**QTS Professional Skills Test - Numeracy**

**General advice**

**Mental Arithmetic**

Ratio and proportion

**Q.T.S. test overview**

Sadly, the tests do not take place here...

Percentage change

Fractions

To simplify fractions, you divide the numerator (top number) by the denominator (bottom number) by the same prime factors (2,3,5,7) to give the equivalent fraction.

E.g. Cancel 6 to its lowest terms

14

6/2 = 3

14/2 = 7

Simplify these to their lowest terms:

32 18 45

36 48 75

Special Arrangements

These are available for students who need them.

The following arrangements are available:

25% and 50%* extra time

on-screen spelling questions in literacy tests*

on-screen mental arithmetic questions in numeracy tests*

paper-based tests (including larger print format)*

*Need to complete an application

Per cent and percentage change

A per cent (%) is a special case of a fraction where the denominator is always 100. For example:

60% = 60 = 6 = 3

100 = 10 = 5

A per cent can be expressed as a decimal by dividing the numerator by 100 i.e. moving the decimal place two places:

75% = 0.75

Mucking about with fractions

Where do they happen?

The tests take place in Pearson Centres around the Country.

When you register to book your Skills Tests, you will have a choice of local test centres.

Saturday appointments are available but be warned - they do go very quickly as all ITT candidates are required to complete their QTS tests over the summer

Why do I need to complete them?

All I.T.T. Programmes now require applicants to complete Q.T.S. Skills tests prior to starting the course.

The aim of them is to assess your literacy and numeracy skills within the professional remit that you will be expected to work in

Where do they happen?

All Q.T.S. skills tests take place in Pearson test centres across the UK.

When you register online to book your skills tests, you will be asked to choose your test centre.

Saturday tests are available but be aware all I.T.T. applicants will be completing theirs over the summer.

What is the test environment like?

You MUST arrive 20 minutes beforehand to hand in your copies of identification

All your items will be placed in a locker and you are not permitted to take anything into the testing area

You will be given your result straight after the exam

What is the structure of the exam like?

The entire test is 48 minutes long

The number of marks available range is 28 (12 mental arithmetic and 16 on screen)

There are currently 2 sections to test

The current pass mark is approximately 63% but this depends on the difficulty of the exam

The exam is the equivalent of a grade B at GCSE

Applying for special arrangements

All special arrangements with the exception of an extra 25% must be applied for with an application.

You will need to provide supporting evidence from a professional.

If you need to book a test with special arrangements, you CANNOT do it online, you would need to contact

0845 450 8867

And if I don't pass?

Don't worry - yet.......

You have 3 attempts at each paper. The first attempt is free, the 2 subsequent attempts are £19.25 each

You are also told which areas you need to work on to improve on your exit slip

Resources

Handouts from today

Common misspellings

Commonly confused words

Homophones

Online Oxford Spelling Test

http://www.oxforddictionaries.com/spelling-challenge/

US VS TH3M

http://games.usvsth3m.com/maths/

(

There is also a literacy one available

)

MP3 files for the tests can be downloaded for free at www.koganpage.com/QTS

(

the files are at the bottom of the page

)

Quizup

Free app available from Apple or Android Store

https://itunes.apple.com/gb/app/quizup/id718421443?mt=8

https://play.google.com/store/apps/details?id=com.quizup.core

DfE Website

Contains practice papers

Guidance about content

Online practice materials

http://www.education.gov.uk/sta/professional

Book resources

Johnson, Jim, 2012, Passing the Literacy Skills Test, third edition, (Achieving QTS Series), Learning Matters Ltd.

Medwell et al, 2012, Primary English: Knowledge and Understanding, sixth edition, (Achieving QTS Series), Learning Matters Ltd

Tyreman, Chris 2012, How to Pass the QTS Numeracy and Literacy Tests, Koganpage.

Ratios are similar to fractions. They show how a number is divided into parts.

