Passing the QTS Numeracy Test
Teachers notes
There are five videos in this series.
1. Introduction to the Test
2. Preparing for the Test
3. Mental Arithmetic
4. Interpreting Statistics
5. General Arithmetic
 1. Introduction to the Test
In the year 2000, the government decided that all newly qualified teachers needed to
demonstrate a good understanding of basic maths, so they introduced a skills test to prove it,
which is run by the Training and Development Agency for Schools (TDA). The bad news is that
trainee teachers have to pass this test before they can qualify as a teacher, but the good news
is that they can take it as many times as they need to pass it. Despite the high levels of anxiety
that seem to be associated with these tests, around 80% of students pass it first time, and
nearly all candidates pass it eventually.
It’s worth realising that the QTS Numeracy skills test doesn’t test the maths you’re going to
teach in the classroom, but the functional maths you’ll need as a practising teacher, such as
when you’re scheduling school trips, planning timetables, and particularly, when you’re tracking
pupil performance.
Maths specialists shouldn’t find the content of the test too difficult, but the style of the test could
come as a surprise, so it’s still worth doing some preparation. And for those who waved
goodbye to maths with a Grade C GCSE some years ago, hoping they’d never need it again, it’s
a good idea to do some serious revision.
 There’s more information about how to prepare for the skills test in the second video of the
series.
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So what’s the test like?
The actual skills test is all done online at a computer. This may seem awkward at first, but
computer-based testing is becoming more common, so it’s important for teachers to have the
same experience as their pupils. The test isn’t done on your own computer nor on one at your
college, but at a dedicated independent test centre. In many places it’s the same centre where
people go to take their driving theory test.
Although it’s an on-screen test, you can use paper and pencil to make notes and do workings,
and there are various arrangements for candidates with special needs, including extra time and
paper-based options. There’s more about this on the TDA website at
http://www.tda.gov.uk/skillstests/specialarrangements.aspx
After taking the test, you get the result straight way - a pass or a fail. In the case of a pass,
there’s no more detail of which questions you got right or wrong, but with a fail, some simple
printed feedback is provided to indicate areas that need further work before you sit the test
again.
The test itself is in two sections. There’s a mental arithmetic section with 12 questions, and a
section that covers both ‘interpreting and using statistical information’ and ‘using and applying
general arithmetic’ with 16 on-screen questions. So there are 28 questions altogether and each
one is worth one mark, all to be done within 48 minutes. The pass mark is about 60 percent,
though this is adjusted slightly from year to year to compensate for the changing difficulty of the
questions. The key fact is that you don’t have to get everything right. In fact about 17 right
answers out of the 28 will usually see you through.
The test starts with the 12 mental arithmetic questions. In this part of the test, a pre-recorded
voice reads each question, and then reads it again. Then there’s a gap of 18 seconds to work
out the answer and enter it in the box on the screen. At the end of the 18 seconds the on–
screen answer box disappears and the next question starts playing. It’s important to realise that
the mental arithmetic test can’t be stopped or rewound - it just keeps going. You can’t use a
calculator, but you can make notes, so you don’t have to do everything in your head.
 There’s more about the mental arithmetic part of the test in the third video of this series.
The next section of the test has a mixture of 16 questions on general arithmetic and interpreting
statistics. These test your ability to apply arithmetic to school scenarios, such as school trips,
test results, timetable planning and budgets, as well as how to make sense of tables of figures,
graphs and charts - the kind of educational data you’re likely to come across once you start
teaching. In this part of the test you can use a calculator, but it has to be the one provided on
the screen. There’s a ‘calculator’ button and when the calculator pops up, you can use the
mouse to move it to where you want it on the screen. You can do any workings on paper, but
the final answer has to be entered on the screen, which can be done in a variety of ways.
In some questions you click on the one correct answer from a multiple choice list, and with
others you need to click on one or more correct answers. In some questions you type your
answer in the box, and in others you point and click on the correct area of say, a table or graph.
In this section you can work at your own pace, ‘flagging’ a question and moving on to the next if
you get stuck, and then going back to those you’ve flagged to have another at them. It’s
important not to get bogged down with one question and then run out of time later, so plan to
spend no more than about two minutes on each question.
 There’s more about how to deal with interpreting statistics questions in the fourth video in this
series, and more about general arithmetic questions in part five.
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 2. Preparing for the Test
When you’re doing your teacher training, you’re expected to organise taking and passing your
skills tests yourself. Although you can take the test as many times as you need to pass it, it’s a
good idea to start making arrangements to take it as soon as you can. Then if you pass, it’s all
over, and you can forget about it, and if you don’t pass, there’s more time to do it again without
getting in a panic.
Because this test is so important - you can’t become a practising teacher without passing it - it’s
well worth preparing for. Your college might provide numeracy support sessions, or maybe you
can arrange some informal help from fellow students who are maths specialists. There are also
books you can buy, with explanations, worked examples and sample questions.
But perhaps the most useful support is on the TDA web site itself at
http://www.tda.gov.uk/trainee-teacher/qts-skills-tests/numeracy.aspx
Here, there’s an explanation of the purpose of the test and what’s in it, and a basic ‘glossary’ of
the mathematical terms and topics you should be familiar with.
The most useful feature on the TDA site is the practice materials. These are sample on-line
tests, similar to the real thing, which you can work through and get a mark at the end. See
http://www.tda.gov.uk/skillstestsonline/numeracy/launch.html. These sample tests also have
useful support options, which you can set up before you run the test. There’s a ‘guide me’
option that gives you some hints, and a ‘show me’ option that explains the answer, and the ‘try
me’ option, which runs the test with no extra information.
