Mathematics SAMPLESamples Assessment Tests: Curriculum · contained in the programmes of study for...

Mathematics Curriculum

Assessment Tests: Samples

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End of Term

Mathematics Test Sample

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1© Copyright HeadStart Primary Ltd

HeadStart Primary End of Term Mathematics Tests

Teachers’ Notes Year 6

Introduction - about the tests

Administration - how to manage the tests

The HeadStart Primary End of Term Mathematics Tests have been developed to help teachers assess children’s progress against the matters, skills and processes (grouped here as ‘objectives’) contained in the programmes of study for the mathematics curriculum.

The end of term tests (A, B and C) provide the option to administer a test at the end of each term.

The three end of term tests, together, cover all the objectives in the Year 6 mathematics curriculum. They provide a summative alternative to the content domain assessments. However, for the purpose of formative assessment, it is recommended that the domain tests are used, particularly for the number domains. This ensures thorough analysis of children’s performance against the curriculum objectives.

Ideally, the class teacher should administer the tests. This gives an overview of the children’s performance and a picture of any potential misconceptions as the test is being completed. Observing and making note of the way children approach and tackle the questions can be an extremely useful indicator towards future teaching and learning.

A pencil or pen is needed - any other necessary equipment is detailed at the top of the front cover of each test. No time limit is set for these tests. Depending on the year group, it may be appropriate to split the tests over two or more sessions.

Primary

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Support during the tests

When deciding upon the amount of support that is appropriate, it is important to remember that it is maths and not reading that is being tested. If a child needs to have all or some of the test read to them, this support should be made available. However, it is also necessary to avoid giving too much assistance; this could mean that results do not realistically reflect a child’s progress in maths.

Teachers have an in-depth knowledge of the children in their care and professional judgement is always the best guide, when considering how much support to provide. It may be that the CD-ROM is used in conjunction with a whiteboard to display and read the pages of the test to aclass or group of children.

The most successful approach is achieved by developing a whole school agreement/policy on how much support is appropriate for each year group. This ensures effective moderation across the school year groups.

Marking - understanding and using the mark scheme

In Year 6, there are 25 questions in each test. Each question carries a maximum of 2 marks. Ideally, the class teacher should mark the tests. As with the administration of the tests, marking gives a clear picture of necessary next steps on an individual, group and class basis.

Some of the questions have several parts. If the number of parts is even, 1 mark is awarded if half or more of the parts are correct. For example, if a question is comprised of 6 calculations, a child getting 3, 4 or 5 of the calculations correct is awarded 1 mark.

If a question has an odd number of parts, 1 mark is awarded if more than half the parts have a correct answer. For example, a 3-part question would need to have 2 parts correct for the award of 1 mark.

Many questions have only one possible answer but the question still carries 2 marks. Some questions have a definite, correct answer but a child may be awarded 1 mark if appropriate working or method is evident. Since ‘appropriate working or method’ could involve a number of possible strategies, the final judgement on whether to award one mark has been left to the professional judgement of the teacher.SAMPLE


Tracking - using the assessments and scaled scores to track progress

Once a test has been marked, a raw score out of 50 can be awarded. Test raw scores should be converted to scaled scores (see conversion charts).

The table below can then be used to identify progress against one of the 6 stages.

The HeadStart assessment and tracking system is intended to be used to support teacher assessment strategies and professional judgement.

It is important to note that the HeadStart assessments and scaled scores cannot be directly correlated to national curriculum test scaled scores, for the following reasons:

• HeadStart assessments test every objective of the national curriculum and are intended fordiagnostic purposes as well as summative purposes.

• HeadStart assessments follow the standard deviation of 15, giving a range of scores from <70to 125+. SATs scaled scores range from 80 - 120.

• HeadStart assessments identify a range of scaled scores within an expected band either side ofa mean score of 100. SATs scores identify the expected score of 100.

Year 6

Scaled Score Stage

0 - 75 Emerging Below average range76 - 95 Developing

96 - 100 Progressing Average range101 - 112 Secure

113 - 122 Mastering Above average range123 + Exceeding

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Using the scaled score model to make a tracking judgement

Each test should be administered at an appropriate point towards the end of each term. Some teachers may decide to present the tests to children at the beginning and at the end of the terms. This would enable progress to be tracked over each term, as well as across the three terms of the school year.

To establish the stage achieved, the directions in the table below should be followed. The table shows an example of a child who has completed TEST A.

A Year 6 child completing TEST A

TEST A: 32 scored out of 50

Use the raw score/scaled score conversion chart to convert the raw score of 32 to a scaled score of 103.

Therefore, a child with a scaled score of 103 is working at the ‘Secure’ stage (see table on page 3).

NB: This data should always be used in conjunction with ongoing teacher assessment.

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Test analysis software is also available from HeadStart Primary. Tests can be marked directly into the software; detailed performance analysis is then automatically generated for individuals, groups and classes.

Please visit www.headstartprimary.com for more information.

Every test question is underpinned by a statutory objective from the Year 6 mathematics curriculum. There is an objectives grid for each test, on which children’s performance can be recorded. The grids can be enlarged to A3 to make recording easier and clearer.

