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

FSMQ Level 2 Higher Core Unit scheme of work

Note: AQA have decided to discontinue this certificate. The last exams will be in the June 2018 series.

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  = \pi \times d = 2 \pi r
and arc length of circles for fractions of circles

· Area of circle  = \pi 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
= 3.28l 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 = l \times b \times 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 \frac {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 \sqrt 3 and  \small - \sqrt 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 \frac{\textup{sum~of~observed~values}}{\textup{number ~of~observations}} or

\small \frac {\sum 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.

 

Topic area

Content

Nuffield resources The links below go to pages from which you can download the resources, some recently revised.

Compare datasets

(12 hours)

Use measures of location and range together with statistical diagrams to come to conclusions about the data from which they have been derived.

Include comparisons with other data of a similar nature. 

Consider whether alternative measures/diagrams would be more/less useful to highlight the findings. 

Identify what it is not possible to conclude from the data, and consider what extra information / data is needed.

Acid rain 
Worksheet explains how acid rain is produced and requires students to analyse thedata given in the accompanying spreadsheet.

Heights and weights (assignment)  
Data set of girls’ and boys’ heights and weights. Students select data, then calculate statistical measures and draw statistical diagrams. 

Body Mass Index (assignment)   
Involves collecting and illustrating data using a spreadsheet.

Computer survey (assignment)   
Students design a questionnaire about computer usage, carry out a survey and analyse the results

Football figures    
Spreadsheet containing 2007-8 data for each premier league club. Teacher notes suggest uses.

House prices  
Two versions, both with large data sets of house prices showing how they have changed in different locations over long and short periods of time. In Version A students draw and interpret statistical diagrams and calculate statistical measures by hand. In Version B students use a spreadsheet to create the statistical diagrams and calculate statistical measures, then interpret them.

Part-time work survey 
Investigation into students’ paid employment (questionnaires, averages and range, charts and graphs).

Music Festival  
Students use weather data to decide which is the best month for an outdoor event. Two versions – for use with calculator or spreadsheet.

HE applications   
Data sheets and spreadsheet giving gender, age, ethnic origin and other information about HE applicants. 

Heart rate  
Students are shown how to measure heart rate and then asked to plan and carry out an investigation.

Five a day   
Investigation to find out to what extent people understand and follow government advice to eat five portions of fruit and vegetables per day.

Larks and owls (assignment)  
Assignment in which students carry out an investigation involving sleep.

Crime in the regions (assignment)   
Assignment in which students compare crime figures for their region with other regions.

Cemetery mathematics (AMP activity) 
Learners collect data from a local graveyard or cemetery to test a hypothesis they themselves have chosen (such as people live longer than they used to or women live longer than men)

Reaction times (AMP activity)  
Learners design an experiment to measure reaction times and are asked to display results in a clear and interesting way. 

 

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 \frac {k}{V}). 

Use substitution of values into a given expression for a model
(\small y = mx + c, \small y = kx^2 + c) to find unknown constants

Look for patterns in data fitting proportional
(\small y = mx),  linear
(\small y = mx + c) and quadratic models (\small y = 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 \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 \sqrt 3 and \small - \sqrt 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 resources
The links below go to pages from which you can download the resources, some recently revised.

Currency
(3 hours)

Use exchange rates to convert amounts between currencies.

Convert currency  
Interactive spreadsheet for practice in converting between £ and euros and £ and dollars

Money calculations involving fractions and percentages
(9 hours)

Read and use information given in tables and use fractions, decimals and percentage in a range of contexts involving money. Include:

· Finding fractions and percentages of quantities (such as discounts, VAT on order forms and bills)

· Calculating new values given a starting value and the percentage rate (such as amount in an account after interest is added, sale price after a reduction, wage after a percentage rise).

Use spreadsheets to record and work out values.

Find percentage  
Find percentage without a calculator and on a spreadsheet.

Sale   
Students use a spreadsheet to work out sale prices and check their results.

Work out VAT 
Find VAT without a calculator and on a spreadsheet.

Wages and overtime 
For giving students practice in working out overtime rates. 

Savings and interest
Relatively straightforward worksheet to give students practice with working out interest and amounts in accounts after one year.

Firefighters’ pay    
Students compare rises of 11%, 16% and 40% in the annual pay of four different ranks of firefighters, and the difference this might make to a fireman’s savings.

Bills   
Simulated bills, exercise, sample exam questions and assignment. Includes use of a spreadsheet.

