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Ma KEY STAGE 1 LEVELS 2–3 2002 Mathematics test Teacher’s guide Key stage 1 2002 Mathematics booklet Name Score Level and gradeFirst published in 2002 © Qualiﬁcations and Curriculum Authority 2002 Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, provided full acknowledgement is given. Produced in Great Britain by the Qualiﬁcations and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Ofﬁce and Queen’s Printer of Acts of Parliament. The Qualiﬁcations and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act 1993. Qualiﬁcations and Curriculum Authority 83 Piccadilly London W1J 8QA www.qca.org.uk/
Contents Background information 2 Speciﬁc guidance: English as an additional language and special educational needs 4 Administering the test 8 Marking the test 15 Finding the level 21 Age standardised scores 22 Teacher’s guidance on assistance for the written questions This guidance is provided in the central pullout section in this booklet.
Background information Children to be tested This test should be used with all children judged by the teacher to have attained level 2 or above in mathematics overall. In addition, you may wish to administer the test to those children who achieved very highly on all parts of the level 1 task. Structure of the test The materials include: a test booklet for each child; administration and marking instructions contained in this Teacher’s guide; a grid providing programme of study references for optional use. The test includes material drawn from the key stage 1 programme of study both for Number and forShape, Space and Measuresin the 2000 national curriculum order. There are two parts to the test. The ﬁrst part comprises ﬁve questions (and one practice question) which are to be read aloud to the children by the teacher and have been devised to be accessible to the majority of children entered for the test. The second part comprises 29 written questions (and one practice question). The test, therefore, has 34 questions in all, but may be divided into sections and spread over two sessions if appropriate. The questions have been ordered approximately by their degree of difﬁculty, as informed by the outcomes of the trials of the test. This test was developed in consultation with a group of year 2 classroom teachers, and was subjected to three types of trial with a nationally representative sample of approximately 3,000 children. Children in one particular class or school may ﬁnd it easier or harder than this sample. It is important that all children are given an opportunity to attempt as many questions as they can in the written test. An evaluation study of the performance of a group of children who just attained level 2 in an earlier test showed that each of the more difﬁcult questions, towards the end of the test, was answered correctly by at least one child in this group. If a child is unable to cope with one written question, he or she should be encouraged to move on to the next question. Timing The test should be carried out and completed during the month of May 2002. It should not be necessary for the test to be taken in more than two sessions. 2
Children may beneﬁt from a break after about 30 minutes. These sessions should normally take place on the same day or on consecutive days. There is no time limit for either part of this test. In previous tests comprising 30 written questions, trialling showed that most children demonstrated what they could do in about 45 minutes, after a short introduction. You should use your discretion to give the children enough time to ﬁnish all the oral and written questions they can do. Grouping children for the test Both the oral and written parts of the test can be administered to all the children at the appropriate levels together, in small groups or individually. For the written part of the test, you may give help with reading (see the central pullout section Teacher’s guidance on assistance for the written questions). Your decision about grouping, therefore, should reﬂect the needs of the children in your class and their ability to work independently. Further guidance on grouping and reading the test is included on page 5. Assistance This test does not require the use of staff beyond those normally available in the classroom. However, it may be administered, under the direction of the teacher, by any competent and informed person such as a language support teacher, teaching assistant or special educational needs support staff. These staff should have a copy of the pullout section mentioned above. The teacher, however, remains responsible for the assessments. Parents of children in the class should not administer the test. Detailed guidance on supporting children during the test is provided on pages 10 –12 for the oral questions and on pages 13–14 and also in the central pullout section for the written questions. Any personadministering the test should be familiar with this guidance and have it to hand during any administration of the test. Age standardised scores This year, the table of age standardised scores for the test is contained within this Teacher’s guideand not in a separate booklet. The use of this table remains optional. Optional grid for test analysis For the ﬁrst time, QCA has produced this year a grid giving programme of study references for each question, which will allow teachers, if they wish, to analyse the performance of the children in their class. QCA would welcome feedback on whether this grid is useful or not. 3
Speciﬁc guidance: English as an additional language and special educational needs You can be ﬂexible in your arrangements for the test as long as any adaptations do not invalidate the assessments. The range of children’s needs is such that it is neither sensible nor possible to provide detailed advice to cover every individual circumstance. You should use your professional judgement and your knowledge of individual children to decide how best to make the test accessible to all children while maintaining the rigour of the assessment. Examples of permissible adaptations include: using tactile shapes and number cards; photocopying on to coloured paper; enhancing shading and/or emboldening lines on diagrams, charts and graphs; cutting out, enlarging, embossing or mounting diagrams; using adhesive to attach materials to a table; using mechanical and technological aids, including computers but not calculators; rephrasing parts of the written questions as indicated in the central pullout section of this booklet. There may be some children who have difﬁculty with the test layout and procedures. These children may be willing to ask for help, and you will be able to ensure they receive the support they need. However, other children may be reluctant to ask. As well as offering reassurance to the whole group, you may need to be active in watching for children who are having problems with reading or with writing responses. Children’s responses Children may convey what they know or understand by any means appropriate to them: talk, sign, writing, gesture, pictures, models, mime or any combination of these. A wide variety of forms of communication is acceptable. Children learning English as an additional language Children who are learning English as an additional language may be given access to the test in any way that is usual for them. If language support is available, the questions may be translated and children may respond in a language other than English. It is not intended that children are provided with a comprehensive written translation of the paper. As with all children, you may read the questions aloud in English. You may also give a fuller explanation of the context of the questions, but it is important to ensure that you do not give any additional interpretation of the mathematics or mathematical vocabulary in doing this. 4
