Numeracy Guidebook for

NMWCTE ITT courses

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Our vision:

To educate, support and motivate students to become excellent and creative teachers, who will inspire and empower all learners to reach their potential

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Introduction 3

Synopsis of personal Numeracy skills and Numeracy in the Classroom 4

Assessment of trainees’ personal numeracy skills 4

Overview and procedures at interview 4

Initial audit and numeracy support 5

Tracking trainees’ personal numeracy skills 6

Key assessment points 6

The self-assessment numeracy matrix 7

Numeracy skills in the classroom – mentor assessment and grading 8

Assessing trainees’ ability to develop numeracy skills in the classroom 8

The grading of the application of numeracy in the classroom. 8

Examples of comments, grades and targets. 9

Summative data collection points 9

Planning for numeracy 10

Lesson Plan Exemplars 12

Foundation phase 12

Primary 15

Secondary (science) 18

Design and technology (secondary) 21

References and further reading (for planning/personal numeracy) 24

Acknowledgements 24

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Contents

INTRODUCTION

The aim of all the skills guidebook series is to provide consistency in the Centre’s provision and procedures in relation to all key skills. The Numeracy Skills guidebook is designed for use by trainees, tutors and mentors to ensure shared knowledge and understanding across the centre (university and school based) and within the ITT courses regarding Numeracy skills. The four courses at the centre are:

BA (QTS) Bangor UniversityBSc (QTS) Bangor UniversityPGCE (Primary) Bangor UniversityPGCE (Secondary) Bangor and Aberystwyth Universities

This guidebook addresses two aspects of numeracy within ITT courses provided by the North and Mid Wales Centre of Teacher Education:

the development and assessment of trainees’ and students personal numeracy skills; the development and assessment of trainees’ and students’ ability to implement the

numeracy framework in the classroom.

The guidebook will also include:

exemplars of cross curricular skills lesson plans across all phases to demonstrate effective planning that will also serve as a starting point for discussion and analysis

o during school experience skills briefing session o during mentor and tutor training dayso and as possible focus in weekly mentor and tutor meetings

general literature, documents and websites to provide ideas, critical references and practical activities when applying numeracy in the classroom.

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Synopsis of personal Numeracy skills and Numeracy in the Classroom within the North and Mid Wales Centre of Teacher Education:

Personal numeracy skillsAll courses will ensure that all trainees are assessed as having functional personal skills in numeracy applicable in a professional teaching context, appropriate to the phase and subject of study. All courses will also ensure that all trainees’ personal skills in numeracy are regularly and accurately assessed throughout their training and at the point that trainees are assessed against the QTS Standards at exit (as set out in WG document number 127/2013, Requirements for initial teacher training courses at higher education institutions in Wales).

Numeracy in the classroomAll courses will develop trainees’ ability to plan effectively for the teaching of numeracy and to address learners’ needs appropriate to their phase and subject and subject area. Trainees will become familiar with the skills expected of learners to develop throughout their time in school, from ages 5 to 14. They will become adept at recognising opportunities to apply numeracy in context within their lessons and will use the Numeracy Framework to plan for and assess learners’ progress (as set out in WG document number 120/2013 National Literacy and Numeracy Framework. To support schools in introducing the National Literacy and Numeracy Framework.) All courses will assess trainees’ ability to plan and deliver lessons which implement the numeracy framework; this assessment will contribute to the grading of trainees against the QTS standards during school experience and at exit. All grading will conform to guidelines outlined in the booklet “Grading Accurately and Consistently” and criteria specific to numeracy are included later in this document.

Assessment of trainees’ personal numeracy skills

Overview

All trainees’ numeracy skills will be assessed at interview when applying for all QTS courses. Once accepted onto the course they will be subjected to an initial audit to identify areas of numeracy in which they need to develop. A small number of trainees will be identified for extended support in small classes customised to address their needs. All trainees will be expected to access online materials to improve their numeracy during courses and their progress will be monitored in their professional development documents profile (PDD-Secondary) or personal progress file (PPF- primary) and formally assessed on exit. The final audit will inform their career entry profile and enable them to continue their progress in their first year of teaching

Procedures at interview

All trainees will sit the half hour all Wales numeracy test agreed by UCET in response to the guidance given in WG document number 120/2013 Requirements for initial school teacher training courses at higher education institutions in Wales. Candidates who have recognised additional learning needs such as dyslexia will be accorded an additional 10 minutes (this complies with both Universities’ code of practice for the provision for students with additional learning needs). Candidates must achieve a minimum 50% to be accepted to all courses. Should they show particular promise in other areas at

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interview then they will have the opportunity to retake the test once and once only to gain access to the course.

The numeracy test will focus on the functional mathematical skills required by teachers in their professional role; calculators will not be allowed. English and Welsh versions of the question paper will be provided and applicants can choose to answer in either language.