All the national curriculum objectives are covered over the three end of term tests.

The grids can be used to identify children’s performance against each of the objectives.

The grids can be used, in conjunction with ongoing teacher assessment,to identify which objectives need further reinforcement.

This analysis can be used to inform planning. (Identification of strengths and weaknesses enables teachers to be aware of the necessary emphasis to place on teaching the objectives when they are next met.)

The grids can be used to identify strengths and weaknesses of the whole class or groups. Groups might include boys/girls, children with special educational needs, children who have English as an additional language, pupil premium children, high achievers etc.

After all three tests have been completed, diagnostic information can be passed to the next year group teacher.

Analysis and assessment for learning - using the objectives analysisgrids to identify strengths and weaknesses

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Y6 End of term:TEST B


2 marks

2 marks

1

a

b

c

d

a

2

b

End of term: TEST B You will need a pencil and a ruler.

Page Total

Name Class Date

Year 6

Write TRUE (T) or FALSE (F) after these statements.

1 pints is about 1 litre.

3 kilometres is about 1 mile.

6.5 centimetres is about 1 inch.

1.6 kilometres is about 1 mile.

34

8935 8628 8715 8346

Put the following numbers in order of size, starting with the smallest.

smallest largest

4,162,352 4,126,325 4,126,352

smallest

largestSAMPLE



2 marks

2 marks

3

4

a

b

c

Use this box for your working out.

Page Total

Container A measures 7cm x 8cm x 6cm.Container B measures 7cm x 7cm x 7cm.

Which container has the greater volume?

Use the box below to explain how you know.

A BTick ( ) or

Solve the following.

0.3 x 3

7.56 x 6

5.85 x 29

=

=

=

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people

2 marks

2 marks

5

6

Page Total

18,567 people watched athletics this Sunday. This was 5348 people more than watched last Sunday.

How many people watched last Sunday?

Plot the points below onto the full co-ordinate grid. Join the dots to make a rectangle. Use a ruler.

4

-3

3

-4

2

-5

5

-2

6

-1

1

-6

-1 6-3 4-5 2-2 5-4 3-6 10

(2,3)

(-2,3)

(-2,-3)

(2,-3)SAMPLE



2 marks

2 marks

2 marks

7

a d

b

c

e

f

8

a

b

c

9

Page Total

Simplify the following fractions.

2 9

8

3

3

15

6 27

16

12

15

18

= =

=

=

=

=

I think of a number, add 3.8 and multiply by 8.

The answer is 78.4

What is my number?

-15

+26

-84

and

and

and

+7

-9

+49

difference

difference

difference

Calculate the difference (across zero) between the pairs of numbers below.

=

=

=SAMPLE



Set out your calculations in this box.

2 marks

2 marks

10

11

a

b

Page Total

Mr and Mrs Khan worked out that they would need exactly 4386 bricks to build a wall around their garden.

The builders yard sells bricks on large pallets of 1000 and smaller pallets of 100.

How many pallets of each would Mr and Mrs Khan need to buy?

pallets of 1000 bricks

pallets of 100 bricks

Use a formal written method of short division to solve the following. Show your remainder as a whole number.

420 ÷ 11

8382 ÷ 12

=

=

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2 marks

2 marks

A A

12

98o110o

75o

a b

13

Page Total

Calculate the size of the missing angle A in the shapes below.

o o

68o

54o

A = A =

The formula for the area of a rectangle is A = l x w(Area = length x width)

Look at the shape below.

Circle the equation which describes the area of the shape.

8cm

6cm

A = 8 x 6 + 1 A = 6 x 8 x 4 A = (4 x 5) + (6 x 4)

drawing is not

to scale

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16

2 marks

2 marks

2 marks

14

a

b

c

15

You’ll need to use a formal

written method.

Page Total

Badges cost 30p each. Look at the formula below which shows how to calculate the cost of any number of badges.

Total cost = 30n pence

What does ‘n’ stand for?

Look at the number 8,594,127.

What is the value of the digit 1?



Khadeeja knew that meant 1 divided by 8.

She wanted to work out the decimal fraction equivalent of .

Use the big box below to show how she would work it out.

Put your answer in the small box.

1

1

8

8

SAMPLE



2 marks

2 marks

17

18

a

b

c


Page Total

Mr Jones wanted to buy some ham.

The shopkeeper weighed slices of ham measuring 792 grams.

Mr Jones said it was far too much and he wanted of that amount.

How much ham would this be?

14

g

Circle the common factors of 12 and 48.

Circle the common multiples of 2 and 3.

Circle all the prime numbers.

2

9

6

8

16

49

5

24

11

6

38

61

4

12

18

73

30

29

9

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2 marks

2 marks

a b

19

20

a

b

c

Don’t forget to write . in its simplest

form!

c

Page Total

435 x 17 5863 x 38= =

Use the formal written method of long multiplication to solve the following.

Multiply the fractions below.

