature this afternoon was 4°C and now it is -2°C, by how many
degrees has the temperature dropped?
4°C to -2°C is 6°C
When subtracting a negative it becomes add -(-3) +3
When adding a negative it changes to subtract +(-3) -3
When multiplying a negative by a negative the answer is positive (-3) x (-4) = 12
When multiplying a negative by a positive the answer is negative (-3) x 4 = -12
Calculate: Calculate:
(-6) + 10 4 x (-6)
= 4 = -24
Calculate: Calculate:
(-8) – (-5) (-15) x (-3)
= -8 + 5 = 45
= -3
Calculate: Calculate:
12 + (-5) (-12) x 6
=12 – 5 = -72
=7
-2 -1 0 1 2 3 4 5
Order of Operations - BODMAS
BODMAS is the acronym we teach in maths to enable pupils to remember the
right sequence for carrying out mathematical operations.
Scientific calculators use this rule but basic calculators only do the order the
sum is typed in so be careful!
What do you think the answer to 2 + 3 x 5 is?
Is it: (2 + 3) x 5 or 2 + (3 x 5)
= 5 x 5 = 2 + 15
= 25 = 17
We need to use BODMAS to get to the right answer.
Bracket work Of/Others Divide Multiply Add Subtract
So according to BODMAS, multiplication gets done before add therefore 17 is
the correct answer from above.
‘O’ is for of e.g. ½ of 14, or order e.g. 23
Sometimes you might read BOMDAS – this is the same as x ÷ can be swapped
or sometimes BIDMAS where the I means index instead of order.
WORKED EXAMPLES
1. 10 + 2 x 7 BODMAS 2. 12 – 10 ÷ 2 BODMAS
= 10 + 14 = 12 – 5
= 24 = 7
3. ½ of (4 x 5) – 3 BODMAS 4. 4 + 23 x 3 BODMAS
= ½ of 20 – 3 = 4 + 8 x 3
= 10 – 3 = 4 + 24
= 7 = 28
NOTE: MULTIPLICATION AND DIVISION HAVE EQUAL PRIORITY AND
ADDITION AND SUBTRACTION HAVE EQUAL PRIORITY BUT BOMDAS,
BOMDSA, BODMSA DON’T SOUND RIGHT HENCE WE STICK TO BODMAS!
EXAMPLES OF OTHER SUBJECTS WHO USE NUMBER AND NUMBER
PROCESSES:
Languages – teaching numbers and giving sums in
French and German.
PE – keeping scores.
IT – in spreadsheets.
Music – beats to the bar, intervals between notes.
TECH – in drawing with ± for error. Geography – climate graphs,
negative numbers on tundra
graphs.
History – timelines.
HE – reading scale to set the oven.
Science – recording data.
Fractions – Non Calculator
At Second Level we expect pupils to be able to:
calculate common fractions of 1 or 2 digits e.g.
2
1of 8 = 4
5
1 of 35 = 7
10
1 of 90 = 9
3
1 of 39 = 13
calculate common fractions e.g.
3
2of 9 = 6
5
3 of 35 = 21
10
3 of 90 = 27
At Third and Fourth Levels we expect pupils to:
work with equivalent fractions e.g. 10
6=
5
3
use equivalences of widely used fractions and decimals e.g. 3
0.310
calculate widely used fractions mentally e.g. 2
1,
10
1,
10
3 , 5
3……
use equivalences of all fractions, decimals and percentages 3
0.310
= 30%
add, subtract, multiply and divide fractions.
Vocabulary:
Numerator – number on the top.
Denominator – number on the bottom.
Rule for calculating a fraction:
divide by denominator then multiply by numerator
Some pupils find it easier saying divide by bottom then multiply by top
but try and encourage them to use the proper vocabulary.
WORKED EXAMPLES
Add and Subtract Multiply Divide
If denominators are
the same just
add/subtract the
numerators.
10
7 -
10
4
= 10
3
If denominators are
different, find
common denominator
first, then
add/subtract the
numerators.
=
If you have whole
numbers work with
them first.
12
1+ 2
5
4
=310
5 +
10
8
=310
13
=410
3
Multiply numerators together
then multiply denominators
together.
4
2 x
5
3
= 20
6
= 10
3
Sometimes pupils say
“top x top, bottom x bottom”
but again try to get them to use
the correct vocabulary.
Cancelling first if you can
before you multiply:
5
3 x
8
25
= 5
3 x
8
25
= 8
15
Change ÷ to x then invert
the second fraction.
