Nuffield Mathematics teaching resources are for use in secondary and further education

# FSMQ Level 2 Higher Core Unit scheme of work

The content of this unit is based on the subject content of the FSMQs that are components of the Certificate in Use of Mathematics qualification.

Suggested schemes of work are given below. These assume that you will also be covering the content of two Level 2 FSMQs (Financial calculations, Shape and space, Handling data, Algebra and graphs) either before or alongside that of this core unit. You should select just one of the six work schemes according to which two Level 2 FSMQs you are also using. The work scheme describes the extra topics that you will need to cover for your learners to be prepared for the core examination. Each of the three alternatives recommends a total of 60 guided learning hours including an allocation of time for revision which should include some of the topics from the two FSMQs that you are also using.

If your students are studying one or two of the equivalent FSMQs at Level 1 (that is Money management, Using spatial techniques and/or Using data) you will also need to cover the Level 2 topics in these areas in the higher core content.

Note that the AQA assessment of this core unit is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments listed below which have not yet been updated. These have been included for possible use as classroom activities but will not form part of the assessment of this core unit. Also note that the AMP activities were not written specifically for this core unit and may include some work that is beyond that needed.

## Work Scheme A

Use this scheme of work if your students are also studying Financial calculations and Handling data.
In this case, for the core unit you will need to cover the topic areas listed below which involve shape and space and algebra.

You should introduce the following and include them wherever possible during this part of the course:

• use of geometrical terms: parallel, perpendicular, bisect, perpendicular bisector, mid-point, horizontal, vertical, line, line segment, regular, similar, congruent, polygon (pentagon, hexagon, octagon)
• use of appropriate instruments (ruler, tape measure, protractor) to make measurements to appropriate levels of accuracy with appropriate units and correct notation
• effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic
• checking calculations using estimates, inverse operations and alternative methods.
 Topic area Content Nuffield resource The links below go to pages from which you can download the resources, some recently revised. Measure lengths (2 hours) Use ruler and tape measure to measure objects using metric and imperial units (m, cm, mm, in, ft)  · to the nearest whole unit · to an appropriate level of accuracy (include significant figures and decimal places) Record dimensions in tables and in diagrams. Discuss accuracy of measurements and how it affects subsequent use.  Recognise that measurements expressed to a given unit can have a maximum error of half a unit. Measure it Slide presentation to demonstrate and check that students can measure in centimetres and millimetres. Worksheet for recording measurements. Paper sizes (AMP activity) Learners consider the relationships between paper sizes within one range and the relationships between ranges (A and B series of international paper sizes). Errors (Use the first part only) Slide presentation showing errors in measurements and how errors accumulate in calculations involving measurements.  Accompanying notes and worksheets. Convert measurements (2 hours) Convert within and between metric and imperial systems: metric (mm, cm, m, km), imperial (inches, feet, yards, miles).  Include the use of conversion factors. Convert lengths   Worksheet, bingo and dominoes games providing practice in length conversions. Convert it!   Interactive spreadsheet for practice in converting metric lengths and distances. Use protractor (1 hour) Measure angles in degrees. Angles   Slide presentation and activity measuring and classifying angles. Calculate perimeters and areas of 2D shapes (5 hours) Use measurements of length, in both metric and imperial units, to calculate: · Perimeters and areas of rectangles, triangles, trapezia and parallelograms · Circumference of circle  $=&space;\pi&space;\times&space;d&space;=&space;2&space;\pi&space;r$ and arc length of circles for fractions of circles · Area of circle  $=&space;\pi&space;r^2$ and areas of sectors of circles  using  $\pi$ button on a calculator and giving correct units Include shapes involving combinations of rectangles and triangles. Use formulae for perimeters and areas expressed in words and symbols. Perimeter and area  Slide presentation, information sheet and worksheet covering the perimeter and area of rectangles and shapes made from rectangles. Also 24 sets of 3 cards for learners to match.  One card gives the dimensions of a rectangle or shape made from rectangles, one gives its perimeter and one its area. Circle matching cards   Twelve sets of three cards for learners to match. One card shows a real object with its diameter, one gives its circumference and one its area. Design a table (AMP activity)   Students use given body measurements to design a table for five people which can be extended for use by eight/ten people.