E.g. Divide 60 in the ratio 1:3

Method:

Work out the number of parts in the whole. In this case, 4 (1 + 3 = 4)

Work out the proportional parts, 1/4 and 3/4

Multiply the whole number (60) by the proportional parts

60/4 = 15

(60/4) x 3 = 45

**Group Activity!**

**Each team is given a problem to work out; each problem is different. You will have 6 minutes to work it out then you will have to present your answer to the rest of the class.**

Simplifying ratios

If you've grasped simplifying fractions, this should be pretty straightforward.

Ratios are simplified in a similar way to fractions; cancelling both sides by a common factor.

The ratio of boys to girls in a science class of 28 is 16:12. Express this ratio in its simplest terms.

16:12 = 8:6 = 4:3 so for every 4 boys, there are 3 girls.

Lack of Knowledge

This is the main reason students fail

Revise and practise, practise, practise.

You are expected to have GCSE grade B level knowledge to successfully complete this exam.

Pressure of time

The test lasts for 48 minutes with 12 of those minutes allocated to the mental arithmetic part.

This leaves 36 minutes for the longer questions.

Do not attempt to work every single equation out mentally, use the pen and paper to help you.

Maths phobia

A combination of the aforementioned stumbling blocks can lead to this.

A lack of knowledge and an inability to cope under pressure can led to a vicious circle.

Calculator Skills

You will not have a hand held calculator to work with. It will be an on-screen calculator.

It will also not be a scientific calculator so you will be unable to insert brackets.

Practising the online tests will help you get used to the calculator provided.

Inputting your answers

When typing numbers into answer boxes:

always give your answer as a number not words

do not enter any additional numbers, letters, spaces or symbols or your answer may be marked as incorrect

do not enter any zeros in front of your answer, eg enter 21 rather than 021 or 12.5 rather than 012.5

enter fractions using the 'forward slash' key, eg 'one-half' should be entered as 1/2

enter 24-hour clock times using a colon, eg 14:30

enter decimal numbers using a ‘full stop’ for the decimal point, eg 12.5

there is no need to type the units (ie £, pupils, %) if they are already specified

Coping with the anxiety

Revision and planning can help alleviate some of the pressure beforehand.

If you feel anxious during the exam, close your eyes, put down anything in your hands and take deep breaths, then open your eyes and try again.

**Don't be scared!!**

Addition

Right, let's start off easy.

Add together 547 and 142.

Subtraction

This can sometimes be a little difficult.

A nifty trick is to subtract more than you need (typically hundred or thousand) then add the difference back on.

E.g.

927 - 68 = 927 - 100 + 32 = 827 + 32 = 859

Multiplication

We can use the same method as before when we were adding; breaking it down into tens, hundreds e.t.c.

Multiply 532 by 3.

(500 x 3)+(30 x 3)+ (2 x 3) = 1500+90+6

Answer = 1596

Division

This is the trickiest beast of them all.

There are several ways to do this, again, there is no right or wrong way, it's just whatever works for you.

Two methods:

The 'old fashioned' way:

547

+142

689

OR

Break down into smaller values:

547 = (5x100)+(4x10)+7

142 = (1x100)+(4x10)+2

So..... (6x100)+(8x10)+(9)

Answer = 689

Old fashioned method

Place value

As before with the addition work. Break down the numbers into their place value e.g.

864/4 = (800/4)+(60/4)+(4/4)

= 200+15+1

= 216

Factorising

The following rules are helpful when dividing:

If the last digit is 0,2,4,6 or 8, it will divide by 2

If the last digit ends in 0 or 5, the number will divide by 5

If the last digit ends in 0, it will divide by 10

If the last two digits divide by 4, the number will divide by 4

You can break down (factorise) large numbers by dividing them by prime numbers. (A prime number being a number that is divisible by itself and 1)

Prime Numbers

The first six prime numbers are, 2,3,5,7,11 and 13.

Start with the smallest of these and continue with it if possible. Otherwise try the next one.

