Non-Verbal Reasoning - galorepark.co.uk Samples/Non... · • 11+ Non-Verbal Reasoning Practice Papers 2 Three steps to examination success

11+For 11+, Pre-Test and independent school exams, including CEM, GL and ISEB

Non-Verbal Reasoning

Find out more about our new series at: galorepark.co.uk/nvrsample

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Samples from:

27544 Non- Verbal Reasoning sampler booklet v6.indd 1 05/05/2016 11:05

A Guide to your Non-Verbal Reasoning Sample PagesGalore Park’s brand-new Non-Verbal Reasoning range has just been published! This new 11+ revision range has been written specifically for independent school entrance exams, including CEM, GL and ISEB. Galore Park has worked with 11+ tutors, independent school teachers, test writers and specialist authors to create this series.

Included in this sample are pages from a key topic within non-verbal reasoning – matrices – to show how a topic is revised, practised and tested throughout the range.

• 11+ Non-Verbal Reasoning Study and Revision Guide

• 11+ Non-Verbal Reasoning Workbook (Age 9-11)

• 11+ Non-Verbal Reasoning Practice Papers 2

Three steps to examination success

The range has been constructed to help pupils follow three steps to examination success...

Study and Revision Guide 1

Learn the skills and understand the question types for all pre-tests and 11+ independent school entrance exams.

Workbooks 2

Increase exam confidence with over 160 questions in each of the books, with even more question variationsand application of knowledge learned in the Study and Revision Guide.

Practice Papers 3

Perfect exam technique by practising with a variety of exam-paper styles under time pressure. Books 1 and 2 contain four training tests, nine model exam papers and fully explained answers for final test preparation.

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ContentsA Guide to your Non-Verbal Reasoning Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pages 2-5

• Three steps to examination success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 2

• Contents and Progress Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 3

• Working through the books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4

• Detailed answers throughout the range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5

• The Learning Ladders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5

11+ Non-Verbal Reasoning Study and Revision Guide . . . . . . . . . . . . . . . . . . . . . . . . . Pages 6-7

11+ Non-Verbal Reasoning Workbook (Age 9-11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pages 8-9

11+ Non-Verbal Reasoning Practice Papers 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pages 10-11


Contents and progress recordUse these pages to record your progress. Colour in the boxes when you feel confi dent with each skill and note your scores for the ‘Test yourself’ and workout questions.

● How to use this workbook 5

● Most unlike ........................................................................... 8

● Matching features 1 ...........................................................10

● Applying changes 1 ............................................................12

● Matching 2D and 3D shapes 1 .......................................14

● Matching features 2 ...........................................................16

● Applying changes 2 ............................................................18

● Matching 2D and 3D shapes 2 .......................................20

● Following the folds 1 .........................................................22

● Matching a single image 1 ...............................................24

● Translating and combining images 1 ............................26

● Following the folds 2 .........................................................28

A Numbers, shapes and relationships

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B Position and direction

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● Working with 2D shapes ..................................................40

● Working with 3D shapes ..................................................41

Maths workout 1

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Contents and Progress Record

Throughout the 11+ Non-Verbal Reasoning range, we have included these handy contents pages, specifically designed to easily track progression throughout the books. Once pupils feel confident with a skill, they can colour in or tick the boxes correlating to the area they have completed, and easily note scores and times for end-of-unit tests.

Clear chapter headings divide revision into manageable chunks.

Boxes to colour in when a topic has been completed. Allows teachers to easily track topics revised.

Easily record test scores.

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To view the full contents lists of all 6 books in the range, visit galorepark.co.uk/nvrsample.

All of these great features are included across the whole 11+ and Pre-Test range, across a number of subjects. View the full range at galorepark.co.uk/nvrsample.


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Working through the books

Throughout the 11+ Non-Verbal Reasoning range, we have included handy headers for pupils to easily follow during independent revision. Across the Study and Revision Guide, Workbooks and Practice Papers, they include:

Chapters that link together types of questions testing similar skills

Chapter introductions to explain how the skills link in with work already covered in maths

Thinking skills and games for pupils to practise with friends and family to build skills and to test everybody else’s at the same time!