Invoices  
Explain and check calculations. Includes use of a spreadsheet.

Mobile phone tariffs 
Enter values onto spreadsheet, explain calculations, then choose the most suitable tariff.

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.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Comparisons
(8 hours)

Use fractions, decimals and percentages to make comparisons.

Select the best buy in a range of contexts.

Express two or three quantities as a ratio, divide a quantity in a given ratio (e.g. 2 : 3 : 5) and use ratios to make comparisons (between 2 or 3 values)

(May also require conversion of units such as kg to g, litres to ml)

Best buys
Examples and worksheet.

Ratios
Activities giving learners practice in simplifying ratios.

Party time  (assignment) 
Use on-line shopping to find best buys and cost a party. Optional use of spreadsheet

The best buy (assignment) 
Assignment with structured section on best buys followed by an extension that gives students the opportunity of working independently.

Recording financial transactions
(6 hours)

Credits, debits and running totals, using both positive and negative numbers.  Draw line graph by hand to show how balance varies over time.

Use a spreadsheet to carry out and record financial calculations (including the use of negative numbers). 

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 Handling data allowing possible combination of work)

 

Student budget 
A spreadsheet showing a student’s bank balance over a term and a worksheet based on it.

Car costs (assignment) 
Assignment and sample exam questions supported by three data sheets. Assignment requires use of a spreadsheet to keep an account of the cost of running a car.

Bank balance
Game in which learners enter items onto bank balance statements and calculate the resulting balances.

Spot the errors  
Simulated invoice, phone bill and bank statement for learners to check (several errors on each). Also provided with spaces for students to complete.

Bank statement (assignment)  
Create and analyse a spreadsheet to show income and expenditure.

Plot and interpret line 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 behavior in real world terms.

Calculate the gradients of linear graphs in appropriate units and understand their physical significance.

Reaction rates
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).

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

Crushed calcium carbonate
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.

 

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 \frac {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 \sqrt 3 and \small - \sqrt 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 = \pi \times d = 2\pi r
and arc length of circles for fractions of circles

· Area of circle = \small \pi r^2 and areas of sectors of circles using \small \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 \frac {\textup{sum~of~observed~values}}{\textup{number~of~observations}} or \small \frac {\sum 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.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Compare datasets 
(9 hours)

Use measures of location and range together with statistical diagrams to come to conclusions about the data from which they have been derived. Include comparisons with other data of a similar nature. 

Consider whether alternative measures/diagrams would be more/less useful to highlight the findings. Identify what it is not possible to conclude from the data and consider what extra information /data is needed.

Acid rain   
Worksheet explains how acid rain is produced and requires students to analyse thedata given in the accompanying spreadsheet.

Heights and weights (assignment)
Data set of girls’ and boys’ heights and weights from which students select data, then calculate statistical measures and draw statistical diagrams. 

Body Mass Index (assignment)
Involves collecting and illustrating data using a spreadsheet.

Computer survey (assignment)  
Students design a questionnaire about computer usage, carry out a survey and analyse the results

Football figures  
Excel spreadsheet containing 2007-8 data for each premier league club. 

House prices  
Two versions, both with large data sets of house prices showing how they have changed in different locations over long and short periods of time.
In Version A, students draw and interpret statistical diagrams and calculate statistical measures by hand.
In Version B, students use a spreadsheet to create the statistical diagrams and calculate statistical measures, then interpret them.

Part-time work survey   
Investigation into students’ paid employment (questionnaires, averages and range, charts and graphs).

Music Festival   
Students use weather data to decide which is the best month for an outdoor event.  Two versions – for use with calculator or spreadsheet.

Heart rate  
Students are shown how to measure heart rate and then asked to plan and carry out an investigation.

Five a day 
Investigation to find out to what extent people understand and follow government advice to eat 5 portions of fruit and vegetables per day.

HE applications  
Data sheets and spreadsheet giving gender, age, ethnic origin and other information about HE applicants. Worksheet and teacher notes suggest uses.

Larks and owls (assignment)  
Assignment in which students carry out an investigation involving sleep.

Cemetery mathematics (AMP activity)  
Learners collect data from a local graveyard or cemetery to test a hypothesis they themselves have chosen (such as people live longer than they used to or women live longer than men)

Reaction times (AMP activity)
Learners design an experiment to measure reaction times and are asked to display results in a clear and interesting way.

