Entry Tests Guide
Mental Arithmetic
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INTRODUCTION
Schofield & Sims
How to use the Entry Tests Mental Arithmetic makes it easy for teachers to provide work for different abilities within a class or group, using two Entry Tests to help you select the right book for each pupil or class. Pupils working significantly above or below age-related expectations can work on the book best suited to their needs. This means that all pupils will be working at their own pace, giving you the time to support those who need your help, including those with additional needs or disabilities. Two Mental Arithmetic Entry Tests are available in this guide: • Entry Test A is suitable for lower Key Stage 2 and covers Mental Arithmetic 1 to 3 • Entry Test B is suitable for upper Key Stage 2 and covers Mental Arithmetic 4 to 6. Both Entry Tests are designed to help you establish the starting point for each pupil. You may wish to test all the class or, if you are already using the series, only those whose competency in mathematics you are unsure of.
Administering the Entry Tests Before administering the Entry Tests, ensure that you have a sharp pencil, a photocopy of the appropriate test and some spare paper for each pupil. Entry Tests can also be downloaded from our website: www.schofieldandsims.co.uk/free-downloads Explain to the pupil or the class the following points: • the purpose of the test is to make sure that the maths work they do on a daily basis is at a suitable level – not too easy or too difficult for them • only the individual and the teacher will know the results of the test • the test is not timed but is likely to take up to an hour • the questions are arranged to become increasingly difficult as they work through the test • there will come a point when they are unable to answer any more questions – and at this point they may read quietly so as not to disturb others who are still working • they should try to do their best. You may then distribute the Entry Test and tell pupils to start.
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INTRODUCTION
Mental Arithmetic Entry Test Guide
Marking the Entry Tests Use the Entry Test marking keys on page 8 to mark the test. One mark is given for each correct answer. Where a question has two parts, give half a mark for each part. The table below indicates which Mental Arithmetic book will be most suitable for each child, based on their Entry Test score.
Entry Test
Entry Test A
Entry Test B
Entry Test score
Next step
0–8
Begin with the Mental Arithmetic Introductory Book.
9–13
Begin with Mental Arithmetic 1.
14–18
Would benefit from working on Mental Arithmetic 1 for consolidation but, if confident, could start Mental Arithmetic 2.
19–28
Begin with Mental Arithmetic 2.
29–33
Would benefit from working on Mental Arithmetic 2 for consolidation but, if confident, could start Mental Arithmetic 3.
34–40
Begin with Mental Arithmetic 3.
41–45
Would benefit from working on Mental Arithmetic 3 for consolidation but, if confident, could start Mental Arithmetic 4.
46–50
Begin with Mental Arithmetic 4.
0–15
Take Entry Test A for more information or begin with Mental Arithmetic 3.
16–20
Begin with Mental Arithmetic 4.
21–25
Would benefit from working on Mental Arithmetic 4 for consolidation but, if confident, could start Mental Arithmetic 5.
26–29
Begin with Mental Arithmetic 5.
30–33
Would benefit from working on Mental Arithmetic 5 for consolidation but, if confident, could start Mental Arithmetic 6.
34–40
Begin with Mental Arithmetic 6.
41–50
Achieving well but, for consolidation, work on Mental Arithmetic 6.
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Schofield & Sims Mental Arithmetic
Name:
Entry Test A
Class/Set: Date:
Answer 1
Answer
Increase 6 by 5.
15 400 + 70 + 5 =
2 Name the month which is three
16 26 + 78 =
months after December. 3
20p + 30p =
4
Write this number in figures.
17 What number is added to 306
p
to make 376? 18 £3.00 – £1.80
£
4 tens 7 units 19 How many times smaller is 54
than 540?
5
63 – 7 =
6
4 + 4 + 4 + 4 + 4 + 4 =
7
×
20 28 March is the first day of a holiday
=
which ends on 6 April. How many days?
square has A equal sides and right angles.
21 What fraction of the whole strip is 8
Add 30cm to 40cm.
cm
9
rite the number that is 5 more W than 14 minus 9.
a shaded
a
b unshaded?
b
10 Two faces on a
cylinder are the same. What shape are they? 11 How much longer is 1m than 57cm?
22 How many Scores
cm
Jay
Emily
22
18
as their favourite animal?