It is particularly important when assessing children for whom English is an additional language that sufﬁcient time is given for the children to show their best attainment without pressure. Special educational needs This test is designed to be used with all children at the appropriate level, but additional consideration should be given to children with special educational needs. Usually, the most appropriate conditions for testing will be those in which the children normally work well. If you judge it appropriate, you may go through the whole test, reading out each question to a group and waiting for the children to write their answers before continuing (the ‘look and listen’ method). This is a legitimate way to administer the test to children who would otherwise have difﬁculties in accessing the test. It is, however, unlikely to be the best method for whole class administration, as the test would then need to be read out to suit the pace of the slowest child.This would mean that children who wanted to work more quickly could become bored with waiting and possibly not demonstrate their best attainment. Some research that QCA has carried out has shown that ﬂuent readers can sometimes perform better if helped by the ‘look and listen’ technique, as they can otherwise skim read questions and misread what needs to be done. However, QCA feels that, in general, children who read ﬂuently can best be helped by the teacher stressing the importance of reading the questions carefully, asking for help with reading unfamiliar text and checking what they have read and how they have responded. Nevertheless, QCA recognises that teachers are in the best position to judge whether ﬂuent readers would beneﬁt or not from ‘look and listen’. You can administer the test to smaller groups of children or on an individual basis and adopt any strategies suggested in this guide. You may describe the pictures to the children or provide them with any objects that convey to them what is in the pictures. You may use overhead projector transparencies of any parts of the test paper to direct children’s attention to what they have to do. Children with hearing impairments Children who have hearing impairments may need particular help with reading. The questions may be presented to the child in sign. A variety of forms of communication can be used for presentation and response, including British Sign Language (BSL), sign supported English (SSE) and Makaton vocabulary. For children who sign, use should be made of a skilled adult signer who is familiar to the child. Since this person may not be the teacher, there is a need for the teacher and the signer to be clear about how the test will be presented. The nature of BSL may demand that some questions are restructured. In restructuring, take care that the signs used neither give clues to the answer or the mathematics to be used nor cause confusion, and that the questions are restructured only where the sign language itself necessitates it. You may also give 5
a fuller explanation of the context of the questions, but it is important to ensure that you do not give any additional interpretation of the mathematics and mathematical vocabulary in doing this. If the child responds orally, the person administering the test will need to be familiar with the hearing impaired child’s voice to ensure responses are understood accurately. You should ensure that children with hearing impairments understand the contributions made and questions raised by other children prior to the start of the test. The oral questions – additional guidance for teachers of children with hearing impairments There are ﬁve questions (and one practice question) which are to be read aloud to the children by the teacher. These questions come at the beginning of the test, but they may be administered to children with hearing impairments during a separate session or at the end of the test. The oral questions should be administered by a familiar adult whom the child is used to lipreading; this could be the child’s special support assistant. Children with hearing impairments should be given enough time to lipread the question, process the information and ﬁnd the appropriate part of the answer sheet to write the answer. Each question may be written out as a ﬂash card or projected as an overhead projector transparency if this will make it more accessible for these children. Teachers of hearing impaired children may reword questions using more familiar syntax if necessary. However, considerable care should be taken in order to avoid altering the nature of the assessment within any question. For example: question 2:Usea girl instead ofHannah. question 3:Find box d. Work out the sum of 13 and 7. If the child cannot lipread, use ﬂash cards with 13 and 7 on them. Write your answer in box d. Children with visual impairments Children with visual impairments may have the test presented to them, and make their responses, in any way that is usual for them, but care should be taken to avoid altering the nature of the questions. All usual low vision aids should be used, and real objects may be used where appropriate. Materials may be enlarged, reduced, cut up, brailled, etc, to increase accessibility for individual children, and children may hand write their answers, use computer facilities, braille or dictate answers to an adult scribe. Help may be given to interpret pictures and diagrams, as long as this does not invalidate the assessment being made. 6
Braille The test is available in grade 2 braille, free of charge, from: Pia Victoria Street Cwmbrân NP44 3YT Tel: 0870 321 6727 Fax: 0870 321 6429 Modiﬁed large print Teachers of children with special educational needs should be aware of a modiﬁed large print version of the test. Although designed for children with visual impairments, this modiﬁed large print paper may be used by other children who have special educational needs. For example, some children with particular physical difﬁculties may ﬁnd it more accessible than the unmodiﬁed paper. The modiﬁed large print paper is produced on A4 size paper using bold print, simpliﬁed diagrams and illustrations with all extraneous information removed. Copies of the modiﬁed large print test are available free of charge. Examples can be seen on the QCA website at www.qca.org.uk/ca/tests/modiﬁed_tests Time for the modiﬁed tests Children using braille or modiﬁed large print tests are likely to need more time to complete the tests than fully sighted children to take account of their slower reading speeds. You will wish to make this clear to the children and to organise the classroom as appropriate. You may ﬁnd it helpful to administer the tests in more than one part. Additional teacher notes have been produced to accompany modiﬁed large print and braille versions of the tests. You should refer to these notes before administering and marking the tests. Children with physical disabilities Children with physical disabilities may have the test presented to them, and make their responses, in any way that is usual for them, for example the teacher scribing dictated answers, the use of enlarged form or the use of a computer. Children with emotional and behavioural difﬁculties Children with emotional and behavioural difﬁculties may have problems maintaining their attention for extended periods of time. For this reason, the test could be administered to this group of children in smaller parts, over a number of sessions, rather than at two sittings. 7 Minor changes have been made to the text in the braille version. A print version of the modiﬁed text for braillists is included with the braille materials. Additional teacher’s notes for the braille test will also be included with the materials. You should have ordered these test materials by photocopying the order form on page 41 of the 2002 Assessment and reporting arrangements booklet for key stage 1. Additional teacher’s notes will be included with the modiﬁed large print materials.