1 1

1 2

2 5

3 4

3 7

6 5

=x

=x

= =xSAMPLE



2 marks

2 marks

21

a b

c d

22

Page Total

The shaded square shows the base of each shape.

Circle the net which will not make an open cube.

25% of £30075% of £96

Which is more? Tick ( ) the box.

orSAMPLE



2 marks

2 marks

2 marks

23

23 24 25

24

25

TEST TOTAL PERCENTAGE SCORE

%50

End of Test B Page Total

How many children prefer apples?

Use the pie chart to answer questions , and .

The pie chart below shows the number of children who prefer apples, oranges or pears. Altogether, 24 children are represented by the chart.

What fraction of the children prefer oranges?

25% of the children who prefer apples are girls and half of the children who prefer pears and oranges are girls. How many of the children are girls, altogether?

90o

90o180o

pears

oranges

apples

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© Copyright HeadStart Primary Ltd

ANSWERS: END OF TERM TESTS

TEST B

1) a)F b)T c)T d)F(2 marks for all 4 correct, 1 mark for2 or 3 correct)

2) a)8346, 8628, 8715, 8935 b) 4,126,325, 4,126,352, 4,162,352(2 marks for 2 correct, 1 markfor 1 correct)

3) B; indication that A has an area of336cm² and B has an area of 343cm²(2 marks for a correct answer)

4) a)0.9 b)45.36 c)169.65(2 marks for all 3 correct, 1 markfor 2 correct)

5) 13,219(2 marks for a correct answer)(1 mark for appropriate working butan incorrect answer)

6) rectangle drawn appropriately(2 marks for a correct answer)

7) a)1/3 b)1/2 c)1/4 d)1/3 e)1/5 f)5/6(2 marks for all 6 correct, 1 mark for 3, 4 or 5 correct)

8) 6(2 marks for a correct answer)

9) a)22 b)35 c)133(2 marks for all 3 correct, 1 markfor 2 correct)

10) 4 pallets of 1000, 4 pallets of 100(2 marks for a correct answer)

11) a)38 r2 b)698 r6(2 marks for 2 correct, 1 mark for 1 correct)

12) a)58° b)77°(2 marks for 2 correct, 1 mark for 1 correct)

13) A = (4 x 5) + (6 x 4) circled(2 marks for a correct answer)

14) number of badges(2 marks for a correct answer)

15) a)100 b)90,000 c)8,000,000(2 marks for all 3 correct, 1 markfor 2 correct)

16) 0.125(2 marks for a correct answer) (1 mark for appropriate working but an incorrect answer)

17) 198g(2 marks for a correct answer)(1 mark for appropriate working but an incorrect answer)

18) a)2, 4, 3, 6 circled b)24, 12, 30 circled c)11, 29, 61 circled(2 marks for all 3 correct, 1 markfor 2 correct)

19) a)7395 b)222,794(2 marks for 2 correct, 1 mark for 1 correct)

20) a)1/12 b)2/21 c)10/30, 1/3(2 marks for all 3 correct, 1 mark for 2 correct)

21) c circled(2 marks for a correct answer)

22) 25% of 300 ticked(2 marks for a correct answer)


24) 1/4(2 marks for a correct answer)


Year 6

SAMPLE

© Copyright HeadStart Primary LtdEnlarge to A3 for added clarity

Question Objectives

Children’s Names

1.

3.

5.

8.

11.

14.

2.

4.

7.

10.

13.

6.

9.

12.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

Scaled Scores

Children’s Scores

Tota

l cor

rect

per

qu

estio

nPe

rcen

tage

per

qu

estio

n

End of term YEAR 6

TEST B: ANALYSIS GRID

know conversions between metric and imperialmeasures (m 1)

use common factors to simplify fractions (fdp 1)

recognise when it is possible to use the formula forthe area of a rectangle (A = l x w) (m 5)

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication (asmd 1)

multiply one-digit numbers with up to two decimalplaces by whole numbers (fdp 8)

solve a problem involving rounding a number toa required degree of accuracy (npv 4)

associate a fraction with division and calculate a decimal fraction equivalent to a simple fraction (fdp 6)

use percentages to compare amounts of money (rpa 2)

compare and order numbers up to 10,000,000 (npv 1)

solve a ‘think of a number problem’ using theinverse (asmd 8)

use a simple formula (rpa 5)

multiply simple pairs of proper fractions, writing the answer in its simplest form (fdp 4)

decide on the appropriate number operation andsolve a problem (asmd 7)

divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate (asmd 3)

solve a problem involving scaling by division (mass) (rpa 3)

interpret information presented in a pie chart (s 1)

calculate and compare the volume of a cube anda cuboid (m 7)

calculate intervals (differences) across zero (npv 3)

determine the place value of digits in numbers upto 10,000,000 (npv 1)

recognise the net of an open cube (g 2)

plot co-ordinates in all four quadrants to make arectangle (g 6)

find the size of a missing angle in triangles andquadrilaterals (g 3)

identify common factors, common multiples andprime numbers (asmd 5)

interpret information presented in a pie chart (s 1)

use information presented in a pie chart to solve a problem (s 1)SAMPLE

© Copyright HeadStart Primary Ltd 1

HeadStart Primary End of Term Mathematics TestsScaled Scores Year 6

Standardising the maths assessments

HeadStart Primary has conducted an extensive analysis, using a national sample of pupils for each assessment test, in order to produce a set of scaled (standardised) scores.