 Topic area Content Nuffield resource The links below go to pages from which you can download the resources, some recently revised. Calculate surface area and volume of 3D shapes (4 hours) Find surface areas and volumes of cuboids, prisms (including triangular) and cylinders giving values in correct units. Volume   Slide presentation, information sheets and worksheet covering the volume of cuboids. Use of formulae (5 hours) Substitute values into given formulae and functions using BIDMAS to find secondary data (including formulae with multiples and fractions, powers and brackets). Include use of formulae · to convert units such as using $L$ = 3.28$l$ to convert $l$ metres to $L$ feet. · to find the surface area and volumes of spheres, hemispheres and cones Use formulae (for single plane shapes or solids) for perimeters, areas and volumes, together with known values to find one unknown length (for instance given $V&space;=&space;l&space;\times&space;b&space;\times&space;h$ and values for $V$, $l$ and $h$, find $b$). Hot water tank: Formulae   Slide presentation, notes and exercise. Students learn to substitute values into formulae, and to use a calculator to evaluate expressions. Goldfish bowl: rearrange formulae Students practise rearranging formulae. There is a worksheet for individual work, or a set of cards for group work to develop this skill. Solve problems (5 hours) Solve problems involving lengths and angles, deciding on the correct arithmetic to use (adding, subtracting, multiplying, dividing) Use ideas of similarity in terms of enlargement and scale factors (include finding unknown sides in similar triangles). Length problems  Twelve problems set in a range of real contexts to solve. How much will it cost?  Taking measurements from scaled elevations of a house, then finding area and cost of painting. Costing the job   Students take measurements from scaled elevations of a house to find the wall area to be painted and then work out the cost. 'How much will it cost?’ is an easier version. Pythagoras’ Theorem  (4 hours) Use Pythagoras theorem to calculate unknown lengths including use of the formula c2 = a2 + b2 in 2D problems. Pythagoras   Slide presentation, notes and worksheet.  Links to useful websites. Recognise and classify plane shapes (2 hours) Shapes to include: · triangles including obtuse-angled, acute-angled, equilateral, isosceles and right-angled ·  quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite · other polygons including pentagons, hexagons, octagons – understanding that regular polygons have equal sides and equal angles Name the shape  Slide presentation and activity naming and classifying shapes. What am I?   24 pairs of cards for learners to match. One card gives a 2D or 3D shape and its name, the other a description. Drawing shapes in Word Shows students some of the basic drawing techniques available in Word.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Plot and interpret graphs of real data (5 hours) Plot accurate graphs of data pairs by hand and using either a graphic calculator or function plotting software, ensuring that the graphs are correctly scaled and labelled.  Use coordinates in all 4 quadrants where appropriate. Fit straight/curved lines by eye as an approximate fit to data and consider intercepts and long term behaviour in real world terms. Calculate the gradients of linear graphs in appropriate units and understand their physical significance. Crushed calcium carbonate Data and line graph of a chemical reaction for interpretation. Matching graphs and scenarios    Twelve pairs of cards for students to match.  One card in each pair shows a graph and the other gives a description of the real situation that the graph represents.  Slide presentation to aid discussion (same graphs with titles and labels). Road test    Use data from a road test on a sports car for practice in drawing and interpreting graphs.  Optional use of spreadsheet. Melting and freezing points (assignment)  Students draw and interpret a graph using data from an experiment to find the melting point of wax Experiments    List of seven experiments that generate linear and non-linear data.  Students are asked to find appropriate algebraic models. Proportional, linear and quadratic functions and their graphs (6 hours) Use functions to find data pairs of the form y = mx + c and y = kx2 + c including functions in terms of variables other than y and x. (such as s = 5t2, P = $\small&space;\frac&space;{k}{V}$).  Use substitution of values into a given expression for a model to find unknown constants. Look for patterns in data fitting proportional (y = mx),  linear (y = mx + c) and quadratic models (y = kx2) have and consider the main features of their graphs and their differences. Use graphs (including the y = mx + c and y = kx2 + c types) to determine the values of functions and to solve equations. Find the approximate solution of linear simultaneous equations by finding the point of intersection of two straight lines. Linear graphs Slide presentation and activity to introduce linear graphs. Hire a coach Introduces the concepts of gradient and intercept for linear graphs using Excel. Graphs of functions in Excel  This activity shows students how to draw graphs of algebraic functions in Excel. Spreadsheet graphs   Interactive spreadsheet graphs introducing the shape and main features of proportional and  linear graphs (ignore inverse proportional and quadratic sheets). Linear relationships    Example and exercise involving proportionality and other linear relationships in scientific contexts. Match linear functions and graph     Twelve sets of cards, each containing a linear graph, its equation and the real situation it represents – for students to match. Non-linear graphs    Draw graphs from data and formulae then use them to solve problems in real contexts. Includes slide presentation. Plumbers’ prices  Introduction to the graphical solution of simultaneous equations using Excel in real contexts. Can be used as a follow-up to 'Hire a coach'. Circuit boards (assignment) Students investigate the cost efficiency of two machines using graphical and algebraic techniques.