7
13
tiger
9
9
12 How many children chose giraffe
more did Emily score than Jay?
giraffe monkey
23
Two children =
12 11 1 10 2
9 8 4 7 5 6
13 Write the two missing numbers
in this sequence. 0, 8, 16,
, 32,
1 5 1 5
1 5
1 5
1 5
T he circle is one whole one. How many fifths in four whole ones?
For use with Schofield & Sims Mental Arithmetic.
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min
, 48 24
14
3
ow many H minutes from the time on the clock to ten to six?
3 6 10 + 10 =
25 What is the missing number?
×6=8×3 26 1kg costs 45p. 200g costs
4
p. p © Schofield & Sims Ltd, 2016.
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Answer
Answer
27 Which of these angles is an
Favourite sport
40
acute angle?
ow many H votes are shown on this bar chart altogether?
6 W
4
Y
X
2
V
nearest kilometre. 1
nc e fo ot ba ll sw im mi ng
28 Write 4km 600m to the
da
te n
ni s
0
km
41 What is the missing number?
1
29 Add 4 of 20 to 8 of 48.
9×8=
× 12
30 Nine pieces of wire each 42 Each side of this
measure 6cm. Find the total length of the pieces in millimetres.
octagon is 0.6cm long. What is the length of its perimeter in millimetres? mm
mm
31 Divide 1m by 5. Answer
in centimetres
cm
32 Add three hundred to one thousand
43
and ten. Answer in digits. 33 Write these decimals in
How much is saved on each toffee apple by buying four at a time?
ascending order. 5.79
5.31
4.87
4.09
Toffee apples 51p each or 4 for £1.96
p
5.33 44 Write, in 24-hour clock format, the
correct time for each digital clock if 34 Write as £s the value of
fifty-nine 5ps.
£
a clock X is 16min fast
a
b clock Y is 35min slow.
b
35 The perimeter of a square is 60mm.
Find the length of one side.
mm
3 36 Write the
coordinates of A.
2
10 15
23 50
X
Y
45 Find the difference in grams
(
,
between 1.7kg and 2.3kg.
)
g
1 A 1
2
3
46 6.71 = 100
4
47 3 A square has
37 How many times larger than 35 is
a three hundred and fifty
a
b three thousand five hundred?
b
2 1 1
38
12 11 1 10 2
9
3
8 4 7 5 6
T his clock is half an hour fast. Write the correct time in digits using a.m. or p.m.
50°
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4
, )
90°
1
Y
of angle Y in degrees.
°
1
49 Find 2 of 5 2 .
17 8 10 – 10 =
For use with Schofield & Sims Mental Arithmetic.
3
48 Find the size
afternoon
39
2
vertices at (4, 0) (2, 0) (2, 2) and (x, y). What are the values of x and y? (
50 6 £4.08
5
£ © Schofield & Sims Ltd, 2016.
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Schofield & Sims Mental Arithmetic
Name:
Entry Test B
Class/Set: Date: Answer
1
200 – 96 =
2
Increase 250 by 13 of 90.
3
£50.00 – five 5ps =
4
5.07 × 100 =
5
TTH Th H
Answer 12 How many hours and minutes
from time X to time Y?
23 50
X
Y
£
13 5l ÷ 4 = U
ml ml
are given. Find the area of a both the sides
a
cm2
b both the ends
b
cm2
c
c
cm2
the top and bottom. top
6
Find
a the perimeter of this square
a cm
b its area.
b cm2
min
14 The measurements of the box
rite the number W shown on the abacus in words.
5cm
T
10 15
h
side
end
8cm
6cm
9cm
15 How many degrees in one-eighth 7
474 563 + 403 003 =
8
hich year is represented by the W Roman numerals MCMLXXXVII?
9
annah left home at 09:00. H She stopped for coffee at a café. How far from home was the café?
of a full turn?
°
16 Increase £8.50 by 10%.
£
17 Which of these are equivalent
to 80%? km
8 10
0.75 0.08
1 8
4 5
0.8
Distance from home in km
Hannah’s journey 20
18 0.07 × 8 =
15
19 Which of these shapes will have a
10
circular face when cut horizontally and a triangular face when cut vertically?
5 0
09:00
10:00
11:00
12:00
13:00
Time
3
sphere
10 A jug when 4 full holds 600ml.
How many millilitres does it hold 1
when it is 8 full?
cone
cylinder
20 Change this improper fraction
to a mixed number. 27 8
ml
21 What percentage of 24p is 6p?
11 Find the two missing numbers in
%
the sequence. 80, 8,
22 102 – 87 =
, 0.08,
For use with Schofield & Sims Mental Arithmetic.
