Numeracy Across the Curriculum St Alban’s Catholic High School Influencing Attitudes • Poor learning experiences and fear of getting the ‘wrong’ answer contribute to the negative impression many adults have of mathematics. Problems can be created if these views are passed on to pupils by staff or parents. • Some teachers may put pupils under pressure in their lessons to perform mathematical routines that are insufficiently developed or are unfamiliar, this can reinforce negative feelings which pupils may already have. • Some teachers may avoid the mathematical elements of their subject, thereby losing opportunities to demonstrate the necessity of mathematics. Aims of the day • To introduce teachers to the underlying principles of the National Numeracy Strategy. and • To begin the process of ensuring that there exists a consistency of practice across the curriculum. Approaches to Mathematics Estimation Skills 48.34 / 5.13 = 50 / 5 = 10 14.56 x 10.6 = 15 x 11 = 165 15 x 10 = 150 E stim ation G am e 1 4 .49 1 638 2 0 .1 5 .67 54 9 .6 1 26 .7 2 30 7 1 43 .9 9 52 9 6 .6 E stim ation G am e 1 4 .49 1 638 2 0 .1 5 .67 2.1 x 6.9 42 x 39 62.31 / 3.1 6.8 x 0.9 54 9 .6 1 26 .7 2 30 5130 / 95 62 / 9.8 12.8 x 9.9 930 / 31 7 1 43 .9 9 52 9 6 .6 4 8 .51 / 6 .9 3 1 1 .9 x 12 .1 26 / 0.5 46 x 2.1 Mental Calculations 45 + 46 = 2039 - 1996 = 60 - 19 = 37 + 198 = 23 x 42 x 40 2 20 800 40 3 120 6 800 + 40 + 120 + 6 = 966 16 x 54 10 x 54 = 540 + 5 x 54 = 270 + 1 x 54 = 54 16 x 54 = 864 16 x 54 - 2 x 54 = 108 20 x 54 = 1080 4 x 54 = 216 16 x 54 = 864 38724 387 10 x 24 = 240 147 5 x 24 = 120 27 1 x 24 = 24 3 Answer: 16 r 3 or 16 3/24 - 32024 1 x 24 = 24 2 x 24 = 48 4 x 24 = 96 8 x 24 = 192 192 + 96 = 288 + 24 = 312 32024 1 x 24 = 24 2 x 24 = 48 4 x 24 = 96 8 x 24 = 192 192 + 96 = 288 + 24 = 312 Answer: 1+4+8 =12 r 8 or 12 8/24 Problem Solving and Discussion Brainteaser 1 Solve the following brainteaser, without discussing it. In a mathematics test, no two pupils scored the same. Brian scored less than 4 and Julie scored more than 6, but did not get full marks. Simon’s score was the sum of Brian’s and David’s. Rachel scored three times as many as Brian. Brian, Julie and Rachel all scored even numbers, while Simon’s and David’s scores were both odd. David’s score was half of Rachel’s. What did each pupil score out of 10? Brainteaser 1 Brian 2 out of 10 Julie 8 out of 10 Simon 5 out of 10 David 3 out of 10 Rachel 6 out of 10 Brainteaser 2 Real-Life Graphs Washing Up Give a plausible explanation for the shape of this graph. © Cr own copyright 2001 Scales 0 10 3 © Crown copyright 2001 Scales 0 20 6 © Crown copyright 2001 Scales 2 3.5 © Crown cop yright 2001 7 Mental Imagery Listen carefully and draw what you see in your mind. Some possible visualisations The Handling Data Cycle Common difficulties in Handling Data • 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 Common difficulties in Handling Data • 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 Common difficulties in Handling Data • 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 The Handling Data Cycle Handling Data Video The Ofsted framework for school inspection (September 2012) When evaluating the achievement of pupils, inspectors consider how well: • pupils develop a range of skills, including reading, writing, communication and mathematical skills, and how well they apply these across the curriculum [Section 52 Page 17] The Way Forward • 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 • References to reasoning, communicating, investigating and problem solving in schemes of work The Way Forward • References to Mental Imagery and oral work • An ongoing part of the School Improvement Plan • References to Numeracy included in Departmental Schemes of work • Glossary • Displays in classrooms Cross-Curricular Priorities • To improve accuracy, particularly in calculation, measurement and work involving formulae • To improve interpretation and presentation of graphs, charts and diagrams • To improve reasoning and problem solving Cross-Curricular Priorities O p p o rtu n itie s e xist to im p ro ve in te rp re ta tio n a n d p re se n ta tio n o f g ra p h s, ch a rts a n d d ia g ra m s Year 7 Year 8 Year 9 Maths in other Subjects By referring to your schemes of work please identify what opportunities exist in your subject area, that satisfy the cross-curricular numeracy objectives. Please go to the following rooms Design and Technology Geography, June and Dennis Science History and RE and Chris ICT and Celia Languages Music, Art and PE Caroline and Maureen S1 S2 S3 S4 S5 S6 PSA PSA Numeracy Across the Curriculum St Alban’s Catholic High School Calculator skills expected by the end of Year 6 • 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 Calculator skills expected by the end of Year 6 • 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 Calculator Skills Q 1. Q 2. Q 3. 23 2 33 233 0.66666 2 -2.33333 Q 4. 2 (3 3) No solution Q 5. 2 3 4 14 3 . 1 4 . 23 1.397 Q 6. 4 . 6 2 . 04 6 3 .1 6 .3 1 .6 3 Q 7. 203.79

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