252 can be factorised as follows:

252/2 = 126

126/2 = 63

63/3 = 21

21/3 = 7

252 = 2 x 2 x 3 x 3 x 7

Divide 504 by 4

Adding and subtracting

Two steps:

make sure the denominators are the same

add the numerators together

e.g. 2 + 3 = 5

7 7 7

Multiplication and division

To multiply fractions all you do is multiply the two numerators together and the two denominators together. Then simplify.

e.g. 1 x 3 = 1 x 3 = 3 = 1

6 8 6 x 8 48 16

Division of fractions is similar, except the fraction on the right-hand side must be turned upside down then multiplied with the fraction on the left.

e.g. 1 / 3 becomes 1 x 8 = 8 = 4

6 8 6 x 3 18 9

BUT

If the denominators are not the same, you need to find the lowest common denominator.

e.g.

1 + 3

6 8

We know 6 and 8 multiply to give 48, but, this is not the lowest denominator.

1 = 8 3 = 18

6 48 8 48

These fractions are both divisible by 2, therefore,

4 + 9 = 13

24 24 24

Decimals and fractions

0

1

0.5

1/2

0.25

1/4

0.75

3/4

1/1000

0.001

0.125

1/8

0.375

3/8

Addition and subtraction of decimals

The decimal should be aligned

e.g. 0.68 + 0.062 + 0.20

Should be written as

0.680

0.062

0.200 +

0.942

Calculating percentage figures

To calculate a percentage figure, you multiply by the per cent expressed as a fraction or a decimal. For example:

Find 25% of 120

25% = 25/100 = 0.25; 0.25 x 120 =2.5 x 12 = 30 or

25% = 25 = 1 1 x 120 =/4 = 30

100 4 4

OR 120/4 = 30

Percentage change = change in value

original value x100

A school bus accelerates from 40mph to 60mph. What is the percentage increase in speed?

Percentage change = 60 - 40 x 100

40

= 20 x 100

40

=0.5 x 100

= 50%

Percentage decrease

A school mini-bus brakes from 60mph to 40mph. What is the percentage decrease in speed?

Percentage change = 60 - 40

60 x 100

= 20

60 x 100

= 1 = 33.3%

3

Question time!!

Tips for answer mental arithmetic questions

Each question is read out twice with no pause in between. You then have

18 seconds

to type your answer before the next is read out

Write down any numbers and attempt the question straightaway without waiting time for it to be read for second time

Do not continue with any question beyond the allotted time. Leave it and move onto the next question.

Most questions involve more than arithmetic process

there are no right or wrong methods. Your answers are marked by a computer

The context of the question is irrelevant

School dinners cost one pound and eighty-five pence each. A pupil pays in advance for a week's dinners. What is the correct change out of a ten pound note?

A school with nine hundred and fifty places has an occupancy rate of ninety-four per cent. How many more pupils could it take?

A school has two hundred and ninety boys and three hundred and ten girls. How many girls would you expect there to be in a representative sample of one hundred and twenty pupils?

An exam finished at twelve twenty-five hours having lasted one and three-quarter hours. At what time did the exam start?

In a sponsored run, a pupil completed twenty laps around a four hundred metre track. How many miles did he complete if one kilometre is equal to five-eighths of a mile?

In a secondary school with nine hundred pupils, four out of five own a mobile phone. How many pupils do not own a mobile phone?

A sponsored walk by five hundred pupils raised six thousand, nine hundred and fifty pounds for charity. What was the average amount raised per pupil?

A school trip to the Tate Gallery took two hours and fifteen minutes by coach, travelling at an average speed of forty miles per hour. How far away was the gallery?

A pupil gained thirty marks out of fifty in one Maths exam and sixteen marks out of twenty-five in a second Maths exam. What was the average percentage for the two tests assuming the weightings were equal?

What is sixty-two and one half per cent as a decimal fraction to one decimal place?

A school skiing trip costs seven hundred and twenty pounds per pupil with a fifteen per cent deposit. How much is the deposit in Euros if there are one point two five Euros to the pound?

Teachers at a school have four hours and twelve minutes contact time per day. What is the contact time per week?

Decimals and measurements

Algebra

Rounding up, rounding down

Sometimes the numbers you obtain from a calculation give a higher level of accuracy than is required for sensible answer.

e.g. 3.75 x 4.29 = 16.0875

To correct the answer, you need to shorten the number of decimal places (d.p.) to 1d.p. 2d.p. or 3d.p.

