1. What Mathematics should we teach in KS3 science? Dave Whittle, Hampshire Science Inspector/Advisor

3. Hopefully you are familiar with this document …

4. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V.

5. A quick discussion … 1.What discussions have you had with your maths department? 2.If you have had the discussions, what have been the key outcomes? 3.Have you discussed the ‘increasing mathematical’ challenge within the new GCSE specs (and hence within KS3) with your department? What were the outcomes?

6. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V. recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian planerecognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane interpret mathematical relationships both algebraically and graphically interpret mathematical relationships both algebraically and graphically reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraicallyreduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically Let’s have a look at that old favourite … graphs

7. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V. describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical dataconstruct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

8. You need to talk to your maths department about a)When you need to use graphing skills in science b)When do they teach graphing skills? c)What language should you agree to use? d)How will you deal with the differences? It is worth noting that in science we often don’t fully utilise sketch graphs as a means of helping students develop their thinking … and developing predictions.

9. Simple example … a)Are older people always taller? b)How does the size of as magnet affect it’s strength? c)How does the amount of solute that will dissolve in water vary with the temperature of the solvent? d)How does the population of spiders in the ‘environment area’ change over a year? e)How does the rate at which hydrogen is produced when a metal reacts with an acid vary with the size of metal lumps?

10. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V. understand and use place value for decimals, measures and integers of any sizeunderstand and use place value for decimals, measures and integers of any size

11. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V. describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical dataconstruct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs. describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

12. Aspect of mathsRelative frequency Exemplification Graph work18%Constructing graphs Identifying and interpreting linear and non linear relationships Extrapolating and interpolating Identifying critical points Understand gradient represents how rapidly the DV changes with IV Comparing and measuring gradients Measurement and units 18%Measurement of angles, distance, area, volume, time, mass, p.d, current, mass, force, temperature. Use appropriate units Convert units (mass, distance, area) Use unconventional scales (graticules and pH) Judging error15%Quantifying the range of repeated measurement (answer +/-) Including error bars in graphs Judging the extent to which a conclusion can be trusted after considering error. Algebra14%Re arranging simple y=mx equations Substituting values into equations to calculate solutions Ratios10%Working out how many times bigger something is that an other Scaling up, ratios Number7%Using place value accurately Use negative numbers as part of a continuous number line Quote results to no more significant places than the data from which answers were derived Simple statistics6%Calculating mean, mode and median Concept of rate3%Rate as the concept of a quantity changing with time e.g. speed, rate of reaction Estimating3%Estimating sizes, times, distances using and understanding of scale Geometry3%Calculating areas of circles, rectangles and compound shapes Calculating volumes Calculating surface area. Converting units3%Converting g into kg, sec into minutes and hours, mm into cm, m and km, J into kJ, mA into A, mV into V. use and interpret algebraic notationuse and interpret algebraic notation substitute numerical values into formulae and expressions, including scientific formulaesubstitute numerical values into formulae and expressions, including scientific formulae understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factorsunderstand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors simplify and manipulate algebraic expressions to maintain equivalence by:simplify and manipulate algebraic expressions to maintain equivalence by: understand and use standard mathematical formulae; rearrange formulae to change the subject understand and use standard mathematical formulae; rearrange formulae to change the subject model situations or procedures by translating them into algebraic expressions or formulae and by using graphsmodel situations or procedures by translating them into algebraic expressions or formulae and by using graphs recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian planerecognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

13. So we all need to talk to the Head of Maths – develop the idea of mutual support … we can use their expertise in teaching the maths … they can use science as a context in which to use maths to solve problemsSo we all need to talk to the Head of Maths – develop the idea of mutual support … we can use their expertise in teaching the maths … they can use science as a context in which to use maths to solve problems It is also worth looking at, and discussing this …It is also worth looking at, and discussing this … Working mathematically Working mathematically

14. Solving problems – students should … develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problemsdevelop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematicsdevelop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics begin to model situations mathematically and express the results using a range of formal mathematical representationsbegin to model situations mathematically and express the results using a range of formal mathematical representations select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

15. Reflection What are the issues for your department?What are the issues for your department? What will you do …What will you do … –Next week? –Before Easter? –During the summer term? Who do you need to talk to?Who do you need to talk to? What can we do to help?What can we do to help?