Standardising test scores fulfils two primary purposes:

(1) It enables a child's performance to be compared to the performance of other childrentaking the same test.

(2) It enables comparisons of performance across a range of tests, irrespective ofindividual test difficulty or number of questions etc.

The standardisation process

The test raw scores have been standardised so that the mean average of the sample is 100, with a standard deviation of 15. The standard deviation is the measure of the spread of scores away from the mean; usually in educational assessments, this is set as 15 for one standard deviation. Normal distribution suggests that around 68% of scores are within one standard deviation (i.e. 85-115).

Linking the scaled scores to HeadStart tracking stages

Scaled Score Stage

0 - 75 Emerging Below average range76 - 95 Developing

96 - 100 Progressing Average range101 - 112 Secure

113 - 122 Mastering Above average range123 + Exceeding

SAMPLE

© Copyright HeadStart Primary Ltd2

The HeadStart assessment and tracking system is intended to be used to support teacher assessment strategies and professional judgement.

It is important to note that the HeadStart assessments and scaled scores cannot be directly correlated to national curriculum test scaled scores, for the following reasons:

• HeadStart assessments test every objective of the national curriculum and are intendedfor diagnostic purposes as well as summative purposes.

• HeadStart assessments follow the standard deviation of 15, giving a range of scores from<70 to 125+. SATs scaled scores range from 80 - 120.

• HeadStart assessments identify a range of scaled scores within an expected band eitherside of a mean score of 100. SATs scores identify the expected score of 100.

Using the assessments and scaled scores to track progress

SAMPLE

Raw Score Scaled Score

0 59

1 60

2 62

3 63

4 65

5 66

6 67

7 69

8 70

9 71

10 73

11 74

12 75

13 77

14 78

15 80

16 81

17 82

18 84

19 85

20 86

21 88

22 89

23 90

24 92

25 93


26 95

27 96

28 97

29 99

30 100

31 101

32 103

33 104

34 105

35 107

36 108

37 110

38 111

39 112

40 114

41 115

42 116

43 118

44 119

45 121

46 122

47 123

48 125

49 126

50 127

Year 6 - HeadStart Mathematics End of Term Test A


SAMPLE


0 58

1 59

2 61

3 62

4 63

5 65

6 66

7 68

8 69

9 71

10 72

11 73

12 75

13 76

14 78

15 79

16 81

17 82

18 83

19 85

20 86

21 88

22 89

23 91

24 92

25 94


26 95

27 96

28 98

29 99

30 100

31 102

32 104

33 105

34 106

35 108

36 109

37 111

38 112

39 114

40 115

41 116

42 118

43 119

44 121

45 122

46 124

47 125

48 127

49 128

50 129

Year 6 - HeadStart Mathematics End of Term Test B


SAMPLE


0 57

1 59

2 60

3 61

4 63

5 64

6 65

7 67

8 68

9 70

10 71

11 72

12 74

13 75

14 76

15 78

16 79

17 81

18 82

19 83

20 85

21 86

22 87

23 89

24 90

25 92


26 93

27 94

28 96

29 97

30 99

31 100

32 101

33 103

34 104

35 105

36 107

37 108

38 109

39 111

40 112

41 114

42 115

43 116

44 118

45 119

46 120

47 122

48 123

49 125

50 126

Year 6 - HeadStart Mathematics End of Term Test C


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Content Domain

Mathematics Test Sample

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HeadStart Primary Content Domain Mathematics Tests Teachers’ Notes Year 6

Introduction - about the tests

The HeadStart Primary Mathematics Tests have been developed to help teachers assess children’s progress against the matters, skills and processes (grouped here as ‘objectives’) contained in the programmes of study for the mathematics curriculum.

In the Year 6 curriculum, there are 8 distinct content domains. For organisational purposes, Ratio and Proportion/Algebra have been combined into one test.

There are 3 tests for each domain - TEST A, B and C. The content of each test is purposely very similar so that it is possible to assess children’s progress over the year, on a like-for-like basis. It is not intended that all 3 tests are completed for every domain. Individual schools will choose to organise the delivery of the maths programmes of study in line with their overall curriculum design. The HeadStart Primary Tests are designed to fit any curriculum organisation.

It may be, for example, that in Year 6, a school chooses to teach and assess all the ‘NUMBER’ domains every term, but decides to spread the teaching of RATIO AND PROPORTION/ALGEBRA, MEASUREMENT, GEOMETRY and STATISTICS across the 3 school terms. This could mean that the 3 ‘NUMBER’ domains are tested every term, but the remaining 4 domains are only tested once in each term over the year. This is only one possible model, and all permutations of domain teaching and assessing are available, depending on the requirements of the school.