A sample test is available at https://www.bangor.ac.uk/addysg/courses/PGCEs/docs/Numeracy_test-exemplar.pdf

The test is similar to those set for ITET courses in England and additional support can be found here: http://sta.education.gov.uk/professional-skills-tests/numeracy-skills-tests

Initial audit and numeracy support

The Centre provide an initial audit on entry during the first two weeks of all courses. (See Appendix 1 for a copy of the audit)

All trainees who gain less than 50% in these tests are required to attend additional numeracy classes. However, tutors may recommend that other trainees attend especially if their first subject area is science or during the primary phase; all trainees are welcome to attend the sessions voluntarily. The number of timetabled support lessons provided are:

PGCE (Primary and secondary) 6 hours

BA and BSc (QTS) 6 hours per year

These additional classes will focus on basic concepts such as proportion; ratio; efficient mental and written methods; decimals, percentages and fractions; shapes and measures and data handling. As these classes are intended to be small, content is tailored to individual learners’ needs.

These sessions are timetabled across complete courses for both PGCEs and in the first and second year of the BA and BSc courses. Additional individual one to one sessions will be provided to cater for individual needs on the BA and BSc courses, especially in the third year

In addition to these support sessions, all primary trainees (PGCE and BA) attend mathematics subject knowledge sessions which combine subject knowledge with effective pedagogic approaches to mathematics and numeracy.

Those gaining higher than 50% in the numeracy audit are required to identify areas of their own numeracy requiring development. They will study independently using online materials developed by the centre and linked to other websites aimed at improving numeracy skills. These online materials are embedded in all courses’ Blackboard sites and students track their own progress throughout the year using the numeracy tracker in their PDD(secondary) or PPF(primary)noting their attainment at the following key points:

PGCE (Secondary and Primary): end of SE1, end of SE2

BA, BSc: end of SE1, SE2 and SE3

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All trainees will then be audited using Test B towards the end of each course. The results of the audit exit will identify targets for the Career Entry Profile which will be the basis for further development as part of the statutory induction period for each newly qualified teacher (NQT).

Tracking trainees’ personal numeracy skills

There are two aspects to the tracking of trainees’ numeracy skills:

Test based audits Trainee self-audit

The test audit will assess key numeracy skills needed by all teachers whilst the self-audit will target a wider set of key numeracy skills selected from the numeracy framework.

The self-audit identifies areas for development and each question is linked to specific support materials via Blackboard.

The key assessment points are as follows:

PGCE Primary and secondary

Activity When Assessor

Initial audit (Test A) Sept Tutor

Response to the initial audit and personal reflection Start of PY1 Trainee

Second self-audit within the PDD Start of PY2 Trainee

Exit audit (Test B) to inform CEP June Tutor

BA (Primary), BSc (D&T)

Activity When Assessor

Initial audit (Test A) Entry to year 1 Tutor

Response to the initial audit and personal reflection in PPF Start of Year 1 Trainee

Interim audit End of year 1 Trainee

Response to the initial audit and personal reflection in PPF Start of Year 2 Trainee

Exit audit (Test B) to inform CEP End of year 2 Trainee

Identify trainees needing further support Start of year 3 Tutor

The self-assessment matrix is shown on the next page.

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Personal Numeracy AuditPlace a tick or cross in the first and final columns to signify which questions were correct in the two tests. At the end of each School Experience you should place a number in the shaded boxes

1 = full understanding 2 = partial understanding 3 = insufficient understandingUnless you have full understanding you should use the Blackboard Numeracy pages to help you develop your knowledge in the identified area

Numeracy Skill Test AAudit

Test BSE1 SE2

1. use appropriate strategies for multiplication, including application of known facts

2. use appropriate strategies for division, including application of known facts

3. use efficient written methods to add, subtract and multiply numbers with up to 2 decimal places

4. use ratio and proportion to calculate quantities.

5. use common metric units of measure, convert between related units and carry out calculations

6. calculate using foreign money and exchange rates;

divide numbers with up to 2 decimal places

7. calculate percentages of quantities using non-calculator methods where appropriate;

use equivalence of fractions, decimals and percentages to compare proportions

8. use timetables and time zones to calculate travel time.

9. make links between speed, distance and time.

10. calculate the outcome of a given percentage increase or decrease

11. express one quantity as a percentage of another;

simplify a calculation by using fractions in their simplest terms

12. interpret graphs that describe real-life situations, recognising that some graphs may be misleading;

use mean, median, mode and range to compare two distributions

13. calculate areas of compound shapes and volumes of simple solids (e.g. cubes and cuboids)

14. convert temperatures between appropriate temperature scales.

Note that the numbers in the first column correspond to the questions in Test A and Test B Total A Total B

Trainee Signature: ____________ Tutor signature: ___________________ Date_________

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Numeracy skills in the classroom

Assessing trainees’ ability to develop learners’ numeracy skills in the classroom.

Whenever appropriate, trainees should be developing learners’ numeracy skills with reference to the numeracy framework, planning clear learning objectives and success criteria and applying pedagogy based on sound theory and recognised good practice. Planning and implementation should be supported by effective assessment of pupils’ attainment in numeracy using appropriate questioning.

We acknowledge that some secondary subjects will not be planning for numeracy as often as others but all trainees will be supported during University sessions either in numeracy/mathematics specific sessions (primary) or during their subject specific sessions (secondary). The unique nature of each secondary subject means that designing meaningful numeracy activities is more suited to the subject based sessions.