Administering the test Resources For both the oral and written questions, each child will need: a copy of the test booklet; a pen or pencil; a centimetre ruler with which they are familiar; a rubber (optional). You may obtain more useful diagnostic information if you encourage your children to leave their working out on the page and to cross out their mistakes rather than rub them out. If rubbers are not provided: – you should tell the children that they may cross out any answers they wish to change; – you should keep a rubber in readiness for children who wish to change answers they have drawn (such as lines or shapes) where changes may be clearer by rubbing out rather than by crossing out. You should also provide: structured apparatus consisting of tens and units for each group working at the same table. This must be available in sufﬁcient quantity to allow children to select as much or as little as they wish. Please note: No other support materials should be given to the children, for example clocks or clock faces, number lines or squares, addition squares, multiplication squares, calculators or any representation of money (toy or real). Wall displays such as tables charts, number lines or number squares should be covered or removed. Wall clocks do not need to be removed. 8 Number apparatus must be structured into tens and units (Uniﬁx cubes in sticks of tens and ones, Dienes tens and ones, etc) to discourage unhelpful counting in ones rather than the use of tens where appropriate. If interlocking cubes are used, each rod of ten cubes should be made up of one colour only. At least two different colours of rods should be provided. In this way, children can identify a group of ten easily as they calculate. However, you should not intervene if a child dismantles the structured tens when working.
Administering the test fairly In order to ensure that the test is administered fairly in different classrooms, it is important that all teachers behave in a similar way while the test is in progress. THEREFORE YOU MUST: ensure that children can work undisturbed, individually and without access to materials that could give them an unfair advantage. Changes to the usual classroom layout may be necessary. It is important that you decide on seating arrangements before the start of the test, in order to avoid any unnecessary confusion; ensure that the children work on their own and that they do not discuss questions or copy answers. Some teachers have found one or more of the following strategies helpful to ensure that children cannot see each other’s work: seating children at the ends of tables; seating children individually in a larger space; providing a blank sheet of paper to cover completed work on the open page; using large picture books, etc, to create table screening between children; observe the children throughout the test to ensure that they do not copy or distract each other; ensure that wall displays, etc, in the classroom do not give the children an unfair advantage, for example tables charts or number squares or number lines should be covered or removed. However, it is not necessary to remove wall clocks; encourage the children to stay on task and to work at an appropriate pace, moving on to the next question promptly when it is clear that they cannot spend any more time productively on the question they are working on; encourage the children to check all their work carefully when they have ﬁnished. DO NOT: give help with the mathematics, as this will invalidate the assessment; represent questions on addition or subtraction vertically when they are presented horizontally in the test booklet; suggest to the children the mathematical operation to use; give clues which help the children to interpret what any question requires them to do; rephrase or rewrite, except where indicated in the guidance in the central pullout section of this booklet; prompt the children to conﬁrm or change answers by pointing, frowning, smiling, head shaking or nodding, offering rubbers or asking leading questions. Teachers of children with special educational needs should refer to the further guidance on pages 5–7 of this guide. 9
Starting the test When you have seated the children, give each child a test booklet and make sure they have the resources they need. Ask the children to write their name in the space provided on the front of the booklet and introduce the test in your own words, making sure you cover the points outlined in ‘Introducing the oral questions’ (below) then in ‘Introducing the written questions’ (page 13) at the appropriate times. To ensure that the testing is carried out in a standard way in all schools, it is important that your introduction does not exceed this information. Introducing the oral questions These questions will be read aloud by you. The ﬁrst question is a practice question. It is not part of the assessment, so you can spend as much time as you wish helping the children to understand the format, what they should do and where they should write their answer. Children are allowed to use space on the test paper for working out their answers if necessary. There is no time limit on each question, so the length of time taken will depend on the speed of the children. Proceed from one question to the next when you feel that all the children have had ample opportunity to ﬁnd the answer. The text to be read aloud is shown in italics in the next section, ‘Working through the oral questions’. The language highlighted in bold text is part of the assessment, and you should not rephrase it or give explanations of terms used. Tell the children: I will read aloud some questions for you to answer. The ﬁrst question is a practice question which we will all do together. I will read each question twice, leaving a short gap in between. If you want to hear the question a third time, put up your hand. I will explain how to write answers to each question. You must listen very carefully to what I am saying. You will have plenty of time to work out the answers. You must work on your own and you must not call out the answers. If you make a mistake, you should cross it out / rub it out neatly* and write the answer clearly[*as appropriate]. When you have ﬁnished answering a question, look up so that I know you have ﬁnished. 10