Learning pages to introduce one type of question or set of skills across two pages

End-of-chapter tests to give pupils a chance to try out skills learnt in a short test

6 M

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Matrices using numbers and shapesSkill definition: Solve Matrices questions that use numbers and shapes.

l Matrices are grids with patterns that work in different directions.l In this learning spread you will practise questions with matrices that use numbers,

scale, proportion, 2D and 3D shapes, shading, line styles and angles.l As explained on pages 22–23 in Chapter 1, most matrices have:

• two rows and two columns (top picture), or• three rows and three columns (second picture).

l Patterns work down as well as across, and sometimes diagonally. They often include short number sequences. In the grid containing triangles shown here, the rows have an identical shade pattern and the columns have an identical number pattern.

l Matrices with three rows and columns often have diagonal patterns, as shown in this coloured grid. If a question has three different pictures on a single row, look for diagonal patterns. These should repeat every third diagonal. Colouring diagonal patterns can make it clearer to see how they work.

MethodOne of the options on the right completes the pattern in the grid on the left. Circle the letter beneath the correct answer.

a b c d e

l Begin by breaking down the question into the different features to find the missing square. There seem to be patterns with shape, number of shapes and shading.

l Follow one pattern at a time to discover the rules:• the shapes are different on each row• the number of shapes changes in each column (decreasing by one from left to right)• the shading changes in a diagonal pattern working top left to bottom right.

l Now work out what features you would expect from the missing square:• the shape in the bottom row should be a diamond• the number of shapes in the middle column should be two• the diagonal, working top left to bottom right, that links to

this empty box is striped (colour the diagonals, as described above if you find this difficult to see).

This means you are looking for two diamonds with a diagonal background. So the answer must be option d.

Look out for distractors in questions. Not every feature in Matrices questions changes, like the oval in this question.

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Matrices using num

bers and shapes

91

Train

1 There are two rules for this Matrices question: there is a different fruit in each row and the fruits change in size from one column to the next. Use your imagination to complete the missing squares with fruits of different sizes!

Try

One of the options on the right completes the pattern in the grid on the left. Circle the letter beneath the correct answer.

2

a b c d e

Test

3

a b c d e

4

a b c d e

5

a b c d e

Test time: 02:00

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Try

Train

Test

Some not-too-difficult questions for pupils to take a close look at to understand how they work.

Questions to introducepupils to usingthe skills.

Timed questions to see what real exam questions are like. The last one will be difficult, so if the pupil can do this one, the skill is nearly mastered.

11+ Non-Verbal Reasoning Study and Revision Guide


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The Learning Ladders

These Learning Ladders appear throughout the 11+ Non-Verbal Reasoning range, to show pupils how skills in non-verbal reasoning link to the familiar areas of maths that they have already learnt in school. Their ability to problem-solve will develop as they step up the ladder, bringing together all of their knowledge to solve the most challenging questions by the time they reach the top.

Handling data

MatheMaticS LeaRNiNg LaDDeR

Algebra

Position and direction

Measurement Properties of shapes

Working with proportion Fractions

Number and place value Calculations

Handling dataMatrices

Example:

Challenging

Foundation

Problem-solving

Knowledge-based questions

Links to

Now that you’re familiar with the features of the range, we hope you enjoy using your sample pages! All pages have been selected based on a key topic in non-verbal reasoning. We have provided pages that you can photocopy to use in your class to see how well the range could work for your pupils.

Now try for yourself

Matrices

NoN-veRbal ReaSoNiNG LeaRNiNg LaDDeR

Connections with codes Sequences

TranslationRotationReflectionPlacement

Shapes and shading 2-D views of 3-D shapesLine styles and angles

Working with proportion

Working with numbers

Detailed answers throughout the range

All the answer explanations tie into the teaching given and tie into the maths that pupils will have learned in school. So if, for example, the question involves scaling and angles, the answer explanation will make this clear. This approach has been followed in order to support you and your pupils in reviewing questions they may have found challenging and so provide ideas for patterns to look out for when practising further questions.