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Answer
Answer
23 16 – 6 × 2 + 8 ÷ 2 = 24
36 What is the length in millimetres
£14.63 = 7
when an 11.5cm line is enlarged by a scale factor of 6?
£
25 Calculate the reflex angle AOC. A
37 How many thousandths
°
in 12 of 0.01?
B 108°
mm
6
38 7 ÷ 4 =
38° C
O
3
2
39 1 8 + 5 = 26 Harry missed the 08:48 train by
10min. How long did he have to wait for the next train at 10:25? 27
h
40 Find the circumference of a wheel
min
of radius 3cm. π = 3.14
What fraction 1 of the circle 4 is shaded?
41 These two hexagons are similar.
1 3
28
cm
What is the scale factor of enlargement?
3 1 10 × 2 =
1.5cm
6cm
29 The graph shows the speed of a car.
Use the graph to find the time taken by the car to travel 20km.
min 42 What is half of 3.75?
Distance in km
50 40 30
43 Arrange in descending order.
20
3 4
10
4 5
2 3
1 2
5 8 >
>
>
>
0 0 10 20 30 40 50 60 Time in minutes
44 London
30 Change 5.2m to millimetres.
45 39 44 36 43
mm
31 252 ÷ 28 = 32 The diameter of a circle is 4cm.
Its circumference is 3.14 times this length. What is the perimeter of the semicircle?
prime numbers.
cm
46 If m = 7, n = 5, evaluate
(m + n) × (m – n).
34 Point A is at (–3, –2). Write the
47 What is the order
(
of rotational symmetry of a regular pentagon about its centre?
, )
y 3 2 1 –3 –2 –1 0 1 2 3 –1 –2 A –3
mm
45 Express 70 as the product of three
33 Divide £135 in the ratio of 5:4.
coordinates of its reflection in the y-axis.
T his table shows the number of millimetres of rain each week for 5 weeks. What is the mean rainfall to the nearest millimetre?
x
48 A train goes at 78kph for 20min.
How far does it travel?
km
49 True or false? 7 < √80 < 8 35 A coat costing £45 is reduced by
20%. How much do I pay? For use with Schofield & Sims Mental Arithmetic.
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50 Write 24 × 25 as a number.
£
7
© Schofield & Sims Ltd, 2016.
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Entry Test A marking key
Entry Test B marking key
1
11
26 9p
1
104
26 1h 27min
2
March
27 V
2
280
27
5 12
3
50p
28 5km
3
£49.75
28
3 20
4
47
29 11
4
507
5
56
30 540mm
6
4 × 6 (or 6 × 4) 24
31 20cm
7
4
4
32 1310
8
70cm
33 4.09
9
10
5.33
29 15min
5 ten thousand six
4.87 5.79
5.31
hundred and four
30 5200mm
6
a 36cm
31 9
7
877 566
32 10.28cm
8
1987
33 75:60
9
4km
34 (3, –2)
b 81cm2
34 £2.95 10 100ml
10 circle
11 0.8
11 43cm
36 (3, 0)
12 6
37 a 10
13 24
35 £36
35 15mm
40
14 20 15 475
12 13h 35min
b 100
38
9 10
39 1 40
c 96cm2
40 18.84cm 41 4
16 £9.35 42 48mm
31
b 60cm2
15 45°
18 £1.20
3 14
14 a 80cm
41 6
17 70
37 5
2
40 16
16 104
36 690mm
13 1250ml
38 3.55 p.m. 39
0.008
8 4 17 10 5
43 2p
42 1.875
0.8 43
4 3 2 5 1 5 > 4 > 3 >8 > 2
18 0.56 19 10
44 a 09:59
20 10
44 41mm
b 00:25
19 cone
45 600g 5
21 a 8
b 38
3
45 2 × 5 × 7
20 3 8
671
46 24
46 100
21 25%
22 2
47 (4, 2)
22 15
23 35min
48 40°
23 8
48 26km
9 10
49 2 4
24 £2.09
49 false
50 £0.68
25 214°
50 600
24
25 4
3
For use with Schofield & Sims Mental Arithmetic.