 Topic area Content Nuffield resource The links below go to pages from which you can download the resources, some recently revised. Areas under graphs (4 hours) Calculate estimates of areas under graphs and understand their physical significance (if any) using the formula for the area of a trapezium (and triangle if necessary). Speed and distance Slide presentation to introduce area under a speed-time graph accompanied by examples for students to try.  Optional use of spreadsheet/graphic calculator. Equations  (4 hours) Form and solve exactly equations where the unknown appears in only one term (such as 2x2 + 14 = 20 with solutions $\small&space;\sqrt&space;3$ and  $\small&space;-&space;\sqrt&space;3$) and equations where the unknown appears two terms each of the same power (such as 4x – 2 = 2x + 8 and 3x2 + 4 = 20 – x2) Algebraic expressions Slide presentation, information sheet, practice sheet and application to perimeters and areas. Use timetables (2 hours) Read and use timetables using 12 and 24-hour clocks.  Find the length of time for a journey. Every second counts (AMP activity)   Learners use maps and timetables to find how far they could travel in one hour. Revision (9 hours) Revise topics across the whole core content (including finance and data topics). Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

## Work Scheme B

Use this scheme of work if your students are also studying Financial calculations and Shape and space. In this case, for the core unit you will need to cover the topic areas listed below which involve data and algebra. Note that some of the data topics (such as interpretation of statistical diagrams and line graphs) are similar to those in the Financial calculations content.  You may wish to extend the work done for Financial calculations to include these rather than studying them separately.

You should introduce the following and include them wherever possible during this part of the course:

· using tables to record results

· using spreadsheets to carry out calculations and display results in tables and statistical charts and graphs

· effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic

· checking calculations using estimates, inverse operations and alternative methods.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Averages and range (5 hours) Discuss the difference between discrete and continuous data. Choose and find appropriate measures of location: mean (from $\small&space;\frac{\textup{sum~of~observed~values}}{\textup{number&space;~of~observations}}$ or $\small&space;\frac&space;{\sum&space;x&space;}{n}$), mode, median including use of calculator and spreadsheet. Choose and find appropriate measures of spread: range and inter-quartile range. Use these to compare datasets. On average  Examples and exercises on mean, mode and median. Coffee shop   Table of information about customers at a coffee shop. Use on paper or in spreadsheet form for discussion and practice of statistical techniques. Draw and interpret statistical diagrams (9 hours) Draw pictograms, bar charts and pie charts. Plot scatter graph, draw line of best fit through the mean point and use it to estimate missing values. Consider correlation (positive, negative, strength of correlation, no correlation). Draw histograms (with equal class widths) and stem and leaf diagrams (including back-to-back).  Consider the use of techniques which aim to mislead or exaggerate findings (such as manipulation of axes/ using area to exaggerate findings/choosing to omit some data). (There is some overlap with the content of 'Financial  calculations' allowing possible combination of work) Draw pie charts in Excel  Activity showing students how to draw a pie chart in Excel and change its appearance. Pie charts Activity showing students how to draw a pie chart by hand. Also includes practice exercise with real data – can be used as follow-up to ‘Draw pie charts in Excel’ activity. Draw histograms in Excel   Instructions explaining how to construct an accurate histogram and frequency polygon in Excel. Safety on the roads  Graphs and charts for interpretation. Mineral water (assignment)  Tabulated data and charts about the mineral content of various bottled waters. Students are asked to interpret and analyse this information. Solar eclipse    Lots of data for discussion and suggestions for analysis. Election results    Spreadsheet containing the 2005 and 2010 General Election results. Select local data for practice in drawing charts, finding percentage, and so on.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Plot and interpret graphs of real data   (5 hours) Plot accurate graphs of data pairs by hand and using either a graphic calculator or function plotting software, ensuring that the graphs are correctly scaled and labelled.  Use coordinates in all four quadrants where appropriate. Fit straight/curved lines by eye as an approximate fit to data, and consider intercepts and longterm behaviour in real world terms. Calculate the gradients of linear graphs in appropriate units and understand their physical significance. Matching graphs and scenarios    Twelve pairs of cards for students to match.  One card in each pair shows a graph and the other gives a description of the real situation that the graph represents.  Slide presentation to aid discussion (same graphs with titles and labels) ---------------------------------------------------------------------------------------- Crushed calcium carbonate    Data and line graph of a chemical reaction for interpretation. Interpreting curves   Discussion sheets and exercise on interpreting and sketching line graphs. Focuses on the shape of graphs. Road test  Use data from a road test on a sports car for practice in drawing and interpreting graphs.  Optional use of spreadsheet. Melting and freezing points (assignment)   Students draw and interpret a graph using data from an experiment to find the melting point of wax. Reaction rates Drawing and interpreting graphs using data provided from chemical reactions. Requires graphs to be drawn using spreadsheet and by hand. Experiments List of seven experiments that generate linear and non-linear data.  Students are asked to find appropriate algebraic models. Proportional, linear and quadratic functions and their graphs (6 hours) Use functions to find data pairs of the form y = mx + c and y = kx2 + c including functions in terms of variables other than y and x (such as s = 5t2, P = $\small&space;\frac&space;{k}{V}$).  Use substitution of values into a given expression for a model ($\small&space;y&space;=&space;mx&space;+&space;c$, $\small&space;y&space;=&space;kx^2&space;+&space;c$) to find unknown constants Look for patterns in data fitting proportional ($\small&space;y&space;=&space;mx$),  linear ($\small&space;y&space;=&space;mx&space;+&space;c$) and quadratic models ($\small&space;y&space;=&space;kx^2$) have and consider the main features of their graphs and their differences.  Use graphs (including the y = mx + c and y = kx2 + c types) to determine the values of functions and to solve equations. Find the approximate solution of linear simultaneous equations by finding the point of intersection of two straight lines. Currency conversion Introduction to conversion graphs and direct proportionality in the context of currency conversion  Includes use of a spreadsheet. Linear graphs   Slide presentation and activity to introduce linear graphs. Shorter by helicopter    Students plot graphs of real data to compare the straight-line distances between towns with the distances by road. Circles (assignment)    Students measure circular objects and find $\small&space;\pi$ from the gradient of a graph. Non-linear graphs    Draw graphs from data and formulae, then use them to solve problems in real contexts. Includes slide presentation. Hire a coach   Introduces the concepts of gradient and intercept for linear graphs using Excel. Plumbers’ call-out   Students complete data tables, then draw, read and interpret linear graphs where the intercept on the y axis is not zero. Interpretation includes finding where two linear graphs meet. Graphs of functions in Excel  shows students how to draw graphs of algebraic functions in Excel. Spreadsheet graphs  Interactive spreadsheet graphs introducing the shape and main features of proportional and  linear graphs (ignore inverse proportional and quadratic sheets). Linear relationships    Example and exercise involving proportionality and other linear relationships in scientific contexts.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Areas under graphs (5 hours) Calculate estimates of areas under graphs and understand their physical significance (if any) using the formula for the area of a trapezium (and triangle if necessary). Speed and distance Slides to introduce area under a speed-time graph accompanied by examples for students to try. Optional use of spreadsheet/graphic calculator. Formulae and equations  (6 hours) Substitute values into formulae and functions using BIDMAS to find secondary data (including formulae with multiples and fractions, powers and brackets). Form and solve exactly equations where the unknown appears in only one term (e.g. 2x2 + 14 = 20 with solutions $\small&space;\sqrt&space;3$ and $\small&space;-&space;\sqrt&space;3$ ) and equations where the unknown appears two terms each of the same power (such as 4x – 2 = 2x + 8 and 3x2 + 4 = 20 – x2) Hot water tank: Formulae  Slide presentation, notes and exercise. Students learn to substitute values into formulae, and to use a calculator to evaluate expressions. Goldfish bowl: rearrange formulae  Students practise rearranging formulae. There is a worksheet for individual work, or a set of cards for group work to develop this skill. Algebraic expressions  Presentation, information sheet, practice sheet and application to perimeters and areas. Use timetables (2 hours) Read and use timetables using 12 and 24 hour clocks.  Find the length of time for a journey. Every second counts (AMP activity) Learners use maps and timetables to find how far they could travel in 1 hour. Revision (10 hours) Revise topics across the whole core content including finance and shape and space topics. Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

## Work Scheme C

Use this scheme of work if your students are also studying Shape and space and Handling data.