4
3 ÷
5
2
=4
3 x
2
5
= 8
15
If you have mixed
fractions, change them to
top heavy first then follow
diving process.
33
1 ÷ 1
5
2
= 3
10 ÷
5
7
= 3
10 x
7
5
=21
50
5
6
X3
1 1
2 3X2
3 2
6 65
1
Fractions – Using a Calculator
From Third level onwards we also expect pupils to be able to use their
fraction button on their calculator for adding, subtracting, multiplying and
dividing fractions.
The following guide is for the calculator model fx-83GT PLUS as this is the model we
sell in the Maths department but most fractions buttons work in a similar manner.
WORKED EXAMPLES FOR fx-83GT PLUS
8
1+
6
5
Press button, then type in: 1 8 + 5 6 = 24
23
35
2 - 1
4
3
Press shift button, then type in: 3 2 5 - shift 1 3 4 = 20
33
Decimal Fractions
When calculating adding, subtracting and dividing sums, the decimal points
should be lined up in a column.
When multiplying or dividing decimals by 10, 100, 1000 etc… we talk about
moving up (for multiply) and down (for divide) the HTU columns. The number of
columns you move depends on how many zeros are in the multiplier e.g. x10
move up one column, ÷100 you move down two columns (see measurement notes).
When multiplying by other numbers, decimal points need not be in line. Multiply
as if whole numbers, then count number of figures in total after the decimal
points and put same amount of numbers after decimal point in the answer.
When dividing a decimal by a decimal, multiply both numbers you are working
with by 10, 100 or 1000, so that you always divide by a whole number.
When talking about money in pounds and pence it has to be to two decimal
places.
WORKED EXAMPLES
1. 46 + 2.8 + 0.23 2. £7.1 0 – £1.84
46.00 7. 1 0
2.80 - 1. 8 4
+ 0.23 £5. 2 6
49.03 1
3. 2.3 x 10 4. 2.4 x 23.7
(do 24 x 237)
2.3 3 moves up one column
=23.0 can put zero where 3 was 23.7
or leave as 23 x 2.4
948
4740
56.88
4. 0.6944 ÷ 0.08
Multiply both numbers by 100 so you are dividing by whole number to get:
69.44 ÷ 8=
8.688 69.44
Fill in gaps
with 0’s so
each number
is to 2
decimal place
0 1 6 1 1
2 numbers in
total after
decimal point
same in
answer
Percentages – Non-Calculator
At Second Level we expect pupils to be able to:
calculate common percentages of 1 or 2 digits by changing them first into the
equivalent fraction e.g.
50% of 18 10% of 50 25% of 36 75% of 20
= of 18 = of 50 = of 36 = of 20
= 9 = 5 = 9 = 15
At Third and Fourth Levels we expect pupils to:
calculate 20%, 1%, 333
1 %, 5%, 17
2
1 % by changing them first into the
equivalent fraction and use combinations to find other amounts, e.g.
1
25%4
1 1
33 %3 3
1
1%100
150%
2
2 266 %
3 3
110%
10
375%
4 5% 10% 2
12 % 5% 2
2
be able to convert between fractions, decimal fractions and percentages and
decide which equivalence is best for their working.
WORKED EXAMPLES
Find 36% of £250
10% = £25 (ie 10
1of 250)
30% = £75 (10% x 3)
5% = £12.50 (10% 2)
1% = £2.50 (10% 10 or 100
1of 250)
36% = £90 (answers for 30% + 5% + 1%)
Express two fifths as a percentage
2 4 40
40%5 10 100
(always want to get denominator multiplied up to 100)
Percentages – Non-Calculator continued
You buy a car for £5000 and sell it for £3500, what is the percentage loss?
Loss = £5000 - £3500 = £1500
% loss = original
difference
=5000
1500
= 50
15
= 100
30
= 30 % So percentage loss is 30%
A TV has a price tag of £350. It is now in a ‘15% off’ sale.
What is the new price?
10% of 350 = 35
5% = 17.50
so 15% = 35.00
+17.50
52.50
14 9
New price = 23510.10 0
– 5 2 .5 0
297 .5 0 Hence new price is £297.50
Percentages – Using a Calculator
At Second Level we expect pupils to be able to:
calculate common percentages of 1 or 2 digits by changing them first into the
equivalent decimal fraction e.g.
50% of 196 25% of 136
= 0.5 x 196 = 0.25 x 136
= 98 = 34
At Third and Fourth Levels we expect pupils to:
calculate 27%, 1%, 32%, 2%, 17 % by changing them first into the equivalent
decimal fraction be able to convert between fractions, decimal fractions and percentages and
decide which equivalence is best for their working.