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ABOUT MENTAL ARITHMETIC
Mental Arithmetic Entry Test Guide
Overview Mental Arithmetic is a unique resource providing varied and frequent practice of core mathematical processes and concepts. A trusted favourite for homework and classroom use, each book contains over 1,500 carefully structured questions, combining numerical calculations, written problems, and one- and two-step challenges to strengthen core skills.
Four steps to using Mental Arithmetic Mental Arithmetic offers a structured and effective approach to developing confidence and fluency. The series is organised by ability rather than age, so we recommend pupils use the free Entry Tests to decide on the most suitable starting point before beginning regular practice. 1. Initial assessment – Assess what level pupils are working at using the Entry Tests or National Curriculum Charts that are available in this guide or as a free digital download on the Schofield & Sims website. 2. Rigorous, daily maths practice – Schedule 10–20 minutes a day for pupils to work through part of a Mental Arithmetic book test. Many schools find that the easiest time to fit in Mental Arithmetic sessions is either at the beginning of the day, as an early morning starter, or as homework. 3. Effective marking and feedback – Organise weekly group marking sessions to quickly and easily identify areas of difficulty and provide immediate feedback. Where further diagnostic assessment is required, use the Diagnostic Checks provided in the Teacher’s Guides to assess the exact nature of a pupil’s difficulties. 4. A positive maths culture – Encourage children to take pride in the development of their maths skills and monitor their own progress using the Progress Tests and Achievement Charts in each pupil book. Reward those whose achievements are especially significant with editable certificates available from the Schofield & Sims website.
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ABOUT MENTAL ARITHMETIC
Schofield & Sims
More ways to use Mental Arithmetic Mental Arithmetic may be used in many different ways, including: • individual work, with pupils who are confident with the maths concepts covered • maths recovery, to assess new or struggling pupils and to improve mental fluency • paired work, allowing pupils who lack confidence in some concepts to discuss the questions and think of possible ways to answer them • group or whole-class work, working through a set of questions with a group of pupils after they have answered them • homework, with parents and carers encouraging children to explain their working methods.
Mental Arithmetic and the National Curriculum By providing rich and varied maths practice and on-going formative assessment, Mental Arithmetic meets the requirements of the National Curriculum, enabling pupils to consolidate their essential maths skills and develop a deeper understanding of the topics covered. The range of topics per test encourages pupils to think mathematically and apply all that they have learnt when answering each question, as well as helping them to improve their mental fluency. The table below indicates which Mental Arithmetic book may be most suitable for your class, based on end of year expectations in the National Curriculum. First Mental Arithmetic is available for younger children. Pupils at risk of not meeting end of year expectations
Pupils on target to meet end of year expectations
Pupils on target to exceed end of year expectations
Year 3
Mental Arithmetic Introductory Book
Mental Arithmetic 1
Mental Arithmetic 2
Year 4
Mental Arithmetic 1
Mental Arithmetic 2
Mental Arithmetic 3
Year 5
Mental Arithmetic 3
Mental Arithmetic 4
Mental Arithmetic 5
Year 6
Mental Arithmetic 4
Mental Arithmetic 5
Mental Arithmetic 6
Pupils should demonstrate mastery of the curriculum content for their year group before they are allowed to move on to a later book in the series. The increase in difficulty within each book will challenge and extend more able pupils, providing comprehensive practice and highlighting any gaps in their understanding.
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ABOUT MENTAL ARITHMETIC
Mental Arithmetic Entry Test Guide
Individual test structure Each pupil book test is in three parts, A, B and C. Part A: contains questions where the use of language is kept to a minimum, and symbols and numbers are used. Part B: contains questions where mathematical language is used. Part C: contains written questions that involve one- or two-step problem solving.
SECTION 2 | Test 11
Schofield & Sims
A 1
C
Answer Th H
T
Write in words the number shown on the abacus.
U
1
Answer
Which of these is a pair of parallel lines? d
e
b a
hundreds
2
2400 =
3
£5.00 – £3.99 =
4
80min + 40min =
5
2 2 kg + 600g =
6
110 + 10 =
7
1
1
H
kg
min
h
min
g
kg
g
A baguette is 2 m long. How many centimetres does another baguette measure which is one and a half times as long?
cm
4
How much change from a £5 note after buying three aeroplanes?
p
£1.50
(6 × 5) + (8 × 7) =
9
7m cost 56p. 1m will cost
10
(9 × 12) – 8 =
p.
p
Answer
+ 6 = 2076
1
2000 +
2
£0.35 + £0.26 + £0.37 =
3
What number is 100 times greater than 11?