The domains are:NUMBER - Number and place valueNUMBER - Addition, subtraction, multiplication and divisionNUMBER - Fractions (including decimals and percentages)RATIO AND PROPORTION/ALGEBRAMEASUREMENTGEOMETRY - Properties of shapes / Position and directionSTATISTICS

Primary

SAMPLE


Timetabling - when to administer the tests

The tests have been designed to assess a thorough content coverage of each domain. The statutory objectives are assessed, almost without exception. (A small number of objectives, or parts of objectives are related to a practical activity that cannot be assessed using a paper-based test.)

Much of the non-statutory guidance is also covered and assessed, since this often underpins the conceptual understanding of the statutory objectives. The main purpose of testing should be a formative one, and only a comprehensive coverage of the curriculum can lead to meaningful assessment for learning, performance analysis and future planning.

The tests have been designed to provide maximum flexibility regarding when they should be carried out. It is for schools to decide upon the optimum testing frequency in order to facilitate meaningful data analysis, without overloading the curriculum with formal assessments.

Children’s progress can be measured against age-related expectations. The system incorporates identification of 6 stages; Emerging, Developing, Progressing, Secure, Mastering and Exceeding.

Progress can be tracked at any time throughout the school year. Although it is possible to track progress after the completion of each test, an overall judgement made every term would present a clear indication of children’s performance. The test scores can be recorded and converted for tracking purposes, at an appropriate point, according to the policy of the school. The information gleaned from making a tracking judgement once a term would be wholly appropriate for reporting to parents and as evidence in Ofsted inspections.

Administration - how to manage the tests

Ideally, the class teacher should administer the tests. This gives an overview of the children’s performance and a picture of any potential misconceptions as the test is being completed. Observing and making note of the way children approach and tackle the questions can be an extremely useful indicator towards future teaching and learning.

The test papers can be photocopied from the book or printed from the CD-ROM. The pages are numbered for the benefit of the children completing the test. At the bottom of each page, the year group, domain and test is identified. So, ‘Y6: npv - A’ is Year 6, NUMBER - Number and place value, TEST A.SAMPLE


Marking - understanding and using the mark scheme

In Year 6, there are 15 questions in each test. Each question carries a maximum of 2 marks. Ideally, the class teacher should mark the tests. As with the administration of the tests, marking gives a clear picture of necessary next steps on an individual, group and class basis.

Some of the questions have several parts. If the number of parts is even, 1 mark is awarded if half or more of the parts are correct. For example, if a question is comprised of 6 calculations, a child getting 3, 4 or 5 of the calculations correct is awarded 1 mark.

If a question has an odd number of parts, 1 mark is awarded if more than half the parts have a correct answer. For example, a 3-part question would need to have 2 parts correct for the award of 1 mark.

Many questions have only one possible answer but the question still carries 2 marks. Some questions have a definite, correct answer but a child may be awarded 1 mark if appropriate working or method is evident. Since ‘appropriate working or method’ could involve a number of possible strategies, the final judgement on whether to award one mark has been left to the professional judgement of the teacher.

A pencil or pen is needed - any other necessary equipment is detailed at the top of the front cover of each test. Since the primary purpose of the tests is formative, no time limits are set for any of the tests.

Support during the tests

When deciding upon the amount of support that is appropriate, it is important to remember that it is maths and not reading that is being tested. If a child needs to have all or some of the test read to them, this support should be made available. However, it is also necessary to avoid giving too much assistance; this could mean that results do not realistically reflect a child’s progress in maths.

Teachers have an in-depth knowledge of the children in their care and professional judgement is always the best guide, when considering how much support to provide. It may be that the CD-ROM is used in conjunction with a whiteboard to display and read the pages of the test to aclass or group of children.

The most successful approach is achieved by developing a whole school agreement/policy on how much support is appropriate for each year group. This ensures effective moderation across the school year groups.

SAMPLE


Tracking - using the tests to track children’s progress

Once a test has been marked, a score out of 30 can be awarded. When a tracking judgement is required, test scores should be converted to a percentage (see page 5 Teachers’ Notes).

The table below can then be used to identify progress against one of the 6 stages. The table uses percentage scores for conversion, so tracking judgements can be made after any number of tests have been completed.

Although it is possible to make a tracking judgement after the completion of just one test, this is not recommended. A termly calculation, made after the completion of a number of tests, will provide more reliable information.

The assessment system is intended to be used by teachers as a tool to support their professional judgement.

0 - 25

26 - 50

51 - 63

64 - 75

76 - 88

89 - 100

Percentage Score

Year 6

Stage

Emerging

Developing

Progressing

Secure

Mastering

Exceeding

Below average range

Above average range

Average range

0 – 50% Below average range 51 – 75% Average range76 – 100% Above average range

SAMPLE


NUMBER - Number and place value (20 out of 30)

NUMBER - Addition, subtraction, multiplication and division (20 out of 30)

NUMBER - Fractions (including decimals and percentages) (19 out of 30)

RATIO AND PROPORTION/ALGEBRA (17 out of 30)

has a total score of 76 out of 120

Percentage score = ( × 100 ) = 63%

Therefore, a child scoring 63% is working within the 'Average range' in the ‘Progressing’ stage. (It is worth noting that the child is close to achieving the ‘Secure’ stage.)