Working through the oral questions Ask the children to turn to page 3 of their booklet. Explain: the boxes are for you to write your answers in; the letters below each box show you which box to use for each question; you can do any working out in the white spaces around the boxes, if you need to. Where necessary, you can show the children how to draw a tick, cross, etc. Remember to repeat each question. Repeat the bold textonly. Practice question This is a practice question for us to do together. Find box a. [Help with locating the box where necessary.] Write the number which comes between 13 and 15. Write your answer in box a. Afterwards, ensure that the children know the number they should have written, and discuss methods the children used to work out the answer. Allow any children to change their answer to the correct one by crossing out or rubbing out, to make sure they know the way to correct errors. Question 1 Look at the number grid with b written below it. Write the number 24 in the correct place on the grid. Question 2 Turn over the page. Find box c. At the shop, all packets of crisps cost the same. Hannah buys 2 packets. She pays 40 pence. How much does one packet cost? Write your answer in box c. 11 Teacher: Teacher: Teacher:
Question 3 Find box d. Work out the sum of 13 and 7. [Stress the ‘teen’ in 13 to avoid confusion with 30.] Write your answer in box d. Question 4 Look at the shapes in box e on the next page. One of these shapes has one right angle and three straight sides. Tick this shape. Question 5 Find box f. Imagine a number line. What number is halfway between 11 and 19? [Stress the ‘teen’ in 19 to avoid confusion with 90.] Write your answer in box f. 12 Teacher: Teacher: Teacher:
Mathematics test Teacher’s guidance on assistance for the written questions These centre pages may be pulled out for manageable reference during the test. Any person administering the test should have a copy of these pages available for reference during the test. You must notread numerals, symbols or abbreviations (eg ‘5 + 10 =’ or ‘10p’) unless otherwise stated. Key stage 1 2002 Mathematics booklet Name Score Level and grade Ma KEY STAGE 1 LEVELS 2– 3 2002
2 6 Practice question Only oneof these is correct. Draw a tick (# ) on it. Only oneof these is correct. 6 Draw a tick (# ) on it. 5+7 =10 8+5 =18 10 + 10 = 19 9+6 =15 12 + 4 = 14 85 =7 99 =0 9+2 =12 7 72a eCk+ wg y Ch Cu h4+mNa ,v 3 –Nm{ m kNlhh wy Cu h4+mNa –s You may read and rephrase any of the words except‘square’. You may also read ‘B5’and ‘D2’but do not explain how these relate to the grid. You may read and rephrase any of the words. You may read letters ‘A’to ‘E’on the grid. Do notread the numerals ‘1’to ‘5’.
3 8 Amy has these coins in her purse. 8 How much is in Amy, s purse? Amy spends10p 9 How much does she have left? p p 9 1aNa Ch m hae lp 12pencils. 10 How many is half the set? pencils You may read and rephrase any of the words except ‘coins’which may be read but not rephrased. You may read and rephrase any of the words except ‘How much’ which may be read but not rephrased. You may read but onlyrephrase ‘Amy’. Read ‘10p’ as ‘this amount of money’. Make sure that children attempt question 9. This question was missed by some children in the trials. You may read and rephrase any of the words in this question. Read ‘12’ as ‘this number of’. You may read but onlyrephrase ‘set’.
4 10 Pencil Cis the longest pencil. 11 Order the rest of the pencils. You may use a ruler. 11 Pll+ me e2aha hCiuh} cs 6NCea e2a /ChhCui hCiu Cu amk2 7l8} } – { + 25 18 = 7 10 2 = 20 84=2 You may read any of the words or letters on this page but do not rephrase. If you are uncertain whether a child has written ‘t’ or ‘+’ in an answer box, you may ask the child to make clear which one they have chosen. You may read and rephrase any of the words except ‘sign(s)’which may be read but not rephrased.
5 12 13 Draw a ring around the twoletters which are made with straight lines only. 14 Draw a ring around each evennumber. 35 28 29 11 16 Class 2 counted the letters in their names. They sorted some of them. 15 Draw arrows to show where these other names belong. Tomis done for you. 13 You may explain ‘arrows’ by indicating the one for Tom. Do nothelp with the interpretation of the table. You may read but do not rephrase any of the words on this page. You may read, but onlyrephrase ‘Draw a ring around’. You may read and rephrase any of the words except ‘even number’ which can be read but not rephrased.
6 Gemma asked children which fruit they like best. 16 How many children did Gemma ask altogether? 17 Write the missing numbers in this sequence. children 14 3children need 6counters each. 18 How many do they need altogether? 19 Write the total. 36 + 29 = counters 15 You may read any of the words in this question but onlyrephrase ‘Gemma’. For ‘7’,‘4’, ‘6’ and ‘3’, say ‘this number’. You may read but do notrephrase. You may indicate the two empty boxes but do not help with the interpretation of the sequence. You may read the numbers ‘3’and ‘6’. You may read any of the words in this question but onlyrephrase‘counters’. You may read but do not rephrase.
7 20 Draw a tick (# ) on the clock which shows half past three. 16 21 How heavy is Peter? Peter is kg 17 You may read but onlyrephrase ‘Peter’. You may read any of the words on this page, but do notrephrase.