WORKED EXAMPLES
Find 32% of £250
= 0.32 x 250
= £80
Calculate 672
1% of 425m to the nearest cm.
= 0.675 x 425
= 286.875
= 286.88m
Calculate the percentage profit on buying a painting for £35,000 and selling it
for £42,500.
% profit = difference x 100
original
= 42500 – 35000 x 100
35000
= 7500 x 100
35000
= 21.4% profit (1d.p.)
IT IS BETTER TO AVOID THE PERCENTAGE BUTTON
ON THE CALCULATOR AS IT CAN CARRY OUT DIFFERENT FUNCTIONS
BASED ON THE CALCULATORS MANUFACTURER.
Biology talk about % change but
working is still the same.
Ratio and Proportion
At Third and Fourth Level we expect pupils to be able to:
know ratios are used to compare different quantities
simplify ratios
know a ratio in which one of its values is ‘1’ is called a unitary ratio e.g. 1:2
if sharing money in given ratios, pupils must
1. Calculate the number of shares by adding the parts of the ratio
together
2. Divide the given quantity by the number of shares to find the value of
one share
3. Multiply each ratio by the value of one share to find how the money has
been split.
WORKED EXAMPLES
1. The ratio of cats to dogs in an animal shelter is 4:7. If there are 35 dogs in
the shelter, how many cats are there?
Cats Dogs
4 7
20 35
So there are 20 cats.
2. £35 is split between Jack and Jill in the ratio 3:2.
How much does Jack receive and how much does Jill receive?
Number of shares = 3 + 2 so 5 shares in total
Value of 1 share = £35 ÷ 5
= £7
Jack’s share = 3 × £7
= £21
Jill’s share = 2 × £7
= £14 (check by adding the values of the
shares: £21 + £14 = £35)
PUPILS SHOULD ALWAYS BE ENCOURAGED TO
CHECK THEIR ANSWERS BY ADDING THE VALUE OF THE SHARES.
X 5 X 5
What do you multiply
7 by to get 35?
Multiply 4 by the same
Number.
EXAMPLES OF OTHER SUBJECTS WHO USE FRACTIONS, DECIMAL
FRACTIONS AND PERCENTAGES:
PE - 4
1,
2
1and
4
3turns in pivoting. TECH – scales in orthographic drawings.
Geography & Modern Studies – percentages to create graphs.
Science – problem solving, investigations and graphs.
Percentage change in mass.
HE – calculating 2
1 measures for
2
1 portions.
Money
At Second Level we expect pupils to be able to:
understand the meaning of profit and loss and be able to calculate that
value.
At Third and Fourth Level we expect pupils to be able to:
calculate percentage profit/loss
calculate interest
exchange £’s into foreign currency and back again
calculate what situation is best value for money.
WORKED EXAMPLES
Calculate the profit if you bought a bike at £120 and sold it on for £155.
Profit = 155
-120
£ 35
My bank gives me an interest rate of 4% p.a. I deposit £680 in my account for
one year.
How much interest will I receive?
4% of 680
= 0.04 x 680 (4 ÷ 100 = 0.04)
= 27.2
= £27.20 interest
A bank gives an interest rate of 2.3% p.a. I deposit £1600 in my account and
leave it there for 3 years.
What will the balance in my account be in 3 years time if I don’t take any
money out?
102.3% of 1600 over 3 years
= 1.0233x 1600 (102.3 ÷ 100 = 1.023)
= £1712.96
This method is referred to as the short compound interest method
rather than doing the calculation for each year.
EXAMPLES OF OTHER SUBJECTS WHO USE MONEY:
Languages – explain about various ex-currencies
in Europe and do Euros in more detail.
TECH – theory of plastics.
Modern Studies – allocation of course resources in
relation to council funding.
Business studies – financial education.
HE – calculating the cost of making dishes.
Time Calculations
At Second Level we expect pupils to:
read timetables and schedules to plan activities
convert between the 12 and the 24 hour clock and know when
to write am/pm and hrs
calculate duration in hours and minutes by counting on the required time.
At Third and Fourth Level:
convert between hours and minutes (multiply by 60 for hours into
minutes)
recognise fractions of hours e.g. 15min = 0.25hrs
convert between minutes and hours (divide by 60 for minutes into a
decimal hour). See measure for more detail.
WORKED EXAMPLES
Change 3.15pm into 24 hour time.
3.15 + 12hours = 1515hrs
Change 0845hrs into 12 hour time.
0845hours = 8.45am
How long is it from 0755 to 0948?