The grading of the application of numeracy in the classroom.

When grading trainees’ application of numeracy in the classroom it should be assessed to what extent the trainee is able to:

recognise opportunities to apply numeracy when they arise; use numeracy specific vocabulary correctly; use visual and practical aids to develop pupils’ understanding where appropriate; have appropriate expectations of pupils according to age and prior attainment; respond appropriately to pupils’ misconceptions and errors; assess pupils’ understanding through skilful questioning.

When assessing numeracy the observer should assess whether the above are outstanding, good, in need of development, in need of considerable development or unsatisfactory.

As the numeracy grade will be closely related to pupils’ progress during the lesson the grade given for numeracy should be the same as or one less than that given for S3.3.

For example, in the lesson shown below the grade given for S3.3 was 2 (good) but pupils’ progress in numeracy was only 3+. The corresponding comment is also shown.

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Note that if there is no numeracy observed in the lesson the observer should assess whether the omission is justified or not. If the trainee misses numerous opportunities to plan for numeracy then the trainee should receive a grade 4. When observing note either “missed opportunity” or “n/a”, leaving the grade blank.

We do not expect all trainees to apply numeracy in all lessons; the frequency of numeracy should be appropriate to both phase and subject.

Good application of calculating percentages in an appropriate context but questioning of pupils’ understanding needs further development

Examples of comments, grades and targets.

Comment There was little use of visual aids to help learners use fractions – this needs considerable improvement; your questioning still requires some improvement.

Grade 3

Target: Use the number line and shaded squares to represent fractions pictorially

Comment The good combination of your questioning and responses to pupils’ errors ensured most pupils made good progress.

Grade 2

Target: Plan for questioning which exposes misconceptions (cognitive conflict).

Comment Missed opportunity

No grade

Target: Apply numeracy when reading maps. Scale (proportion) and bearings (angles) are particularly relevant.

Comment The excellent use of counters linked to the number line and followed by appropriate responses to misconceptions ensured all pupils made good progress or better.

Grade 1

Target: Transfer counters number lines to the teaching of fractions and percentages.

Summative data collection points

For each school placement, mentors should grade trainees’ application of numeracy in the classroom within the following documents:

The Interim Report on trainees’ progress and Target Grades

The End of School Placement Report

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Planning for Numeracy

When planning the numeracy content of a lesson we must be careful not to overstate the level of what we are actually doing. For example, in the science activity, learners are measuring the height from which they drop the ball bearing (with a metre rule) and the diameter of the ball bearing (with a 15cm ruler). It is tempting to look at the Numeracy Framework (NF) and choose this statement:

read and interpret scales on a range of measuring instruments (year 6 and year 7)

but if we track back to year 5 we can find this:

use measuring instruments with 10 equal divisions between each major unit, and record using decimal notation, e.g. 4.2cm, 1.3kg

It is arguable whether measuring with a metre rule with 100 division is more advanced so it is best here to focus on the most relevant statements linked to the task and to the identified needs and/or expected age related outcomes of your pupils:

select and construct appropriate charts, diagrams and graphs with suitable scales (KS3) interpret mathematical information; draw inferences from graphs, diagrams and data,

including discussion on limitations of data (KS3)

These two statements are clearly linked to the task and you can also assess your pupils’ progress using their spoken and written responses. There is a similar problem with the angles in KS2 – the elements do not match the year conveniently. Therefore, when including numeracy in your lessons, make sure you are aware of the related statements for both younger and older years.

Context

Note that the first statement within the reasoning strand is:

transfer mathematical skills to a variety of contexts and everyday situations

The pupils are doing this every time they use numeracy skills in your classroom. Draw attention to this and ask them what they have done in maths lessons and in other subjects, for example, Geography. This element has not been chosen for the KS3 science lesson but has been noted in the KS2 D&T lesson as there are fewer D&T targets being met here. The challenge in the KS3 D&T lesson is to limit the number of elements being addressed explicitly as there are so many mathematical concepts emerging naturally from the tasks. The teacher has chosen to look at area and units to make assessment realistic and specific.

The foundation lesson should be seen as one activity within the overall provision that hmay include many other stations and activities. This plan should not take priority over the general planning and structure of the foundation learning

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Assessment

As you have included numeracy in your lesson it is important that trainees record both the opportunity the pupils have had and their attainment of that element. This should be a simple process otherwise it is time-consuming. It should also match the school’s policy for assessing pupils’ progress against the NF.

Trainees should be asking questions and prompting learners throughout the lesson. The exemplars show the type of questions and prompts they should be planning but they are not comprehensive. More importantly, they cannot prepare for all pupils’ responses; how they react to misconceptions, misunderstandings and unforeseen events is part of the delivery of excellent lessons.

Finally, when evaluating the lesson trainees should listen critically to pupils’ oral responses, note the ways in which they work and talk together and evaluate their completed artefacts/problems/written work. These can be linked to the success criteria and contribute to the overall numeracy assessment of the learners.