8 Look at this pictogram. 22 How many girlsare there in the class? There are 12boys in Class 5. 23 Show this on the pictogram. girls 18 Look at these digits. 24 Use all the digits to make the number nearest to 600 25 Tick (# ) the two numbers which total 50 5 3 8 19 You may read but do notrephrase any of the words on this page except ‘Key’ which may be explained as ‘what each of these symbols means’. Do nothelp with the interpretation of the key or the pictogram. For ‘12’, say ‘this number of’. You may read any of the words in this question but do not rephrase. For ‘600’, say ‘this number’. You may remind children to use only these numbers. You may read but do notrephrase any of the words. For ‘50’say ‘this number’. Make sure that the children attempt question 23. This question was missed by some children in the trials.
9 26 Write the missing number in each box. 27 Write the missing number in the box. + 57 = 100 20 Here is a triangle. Tom turns it one quarter turn clockwise. 28 Tick (# ) the triangle which shows how it looks afterthe turn. 21 You may read but do not rephrase any of the words on this page except ‘Tom’ which may be rephrased. You may read but onlyrephrase ‘box’. You may read but do not rephrase the text on the arrows. For ‘1’and‘10’, say‘this number’. You may read but onlyrephrase ‘box’. Do nothelp with the interpretation of the equation.
10 29 Write the answer. 45 } 5 = 30 Write the missing number in the box. 5{4=10 { 22 Anya has £2 She buys 2drinks costing 35p each. 31 How much money does she have left? Show how you work it out in the box. 23 £ You may read but do notrephrase. You may read but onlyrephrase ‘box’. You may read any of the words on this page but onlyrephrase ‘Anya’ and ‘drinks’. You may indicate the box. Remind the children to show their method. They may gain one mark even if their answer is wrong. For ‘£2’ and ‘35p’, say ‘this amount’. You may read the ‘2’in ‘2 drinks’.
11 24 Megan is 109cmtall. Sunil is 137cmtall. 32 How much taller is Sunil than Megan? cm 25 33 Write the answer. 63  37 = There are 440drinking straws in a box. There are 4colours of straws. There is the same number of each colour. 34 How many of eachcolour are in a box? straws You may read but do not rephrase. You may read but do not rephrase any of the words in this question except ‘drinking straws’ and ‘box’which may be rephrased. For ‘109cm’ and ‘137cm’, say ‘this much’. You may read but do not rephrase any of the words on this page except‘Megan’ and ‘Sunil’. For ‘440’, say ‘this number of’. You may read the ‘4’in ‘4 colours’.
© Qualifications and Curriculum Authority 2002
Introducing the written questions Ask the children to close their booklet and to listen carefully while you introduce the written questions. Tell the children: I will do one practice question with all of you, and then you will go on by yourselves. There are many different sorts of question in the test and none will be exactly like the practice question. Read each question, work out the answer and then write it in the space provided in the booklet. There is plenty of space in the booklet, which you can use for working out, writing or drawing your answers. If you are asked to show how you work something out, write or draw how you got your answer since you can get a mark for showing your working. Always read what you are asked to do. Don’t guess. You can have as much help as you need with reading words in the questions, but no help with reading numbers or working out answers.[You may like to explain that this is because this special booklet will help you to ﬁnd out how many questions they can do by themselves.] If you need help with reading, put up your hand but don’t call out. You may use only the apparatus that I have provided(see page 8). [If rods of ten interlocking cubes are provided, you may remind children that they are rods of ten.] If you make a mistake, you should change your answer by crossing or rubbing it out. Some of the questions are harder than others; if you cannot do one question, go on to the next one which might be easier. Go back to the difﬁcult ones later if you wish. You may not be able to complete all the questions, but you should do as many as you can. Some of the questions have pictures which may help you to work out the answers. You can take as long as you need to ﬁnish all the questions you can do. When you have done all you can, check your answers. Don’t discuss the questions with anyone or copy answers. 13
Working through the written questions Ask the children to turn to page 6 of their booklet and ﬁnd the practice question. Help the children to work through the practice question. Allow them to try to answer the question before you discuss it. The practice question is not part of the test, and you can spend as much time as you like helping the children to understand the format, what they should do and where they should write their answers. Ask the children to start working on their own from question 6. You can stop the testing whenever you judge it necessary, for example if you feel a child is becoming too unsettled or has done as much as possible. Assisting children with the written questions Reading the written questions You should give help with reading words as necessary but not with reading numerals or symbolsin the test booklet. You may need to be aware of more ﬂuent readers who do not ask for the help they need to read unfamiliar words. You may wish to write the following words up on the board, and read them through with the whole group before the written part of the test begins: signs, straight, altogether, sequence, pictogram, digits, clockwise. You may also wish to write up any unfamiliar names of children used in the test booklet. You may read them again for any child as necessary during the test. You should not explain these words in any way except where indicated under rephrasingin the Teacher’s guidance on assistance for the written questions. Rephrasing the written questions There should be no written adaptations of the text. However, some instruction words in the test may be rephrased or explained if these are not familiar to the children, since these are generally not mathematical terms and therefore not part of what is being tested. The annotated pages in the Teacher’s guidance on assistance for the written questionsset out exactly which words in each question may be rephrased and give further guidance for supporting children where necessary. It is very important not to exceed the permissible support indicated. Other assistance Apart from the guidance given above and in the Teacher’s guidance on assistance for the written questions, for reading and rephrasing the test, no other assistance is allowed. 14