 

Revision (10 hours)

Revise topics across the whole core content (including finance and algebra topics). Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

 

 

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 \frac{\textup{sum~of~observed~values}}{\textup{number ~of~observations}} or

\small \frac {\sum 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 
(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.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Compare datasets 
(10 hours)

Use measures of location and range, together with statistical diagrams, to come to conclusions about the data from which they have been derived. Include comparisons with other data of a similar nature. 

Consider whether alternative measures/diagrams would be more/less useful to highlight the findings.  Identify what it is not possible to conclude from the data, and consider what extra information /data is needed.

Acid rain  
Worksheet explains how acid rain is produced and requires students to analyse the data given in the accompanying spreadsheet.

Heights and weights (assignment)  
Data set of girls’ and boys’ heights and weights from which students select data, then calculate statistical measures and draw statistical diagrams. 

Body Mass Index (assignment)  
Involves collecting and illustrating data using a spreadsheet.

Computer survey (assignment)  
Students design a questionnaire about computer usage, carry out a survey and analyse the results

Football figures 
Excel spreadsheet containing 2007-8 data for each premier league club. Teacher notes suggest uses.

House prices   
Two versions, both with large data sets of house prices showing how they have changed in different locations over long and short periods of time.

In Version A, students draw and interpret statistical diagrams and calculate statistical measures by hand.

In Version B, students use a spreadsheet to create the statistical diagrams and calculate statistical measures, then interpret them.

Part-time work survey   
Investigation into students’ paid employment (questionnaires, averages and range, charts and graphs).

Music Festival   
Students use weather data to decide which is the best month for an outdoor event.  Two versions – for use with calculator or spreadsheet.

Heart rate  
Students are shown how to measure heart rate and then asked to plan and carry out an investigation.

Five a day  
Investigation to find out to what extent people understand and follow government advice to eat five portions of fruit and vegetables per day.

HE applications  
Data Sheets and spreadsheet giving gender, age, ethnic origin and other information about HE applicants. Worksheet and Teacher notes suggest uses.

Larks and owls (assignment)   
Assignment in which students carry out an investigation involving sleep.

Cemetery mathematics (AMP activity)   
Learners collect data from a local graveyard or cemetery to test a hypothesis they themselves have chosen (e.g. people live longer than they used to or women live longer than men)

Reaction times (AMP activity) 
Learners design an experiment to measure reaction times and are asked to display results in a clear and interesting way.

 

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Currency
(3 hours)

Use exchange rates to convert amounts between currencies.

Convert currency   
Interactive spreadsheet for practice in converting between £ and euros and £ and dollars

Money calculations involving fractions and percentages 
(8 hours)

Read and use information given in tables and use fractions, decimals and percentages in a range of contexts involving money. Include:

· Finding fractions and percentages of quantities (such as discounts, VAT on order forms and bills)

· Calculating  new values given a starting value and the percentage rate (such as amount in an account after interest is added, sale price after a reduction, wage after a percentage rise).

Use spreadsheets to record and work out values.

Find percentage   
Find % without a calculator and on a spreadsheet.

Sale   
Students use a spreadsheet to work out sale prices and check their results.

Work out VAT  
Find VAT without a calculator and on a spreadsheet.

Wages and overtime  
For giving students practice in working out overtime rates. 

Firefighters’ pay    
Students compare rises of 11%, 16% and 40% in the annual pay of four different ranks of firefighters, and the difference this might make to a fireman’s savings.

Bills (assignment)   
Simulated bills, exercise, sample exam questions and assignment.  Includes use of a spreadsheet.

Invoices 
Explain and check calculations. Includes use of a spreadsheet.

Mobile phone tariffs   
Enter values onto spreadsheet, explain calculations then choose the most suitable tariff.

Savings and interest  
Worksheet to give students practice with working out interest and amounts in accounts after one year.

Use timetables
(2 hours)

Read & 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.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Comparisons
(8 hours)

Use fractions, decimals and percentages to make comparisons.
 Select the best buy in a range of contexts.
Express two or three quantities as a ratio, divide a quantity in a given ratio (such as 2 : 3 : 5) and use ratios to make comparisons (between 2 or 3 values)

(May also require conversion of units such as kg to g, litres to ml)

Best buys  Examples and worksheet.

Ratios
Activities that give learners practice in simplifying ratios.