Lesson Plan Exemplars

The following pages detail lesson plans in four different contexts:

Foundation phase Primary Secondary (science) Design and technology (secondary)

When planning for numeracy there should be clear links between the element of the framework, the learning objectives, the success criteria and the questions designed by the trainee. The learning objectives should ideally be based on the higher thinking skills of understanding, analysis and application whilst SCs should be visible or audible evidence of learning.

For example:

Element: Use known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6 (Yr 8)

L.O. Pupils understand the role of place value when multiplying decimals

S.C. Pupils can explain, using a number line or place value, why 0.7 x 6 = 4.2

Questions Show me your calculation on a number line

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PLANNING PRO FORMA Foundation Phase ExemplarName Class: Reception Date: Subject/Context: Creative Development/Physical Development

TRAINEE’S TEACHING SKILLS TARGETS:S3.2.3 assess learners’ progress using the Foundation Phase OutcomesFocus on observation – see AFL box below

LEARNERS’ LEARNING TARGETS:Develop glue skills observed at Continuous Provision sessionSupport CR and HT who had difficulty with tripod grip.

Skills development

Creative Developmentmake choices when choosing materials and resources

Physical Developmentdevelop fine manipulative skills;use and handle a range of tools.

Numeracy/Mathematical DevelopmentRepresent and Communicateuse everyday and mathematical language to talk about their own ideas and choices

Personal Developmentconcentrate for lengthening periods

Learning objectives

Make a personal selection from a range of resources for decorating their bucket

Use fine manipulative skills to handle a glue spatula

Use everyday and mathematical language to describe their buckets

Success Criteria

The child makes choices regarding the size of bucket and the designs

The decoration of the bucket fits the outline. Shapes are regularly fitted

Glue is used without mess/wasting glueResources are stuck accurately with the glue. Shapes do not fall offGlue does not spoil the design

Compare size and describe shapes using key maths words accurately within whole sentences.

Assessment for learning

Record observations on pre-printed stickers and feed into Foundation Phase Compact Profile – Mathematical Development

Observation during activity by teacher and TA

Focus: Note any children showing left hand dominance for individual portfolios and class display board.

LESSON STRUCTURE & DETAILED PLAN OF ACTIVITIESSKILLS DEVELOPMENT Thinking Skills, PSE, ESDGC

Time Lesson activities Ongoing plenary/ AfL

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15 m

35 m

10 m

15 m

Read Billy’s Bucket paying particular attention to Page 5 Show the pupils the choice of materials. Use the Billy puppet to select resources and model vocabulary of size.

Children come to the ‘Cut and Stick’ area to decorate buckets. Children choose a particular size bucket and resources to decorate. Children use PVA glue and spatulas and are encouraged to talk about choices.Encourage use of key words

Encourage description of the 2D metallic shapes: children should describe size, relative size, shape and colour

Support those who need gluing assistanceSupport use of small/medium/largeExtend through challenging questions about the shapesSquare, circle, straight, round etc

TA to initially support CR and HT with tripod grip then model language

Review designs. Prompt improvements

PlenaryIWB prepared presentation: revisit ‘Billy’s Bucket’ Children click and drag decorative items following other pupil’s descriptions using colours, larger, smaller, large, small, medium, circle, square, triangle for extension

Questions and promptsShow me a large/medium/small.....Which buckets are larger/smaller?Tell me about other sizes you can see.

Observe how the children handle the spatula using appropriate tripod grip

Can they scoop glue without overloading and transfer without spillage?

ListenDo pupils describe their choice of decorations. Remodel this and question during activity.

TA to complete the stickers with focus on glue skills for future planning

Children use two stars and wish technique to offer comments on the task

How would you describe that shape........

TA to complete the stickers with focus on mathematical language for profile

CYMRAEG Bob Dydd: Helpwr heddiw to recite the greeting dialogue:Bore da /Pnawn da…(name child)Sut wyt ti? HH to prompt feelings vocabulary/or use hand gestures hapus/wedi blino/trist/eisiau gweithio?Esiteddwch Task related sentences:Ga i…Mae’r bwced yn ... goch, melynLliwiau (see below) KEY WORDS/TERMINOLOGY(Bilingual)Glue/glud, paper/papur, bucket/bwced, red/coch, yellow/melyn, blue/glas, big/mawr, mawr/mwy, small/bach, smaller/llai medium/canoligRESOURCESBuckets; plant pots (small, medium and large) shells, large sequins, glitter, metallic papers cut into 2D shapes, PVA glue Glue spatulas

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LESSON EVALUATIONLearning objectives (from page 1):

Make a personal selection from a range of resources for decorating their bucket

Use fine manipulative skills to handle a glue spatula

Use everyday and mathematical language to describe their buckets

Evaluation of Learning (against LOs)

Nearly all children could independently select materials except J.P. who needed considerable encouragement to participate and B.G. who refused to come to the Cut and Stick area.

Nearly all children managed the task and use the spatula effectively. From previous weeks observations C.R. showed improved use of glue spatula but H.T. needs further support. Consider other activities to develop H.T.’s physical dexterity.

Observational checklist of activity allowed the TA identify which pupils used mathematical vocabulary effectively. See attached assessment checklist. Details to be fed into pupil’s Compact Profile records.