In this case, for the core unit you will need to cover the topic areas listed below which involve finance and algebra. Note that some of the topics (such as use of formulae and misuse of graphs) are similar to those in the Shape and space and Handling data content. You may wish to extend the work done for the other FSMQs to include these rather than studying them separately for this unit.
You should introduce the following and include them wherever possible during this part of the course:

• rounding values as appropriate (such as nearest pence, pound, £100)
• effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic
• checking calculations using estimates, inverse operations and alternative methods

 Topic area Content Nuffield resource The links below go to pages from which you can download the resources, some recently revised. Proportional and linear graphs (8 hours) Use functions to find data pairs of the form y = mx + c and y = kx2 + c including functions in terms of variables other than y and x (such as s = 5t2, P = $\small&space;\frac&space;{k}{V}$).  Use substitution of values into a given expression for a model (y = mx +c, y = kx2 + c) to find unknown constants Look for patterns in data fitting proportional (y = mx),  linear (y = mx + c) and quadratic models (y = kx2) have and consider the main features of their graphs and their differences. Use graphs (including the y = mx + c and y = kx2 + c types) to determine the values of functions and to solve equations. Find the approximate solution of linear simultaneous equations by finding the point of intersection of two straight lines. Linear graphs Slide presentation and activity to introduce linear graphs. Convert currency   Introduction to conversion graphs and direct proportionality in the context of currency conversion  Includes use of a spreadsheet. Hire a coach Introduces the concepts of gradient and intercept for linear graphs using Excel. Graphs of functions in Excel  This activity shows students how to draw graphs of algebraic functions in Excel. Spreadsheet graphs   Interactive spreadsheet graphs introducing the shape and main features of proportional and  linear graphs (ignore inverse proportional and quadratic sheets). Linear relationships   Example and exercise involving proportionality and other linear relationships in scientific contexts. Non-linear graphs   Draw graphs from data and formulae then use them to solve problems in real contexts.  Includes slide presentation. Plumbers’ call-out   Students complete data tables, then draw, read and interpret linear graphs where the intercept on the y axis is not zero. Interpretation includes finding where two linear graphs meet. Formulae and equations (7 hours) Substitute values into formulae and functions using BIDMAS to find secondary data (including formulae with multiples and fractions, powers and brackets). Form and solve exactly equations where the unknown appears in only one term (such as 2x2 + 14 = 20 with solutions $\small&space;\sqrt&space;3$ and $\small&space;-&space;\sqrt&space;3$ ) and equations where the unknown appears two terms each of the same power (such as 4x – 2 = 2x + 8 and 3x2 + 4 = 20 – x2) (There is some overlap with the content of Shape and space allowing possible combination of work) Formulae   Presentation, notes and exercise including a range of formulae involving areas and volumes, interest calculations, temperature conversion and equations of motion. Rearrange formulae   A wide range of formulae from real contexts (areas, volumes, interest calculations, temperature conversion, equations of motion, and so on) for students to rearrange. Includes cards  to help students with the most difficult cases. Algebraic expressions Presentation, information sheet, practice sheet and application to perimeters and areas. Revision (12 hours) Revise topics across the whole core content including shape and space and data topics. Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

## Work Scheme D

Use this scheme of work if your students are also studying Financial calculations and Algebra and graphs.

In this case, for the core unit you will need to cover the topic areas listed below which involve shape and space and data. Note that some of the data topics (such as interpretation of statistical diagrams and line graphs and use of formulae for areas and volumes) are similar to those in the Financial calculations and Algebra and graphs content. You may wish to extend the work done for the other FSMQs to include these rather than studying them separately for this unit.