0755 0800 0900 0948
(5 min) + (1 hr) + (48 min)
Total time is 1 hr 53 minutes
Change 27 minutes into hours
27 min = 27 ÷ 60 = 0.45 hours
EXAMPLES OF OTHER SUBJECTS WHO USE TIME:
Languages – teach pupils to tell time in
German and French.
PE – discussion about time spent on
leisure/exercise and its importance.
Time swimming and running tasks.
Science – physics units on forces.
HE – calculating how long food
takes to cook.
Measurement
At Second Level we expect pupils to be able to:
take part in practical tasks involving timed events
be able to measure an object in mm, cm and m and 2
1m
use different methods to find perimeter, area and volume of simple shapes.
At Third Level onwards we expect pupils to:
Convert between:
mm cm (divide by 10 to convert from mm to cm and multiply by 10 to
convert from cm to mm )
cm m (divide by 100 to convert from cm to m and multiply by 100 to
convert from m to cm)
m km (divide by 1000 to convert from m to km and multiply by 1000 to
convert from km to m)
g kg (divide by 1000 to convert from g to kg and multiply by 1000 to
convert from kg to g)
ml l (divide by 1000 to convert from ml to l and multiply by 1000 to
convert from l to ml)
use the link between speed, distance and time to carry out related tasks.
From decimal work pupils should be aware that when they:
x 10 the numbers move up one column
x 100 the numbers move up two columns etc
÷ 10 the numbers move down one column
÷ 100 the numbers move down two columns etc
In practice, many pupils find it easier to see that the decimal point moves
the appropriate number of places but mathematically this is wrong.
PLEASE DO NOT TALK ABOUT ADDING ON ZEROS WHEN
MULTIPLYING BY 10, 100 ETC AS IT CAN CAUSE CONFUSION
WHEN PUPILS WORK WITH DECIMALS
E.G. 3.7 X 10 DOES NOT EQUAL 3.70
THE SAME GOES FOR TAKING ZEROS OFF WHEN DIVIDING,
PLEASE TALK ABOUT NUMBERS MOVING COLUMNS.
H T U . th
3 . 2 x 10
= 3 2
WORKED EXAMPLES ON PERIMETER, AREA and VOLUME
Calculate the perimeter of the rectangle
P = 14 + 7 + 14 + 7 or P = (2 x 14) +( 2 x 7)
= 42cm = 28 + 14
= 42cm
Calculate the area of these shapes:
A = l x b A = 2
1x b x h
= 9 x 6 = 2
1x 22 x 5
= 54cm2 = 55m2
WORKED EXAMPLES ON SPEED, DISTANCE AND TIME:
Speed = Distance Distance = Speed x Time Time = Distance
Time Speed
or pupils can use the triangle:
Speed = Distance = Time =
To change minutes into a decimal hour you do minutes .
60
To change decimal hours back to minutes you do decimal hour x 60.
14cm
7cm
Perimeter is
the path
around the
outside of a
shape.
9 cm
6cm
22m
5m
D
D
S S T T
Calculate how far a jogger travelled jogging at 8 mph for 22
1hours.
D = S x T
= 8 x 2.5
= 20 miles
Calculate the average speed of a car that travelled 238 miles in 3 hrs 45 mins.
S = D 3 hrs 45 mins : 3 + 45 = 3.75 hrs
T 60
S = 238
3.75
S = 63.5mph (1d.p.)
How long did it take a cyclist to cycle 180km at 29km/hr?
T = D
S
T = 180
29
T = 6.2 hrs (1d.p.) 6.2hours = 6hrs + (0.2 x 60)
= 6hrs 12minutes
BE AWARE THAT IN SCIENCE THEY USE VELOCITY (v) INSTEAD OF SPEED,
DISTANCE (d) AND TIME (t).
EXAMPLES OF OTHER SUBJECTS WHO USE MEASURE:
TECH – measuring length and breadth of materials.
Art & Design – scaling up images from 1cm to 5cm using a grid.
PE - Measuring for long jump/high jump. Nat West athletics tasks.
Science – measuring data in
experiments. Pressure/density
calculations for area and volume.
Friction.
Geography – record
and observe weather
data.
HE – measuring
out ingredients.
Data Analysis
Definitions
Continuous Data – can have an infinite number of possible values within a
selected range e.g. temperature, height and length.
Discrete Data – can only have a finite or limited number of possible values.
Shoe sizes are an example of discrete data since 37 and 38 mean
something, however size 37.3 does not.
Non-Numerical Data– data which is non-numeric e.g. favourite animal,
colours of cars.