Some pupils used both size and comparative size language but a few pupils need more support with comparative (see targets below)

Learners’ targets (carried forward to next lesson)Mrs. Jones to encourage J.P. to make independent choices of play materials during target time.

HT to be offered builders tray activities scooping gloop to improve fine manipulative skills and to be encouraged to use ‘Finger Gym’ provision.

BG to be offered craft activities in the Outdoor Area as this is where he is showing most engagement.

Use observations from Compact Profile to feed into size activity next week during ‘Three Bears’ task. Lower achievers – extend mathematical language to include long, short and consolidate comparativeHigher achievers – extend comparative language of size to all dimensions and other concepts (eg mass)

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PLANNING PRO FORMA KS2 ExemplarName Class Year 6 Date Subject/Context D&TTRAINEE’S TEACHING SKILLS TARGETSManage focus group effectively whilst scanning whole classAllow learners time to reflect Hold regular pit stops within the lesson

LEARNERS’ LEARNING TARGETSTo work more independently when stuckFor GJ and GW to extend their own learning where possible (Activity 2)

Skills development

DCF create using 2D design

Develop thinking skills as regards reducing waste on the length of wood

Numeracytransfer mathematical skills to a variety of contexts and everyday situations

Y5 use measuring instruments with 10 equal divisions between each major unit, and record using decimal notation, e.g. 4.2cm

Y7 measure and draw angles.

Support: Y4 measure on a ruler to the nearest mm and record using a mix of units, e.g. 1cm 3mm

Learning objectives

Understand angles within a context

Measure angles and lengths accurately

Use saw effectively

Consider health and safety

Success Criteria

Explain how to measure an angle using a protractor.

Produce an accurate mitre joint which is symmetrical and which fits

Produce joint without wasting material/having to recut wood

Wear googles and follow procedures

Assessment for learning

Different set of talking partners to previous session (random pairing)Use random name generator

Peer assessment – evaluate partner’s measurements, mitring and frames during mini plenaries

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LESSON STRUCTURE & DETAILED PLAN OF ACTIVITIESSKILLS DEVELOPMENT Thinking Skills, PSE, ESDGC Time Lesson activities Ongoing plenary/ AfL

5 min

5 min

5 min

35 min

10 min

Introduction: (REMEMBER TO EXTEND WAIT TIME)Capture interest – recap on angles. What do we need to remember? Recap on previous work in the design process project. Re-cap on Investigative task with art straws and triangles within structures.

Read the paragraph on Tamil and Tamara to develop independent learning– what does it tell us about the characters?

Share learning objective – what can we learn from the paragraph we have just discussed about today’s task?

Activity 1 – mixed ability. Focus task. Create a FramePairs to choose an angle of 90/45(easy) or 60 or 30 (harder). Discuss what angle will create different frames. Record images of each step with iPads - to be used to write instructions in next session

Activity 2 (higher achievers)Extended task – create mitred equilateral and isosceles triangles. Generalise answers.

Activity 3 (lower achievers)To create a square from one length of wood (three cuts with one pre marked in pairs) and a sharp pencil. Remember ‘Check twice, cut once’ (see TA support)

PlenaryEach pair to discuss their work and thoughts on the task. Guide their response using the prompts and refer to success criteriaUse of visualiser. Choose pairs randomly – time will limit how many can feedback.

Key Questions (assign pairs and random choice)Explain how to measure an angleGive me some angle names……Show me ….. 90, 45, 60, 30….(hands and arms)Explain how you used angles in your art straws project.

Talking partners and lolly sticksDescribe Tamil and Tamara’s charactersWhich one are you similar to and why? Which one would you like to be and why?

Plenary prompts (pairs)We are pleased with.....this is why…..Mistakes from the session.What have we learnt?Explain how angles and joints are linked.What we would do differently next time.Record evaluations in D & T booklet and assess responses for next session.

CYMRAEG pob dyddRydw i yn.... mesur, llifio, torri, gludioRydw i eisiau...darn o bapur, pren, glud pensil, triongl papurMixed ability to use the past tense:Mi wnaethon ni.…lwyddo…ddarganfod…Higher ability to use the future tense: Tro nesa fasen ni yn newid…KEY WORDS/TERMINOLOGY(Bilingual)Mesur yn gywir/measure accuratelyMeitru / mitringOngl / angleLlifio / saw

RESOURCESProtractor, mitre board, junior hacksaw, G clamp, pencil, ruler, rubber, wood lengths, glue, cardboard triangles, lynx jointers, goggles.

HEALTH AND SAFETYRisk assessment undertaken of activity (see copy in file). Use correct safety equipment. Small groups sawing under supervision.

ROLE OF SUPPORT STAFFSupport Activity 3 Record achievement /learners’ thoughts/ achievements on T.A. sheet and discuss with teacher.