NB: This data should always be used in conjunction with ongoing teacher assessment.

Using the percentage scoring model to make a tracking judgement

An example

A Year 6 teacher has decided to make a tracking judgement for the children in the class at the end of the autumn term. The children have been taught the content for the following domains and the tests (TEST A versions) have been completed:

NUMBER - Number and place valueNUMBER - Addition, subtraction, multiplication and divisionNUMBER - Fractions (including decimals and percentages)RATIO AND PROPORTION/ALGEBRA

Step 1 Add together the test scores for each child.

Step 2 Find the overall percentage score for each child.

Step 3 Identify the stage achieved from the percentage score.

This means that a Year 6 child scoring as follows:

76120SAMPLE




Every test question is underpinned by a statutory objective or an objective from the non-statutory notes and guidance. There is an objectives grid for each test, on which children’s performance can be recorded. The grids can be enlarged to A3 to make recording easier and clearer.

The objectives have been labelled to match the bullet points in the Year 6 Programmes of Study as follows:

NUMBER - Number and place value (npv 1 – 4)NUMBER - Addition, subtraction, multiplication and division (asmd 1 – 9) NUMBER - Fractions (including decimals and percentages) (fdp 1 – 11)RATIO AND PROPORTION/ALGEBRA (rpa 1 – 9)MEASUREMENT (m 1 – 7)GEOMETRY - Properties of shapes / Position and direction (g 1 – 7)STATISTICS (s 1 – 2)

The pupil objective record sheet can be used to measure individual performance against each national curriculum objective.

The objectives grids and record sheets can be used, in conjunction with ongoing teacher assessment, to identify which objectives need further reinforcement.

This analysis can be used to inform planning. (Identification of strengths and weaknesses enables teachers to be aware of the necessary emphasis to place on teaching the objectives when they are next met.)

The grids and record sheets can be used to identify strengths and weaknesses of the whole class or groups. Groups might include boys/girls, children with special educational needs, children who have English as an additional language, pupil premium children, high achievers etc.

Analysis and assessment for learning - using the objectives grids and pupil objective record sheets to identify strengths and weaknesses

SAMPLE

Y6: fdp-A


Mathematics Assessment:

Name

Simplify the following fractions.

Class Date

Year 6

Page Total

2

1

7

1

5

4

1

3

12

3

8

2 8

21

5 15

10

16

3 9

24

15

4 12

=

=

=

=

=

=

=

=

=

=

Fill in the boxes so that the fractions are equivalent.

NUMBER - Fractions (including decimals and percentages)

2 marks

2 marks

1

2

TEST A

a

a

d

c

b

c

b

e

f

d

You will need a pencil.

SAMPLE

Y6: fdp-A

2© Copyright HeadStart Primary Ltd Page Total

Complete the boxes below. Look carefully at the signs.

Use an arrow to join the fractions and mixed numbers to the correct place on the number line. One has been done for you.

1 1 1

2

1 1

4 4 10

1

52

5

3

8 8

15 15

12

15

124

8

15

12

8+ +

+ +

--

a

b

c

=

=

=

=

=

=

0 1 2

2 4 1 7 11 15 5 10 10 2

2 marks

2 marks

3

4

SAMPLE

Y6: fdp-A


Fill in the boxes below to add or subtract the fractions below.

Multiply the fractions below.

1

3

1

1

3

4

2

6

6

12

6

12

6

12

+

+ +

-

+

-

=

= =

=

=

=

1 32 2 333 15 15 155

1 1

1 3

2 3

4 2

5 4

3 8

=x

=x

= =x

2 marks

2 marks

5

6

a

c

b

a

b

c

Don’t forget to write . in its simplest

form!

c

SAMPLE

Y6: fdp-A


7

8

Shade some of shape B below to show the answer to ÷ 2.

Sika knew that meant 3 divided by 8.

She wanted to work out the decimal fraction equivalent of .

Use the big box below to show how she would work it out.

Put your answer in the small box.

Page Total

÷ =2

A B

1

3

3

2

8

8

2 marks

2 marks

You’ll need to use a formal

written method.

SAMPLE

Y6: fdp-A


Put the number 784369 through the divide or multiply machines and write the answers in the boxes.


÷ ÷10

784369

100 1000by by by

0.4 x 2

9.43 x 8

8.74 x 34

=

=

=

2 marks

2 marks

9

10

a

a c

b

b

c


SAMPLE

Y6: fdp-A


£

Use a written method of division to solve the following. Show any remainder as a decimal.

Imran’s dad gave Imran a puzzle challenge on his birthday. He said if he could solve the puzzle, he would give Imran the amount in money, as a present. Here is the puzzle:

Add the value of the 2 in 4629.8 to the value of the 6 in 3.624. Now round your answer to the nearest whole number.

Imran solved the puzzle correctly. How much money did he receive as a present?

