A guide for all staff and parents. - Brae High School · Order of Operations - BODMAS BODMAS is the...

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


subtract using decomposition i.e. exchanging one ten for 10 units or one

hundred for 10 tens etc when needed


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


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


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


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


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


(-8) – (-5) (-15) x (-3)

= -8 + 5 = 45

= -3


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


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


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


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


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


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


understand the meaning of profit and loss and be able to calculate that

value.


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


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.


carry out surveys, collate, organise and communicate results.


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.

A guide for all staff and parents. - Brae High School · Order of Operations - BODMAS BODMAS is the...

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