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LESSON EVALUATIONLearning objectives (from page 1):

Understand angles within a context

Measure angles and lengths accurately

Use saw effectively

Consider health and safety

Evaluation of Learning (against LOs)

Most pupils were able to measure accurately within 2°, but nearly half the pupils were unable to explain how to position the protractor and did not know WHY the cross hairs needed to be placed on the vertex of the angle. JK (higher achiever) produced an equilateral triangle and was able to say how he would create a square

Many pupils produced symmetrical joints but those who measured inaccurately produced symmetrical joints but with the overall angle too small – this suggests that they were consistently measuring the wrong angle

Most pupils were able to cut along the marks created using a pencil. Most waste was due to inaccurate marking rather than inaccurate cutting. ALL those in the support group used the material effectively. It is possible that some of these pupils were given too much support.

All pupils followed the safety procedures and wore goggles etc.

Learners’ targets (carried forward to next lesson)

Most pupils need to consolidate their understanding of angle as a measure of turn – this would assist with the placing of the protractor and enable some pupils to attempt the extension angle work.

Ensure that those producing inaccurate mitres are measuring consistently from the 0 line on the protractor. TA to support on this in next maths lesson.

JK should generalise his answers now – alternative task of working with mitre cuts on paper in next maths lesson involving angles.

Gove those in the support group more choice regarding their task – GJ and GW were not sufficiently challenged with the measyuring and cutting today

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PLANNING PRO FORMA KS3 Exemplar (Science) Name Class: Year 8 Date: Subject/Context: Graphing VariablesTRAINEE’S TEACHING SKILLS TARGETS:Allowing time for pupils to give extended answers to questions (see AfL)Developing questioning and prompts before during and after main activity

LEARNERS’ LEARNING TARGETS:Some pupils have difficulties choosing suitable scales on graphs (Emphasise scales in 2s, 5s, 10s, and 20s (factors of 100))

Skills development

Numeracy select and construct appropriate charts, diagrams and graphs with suitable scales (KS3)

interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data (KS3)

Science – Enquiry when carrying out a fair test, control variables appropriately and identify any variables that cannot readily be controlled.consider the number of observations or measurements that need to be made and their range and values to ensure reliability of evidence

Cwricwlwm CymraegLinks to Welsh history - the Pontllyfni Meteorite

Learning objectives

LO1 Understand the concept of independent and dependent variable

LO2 Understand why a range of values need to be recorded for an experiment

LO3 Understand key concepts of graphing (plotting results, choosing scales and ensuring accuracy)

LO4 Analyse results using a graph and link to context

Success Criteria

SC1 I can explain why I change one variable and how one variable affects another.

SC2 I have chosen heights at regular intervals and explained why.

SC3 I can graph my results accurately, explaining my choice of scales.

SC4 I can use my graph to explain the relationship between height and crater size.

Assessment for learning(strategies)

Think pair share in starter.

Focus on wait time for reflection.

Question and prompts throughout (see overleaf)

Lollipop sticks in plenary

LESSON STRUCTURE & DETAILED PLAN OF ACTIVITIES

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SKILLS DEVELOPMENT Thinking Skills, PSE, ESDGC

Time Lesson activities Ongoing plenary/ AfL

10 min

10 min

10 min

15 min

10min

Lead discussion about images shown on ppt: introduce concepts of cause and variable.

Make sure I give enough time to think; discourage shouting outDiscuss variables with students: Demonstrate equipment, drop the ball and show the craterTell them I am changing height (the independent variable) and investigating the effect on the crater size (the dependent variable) Tell them we’ll investigate height vs crater size this time.Show these in a table and on two axes: emphasise independent horizontal and dependent vertical

Hand out worksheets for students to complete. Observe and circulate and respond. LO1 Understand the concept of independent and dependent

variableLO2 Understand why a range of values need to be recorded for an

experiment Bring class togetherStudents to graph the results. They choose the type and scales. LO3Stop lesson draw attention to effective scales – show scales of 2,5,10, Tell groups that one group will present their results.Pupils plot their results and write key inferences from the graphs

LO3 Understand key concepts of graphing (plotting results, choosing scales and ensuring accuracy)

LO4 Analyse results using a graph and link to context

PlenaryChoose one group at random to present their graphs and results. (LOs 1, 2, 3, 4Collect graphs to be assessed and used in the next lesson.

(questions and prompts)Think pair shareWhat might make the craters?What influences the size of the crater? Explain.

Key questions before activity: (think pair share ) What can I change when I drop the ball?What effect does this have on the crater size?How can I measure crater size? (Link to maths – radius and diameter allow pupils to make the connection)How can I investigate the effect of the changes?

Prompts during activity How can you measure more accurately?Show me how you measured…..How have you decided on the different heights?What do you need to write down?

Why is a scale going up in 3s is not a good idea, or 7 or 9?