Party time   (assignment) 
Use on-line shopping to find best buys and cost a party.  Optional use of spreadsheet

The best buy (assignment
Assignment with structured section on best buys followed by an extension giving students the opportunity of working independently.

Recording financial transactions  
(6 hours)

Credits, debits and running totals, using both positive and negative numbers. 

Draw line graph by hand to show how balance varies over time.

Use a spreadsheet to carry out and record financial calculations (including the use of negative numbers). 

Considerthe 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 earlier statistical work allowing possible combination)

 

Student budgets  
A spreadsheet showing a student’s bank balance over a term and a worksheet based on it.

Car costs (assignment)  
Assignment and sample exam questions supported by three data sheets.  Assignment requires use of a spreadsheet to keep an account of the cost of running a car.

Bank balance 
Game in which learners enter items onto bank balance statements and calculate the resulting balances.

Spot the errors 
Simulated invoice, phone bill and bank statement for learners to check (several errors on each). Also provided with spaces for students to complete.

Bank statement (assignment)  
Create and analyse a spreadsheet to show income and expenditure.

Revision (10 hours)

Revise topics across the whole core content (including algebra and shape and space topics). Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

 


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 \pi \times d = \small 2 \pi r and arc length of circles for fractions of circles

· Area of circle = \small \pi r^2 and areas of sectors of circles

using \small \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.

 

Topic Area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Currency 
(3 hours)

Use exchange rates to convert amounts between currencies.

Convert currency   
Interactive spreadsheet for practice in converting between £ and euros and £ and dollars

Money calculations involving fractions and percentages 
(8 hours)

Read and use information given in tables and use fractions, decimals and percentages in a range of contexts involving money. Include:

· Finding fractions and percentages of quantities (such as discounts, VAT on order forms and bills)

· Calculating new values given a starting value and the percentage rate (such as amount in an account after interest is added, sale price after a reduction, wage after a percentage rise).

Use spreadsheets to record and work out values.

Find percentage   
Find percentage without a calculator and on a spreadsheet.

Sale   
Students use a spreadsheet to work out sale prices and check their results.

Work out VAT   
Find VAT without a calculator and on a spreadsheet.

Wages and overtime 
For giving students practice in working out overtime rates.

Firefighters’ pay   
Students compare rises of 11%, 16% and 40% in the annual pay of four different ranks of firefighters and the difference this might make to a fireman’s savings.

Bills (assignment)   
Simulated bills, exercise, sample exam questions and assignment.  Includes use of a spreadsheet.

Invoices
Explain and check calculations. Includes use of a spreadsheet.

Mobile phone tariffs 
Enter values onto spreadsheet, explain calculations then choose the most suitable tariff.

Savings and interest  
Worksheet to give students practice with working out interest and amounts in accounts after one year.

 

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.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Comparisons
(8 hours)

Use fractions, decimals and percentages to make comparisons.

Select the best buy in a range of contexts.

Express two or three quantities as a ratio, divide a quantity in a given ratio (e.g. 2 : 3 : 5) and use ratios to make comparisons (between 2 or 3 values)

(May also require conversion of units such as kg to g, litres to ml)

Best buys  Examples and worksheet.

Ratios 
Activities giving learners practice in simplifying ratios.

Party time (assignment) 
Use on-line shopping to find best buys and cost a party.  Optional use of spreadsheet

The best buy (assignment) 
Assignment with structured section on best buys followed by an extension giving students the opportunity of working independently.

Recording financial transactions 
(5 hours)

Credits, debits and running totals, using both positive and negative numbers.  Drawing line graph by hand to show how balance varies over time.

Use a spreadsheet to carry out and record financial calculations (including the use of negative numbers). 

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 Handling data allowing possible combination of work)

 

Student budgets  
A spreadsheet showing a student’s bank balance over a term and a worksheet based on it.

Car costs (assignment)  
Assignment and sample exam questions supported by three data sheets. Assignment requires use of a spreadsheet to keep an account of the cost of running a car.

Bank balance 
Game in which learners enter items onto bank balance statements and calculate the resulting balances.

Spot the errors
Simulated invoice, phone bill and bank statement for learners to check (several errors on each). Also provided with spaces for students to complete.

Bank statement (assignment)  
Create and analyse a spreadsheet to show income and expenditure.

Revision
(9 hours)

Revise topics across the whole core content (including algebra and data topics). Try specimen and past papers. Discuss data sheet – make up and try questions based on it.

 

 

Page last updated on 02 August 2017