You should introduce the following and include them wherever possible during this part of the course:

• use of geometrical terms: parallel, perpendicular, bisect, perpendicular bisector, mid-point, horizontal, vertical, line, line segment, regular, similar, congruent, polygon (pentagon, hexagon, octagon)
• use of appropriate instruments (ruler, tape measure, protractor) to make measurements to appropriate levels of accuracy with appropriate units and correct notation
• effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic
• checking calculations using estimates, inverse operations and alternative methods.
 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Measure lengths (2 hours) Use ruler and tape measure to measure objects using metric and imperial units (m, cm, mm, in, ft)  · to the nearest whole unit · to an appropriate level of accuracy (include significant figures and decimal places) Record dimensions in tables and in diagrams. Discuss accuracy of measurements and how it affects subsequent use.  Recognise that measurements expressed to a given unit can have a maximum error of half a unit. Measure it   Slide presentation to demonstrate and check that students can measure in centimetres and millimetres.  Worksheet for recording measurements. Paper sizes (AMP activity)  Learners consider the relationships between paper sizes within one range and the relationships between ranges (A and B series of international paper sizes). Errors (Use the first part only)  Presentation showing errors in measurements and how errors accumulate in calculations involving measurements.  Accompanying notes and worksheets. Convert measurements (2 hours) Convert within and between metric and imperial systems: metric (mm, cm, m, km), imperial (inches, feet, yards, miles). Include the use of conversion factors. Convert lengths  Bingo and dominoes games providing practice in length conversions. Convert it!    Interactive spreadsheet for practice in converting metric lengths and distances. Use protractor (1 hour) Measure angles in degrees. Angles   Presentation and activity measuring and classifying angles.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Calculate perimeters and areas of 2D shapes (5 hours) Use measurements of length, in both metric and imperial units, to calculate: · Perimeters and areas of rectangles, triangles, trapezia and parallelograms · Circumference of circle $\small&space;=&space;\pi&space;\times&space;d&space;=&space;2\pi&space;r$ and arc length of circles for fractions of circles · Area of circle = $\small&space;\pi&space;r^2$ and areas of sectors of circles using $\small&space;\pi$ button on a calculator and giving correct units Include shapes involving combinations of rectangles and triangles. Use formulae for perimeters and areas expressed in words and symbols. Perimeter and area   Presentation, information sheet and worksheet covering the perimeter and area of rectangles and shapes made from rectangles. Also 24 sets of three cards for learners to match.  One card gives the dimensions of a rectangle or shape made from rectangles, one gives its perimeter and one its area. Circle matching cards    Twelve sets of three cards for learners to match. One card shows a real object with its diameter, one gives its circumference and one its area. Design a table (AMP activity)   Students use given body measurements to design a table for five people which can be extended for use by eight/ten people. Calculate surface area and volume of 3D shapes (4 hours) Find surface areas and volumes of cuboids, prisms (including triangular) and cylinders giving values in correct units. Volume  Presentation, information sheets and worksheet covering the volume of cuboids. Solve problems (5 hours) Solve problems involving lengths and angles, deciding on the correct arithmetic to use (adding, subtracting, multiplying, dividing) Use ideas of similarity in terms of enlargement and scale factors (include finding unknown sides in similar triangles). Length problems   Twelve problems set in a range of real contexts to solve. How much will it cost?   Taking measurements from scaled elevations of a house, then finding area and cost of painting. Costing the job   Students take measurements from scaled elevations of a house to find the wall area to be painted and then work out the cost. ‘How much will it cost?’ is an easier version. Pythagoras’ Theorem (4 hours) Use Pythagora's theorem to calculate unknown lengths including use of the formula c2 = a2 + b2 in 2D problems. Pythagoras   Presentation, notes and worksheet.  Links to useful websites. Recognise and classify plane shapes (2 hours) Shapes to include: · triangles including obtuse-angled, acute-angled, equilateral, isosceles and right-angled · quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite  · other polygons including pentagons, hexagons, octagons; understanding that regular polygons have equal sides and equal angles Name the shape   Presentation and activity naming and classifying shapes. What am I?    24 pairs of cards for learners to match.  One card gives a 2D or 3D shape and its name, the other a description. Drawing shapes in Word  Shows students some of the basic drawing techniques available in Word.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Use timetables (2 hours) Read and use timetables using 12 and 24 hour clocks.  Find the length of time for a journey. Every second counts (AMP activity)  Learners use maps and timetables to find how far they could travel in 1 hour. Averages and range (5 hours) Discuss the difference between discrete and continuous data. Choose and find appropriate measures of location: mean from $\small&space;\frac&space;{\textup{sum~of~observed~values}}{\textup{number~of~observations}}$ or $\small&space;\frac&space;{\sum&space;x}{n}$ , mode, median including use of calculator and spreadsheet. Choose and find appropriate measures of spread: range and inter-quartile range. Use these to compare datasets. On average    Examples and exercises on mean, mode and median Coffee shop    Table of information about customers at a coffee shop.  Use on paper or in spreadsheet form for discussion and practice of statistical techniques. Draw and interpret statistical diagrams (9 hours) Draw pictograms, bar charts and pie charts. Plot scatter graph, draw line of best fit through the mean point and use it to estimate missing values. Consider correlation (positive, negative, strength of correlation, no correlation). Draw histograms (with equal class widths) and stem and leaf diagrams (including back-to-back).  Consider the use of techniques which aim to mislead or exaggerate findings (such as manipulation of axes/ using area to exaggerate findings/choosing to omit some data). (There is some overlap with the content of Financial calculations allowing possible combination of work) Draw pie charts in Excel    Activity showing students how to draw a pie chart in Excel and change its appearance. Pie charts    Activity showing students how to draw a pie chart by hand.  Also includes practice exercise with real data – can be used as follow-up to ‘Draw pie charts in Excel’ activity. Draw histograms in Excel  Instructions explaining how to construct an accurate histogram and frequency polygon in Excel. Safety on the roads  Graphs and charts for interpretation. Mineral water (assignment)   Tabulated data and charts about the mineral content of various bottled waters. Students are asked to interpret and analyse this information. Solar eclipse    Lots of data for discussion and suggestions for analysis. Election results    Spreadsheet containing the 2005 and 2010 General Election results. Select local data for practice in drawing charts, finding percentage, and so on.