S.I. Units

Areas, borders, perimeters and volumes

Coping with the anxiety

Revision and planning can help alleviate some of the pressure beforehand.

If you feel anxious during the exam, close your eyes, put down anything in your hands and take deep breaths, then open your eyes and try again.

Not scary - just logical

BIDMAS

This is the order of working out problems:

B - Brackets

I - Indices

D - Division

M - Multiply

A - Addition

S - Subtraction

Rearranging formulas

For example:

x = y - z

treat the '=' sign as a mirror. Whatever you do to one side, you must do to the other.

1. Make z the subject

2. Make y the subject

More useful than you think.....

Typical examples of where they come in useful is are: temperature conversion, speed, distance and time, ration and proportion, and VAT and income tax.

Calculation time!!!

Work through the worksheet.

Averages

Mean

Median

Mode - watch out for sneaky bi-modals...

Why and how??

Rules:

If the number to the right of the decimal please you are rounding is:

5 or above, you increase the number in the decimal place by 1

below 5, it remains the same

Important -

only round up at the end of a calculation NEVER DURING a calculation

16.0875 to 3 dp = 16.088

16.0875 to 2 dp = 16.09

16.0875 to 1 dp = 16.1

16.0875 to 0 dp = 16

Weight

The basic unit of weight is the gram (g)

Name Symbol

kilogram kg

gram g

milligram mg

1kg = 1000g 1g = 1000mg

Length

The basic unit of length is the metre (m). These are the four lengths you may encounter:

Name Symbol

kilometre km

metre m

centimetre cm

millimetre mm

1km = 1000m; 1m = 100cm; 1cm = 10mm

Volume

Quantities of fluids (liquids and gases) are measured in litres (l) and millilitres (ml) where 1l = 1000ml.

Remember!

When working out sums with metric units, it is important that all the numbers have all the same units. For example:

Add 5cm to 2m

2m + 5cm = 2 + 0.05 = 2.05m

Area of square = side of length x side of length

Area of a rectangle = l (length) x b (breadth)

Area of triangle = 1/2 x b (base) x h (height)

Area of circle = r

2

Perimeters

Add up all the distance around the shape for straight shapes' - see example on white board

For circles, use the equation 2 r

Volumes

Measurements are generally in cubed units. To calculate:

Volume = area of front face x length

(9 + 11) x 2 = 20 x 2 = 40

Without brackets, this calculation becomes

9 + 11 x 2 = 9 + 22 =31

Letters can also take the place of numbers to describe the 'general case' of something.

The first skill of algebra involves substituting numbers for the letters, for example.......

If x = 5 and y = 7 find:

x + y

2x - y

x +3y - 3

2

Now, let's put the two principles together....

Find x if 3x + y =z

Step 1: Subtract y from both sides

3x = z-y

Step 2: Divide both sides by 3

x = z-y

3

When calculating the median, always add 1 and divide by 2.

Range

The range measures the spread of the data; the maximum value minus the minimum value. For example:

5 5 7 8 3 7 4 1 2 = 8 - 1 = 7

Weighted averages

In a weighted average test, some scores count more than others towards the overall result. Weighted averages are often used in University coursework

Proper easy once you know how.......

Step 1: Convert each mark into its percentage

Step 2: Multiply each percentage mark by its weight

Step 3 : Add the results

E.g. A student scores 16 out of 20 in Test 1 and 32 out of 50 in Test 2. If the tests are weighted 25% for Test 1 and 75% for Test 2, what is the overall percentage?

1. 16/20 = 80%; 32/50 = 64%

2. 80 x 25% = 20; 64 x 75% =48

3. 20 + 48 = 68%

Statistical analysis.... A crash course

Pie charts

Bar charts

Line graphs

Histograms

Cumulative frequency graphs

Box and whisker plots

Upper range

Lower range

Median

Upper quartile

Lower quartile

**GOOD LUCK!!**