56.0 ÷ 5 325.5 ÷ 6= =

Page Total

2 marks

2 marks

11

12

a b

Place value and rounding? Let me think.


Use this box if you need to do any working out.SAMPLE

Y6: fdp-A


%

Thomas divided 258 by 9 but found a recurring decimal number in his answer. He decided to round his answer to 2 decimal places.

Complete the calculation below.

Put a circle around 3 of the values below that are equivalent.

A pair of trainers was reduced by in the sale. Mr Metric couldn’t work out fractions and wanted to know what the reduction was as a percentage.

What did the shopkeeper tell him?

Now circle the answer after rounding to 2 decimal places.


%30

End of Test Page Total

9 258

28.76

60% 0.35 0.6

0.65 25%

28.66 28.67 28.7

1

36

5

25

2 marks

2 marks

2 marks

13

14

15

a

b

SAMPLE

© Copyright HeadStart Primary Ltd Enlarge to A3 for added clarity

ANALYSIS GRIDTESTA B or C

Please mark as Year 6: FRACTIONS (including decimals and percentages)

Question Objectives

Children’s Names

1.

3.

5.

8.

11.

14.

2.

4.

7.

10.

13.

6.

9.

12.

15.

Percentages

Children’s Scores

Tota

l cor

rect

per

que

stio

n

Perc

enta

ge p

er q

uest

ion

use common factors to simplify fractions (fdp 1)

use a common multiple to express fractions in the same denomination (fdp 1)

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions (fdp 3)

use a common multiple to create an equivalent fraction (fdp 1)

compare and order fractions, including fractions >1 (fdp 2)

multiply simple pairs of proper fractions, writing the answer in its simplest form (fdp 4)

divide a proper fraction by a whole number (fdp 5)

associate a fraction with division and calculate a decimal fraction equivalent for a simple fraction (fdp 6)

multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places (fdp 7)

multiply one-digit numbers with up to two decimal places by whole numbers (fdp 8)

use written division methods in cases where the answer has up to two decimal places (fdp 9)

solve a problem involving identifying place value in a decimal number and the need for accurate rounding (fdp 10)

round an answer to a specific degree of accuracy (fdp 10)

recall and use equivalences between simple fractions, decimals and percentages (fdp 11)

use equivalences between fractions and percentages in context (fdp 11) SAMPLE

Y6: rpa-A


Mathematics Assessment: RATIO AND PROPORTION / ALGEBRA

Name

To make 3 cakes, Cal needs 150g of flour and 120g of sugar.

How much flour and sugar would he need to make 5 cakes?

Class Date

Year 6

Page Total


20% of 150 children do not like swimming. How many children do not like swimming?

7% of 300 children go to school by car. How many children go to school by car?

g of sugarandg of flour

2 marks

2 marks

1

TEST A

a

b

2

You will need a pencil.


SAMPLE

Y6: rpa-A


The actual base of Mr Wood’s new shed will be 89 times the size of the square below.

What will each side of the actual base measure in metres?

Page Total

metres

7cm

7cm

25% of £240 75% of £76

Which is more? Tick ( ) the box.

or

drawing is not

to scale

2 marks

2 marks

3

4


SAMPLE

Y6: rpa-A


of the athletics team are girls.

There are 30 children in the team altogether.

How many are boys?

Mrs Green wanted a block of Cheddar cheese.

The shopkeeper weighed a block measuring 891 grams.

Mrs Green said it was far too much and she wanted of that amount.

How much cheese would this be?

Vincent is painting a picture. He mixes 2 portions of red paint for every 3 portions of white paint.

He mixes 25 portions altogether.

How many portions of red paint does Vincent mix?

13

g

portions of red paint

35

2 marks

2 marks

2 marks

6

5

7


SAMPLE

Y6: rpa-A


Solve the following by filling in the missing numbers.

Pencils cost 20p each. Look at the formula below which shows how to calculate the cost of any number of pencils.

Describe the pattern in the number sequence below.

+

-

x

29

52

143

=

=

=

16

Total cost = 20n pence

What does ‘n’ stand for?

63

13

4, 7, 10, 13, 16,

2 marks

2 marks

2 marks

8

9

10

a

b

c

Use this box to describe the pattern.SAMPLE

Y6: rpa-A


Look at the sequence below.

Find the value of ‘a’ in the equations below.

Square represents 26. Look at the equation below.

What does represent?

Liam says the formula for the sequence is (n x 3) + 1

(n = 1st, 2nd, 3rd, 4th number etc)

Use the formula to find the 21st number in the sequence.

4,

( x 3) + 1=

1st7,

2nd10,3rd

13,4th

16,5th

-

x

÷

+=

a a=

a=

a=

24

3

=

=

=

3

a

9

10

6

a

2 marks

2 marks

2 marks

11

12

13

a

b

c

SAMPLE

Y6: rpa-A


a + 1 = 5. Use this information to find the value of ‘a’ and ‘b’.