4
How many millimetres are 1 there in the sum of 7 2 cm 1 and 2 2 cm?
Which of these numbers is a multiple of 9?
6
Four cards cost 12p. How much will 12 cards cost?
7
3
p
49 56
Write the coordinates of point A ( , ).
A
2
p
63 71
1 1
8
2
3
Divide 1040 by 10.
6
Find the total of 37 and 25.
7
Write 4kg 400g to the nearest kilogram.
8
(3 × 8) equals (4 ×
9
Subtract 20 plus 16 from 50.
(
,
)
Write the next two numbers in the sequence. 0.06, 0.07, 0.08, 0.09,
mm
p
4
9
5
7
5
28
B
wk
1
2.01
1.99 8
9
3
9
Write < or > to make this true.
10
Saba saves 20p each week. How long will it take her to save £4?
£ h
c
2
Estimate the number of sweets
kg
Ana
870
)
,
There were 900 sweets in the jar. These were the estimates.
Zarak
Zoe
Leo
926
860
933
Who made the best estimate? 10
Find the missing number.
Flowers cost 70p for 10. What is the cost of 15 flowers?
£
28
This page is from Mental Arithmetic 2.
Why is Mental Arithmetic so effective? • Breadth: The wide range of topics covered means that pupils must apply their full knowledge and skills in answering each question, demonstrating what they know, as well as what they may have forgotten. • Depth: The rich blend of question types in each book not only improves pupils’ vocabulary and mathematical reasoning skills, but also develops their conceptual understanding of number. • Progress: Each test builds on the previous test, revising topics already covered, while at the same time challenging pupils to tackle more complex problems.
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the long-established educational publisher specialising in maths, English and science
Mental Arithmetic provides rich and varied practice to meet the requirements of the National Curriculum for primary mathematics. Trusted by thousands of schools, the series remains a favourite with teachers for building confidence and fluency in maths. Mental Arithmetic helps every child succeed in maths by providing carefully differentiated questions in the volume necessary to build automaticity and confidence, delivering proven results for half a century.
Mental Arithmetic comprises seven one-per-child pupil books with optional answer books, as well as a single Teacher’s Guide. The series develops pupils’ essential maths skills, preparing them for the Key Stage 2 national tests. It may also be used as preparation for the 11+, and with older students for consolidation and recovery. All the books can be used flexibly for individual, paired, group or whole-class maths practice, as well as for homework and one-to-one intervention. Structured according to ability rather than age, the series allows children to work at their own pace, building confidence and fluency. To help parents or tutors select the appropriate book for each child, Entry Tests are provided in this booklet along with instructions on how to use them. They can also be found in the Mental Arithmetic Teacher’s Guide and on the Schofield & Sims website. The Mental Arithmetic Entry Test Guide contains: • An introduction to the series • Explanations of the Pupil Book test structure • A National Curriculum alignment table • Photocopiable Entry Tests • Marking Keys and score guides
Mental Arithmetic Introductory Book 978 07217 0798 3
Mental Arithmetic Introductory Book Answers 978 07217 0853 9
Mental Arithmetic 1 978 07217 0799 0
Mental Arithmetic 1 Answers 978 07217 0805 8
Mental Arithmetic 2 978 07217 0800 3
Mental Arithmetic 2 Answers 978 07217 0806 5
Mental Arithmetic 3 978 07217 0801 0
Mental Arithmetic 3 Answers 978 07217 0807 2
Mental Arithmetic 4 978 07217 0802 7
Mental Arithmetic 4 Answers 978 07217 0808 9
Mental Arithmetic 5 978 07217 0803 4
Mental Arithmetic 5 Answers 978 07217 0809 6
Mental Arithmetic 6 978 07217 0804 1 Mental Arithmetic Teacher’s Guide
Mental Arithmetic 6 Answers 978 07217 0810 2
978 07217 1389 2
Workbooks for Key Stage 1 A separate series for Key Stage 1 is also available in the form of First Mental Arithmetic. These Pupil Books use the same structured ‘A, B, C’ approach as the main Mental Arithmetic series but are presented in an accessible and engaging format to suit the age and attention span of younger children.
For further information and to place your order visit www.schofieldandsims.co.uk or telephone 01484 607080 MATESTLEAF S&S MA 'How to..' Guide_12pp A4.indd 12
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