## Work Scheme E

Use this scheme of work if your students are also studying Shape and Space and Algebra and Graphs.

In this case, for the core unit you will need to cover the topic areas listed below which involve finance and data.

You should also introduce the following and include them wherever possible during this part of the course:

• using tables to record results
• using spreadsheets to carry out calculations and display results in tables and statistical charts and graphs
• effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic.
• checking calculations using estimates, inverse operations and alternative methods.
 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Averages and  range  (5 hours) Discuss the difference between discrete and continuous data.  Choose and find appropriate measures of location: mean (from $\small&space;\frac{\textup{sum~of~observed~values}}{\textup{number&space;~of~observations}}$ or $\small&space;\frac&space;{\sum&space;x&space;}{n}$)  mode, median including use of calculator and spreadsheet. Choose and find appropriate measures of spread: range and inter-quartile range. Use these to compare datasets. On average    Examples and exercises on mean, mode and median. Coffee shop    Table of information about customers at a coffee shop. Use on paper or in spreadsheet form for discussion and practice of statistical techniques. Draw and interpret statistical diagrams  (8 hours) Draw pictograms, bar charts and pie charts. Plot scatter graph, draw line of best fit through the mean point and use it to estimate missing values. Consider correlation (positive, negative, strength of correlation, no correlation). Draw histograms (with equal class widths) and stem and leaf diagrams (including back-to-back).  Consider the use of techniques which aim to mislead or exaggerate findings (such as manipulation of axes/ using area to exaggerate findings/choosing to omit some data). (There is some overlap with the work on line graphs for finance allowing possible combination) Draw pie charts in Excel    Activity showing students how to draw a pie chart in Excel and change its appearance. Pie charts    Activity showing students how to draw a pie chart by hand. Also includes practice exercise with real data – can be used as follow up to ‘Draw pie charts in Excel’ activity. Draw histograms in Excel  Instructions explaining how to construct an accurate histogram and frequency polygon in Excel. Safety on the roads    Graphs and charts for interpretation. Mineral water (assignment)   Tabulated data and charts about the mineral content of various bottled waters. Students are asked to interpret and analyse this information. Solar eclipse   Lots of data for discussion and suggestions for analysis. Election results   Spreadsheet containing the 2005 and 2010 General Election results.  Select local data for practice in drawing charts, finding percentage etc.

## Work Scheme F

Use this scheme of work if your students are also studying Handling data and Algebra and graphs.
In this case, for the core unit you will need to cover the topic areas listed below which involve finance and shape and space. Note that some of the topics (such as use of formulae for areas and volumes) are similar to those in the Algebra graphs content.  You may wish to extend the work done for Algebra and graphs to include these rather than studying them separately for this unit.