Look at the equation below. Find 3 different pairs of values for ‘a’ and ‘b’.

x

+

x

x

x

+

24

b

a

a b

a

a

b

b

b

7

=

=

= =

b

6

a

a


%30

End of Test Page Total

2 marks

2 marks

14

15

SAMPLE


NUMBER - Number and place value

TOTAL % SCORE

TOTAL % SCORENUMBER - Addition, subtraction, multiplication and division

Year 6

Name Class Date

npv1:

npv2:

npv3:

npv4:

asmd1:

asmd2:

asmd3:

asmd4:

asmd5:

asmd6:

asmd7:

asmd8:

asmd8:

read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

round any whole number to a required degree of accuracy

use negative numbers in context, and calculate intervals across zero

solve number and practical problems that involve all of the above

Enter marks for each question (0, 1, 2) into the appropriate boxes to calculate percentage correct for each objective

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

perform mental calculations, including with mixed operations and large numbers

identify common factors, common multiples and prime numbers

use their knowledge of the order of operations to carry out calculations involving the four operations

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

solve problems involving addition, subtraction, multiplication and division

use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

continued on next page

%

%

%

%

%

%

%

%

%

%

%

%

%

%

%

Q1

Q15

Q3

Q8

Q10

Q4

Q5

Q6

Q4

Q7

Q13

Q15

Q8

Q12

Q1

Q14

Q2

Q7

Q9

Q3

Q6

Q12

Q14

Q11 Q13

Q2

Q5

Q11

Q10Q9

INDIVIDUAL PUPIL OBJECTIVE RECORD SHEET

SAMPLE


RATIO AND PROPORTION / ALGEBRATOTAL % SCORE

NUMBER - Fractions (including decimals and percentages)

Year 6

rpa1:

rpa2:

rpa3:

rpa4:

fdp1:

fdp2:

fdp4:

fdp6:

fdp8:

fdp5:

fdp7:

fdp9:

fdp10:

fdp11:

fdp3:

solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

solve problems involving similar shapes where the scale factor is known or can be found

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

use common factors to simplify fractions; use common multiples to express fractions in the same denomination

compare and order fractions, including fractions > 1

multiply simple pairs of proper fractions, writing the answer in its simplest form (for example, 1/4 × 1/2 = 1/8)

associate a fraction with division and calculate decimal fraction equivalents (for example, 0.375) for a simple fraction [for example, 3/8)

multiply one-digit numbers with up to two decimal places by whole numbers

divide proper fractions by whole numbers (for example, 1/3 ÷ 2 = 1/6)

identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

use written division methods in cases where the answer has up to two decimal places

solve problems which require answers to be rounded to specified degrees of accuracy

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions


continued from previous page

rpa5:

rpa6:

rpa7:

use simple formulae

generate and describe linear number sequences

express missing number problems algebraically

%

%

%

%

%

%

%

%

%

%

%

%

%

%

%

%

Q3

Q13

Q15

Q4

Q9

Q11

Q5

Q1

Q3

Q5

Q7

Q2

Q12

Q14

Q2

Q4

Q6

Q6

Q8

Q10

Q7

Q1

%

%

%

Q11

Q12

Q9

Q10

Q8


SAMPLE


TOTAL % SCORE

TOTAL % SCORE

RATIO AND PROPORTION / ALGEBRA (continued)

MEASUREMENT

rpa9:

rpa8:

m1:

m3:

m4:

m5:

m7:

m6:

m2:

enumerate possibilities of combinations of two variables

find pairs of numbers that satisfy an equation with two unknowns

solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

convert between miles and kilometres

recognise that shapes with the same areas can have different perimeters and vice versa

recognise when it is possible to use formulae for area and volume of shapes

calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units (for example, mm3 and km3

calculate the area of parallelograms and triangles

use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places

Year 6continued from previous page

GEOMETRY - Properties of shapes / Position and direction

g1:

g3:

g4:

g5:

g2:

draw 2D shapes using given dimensions and angles

compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

recognise, describe and build simple 3D shapes, including making nets


%

%

%

%

%

%

%

%

%

%

%

Q15

Q14

Q2

Q6

Q13

Q1

Q5

Q13

Q6

Q9

Q11

Q8

Q10

Q15

Q4

Q12

Q5

Q8

Q10

Q7

Q9

Q14

Q3

Q11

Q4

Q7

%

%

%

%

%Q3

Q1 Q2


SAMPLE




TOTAL % SCORE

GEOMETRY - Properties of shapes / Position and direction (continued)

Year 6continued from previous page

TOTAL % SCORE

STATISTICS

s1:

s2:

interpret and construct pie charts and line graphs and use these to solve problems

calculate and interpret the mean as an average

g6:

g7:

describe positions on the full coordinate grid (all four quadrants)

draw and translate simple shapes on the coordinate plane, and reflect them in the axes

%

%

%

%

Q7

Q12

Q15

Q4

Q9

Q6

Q11

Q14

Q3

Q8

Q5

Q10

Q13

Q2Q1

Q13

Q15

Q12

Q14

%

%


SAMPLE

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SAMPLE


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Mathematics SAMPLESamples Assessment Tests: Curriculum · contained in the programmes of study for...

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