1. © Crown copyright 2001 Key Stage 3 National Strategy Numeracy Across the Curriculum

2. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 1 To consider the need to raise standards in numeracy To consider current images of mathematics and mathematicians To introduce the definition of numeracy To consider the need for improving numeracy skills across the curriculum OHT 1.0

3. © Crown copyright 2001 Key Stage 3 National Strategy Views of mathematics Mathematics is … an important subject nothing to do with real life a boys’ subject something you can either do or you can’t about learning rules about right and wrong answers OHT 1.1

4. © Crown copyright 2001 Key Stage 3 National Strategy Points for discussion Consider the definition of numeracy (handout 1.2) Are there any areas of mathematics useful to your subject which you feel are not covered by the definition? Which aspects of the definition are most relevant to the work of your department? Identify the two most important aspects of numeracy you require for each of the Years 7, 8 and 9. OHT 1.2

5. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 1 By Year 9, pupils should: have a sense of the size of a number and where it fits into the number system recall mathematical facts confidently calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculation strategies use proportional reasoning to simplify and solve problems use calculators and other ICT resources appropriately and efficiently to solve mathematical problems, and select from the display the number of figures appropriate to the context of a calculation OHT 1.3

6. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 2 By Year 9, pupils should: use simple formulae and substitute numbers in the measure and estimate measurements, choosing suitable units, and reading numbers correctly from a range of meters, dials and scale calculate simple perimeters, areas and volumes, recognising the degree of accuracy that can be achieve understand and use measures of time and speed, and rates such as £ per hour or miles per litre draw plane figures to given specifications and appreciate the concept of scale in geometrical drawings and maps OHT 1.4

7. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 3 By Year 9, pupils should: understand the difference between the mean, median and mode and the purpose for which each is used collect data, discrete and continuous, and draw, interpret and predict from graphs, diagrams, charts and tables have some understanding of the measurement of probability and risk explain methods and justify reasoning and conclusions, using correct mathematical terms judge the reasonableness of solutions and check them when necessary give results to a degree of accuracy appropriate to the context OHT 1.5

8. © Crown copyright 2001 Key Stage 3 National Strategy Priorities for cross-curricular numeracy To improve accuracy, particularly in calculation, measurement and graphical work To improve interpretation and presentation of graphs, charts and diagrams To improve reasoning and problem solving OHT 1.6

9. © Crown copyright 2001 Key Stage 3 National Strategy Numeracy in Ofsted inspections In relation to numeracy, inspectors should establish: whether there is clear understanding and consistent practice among staff in the development of pupils’ mental skills, written methods of calculation and use of calculators if pupils can identify and use an efficient strategy for the calculations they need to do if pupils cope well with the mathematical demands made in different subjects, or are held back through lack of mathematical knowledge or poor basic skills in numeracy how well numeracy and, where appropriate, other mathematical skills are taught, developed or practised in other subjects OHT 1.7

10. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 2 To consider one school’s approach to numeracy across the curriculum To introduce activities to develop oral communication skills To discuss whether similar activities could be used in other subjects when mathematical skills are required To explore possible areas for inter- departmental co-operation in this type of activity OHT 2.0

11. © Crown copyright 2001 Key Stage 3 National Strategy Managing numeracy across the curriculum Which aspects of the work done in Ledbury on numeracy across the curriculum could be developed in our school? Are there any other activities that might help to raise standards of numeracy across our school? How can we maintain a focus on numeracy skills? OHT 2.1

12. © Crown copyright 2001 Key Stage 3 National Strategy Washing Up OHT 2.2 Give a plausible explanation for the shape of this graph.

13. © Crown copyright 2001 Key Stage 3 National Strategy Scales OHT 2.3

14. © Crown copyright 2001 Key Stage 3 National Strategy Discussion points Consider the activities modelled in this session. Do you use (or might you use) similar approaches to graphical interpretation or reading scales in your own subject? Could your own subject benefit from the group problem-solving approach? Are there are any examples you could offer the mathematics department, to benefit both subjects? OHT 2.4

15. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 3 To discuss situations where the teaching of mathematics can be enhanced by using examples from other subjects To explore opportunities for collaborative planning and teaching of mathematical topics OHT 3.0

16. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 4 To consider the need to raise standards in numeracy To review the school’s existing practice in numeracy across the curriculum by : comparing existing practice with a video of work in another school checking the requirements of the National Curriculum discussing how best to sustain the work already started OHT 4.0

17. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 1 By Year 9, pupils should: have a sense of the size of a number and where it fits into the number system recall mathematical facts confidently calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculation strategies use proportional reasoning to simplify and solve problems use calculators and other ICT resources appropriately and efficiently to solve mathematical problems, and select from the display the number of figures appropriate to the context of a calculation OHT 4.1

18. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 2 By Year 9, pupils should: use simple formulae and substitute numbers in them measure and estimate measurements, choosing suitable units, and reading numbers correctly from a range of meters, dials and scales calculate simple perimeters, areas and volumes, recognising the degree of accuracy that can be achieved understand and use measures of time and speed, and rates such as £ per hour or miles per litre draw plane figures to given specifications and appreciate the concept of scale in geometrical drawings and maps OHT 4.2

19. © Crown copyright 2001 Key Stage 3 National Strategy A definition of numeracy 3 By Year 9, pupils should: understand the difference between the mean, median and mode and the purpose for which each is used collect data, discrete and continuous, and draw, interpret and predict from graphs, diagrams, charts and tables have some understanding of the measurement of probability and risk explain methods and justify reasoning and conclusions, using correct mathematical terms judge the reasonableness of solutions and check them when necessary give results to a degree of accuracy appropriate to the context OHT 4.3

20. © Crown copyright 2001 Key Stage 3 National Strategy Discussion Points Discuss the definition of numeracy and compare it, where possible, with that used in our whole-school numeracy policy How should our policy be updated to incorporate any differences? OHT 4.4

21. © Crown copyright 2001 Key Stage 3 National Strategy Our current numeracy policy How can we judge or measure our success in numeracy across the curriculum? How can we continue to involve all staff (for example, new staff/NQTs)? How can we incorporate any future changes in the curriculum into our numeracy programme? How can we make best use of ICT to improve numeracy? How successful have we been so far in informing and involving parents/governors in improving numeracy? OHT 4.5

22. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 5 To introduce teachers to the Framework for teaching mathematics: Years 7, 8 and 9 To exemplify oral and mental work in mathematics To consider the approach to calculation OHT 5.0

23. © Crown copyright 2001 Key Stage 3 National Strategy Contents of the Framework for teaching mathematics Guide to the Framework Key objectives Yearly teaching programmes Supplement of examples: Years 7, 8 and 9 Vocabulary checklist OHT 5.1

24. © Crown copyright 2001 Key Stage 3 National Strategy Strands of the yearly teaching programmes Using and applying mathematics to solve problems Numbers and the number system Calculations Algebra Shape, space and measures Handling data OHT 5.2

25. © Crown copyright 2001 Key Stage 3 National Strategy Oral and mental work Develop and explain mental calculation strategies, including figuring out new facts from known facts Apply calculation skills in algebra, for example to substitute numbers in expressions or to solve simple equations Develop estimation skills Practise the interpretation of data Develop mental imagery of shapes, movements and constructions Rehearse the use of mathematical vocabulary and develop oral communication skills Develop the ability to generalise, reason and prove OHT 5.3

26. © Crown copyright 2001 Key Stage 3 National Strategy Some of the possible visualisations OHT 5.4

27. © Crown copyright 2001 Key Stage 3 National Strategy Skills of mental calculation Remember number facts and recall them without hesitation Use known facts to figure out new facts Draw on a repertoire of mental strategies to work out calculations, with some thinking time Understand and use the relationships between operations to work out answers and check results Approximate calculations to judge whether or not an answer is about the right size Apply skills to solve numerical problems OHT 5.5

28. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 6 To review the use of calculators within departments To look at progression in calculator skills To explore the features of different types of calculators To contribute to a school policy on calculator use OHT 6.0

29. © Crown copyright 2001 Key Stage 3 National Strategy Calculator skills that pupils need to develop Selecting from the display the number of figures appropriate to the context of a calculation Entering numbers and interpreting the display when the numbers represent money, metric measurements, units of time or fractions Knowing the order in which to use the keys for calculations involving more than one step Using facilities such as the memory, brackets, the square root, cube root, sign change and fraction keys, and the constant facility Judging whether an answer is reasonable OHT 6.1

30. © Crown copyright 2001 Key Stage 3 National Strategy Calculator skills expected by the end of Year 6 (i) Use a calculator to perform a one-step calculation and interpret the result Key in and interpret money and measurement calculations Extend to calculations with more than one step, e.g. 18 x (137 + 258) Recognise rounding errors, e.g. recognise 2.9999999 as 3 Recognise negative numbers and use the sign change key if appropriate OHT 6.2 a

31. © Crown copyright 2001 Key Stage 3 National Strategy Calculator skills expected by the end of Year 6 (ii) Find decimals equivalent to fractions Recognise recurring decimals, e.g. 0.33333333 Start to use memory keys and perform more complex calculations, such as: (234 + 739) ÷ (145 – 89) Have a feel for the size of an answer and check it appropriately OHT 6.2 b

32. © Crown copyright 2001 Key Stage 3 National Strategy Ageing fast OHT 6.3 Juliet works out her age as 6 311 520 minutes. Calculate how old she is (exactly!) in years, months and days. Check your answer by reversing the calculation

33. © Crown copyright 2001 Key Stage 3 National Strategy Comparing calculators OHT 6.4 For each key sequence, predict the outcome when you enter it on a basic calculator and a scientific calculator. Now see if you were right.