15 Marking the test When the children have completed the test, mark each answer right or wrong. The mark scheme helps you to identify appropriate answers and tells you how many marks to allocate to each answer. Mark boxes have been provided in the margin of the test booklet, beside each item. For consistency, it is recommended that you enter 1 (mark awarded) or 0 (mark not awarded) in each mark box. In addition, a box has been provided at the far righthand side of each double page spread to enter total marks that children obtain for the set of questions that appear on the two pages. If a child has altered an answer or the answer is not clear, try to establish his or her ﬁnal intention. You may occasionally need to talk with children individually to check this. Be sure to use open questions that do not suggest the required answer. Any numeric answer is acceptable in word or number form unless otherwise stated. Mark scheme Oral Question Answer Mark Additional guidance Practice14None 124 written as shown1 220(p)1 3201 4Bottom triangle ticked as1Accept any other clear way of shown: indicating the correct shape. Do not award the mark if more than one shape is indicated unless it is clear that the correct one is the child’s ﬁnal choice. 5151
Written 16 Question Answer Mark Additional guidance PracticeTick by 9 m9 e0None 6Tick by 9 p6 e151Accept any other clear way of indicating the correct equation. Do not award the mark if more than one equation is indicated unless it is clear that the correct one is the child’s ﬁnal choice. 7Cross drawn in D2 as1Accept any other clear way of shown: indicating the correct square. Do not award the mark if more than one square is indicated unless it is clear that the correct one is the child’s ﬁnal choice. 841 (p)1 931 (p)1 OR 10p less than the amount given for Q8 even if Q8 was not correctly answered. 106 (pencils)1Accept any other clear way of indicating the correct answer, eg six pencils ringed or a line drawn between the pencils separating them into two sets of six. 11Writes A, B and E as 1Accept also the lengths written in shown: this order instead of the letters: 12cm, 11cm, 9cm or any other clear way of indicating the order. 12Writes the correct2Write 1 and 1 in the mark boxes. operation signs in all three boxes: 25 m18 e7 10 t2 e20 8 d4 e2 OR OR Writes the correct 1Write 0 then 1 in the mark boxes. operation signs in two boxes.
17 Question Answer Mark Additional guidance 13Rings around E and A.1Accept any other clear way of indicating the correct letters. Do not award the mark if extra letters are ringed unless it is clear that the correct two are the child’s ﬁnal choice. 14Rings around 28 and 16.1Accept any other clear way of indicating the correct numbers. If extra numbers are ringed, do not award the mark unless it is clear that the correct two are the child’s ﬁnal choice. 15Matches Sean, Bethan and1The arrowheads do not need to be Lauren as shown: drawn. If extra lines are drawn, do not award the mark unless it is clear that the correct three lines are the child’s ﬁnal choice. Accept any other clear way of indicating the correct set for each name, eg writing the name in each set. 1620 (children)1 17Write 32 and 27 in this1 order in the boxes. 1818 (counters)1 19651 20Botton right clock ticked1Accept any other clear way of as shown: indicating the correct clock. Do not award the mark if extra clocks are ticked unless the child indicates the correct one as his/her ﬁnal choice. 2124 (kg)1 2217 (girls)1 23Draws 6 full circles as1Accept the correct answer drawn shown: under Q23 or elsewhere. Do not accept combinations of whole and half circles. 245831Accept also 500, 80 and 3 written in the digit boxes.
18 Question Answer Mark Additional guidance 25Ticks drawn on 24 and 261Accept any other clear way of indicating the correct numbers. Do not award the mark if extra numbers are ticked unless it is clear that the correct two are the child’s ﬁnal choice. 26Writes 20 and 29 as1 shown: 27431 28Bottom right triangle1Accept any other clear way of ticked as shown: indicating the correct triangle. Do not award the mark if extra triangles are ticked unless it is clear that the correct one is the child’s ﬁnal choice. 2991 3021 31£1.302Award both marks for the correct answer (even if working is unclear or not shown). Write 1 and 1 in the mark boxes. Accept also £130 or £1.30p or £1:30 or £1 30 (with a clear space between the 1 and 3) or any of these in words. OR OR This mark may be awarded 1 If mark awarded, enter 0 then 1 in the for children who: mark boxes. This mark should not be a) have the wrongawarded to children who have an answerbut a correctincorrect answer unless the method methodthat is they communicate is acceptable. (This communicated clearly: might be using numerals, signs, words or diagrams, or any mixture of these.) or b) have written 130 in the Accept £1.3, £13 or £130 or £130p for answer box as evidence 1 mark but not 2 marks. of appropriate working. Examples of some acceptable and unacceptable responses are shown on pages 19 and 20. 3228 (cm)1 33261 34110 (straws)1 Maximum 36 marks