Plenary: Ask other pupils (lollipop sticks)What was important about designing the experiment? LO2Explain independent and dependent variables LO1What was important when plotting the graphs? LO3 What scales did you use and why? LO3 What do the graphs tell us about the crater size? LO4 How is it linked to our first question about meteorites? LO4

CYMRAEG pob dydd: Aim at new pupils:Dewch i mewnEisteddwch .... Tawelwch Task related every day Welsh:Ewch i nôl…..Dangoswch i miEglurwch i mi sut......Question prompts patterns:Beth wnest ti… Beth wyt ti eisiau ..... KEY WORDS/TERMINOLOGY(Bilingual)Axis – echelinGraph – graffDependent – dibynadwyIndependent – annibynnolVariable – newidynRESOURCESWorksheet, graph paperClass set of 2 litre tubs to hold sandBall bearing (approx. 20mm diameter)Sand to 5cm depth in each tubSieve Table salt15cm clear ruler 2 x 1m rules

HEALTH AND SAFETYNormal lab rules in place.No significant hazards; be careful not to get sand in their eyes. Care with heights.ROLE OF SUPPORT STAFFNone present

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LESSON EVALUATIONLearning objectives (from page 1):

LO1 Understand the concept of independent and dependent variable

LO2 Understand why a range of values need to be recorded for an experiment

LO3 Understand key concepts of graphing (plotting results, choosing scales and ensuring accuracy)

LO4 Analyse results using a graph and link to context

Evaluation of Learning (against LOs)

Some pupils gave convincing explanations of dependent and independent but, despite some evidence of understanding (from the graphs) two of the groups’ understanding is either lacking or unproven.

All pupils were able to understand the second LO. All explanations were convincing and JL’s explanation using a diagram with only two points and then using 20 points was particularly illuminating

Nearly all pupils were able to do this efficiently and skills were transferred effectively from the maths department. One group needed to be questioned about their use of “going up in 4s” on their graph but were able to correct their work when prompted. SJ needed support and did not contribute to her group

Few pupils were able to analyse effectively. I am unsure as to whether this was a lack of time, their language skills or a more fundamental inability to think back to the context. Graphing the data seemed to decontextualize the data for many pupils.

Learners’ targets (carried forward to next lesson)

Need to consolidate group B’s use of scales – they need to use appropriate scales unprompted.

The class’ response to LO1 and LO4 suggests that all learners need to have more opportunities to explain their methods at length.

More opportunities are needed to analyse data in context.

SJ needs additional guidance with graph plotting, especially accuracy when using values between axis tick marks.

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PLANNING PRO FORMA KS3 D&T Numeracy ExemplarName: Class: Year 7 Date Subject/Context Drawing for manufacturing and dimensions

TRAINEE’S TEACHING SKILLS TARGETSDevelop effective peer assessment

LEARNERS’ LEARNING TARGETSMinimising waste when designing artefactsFrom maths department: all pupils need to calculate compound areas in context.

Skills development

NC - Skills DESIGNING4. Identify and apply knowledge and understanding about technological, sustainability and heal and safety issues to develop ideas for products that are achievable and practical.6. Explore, develop and communicate design ideas in a range of ways, including annotation, drawings and CAD.8. Evaluate, refine and modify their design ideas as they develop in relation to aesthetics . . . function, safety, properties of materials, components, sustainability and cost.MAKING4. Develop techniques to ensure consistency and accuracy including the use of CAM

THINKINGEntrepreneurial thinking

NUMERACY Y7 Present answers to a given number of decimal placesY7 convert between units of the metric system and carry out calculations.Y8 calculate areas of compound shapes (e.g. consisting of rectangles and triangles)

Learning objectives

Learners will be able to:

1. Produce a drawing suitable for manufacturing product and minimising waste.

2. Produce a detailed dimensioned working drawing to BS 88:88

3. Select and mark out correctly a piece of acrylic for laser cutting

4. Calculate area of material required, and some will be able to calculate part cost and efficiency

Success Criteria

Drawing: Positioning drawing in top left of drawing

area; Minimising waste between parts; Using different colours for cutting and

engraving; ‘Making path’ from lines of drawing to

minimise cutting time

For the dimensioned working drawing I can Apply dimensions in mm and cm Follow conventions from BS 88:88;

correct use of leader lines, arrow heads, position of measurements, title block

Dimension length, radius and diameter using correct symbols and units

Area and cost Calculate surface area of material

required Calculate cost of material for product –

round to 2dp

Assessment for learning

Peer assessment throughout activity

Plenary focus: reflection on success criteria, measurement, area and numeracy skills

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LESSON STRUCTURE & DETAILED PLAN OF ACTIVITIESSKILLS DEVELOPMENT Thinking Skills, PSE, ESDGC

Time Lesson activities Ongoing plenary/AfL5 min

5 min

5 min

35 min

10 min

STARTERBig image of an orthographic working drawing on board as learners enter, with statement “This drawing is a form of language”.

ACTIVITY 1Learners to study 3 good examples of ‘how to set up drawing for laser cut, identifying:

Positioning drawing in top left of drawing area; Use of different coloured lines for cutting and engraving Minimising waste (draw attention to AREA/cost/efficiency)

ACTIVITY 2Learners to study written instructions of drawing dimensioned to BS88:88, and identify:

Use of leader lines Use of small arrow heads Position of dimensions Symbols used for radius and diameter Include measurements in mm and cm

ACTIVITY 3Learners to work independently on producing drawing for their productRecord measurement of material required, and mark out for laser cutting.Calculate surface area of material required. Use area formulae and compound shapes

EXTENSION ACTIVITY 4Learners to calculate cost efficiency measured in proportion of materials wasted.