Working through the sample tests using these support tools is a good way to revise your
mathematical knowledge as well as becoming more familiar with kind of questions you’re likely
to get. Even if you’re a maths specialist, it’s not a good idea to go into the test unprepared.
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 3. Mental Arithmetic
For many trainee teachers, the mental arithmetic section is the most stressful part of the whole
test - and it’s the first thing you have to do. It’s easy to develop a mental block about mental
maths because, unless you’re a maths specialist, you’re probably out of practice and haven’t
used this skill seriously since primary school.
The actual maths in these questions isn’t difficult - it’s doing them against the clock that seems
to bother people. But doing simple maths efficiently and quickly is a skill you’ll need as a
teacher, so it’s important to try and overcome your phobias with preparation and some simple
strategies.
There are 12 mental arithmetic questions, and a pre-recorded voice reads each question twice.
Then there’s a gap of 18 seconds for you to work out the answer and enter it in the box on the
screen. At the end of the 18 seconds the on–screen answer box disappears and the next
question starts. It’s important to realise that you can’t stop or rewind the mental arithmetic test it just keeps going. You can’t use a calculator but you can make notes and jottings, so you don’t
actually have to do everything in your head.
The first time the question is read out, it’s a good idea to write down the numbers. The second
time the question is read out, listen carefully while looking at the numbers and try to picture what
it’s about. Then in the 18 second gap, work out the answer - and when you’ve done that, don’t
forget to put it in the answer box.
If the next question starts before you’ve finished, abandon the question you were doing and
concentrate on the new one, otherwise you’ll just get left behind. If you don’t get it, just forget it!
If you’re secure with your times tables and have a reasonable grasp of arithmetic, these
questions shouldn’t be too difficult. You can write things down and work things out using
traditional written methods, but using a few of the mental maths short cuts that 10 year-olds are
familiar with in primary school will speed things up.
Like so many things in life, to improve a skill you need to practise it, so it’s well worth doing
some mental maths as you go about your day. Is that bus number divisible by three? Is this
restaurant bill correct? What change should I be getting? Is one large pack better value than
three small ones? What would I get with a 2.5% pay rise! Think of it as an exercise - like
athletes do before they compete.
There are practice tests on the TDA website that you can use to develop your skills.
See http://www.tda.gov.uk/skillstestsonline/numeracy/launch.html
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4. Interpreting Statistics
The statistics questions are probably the most unfamiliar for non-maths specialists. These
involve interpreting tables of figures and understanding graphs and charts, usually involving
pupil performance data.
You might ask why you need to know about scatter diagrams and box and whisker plots, but it’s
important to be able to interpret this kind of information when it’s presented to you in this way
during your teaching career. After all, this kind of information is about actual pupils and their
real achievements.
The statistics question generally ask you to interpret the data in some way and come to some
conclusions from it. The strategy these statistics questions is first to try and work out the ‘drama
behind the data’ and to see what story it’s trying to tell you about that cohort of pupils, for
example. To do this, look carefully at the headings of the tables and the axes of the graphs to
see what the table or graph is actually showing you. Then look at the numbers, bars or points to
see what trends and patterns you can see.
These questions are usually in several parts, so it’s vital to work through them step by step,
always checking back to make sure you’re answering the question they’re actually asking. In
the example shown in the video, it wasn’t too difficult to see from the graph that six pupils had
the same reading age as actual age, but the question wanted to know what proportion that was
of the whole class - as a decimal - to one decimal place!
In this section you can leave a question unfinished and go on to the next, and then go back
later, so it’s a good idea to allow about two minutes for each question and then move on.
As this is an online test, don’t forget to enter your answer on the screen. In some cases this
involves entering the numbers in a box, in others clicking one or more correct answer from a
multiple choice list, and in others pointing and clicking on the correct area of say, a table or
graph.
Practise looking at the graphs, charts and tables in newspapers and magazines and check out
what they’re trying to say, and there are sample statistics questions on the TDA website at
http://www.tda.gov.uk/skillstestsonline/numeracy/launch.html
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5. General Arithmetic
Most trainees find the general arithmetic questions the most straight-forward part of the
numeracy test. These involve applying normal arithmetic to school-based scenarios, such as
school trips, test results, timetable planning and budgets. While some of the scenarios may
seem a little far-fetched, there will be many occasions in your teaching career when you’ll need
to sit down and work out, for example, how much time you can give each pupil if you want them
all to read to you each day.
The problem some trainees have is decoding these ‘word questions’ to decide what maths they
need to use, so the first step is to work out what the question is actually asking.
As in the statistics section, these questions are in several parts, so you must work through them
carefully, step by step, always checking to be sure you’re answering the questions that’s
actually being asked.
One useful mathematical concept to revise is ratio and proportion. This comes up in many
guises, such as converting between fractions, percentages and decimals, or between one kind
of units and another, such as currency or distances. It also comes up when scaling amounts up
or down, such as in a recipe, scale drawing or map, or when calculating which is the better
value of two bulk purchases.
As this is an online test done on a computer, don’t forget to enter your answer on the screen. In
some cases this involves entering numbers in a box, and in others selecting one or more correct
answer from a multiple choice list.
Remember, in this section you can leave a question unfinished go on to the next, and go back
to it later, so it’s a good idea to allow about two minutes for each question and then move on.
There are more sample general arithmetic questions on the TDA website at
http://www.tda.gov.uk/skillstestsonline/numeracy/launch.html
Peter Evans
Malcolm Shay
October 2010
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