At Second Level we expect pupils to be able to:
carry out surveys, collate, organise and communicate results.
At Third and Fourth Level we expect pupils to be able to:
carry out surveys, collate, organise and communicate results using
technology
calculate different averages of a data set
i.e. calculate the mean
find the median (middle value of an ordered list) of a data set
find the mode (most common value) of a data set
calculate the measure of a data set
i.e. calculate the range.
Pupils should be aware that each graph needs to have:
A title
Appropriate even scale
Labels on both axes
A key if needed e.g. pictogram
In Second Level axes are mainly given to pupils and they just need to complete the
graph but in Third Level and Fourth Level pupils are expected to set up their own
graph and think of an appropriate scale if not given.
TYPICAL GRAPHS PUPILS SHOULD BE FAMILIAR WITH
Pictogram Bar graph*
Class 1A’s shoe size
Shoe Size
Fre
quen
cy
3.5 4 4.5 5 5.502468
1012
Line graphs
Umbrella sales
*A Histogram is similar to a bar graph but there are two differences:
1) Bar graphs are equally spaced whereas histogram bars sit together.
2) Bar graphs display discrete data whereas a histogram displays continuous data.
Sometimes you do see bar graphs without the spaces but this is bad form.
Vanilla
Chocolate
Strawberry
Key: each =50 people
Favourite ice-cream
0 5 10 15 20 25 30
Time (sec)
10
20
30
40
50
60
70
80
90
100
Dis
tanc
e (c
m)
Exercise and Pulse Rates
Puls
e R
ate
in b
eats
per
min
ute
Time in minutes
0 12 24 36 48 60
16
32
48
64
80
96
112
128
144
160
Mabel
Albert
Exercise and pulse rate
Number of umbrellas
Cos
t in
£’s
Pie Charts
At Second Level pupils can be asked
‘What fraction of the pupils like crisps?’
or ‘How many pupils like crisps?’
At Third Level onwards pupils can be asked to
draw a pie chart.
Favourite colour
Colour Frequency Angle
Purple 5 20
5x 360° = 90°
Yellow 6 20
6x 360° = 108°
Blue 7 20
7 x 360°= 126°
Red 2 20
2 x 360°= 36°
Total 20 Total = 360°
Favourite colour
Scatter graph
A scattergraph allows you to compare two quantities. It allows you to see if
there is a correlation (connection) between the two quantities. Correlation can
be positive, negative or there may be no correlation.
Favourite snack - results from
28 pupils
Crisps
Purple
Yellow
Blue
Red
50 55 60 70 75
1.5
1.6
1.7
1.8
Hei
ght
(met
res)
Weight (kg)
WORKED EXAMPLES
The result of a survey of the number of pets pupils owned is given below:
6, 3, 4, 4, 5, 6, 7, 4, 8, 3
Mean = (6 + 3 + 4 + 4 + 5 + 6 + 7 + 4 + 8+ 3)
10
= 50
10
= 5
Median (the middle of ordered set) : 3, 3, 4, 4, 4, 5, 6, 6, 7, 8
= 4.5
Mode (most common) = 4
Range (highest – lowest) = 8 – 3
= 5
PLEASE NOTE IN SCIENCE RANGE CAN BE GIVEN AS ‘BETWEEN 3 AND 8’
RATHER THAN THE CALCULATION AND ANSWER.
EXAMPLES OF OTHER SUBJECTS WHO USE DATA ANALYSIS:
English – in simple form.
Music – project, comp & performance.
TECH – design research project work. IT – interpreting data.
Reading and interpreting drawings.
PE – research of work on internet, viewing discussion.
Science – project work, practical investigations.
Modern studies – information project on Afghan war.
Geography – fact file on Japan.
Climate graphs.
Ideas of Chance and Uncertainty.
At Third Level we expect pupils to be able to:
give a statement to describe the probability of an event happening
calculate the value of the probability of an event happening.
Statements used:
Impossible unlikely even chance likely certain
Values:
Probability is always expressed as a fraction:
P (event) = number of favourable outcomes
total number of possible outcomes
WORKED EXAMPLES
Q: What is the probability if today is Wednesday then tomorrow is Thursday?
A: Certain
Q: What is the probability of tossing a head on a coin?
A: P(H) = 2
1
Q: What is the probability of picking an ace card from a normal pack of cards?
A: P(ace) = 52
4=
13
1
EXAMPLES OF OTHER SUBJECTS WHO USE IDEAS OF CHANCE AND
UNCERTAINTY:
Modern Studies – crime law and order.
History – causes of industrialisation.