You can find the answers to all of the questions featured in this sample at galorepark.co.uk/nvrsample

Non-Verbal Reasoning Workbook Age 9–11 published by Galore Park A7

5 A small black circle sitting inside the crescent shape, touching but not crossing it; and four short horizontal lines, two coming out to the left from the top and two from the bottom of the crescent should be added

Test yourself1 c position – the larger circle moves down the string; number –

(a) of small black spots reduces by one each time, (b) of lines in the solid zig-zag reduces by one each time, (c) of lines in the dashed zig-zag increases by one each time

Distractors: position – (a) of the zig-zags within the square, (b) of the point where the dashed zig-zag crosses the thread line

2 d number – (a) of circles decreases by two each time, (b) of shaded segments decreases by one each time

Distractors: size of circles; position of shaded sections3 d proportion – shaded section in the circle on the left increases

by a quarter each time; shading – style of shading in the left-hand circle alternates between diagonal stripes and black; angle – (a) the dashed radius line in right-hand circle moves 45˚ clockwise each time, (b) the solid radius line in right-hand circle moves 90˚ anticlockwise each time

Distractors: shading – style of background4 d position – (a) the shaded square moves one place round the

edge of the larger square anticlockwise each time, (b) the white circle is always directly opposite the shaded square, (c) the black circle is one square ahead of the white circle; shading – (a) angle of line shading in the square rotates 45˚ clockwise each time, (b) the central square alternates white and black

Try it outMany different solutions are possible. For example:

ba c ed

Matrices 1 (page 46)Have a go1 The first grid has the same shape in each column and the shading

along each row alternates so: i h white diamond ii a black circle iii e white triangle

In the second grid the pattern moves down the grid in a zig-zag way along the top row from left to right and then back across the middle row and along the bottom row. So the shapes go circle, triangle, diamond, circle, triangle, diamond, and so on while the shading goes stripes, black, black, white, stripes, black, black, white, and so on.

iv g black diamond2 There is a diagonal line from bottom-left corner to top right, the

triangle on the upper left side is divided into two with a line from the top-left corner of the square to the centre of the square. The small triangle on the left has vertical line shading and the small triangle at the top right has horizontal line shading

3 There should be three circles in the square, each one shaded with grid line shading. The number of circles is indicated by the number of crosses in the triangle to their right and their shading is determined by the shading of the triangle beneath them.

4 (a) shading (b) shape (c) line (d) background shading5 This grid has four lines of symmetry – one vertically across the

centre, one horizontally across the centre, and then two diagonal lines of symmetry also passing through the centre. The box should have a wide V-shape drawn in the lower half with the inner angle of the V shaded black, and two thin parallel lines going across the top of the square. It is a reflection of the top square in the grid.

Test yourself1 b the shapes alternate down the columns, so it will be a triangle

pointing left; shading style alternates along the rows so it will have vertical stripes

2 d shape – (a) the symbol in top-left corner of each square is the same along each diagonal line, so there will be a small right-angled triangle across the top-left corner, (b) shape in bottom-left corner is same along each row, so there will be a spade shape; number – of black spots on the right same in each row, so there will be three; shading – one of each style of shading on each row, so spade will be black

3 e number/position – two shapes, one in top-right corner and one in lower left corner (which is in the middle of the grid); shape – (a) the lower left shape in the square is taken from the border of the next square going clockwise, (b) the shape in the upper right corner is from the adjacent border and will be an L-shape; shading – (a) the lower left shape is black, (b) the upper right shape is white

4 b rotation – anticlockwise by 90˚; position – of shaded element of the small circle pattern; orientation – of each element in relation to the sides of the square

Try it outThere are many possible answers. For example:

ba c ed

Connections with codes 2 (page 48)Have a go1 i AN a square with horizontal stripes ii BL a black circle iii CM a white triangle iv BM a white circle v CN a triangle with horizontal stripes vi AL a black square2 i EZ ii DX iii FZ

iv FY v DY3 A one triangle

B two trianglesX no shadingY two shapes shadedZ one shape shaded

4 D zig-zag of three linesE zig-zag of two linesF zig-zag of four linesS circle shaded blackT circle with diagonal cross line shading

5 Completed picture must include an arrow pointing down and a curved line with two black circles on it – the white circles and arrowhead style are distractors and so do not matter.

Test yourself1 b first letter is for shape of base; second letter is for number of

flowers Distractors: lines – presence or absence of leaves; shading – of

shape at base2 e first letter is for position of the shaded shape in the line, so R

for middle; second letter is for the sequence of shapes, so X for rectangle, circle and oval from bottom to top

Distractors: angle – of line across the square3 c first letter is for angle of diagonal dashed line; second letter is

for number of solid straight lines Distractors: orientation – of straight lines;

angle – of intersections of straight lines; size – of curved lines4 d first letter is for the shape of the three diagonal items, so P for

black dots, Q for white dots and R for crosses; second letter is for position of white circle on the top row, L for left and M for right