34. © Crown copyright 2001 Key Stage 3 National Strategy Departmental policy on using calculators Does our scheme of work make it clear when and where pupils are likely to require calculators? Are there times when we will expect pupils to do calculations without resorting to a calculator? Do we make it clear to pupils when and where we expect them to use a calculator and when we expect them not to? How do the calculator skills we expect pupils to use line up with those in the Framework for teaching mathematics? Are there opportunities in our scheme of work to teach or reinforce identified calculator skills? Is our departmental policy consistent with the school policy? OHT 6.5

35. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 7 To become familiar with the approach to handling data in the Framework for teaching mathematics: Years 7, 8 and 9 To explore possible opportunities for handling data across the curriculum To interpret graphs, charts and diagrams To consider common difficulties in handling data OHT 7.0

36. © Crown copyright 2001 Key Stage 3 National Strategy The handling data cycle OHT 7.1

37. © Crown copyright 2001 Key Stage 3 National Strategy Features of handling data in Key Stage 3 Basing work on purposeful enquiry, using situations of interest and relevance to pupils and making appropriate links to other subjects Placing an emphasis on making inferences from data, drawing on a range of secondary sources to ensure that samples are sufficiently large Using ICT as a powerful source of data, and as a means of processing data and simulating situations OHT 7.2

38. © Crown copyright 2001 Key Stage 3 National Strategy Handling data across the curriculum Are all the different stages of the handling data cycle applicable to your subject? Have pupils handled data in any lessons that you have taught recently? Which stages of the handling data cycle were pupils engaged in? Which stages of the handling data cycle could pupils have been engaged in? Which of the distinctive features of handling data were present in the lesson(s)? OHT 7.3

39. © Crown copyright 2001 Key Stage 3 National Strategy Common difficulties in handling data 1 (i) Mean, median and mode are confused or used inappropriately For example, the mean is used when referring to the average monthly rainfall in India Data are represented by inappropriate graphs or charts For example, a pie chart is used to represent the distances of the different planets from the Sun OHT 7.4 a

40. © Crown copyright 2001 Key Stage 3 National Strategy Common difficulties in handling data 1 (ii) Graphs and charts are incorrectly drawn or labelled For example, the bars in a bar chart representing the votes cast for candidates in a school election are joined together or are of different widths Graphs and charts are read incorrectly or interpreted inappropriately For example, the vertical scale marked in thousands on a population graph is misread: 350 000 is read as 350 OHT 7.4 b

41. © Crown copyright 2001 Key Stage 3 National Strategy Common difficulties in handling data 2 Activities are aimless or contexts inappropriate For example, vast quantities of data are collected without any consideration of the purpose of the enquiry Undue time is spent on mechanical skills and there is insufficient emphasis on interpreting data and making inferences For example, pupils are taught to draw pie charts or calculate a mean without understanding of when it is appropriate to use these or how to interpret them OHT 7.5

42. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 8 To agree a set of whole-school numeracy priorities To discuss the need for a whole-school numeracy policy and its possible content To agree a plan of action to sustain developments OHT 8.0

43. © Crown copyright 2001 Key Stage 3 National Strategy Purposes of a whole-school numeracy policy To secure high standards in numeracy across the school To set out the school’s approach to the teaching of agreed numeracy skills To provide a basis against which progress can be judged To record methods, vocabulary and notation that have been agreed To assist the transfer of pupils’ knowledge, skills and understanding between subjects To indicate areas for collaboration between subjects and processes for facilitating such collaboration OHT 8.1

44. © Crown copyright 2001 Key Stage 3 National Strategy Possible contents of a whole- school numeracy policy 1 Agreed approaches to calculation (including calculations involving fractions, percentages, ratio) School policy on calculator use Agreed mathematical vocabulary and notation Lists of units used for measurement Agreed methods for drawing and labelling graphs, charts and diagrams Links with using and applying mathematics – reasoning, communicating, investigating and problem solving OHT 8.2

45. © Crown copyright 2001 Key Stage 3 National Strategy Possible contents of a whole- school numeracy policy 2 Agreement on the order and timing for teaching topics with common content Agreement on any planned collaborative working/ shared activities Guidance for form tutors, where oral and mental work is included in tutorial sessions Advice from the mathematics department on common errors which arise OHT 8.3

46. © Crown copyright 2001 Key Stage 3 National Strategy Objectives for session 9 To ensure that each department’s expectations for pupils’ mathematics are in line with those in the Framework for teaching mathematics: Years 7, 8 and 9 To explore opportunities for continued joint working OHT 9.0