You should introduce the following and include them wherever possible during this part of the course:

• use of geometrical terms: parallel, perpendicular, bisect, perpendicular bisector, mid-point, horizontal, vertical, line, line segment, regular, similar, congruent, polygon (pentagon, hexagon, octagon)
• use of appropriate instruments (ruler, tape measure, protractor) to make measurements to appropriate levels of accuracy with appropriate units and correct notation
• effective and efficient use of a calculator, including understanding how calculators use the rules of precedence in arithmetic
• checking calculations using estimates, inverse operations and alternative methods.
 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Measure lengths (2 hours) Use ruler and tape measure to measure objects using metric and imperial units (m, cm, mm, in, ft)  · to the nearest whole unit · to an appropriate level of accuracy (include significant figures and decimal places) Record dimensions in tables and in diagrams. Discuss accuracy of measurements and how it affects subsequent use. Recognise that measurements expressed to a given unit can have a maximum error of half a unit. Measure it   Presentation to demonstrate and check that students can measure in centimetres and millimetres. Worksheet for recording measurements. Paper sizes (AMP activity)  Learners consider the relationships between paper sizes within one range and the relationships between ranges (A and B series of international paper sizes). Errors (Use the first part only)  Presentation showing errors in measurements and how errors accumulate in calculations involving measurements.  Accompanying notes and worksheets. Convert measurements  (2 hours) Convert within and between metric and imperial systems: metric (mm, cm, m, km), imperial (inches, feet, yards, miles).  Include the use of conversion factors. Convert lengths   Bingo and dominoes games providing practice in length conversions. Convert it!     Interactive spreadsheet for practice in converting metric lengths and distances. Use protractor (1 hour) Measure angles in degrees. Angles   Presentation and activity measuring and classifying angles. Calculate perimeters and areas of 2D shapes (5 hours) Use measurements of length, in both metric and imperial units, to calculate: · Perimeters and areas of rectangles, triangles, trapezia and parallelograms · Circumference of circle = $\small&space;\pi&space;\times&space;d$ = $\small&space;2&space;\pi&space;r$ and arc length of circles for fractions of circles · Area of circle = $\small&space;\pi&space;r^2$ and areas of sectors of circles using $\small&space;\pi$ button on a calculator and giving correct units Include shapes involving combinations of rectangles and triangles.  (Use formulae for perimeters and areas expressed in words and symbols.) Perimeter and area  Presentation, information sheet and worksheet covering the perimeter and area of rectangles and shapes made from rectangles. Also 24 sets of three cards for learners to match. One card gives the dimensions of a rectangle or shape made from rectangles, one gives its perimeter and one its area. Circle matching cards   Twelve sets of three cards for learners to match. One card shows a real object with its diameter, one gives its circumference and one its area. Design a table (AMP activity)   Students use given body measurements to design a table for five people which can be extended for use by eight/ten people.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Calculate surface area and volume of 3D shapes (4 hours) Find surface areas and volumes of cuboids, prisms (including triangular) and cylinders giving values in correct units. Volume  Presentation, information sheets and worksheet covering the volume of cuboids. Solve problems (5 hours) Solve problems involving lengths and angles, deciding on the correct arithmetic to use – adding, subtracting, multiplying, dividing Use ideas of similarity in terms of enlargement and scale factors, including finding unknown sides in similar triangles. Length problems  Twelve problems set in a range of real contexts to solve. How much will it cost?   Taking measurements from scaled elevations of a house, then finding area and cost of painting. Costing the job   Students take measurements from scaled elevations of a house to find the wall area to be painted and then work out the cost. 'How much will it cost?’ is an easier version. Pythagoras’ Theorem  (4 hours) Use Pythagoras theorem to calculate unknown lengths including use of the formula c2 = a2 + b2 in 2D problems. Pythagoras     Powerpoint presentation, notes and worksheet. Links to useful websites. Recognise and classify plane shapes  (2 hours) Shapes to include: · triangles including obtuse-angled, acute-angled, equilateral, isosceles and right-angled, · quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite, · other polygons including pentagons, hexagons, octagons (understanding that regular polygons have equal sides and equal angles) Name the shape    Presentation and activity naming and classifying shapes. What am I?   24 pairs of cards for learners to match. One card gives a 2D or 3D shape and its name, the other a description. Drawing Shapes in Word  Shows students some of the basic drawing techniques available in Word. Make shapes in Word    Activity showing students how to draw their own shapes in Word, with and without gridlines.