PLENARYOne half of learners given an image of an incorrect drawing for laser cutter; the other half of learners given an incorrect dimensioned drawing. Learners to identify mistakes, and suggest corrections. Pupils to work in pairs (one from each half) to suggest improvements to each other’s work.

Prompt to groups;Explain this statement.

Comments used to annotate blank drawings and to be used as success criteria for own work and work of peers for activity 1 and activity 2

Plenary focus (peer assessment)Conventions not followed for dimensioning correctly Wrong measurement used in some

parts Wrong conversion from mm to cm Measurement placed in incorrect

position.Why is cost related to area? How can we use area to minimise waste?How do we round to obtain cost in £?

CYMRAEG bob dyddConsolidate starter activity language patterns:Tasg sbardun heddiw ydi…Edrychwch ar y llun…Anodwch y llun…Beth ydy’r gost?Beth ydy’r arwynebedd?KEY WORDS/TERMINOLOGY(Bilingual)Working Drawing – Lluniad GweithioDimensions - DimensiwnMeasurements – MesuriadauRadius – RadiwsDiameter – DiamedrArrow – Saetharea – arwynebeddround - talgrynnuRESOURCESExemplar sheets for setting up drawing for manufacturingWritten instructions of how to set up dimensioned drawingExemplar dimensioned drawingHEALTH AND SAFETYSee workshop safety manual and general safety plan

ROLE OF SUPPORT STAFFNone available for this lesson

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LESSON EVALUATIONLearning objectives (from page 1):

1. Produce a drawing suitable for manufacturing product and minimising waste.

2. Produce a detailed dimensioned working drawing to BS 88:88

3. Select and mark out correctly a piece of acrylic for laser cutting

4. Calculate area of material required, and some will be able to calculate part cost and efficiency.

Evaluation of Learning (against LOs)

Most groups produced an accurate drawing, however, only one group minimised waste effectively. They did eventually realise their drawing was inefficient but only during the plenary when group A shared their design.

Most groups were able to confirm to the BS but only on most of the criteria. The labelling of radii and diameters was poor by most pupils – see targets below.

This was done well by ALL pupils but two groups did need intervention regarding the safe use of the laser cutting tool.

About half the pupils were able to calculate areas. Many pupils found it difficult to transfer their knowledge from their maths lessons to the D&T lesson difficult. Some pupils explained now area was related to cost in the plenary and this helped other pupils to understand. DR was able to produce a figure of 76% efficiency for her group.

Learners’ targets (carried forward to next lesson)

The whole class needs to consider minimising waste when designing and not after cutting.

Most learners need consolidation of labelling and constructing circles and semi circles as part of their design and conforming to BS 88:88

More opportunities are needed to apply area in context.

DR will need extension material - consider looking at volume of materials and coverings as well as basic areas

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References and useful reading for trainees

Askew, M., Brown, M., Rhodes, V., Johnson, D. and Wiliam, D., 1997.Effective teachers of numeracy. London: Kings College.Barnes, J., 2011. Cross-Curricular Learning 3-14, SAGE Publications Ltd. http://musicmathsmagic.com/page4/files/EffectiveTeachersofNumeracy.pdf

Estyn, 2014. Numeracy in key stages 2 and 3: an interim report. Available at: http://www.estyn.gov.uk/download/publication/337974/numeracy-in-key-stages-2-and-3-an-interim-report-november-2014/ [Accessed 9/7/16]

Fox, S. & Surtees, L., 2010. Mathematics Across the Curriculum: Problem-Solving, Reasoning and Numeracy in Primary Schools, Continuum International Publishing Group.

Haylock, D. & Cockburn, A.D., 2013. Understanding Mathematics for Young Children: A Guide for Teachers of Children 3-8, SAGE.

Kerry, T., 2010. Cross-Curricular Teaching in the Primary School: Planning and Facilitating Imaginative Lessons, Taylor & Francis US.

McDonough, A. & Clarke, D., 2003. Describing the Practice of Effective Teachers of Mathematics in the Early Years, International Group for the Psychology of Mathematics Education. Available at: http://files.eric.ed.gov/fulltext/ED501025.pdf [Accessed June 19, 2016].

Siraj-Blatchford, I. & Großbritannien eds., 2002. Researching effective pedagogy in the early years, Nottingham: Department for Education and Skills.

Thompson, I., 2010. Issues In Teaching Numeracy In Primary Schools 2nd edition., Berkshire, England: Open University Press.

Ward-Penny, R., 2011. Cross-Curricular Teaching and Learning in the Secondary School: Mathematics, Taylor & Francis.

Welsh Government, 2003. The Literacy and Numeracy Framework. [Online] Available at http://learning.gov.wales/resources/browse-all/nlnf/framework?lang=en#/resources/browse-all/nlnf/framework?lang=en [Accessed 16 July 2015]

Welsh Government, 2014. Numeracy Sample Materials [online] Available at http://learning.gov.wales/resources/browse-all/numeracy-sample-materials/?lang=en [Accessed 01/07/16]

Acknowledgements

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The Numeracy ITT guidebook has been produced by the NMWTCE Skills team in collaboration with trainees, tutors, and mentors within the NMWTCE partnership.