19 Examples of acceptable methods (1 mark may be awarded) Although he had added mentally two lots of 35p incorrectly, Davindar has shown that he knows he needs to subtract this amount from £2. He has used a correct and appropriate method. Georgia’s method is clear and appropriate because her working shows evidence of calculating the cost of the two bottles of cola and explaining what money will be left after the purchase even though she has mentally calculated the difference between 70p and £1 as 20p. Although Janine has not shown her working out, it is reasonable to assume that she calculated mentally the difference between £2 as 200p minus 70p giving an answer of 130p. She has failed to convert this correctly to £1.30 but still gets one mark for writing 130 in the answer box since it is assumed that her method of calculation was appropriate. Alexander’s working clearly shows that he knew to subtract two lots of 35p from £2 even though his answer is 10p less than it should be. However, his method is clearly correct and appropriate. Michael has clearly identiﬁed an appropriate sequence of operationswhich could lead to the correct answer. He has made an error in the ﬁrst calculation, leading to his answer being 10p more than it should be. Nevertheless, he has communicated clearlythat he knows to subtract two lots of 35p from £2. Ishmael has created a number line which clearly shows the stages he went through to ﬁnd his answer. He got an incorrect total of £1.20 when he subtracted 25p from £1.90 to give an answer of £1.55. However, he has communicated a reliable, correct method. Davindar Janine Alexander Michael IshmaelGeorgia 0 0 0 0 0 0 Examples of responses from question 31 11 1 1 1 1 £ £ £ £ £
20 Examples of unacceptable methods (1 mark may notbe awarded) Mark’s brief explanation gives no indication of understanding the problem since it is not clearwhat the relationship between counting on in 10s and solving the problem is. Not only would this strategy on its own not lead to a correct answer, but there is no indication that he recognises the need to ﬁnd the difference between two lots of 35p and £2. Jennifer’s working shows no evidence of recognising that she has to subtract two lots of 35p from £2. Her method is neither appropriate nor correct since her attempt at calculating shows that she does not understand the problem. To get an answer of £1.20 instead of £1.30, Nisha can be assumed to have used an appropriate mental method. However, since the answer is incorrect and she has not shown any working, she cannot unfortunately be awarded either mark, as there must be evidence of subtraction. Kevin made a good start by calculating the cost of the two drinks. The text he then wrote in his explanation implies that he knows what to do, but he has not explained in enough detail the method he used to get an answer of £1.50. There is not enough informationfor Kevin to be awarded the method mark. Andrew’s working shows no evidence of recognising that he has to subtract two lots of 35p from £2. His method is inappropriate and incorrectsince his attempt at calculating shows that he does not understand the problem. Chrissie has explained carefully how to calculate how much money would be left if one drink costing 35p was bought. However, this is not sufﬁcient for the working mark,as there must be evidence of subtracting the cost of two drinks from £2. Mark Nisha Kevin Andrew ChrissieJennifer 0 0 0 0 0 0 Examples of responses from question 30 00 0 0 0 0 £ £ £ £ £ £
21 Finding the level Add up each child’s total score out of the maximum of 36 marks (not including the practice questions), and write this total in the box marked ‘Score’ on the front of the child’s test booklet. Then refer to the table below to ﬁnd the level (and grade if level 2), and enter this on the front of the booklet in the box marked ‘Level and grade’. This information will then be available to transfer on to any recording or reporting document. Evidence shows that it is easy to make careless slips in adding up total scores, and these slips could disadvantage the child; thorough checking and rechecking are, therefore, strongly recommended. The key stage 1 mathematics test covers only a limited range of material pitched at level 3. It can indicate only where a child has performed well enough to be awarded level 3 at the threshold. It does not indicate how much further into level 3 or beyond a child might be able to go. However, if a child scores very highly on this test (at or near 100 per cent) you should consider whether assessment at level 4, using the key stage 2 mathematics tests, is appropriate. Number of marks Level 0– 4 No level awarded Level 1 awarded Level 2C awarded Level 2B awarded Level 2A awarded Threshold level 3 awarded 5–7 8–13 14–18 19– 24 25–36
Age standardised scores This section provides age standardised scores from the 2002 key stage 1 mathematics test. The scores are for optionaluse, and you need only refer to this section if you wish. The purpose of the information set out here is to allow you to convert the child’s actual score in the tests – the ‘raw score’ – to an age standardised score. Age standardised scores take into account the child’s age in years and months, so you have an indication of how each child is performing relative to other children of the same age. However, age standardised scores will not affect the child’s level of achievement in the national curriculum as awarded by the outcome of the tests. The tables were calculated from the results of standardisation trials of each test with over 2,000 children in a nationally representative sample of schools. The information in the tables is speciﬁc to each test and cannot be used for any others. Working out age standardised scores You will need each child’s test score and age at the time of testing, in years and completedmonths. For example, a child born on 30 March 1995 and tested on 15 May 2002 would be 7 years and 1 month old. Using the table on page 24, you can convert the raw test score into an age standardised score by: locating the child’s age in years and completed months at the time the test was taken, along the top of the table; locating the child’s raw test score down the left side of the table; reading off the standardised score from where the row and column meet. The average standardised score is 100. A higher score is above average and a lower score is below average. About twothirds of the children will have standardised scores of between 85 and 115. Almost all children fall within the range 70 to 130, so scores outside this range can be regarded as exceptional. Making use of age standardised scores If you choose to ﬁnd the standardised scores, you may use this additional information about the children’s performance in any way you wish. For example: You may decide to inform parents about how a child’s performance in the test relates to his or her age at the time the test was taken, ega standardised score of 112 shows us that the child’s performance was above average for his or her age. You could use the information in planning teaching, for example to identify children whose achievement, although within the expected range, may have been surprising in relation to their age at the time of taking the test, egthese scores were very good for these children once their age was taken into 22