Distractors: position/shapes/shading of the other elements

Try it outThere are many possible answers.

a b c d e

v f striped triangle

ba c edba c ed

ba c edba c edba c eda b c

d e

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a b c d e







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Matrices using num

bers and shapes

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Train


Try


2

a b c d e

Test

3

a b c d e

4

a b c d e

5

a b c d e

Test time: 02:00

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Sample pages from 11+ Non-Verbal Reasoning Study and Revision Guide

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6 M

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a b c d e







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Matrices using num

bers and shapes

91

Train


Try


2

a b c d e

Test

3

a b c d e

4

a b c d e

5

a b c d e

Test time: 02:00

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Sample pages from 11+ Non-Verbal Reasoning Study and Revision Guide

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Visit galorepark.co.uk/nvrsample for answers


C

Cod

es, s

eque

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and

mat

rice

s

46

Matrices 1

Have a go

1 These two grids use the same shapes but they follow different patterns. Select the correct shape for each empty square from the options given.

ba c

i

ii iii

iv v

ihg

fed

i ii iii iv v

Draw the missing pattern in the box provided to answer the next two questions.

2 3

4 Identify the features that are changing along each row. Write them in the spaces provided.

b

a

c

d

5 The pattern in this shape is symmetrical. Draw dashed lines across the shape to show the lines of symmetry. Then draw the missing pattern in the box provided.

(a)

(b)

(c)

(d)

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Matrices 1

47

Test yourself

One of the options on the right completes the pattern in the grid on the left. Circle the letter beneath the correct answer. For example:

a b c d e

1

ba c ed

2

ba c ed

3

ba c ed

4

ba c ed

Try it out

Draw a 3 × 3 grid and create your own pattern using black circles and white circles with different shadings. Leave one square in the grid blank and give fi ve possible answer options. Ask a friend or parent to identify the missing pattern.

Score / 4

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Sample page from 11+ Verbal Reasoning Workbook (Age 8-10) Sample pages from 11+ Non-Verbal Reasoning Workbook Age 9-11

8


C

Cod

es, s

eque

nces

and

mat

rice

s

46

Matrices 1

Have a go

1 These two grids use the same shapes but they follow different patterns. Select the correct shape for each empty square from the options given.

ba c

i

ii iii

iv v

ihg

fed

i ii iii iv v

Draw the missing pattern in the box provided to answer the next two questions.

2 3

4 Identify the features that are changing along each row. Write them in the spaces provided.

b

a

c

d

5 The pattern in this shape is symmetrical. Draw dashed lines across the shape to show the lines of symmetry. Then draw the missing pattern in the box provided.

(a)

(b)

(c)

(d)

9781471849350.indd 46 2/29/16 10:18 PM

Matrices 1

47

Test yourself


a b c d e

1

ba c ed

2

ba c ed

3

ba c ed

4

ba c ed

Try it out

Draw a 3 × 3 grid and create your own pattern using black circles and white circles with different shadings. Leave one square in the grid blank and give fi ve possible answer options. Ask a friend or parent to identify the missing pattern.

Score / 4

9781471849350.indd 47 2/29/16 10:18 PM

Sample page from 11+ Verbal Reasoning Workbook (Age 8-10) Sample pages from 11+ Non-Verbal Reasoning Workbook Age 9-11

9



Paper 9

17

55

ec dba

56

a b c d e

57

a b c d e

58

a b c d e

59

a b c d e

60

da b c e

Record your results and moveon to the next paper.

/ 60 :Score Time

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a b c d e

51

ca b d e

52

a b c d e

53

a b c d e

54

a b c d e

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Sample pages from 11+ Non-Verbal Reasoning Practice Papers 2

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a b c d e

51

ca b d e

52

a b c d e

53

a b c d e

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a b c d e

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Paper 9

17

55

ec dba

56

a b c d e

57

a b c d e

58

a b c d e

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a b c d e

60

da b c e

Record your results and moveon to the next paper.

/ 60 :Score Time

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a b c d e

51

ca b d e

52

a b c d e

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a b c d e

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a b c d e

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Sample pages from 11+ Non-Verbal Reasoning Practice Papers 2

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a b c d e

51

ca b d e

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a b c d e

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a b c d e

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a b c d e

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Non-Verbal Reasoning - galorepark.co.uk Samples/Non... · • 11+ Non-Verbal Reasoning Practice Papers 2 Three steps to examination success