account – perhaps I could be stretching that group with more challenging work. You may be able to identify patterns in results, which indicate teaching and learning issues to be addressed, egthe performance of girls in our middle age group is consistently better than the boys in that group, but this pattern is not repeated in the other two age groups. Why might that be? Is there something we need to think about here? Standardised scores may be averaged across a group, for example the whole class or school. In the ‘average’ class or school, the average score should be close to 100; if it is much above or below this, the performance of your class or school varies from the national average. Similarly, standardised scores could be used to consider differences in performance between boys and girls, or between children who are learning English as an additional language and those who are not, in your school. (This will give you useful information only if the group is reasonably large; the average of just a few children is not a reliable indicator.) National comparisons – using the shaded bands The tables of standardised scores are divided into ﬁve shaded bands. These bands give an indication of how the scores relate to the national population. The band nearest the top of a table contains the scores that correspond to the lowest ﬁfth of the population; the next band, the next ﬁfth; and so on. If a child has a score in the ﬁnal band, you know that his or her score is in the top 20 per cent nationally, once age has been taken into account. *** Very low standardised scores are printed in the table as ***. This means that they would be below the lowest score in the table, but cannot be calculated with the necessary degree of statistical reliability. If an exact score is needed, for example to calculate an average for the class, the next score below (69) should be used as appropriate for these children. Conﬁdence bands Any scores derived from a short test are subject to some margin of error. A margin of error does not mean children have been assessed incorrectly. It is simply a statistical estimate, based on the fact that tests can only sample the particular area of learning which they assess. To indicate how wide this margin of error is likely to be, a ‘90 per cent conﬁdence band’ has been calculated. This means that you can be 90 per cent sure that the child’s true score lies within the conﬁdence band. The 90 per cent conﬁdence band for the mathematics test is 8 marks. So, for example, if a child has a standardised score of 110 in the test, you can be 90 per cent certain that the true score is between 102 and 118. 23
24 6.05 6.06 6.07 6.08 6.09 6.10 6.11 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 7.11 0 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 1 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 2 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 3 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 4 74 73 72 71 71 70 *** *** *** *** *** *** *** *** *** *** *** *** *** 5 78 77 76 75 74 74 73 72 71 71 70 *** *** *** *** *** *** *** *** 6 818079797877767575747372717170************ 7 84838282818079787777767574747372717170 8 87868584838382818079797877767575747372 9 89888787868584838382818079797877767575 10 91 90 90 89 88 87 87 86 85 84 83 83 82 81 80 79 78 78 77 11 93 92 92 91 90 89 89 88 87 86 85 85 84 83 82 81 81 80 79 12 95 94 93 93 92 91 90 90 89 88 87 87 86 85 84 83 83 82 81 13 96 96 95 94 94 93 92 92 91 90 89 89 88 87 86 85 85 84 83 14 98 97 97 96 95 95 94 93 92 92 91 90 90 89 88 87 86 86 85 15 100 99 98 98 97 96 95 95 94 93 93 92 91 90 90 89 88 87 87 16 101 100 100 99 98 98 97 96 96 95 94 94 93 92 91 91 90 89 88 17 102 102 101 100 100 99 98 98 97 96 96 95 94 94 93 92 92 91 90 18 104 103 103 102 101 101 100 99 99 98 97 97 96 95 95 94 93 92 92 19 105 105 104 103 103 102 101 101 100 99 99 98 97 97 96 95 95 94 93 20 107 106 106 105 104 104 103 102 102 101 100 100 99 98 98 97 96 96 95 21 108 108 107 106 106 105 104 104 103 102 102 101 100 100 99 98 98 97 96 22 110 109 109 108 107 107 106 105 105 104 103 103 102 101 101 100 99 99 98 23 112 111 110 110 109 108 107 107 106 105 105 104 103 103 102 101 101 100 99 24 113 113 112 111 111 110 109 108 108 107 106 106 105 104 104 103 102 102 101 25 115 114 114 113 112 112 111 110 109 109 108 107 107 106 105 105 104 103 103 26 117 116 115 115 114 113 113 112 111 111 110 109 109 108 107 106 106 105 104 27 119 118 117 117 116 115 115 114 113 113 112 111 110 110 109 108 108 107 106 28 121 120 119 119 118 117 117 116 115 115 114 113 113 112 111 111 110 109 108 29 122 122 121 121 120 119 119 118 118 117 116 116 115 114 114 113 112 111 111 30 124 124 123 123 122 122 121 121 120 119 119 118 117 117 116 115 115 114 113 31 127 126 126 125 125 124 124 123 122 122 121 121 120 119 119 118 118 117 116 32 129 128 128 127 127 127 126 126 125 125 124 124 123 122 122 121 121 120 119 33 131 131 130 130 130 129 129 128 128 128 127 127 126 126 125 125 124 124 123 34 133 133 133 133 132 132 132 131 131 131 130 130 130 129 129 129 128 128 127 35 136 135 135 135 135 135 135 135 134 134 134 134 134 133 133 133 133 133 132 36 137 137 137 137 136 136 136 136 136 136 136 136 136 136 136 135 135 135 135 Age in years and months Mathematics test Raw score Very low scores are printed in the table as ***. This means that they would be below 70.
EARLY YEARS NATIONAL CURRICULUM 5 –16 GCSE GNVQ NVQ OTHER VOCATIONAL QUALIFICATIONS GCE A LEVEL For more copies (for any purpose other than statutory assessment), contact: QCA Publications, PO Box 99, Sudbury, Suffolk CO10 2SN (tel: 01787 884444; fax: 01787 312950) Order refQCA/02/873 (teacher pack) QCA/02/874 (pupil pack) J018611/2