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

Foundation Core Unit

Level 1 AQA Certificate in use of mathematics Core unit scheme of work

The content of this Foundation unit is based on the subject content of the FSMQs which are components of the AQA 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 1 FSMQs (Money management, Using spatial techniques, Using data) either before or alongside that of this core unit. Select just one of the three work schemes according to which two Level 1 FSMQs you are also using. The work scheme describes the extra topics you will need to cover for your learners to be prepared for the core examination.  Each of the three options recommends a total of 60 guided learning hours, including an allocation of time for revision; this should include some of the topics from the other two FSMQs you are using.

If your students are studying one or two of the equivalent FSMQs at Level 2 (that is Financial calculations, Shape and space and/or Data handling) you may be able to omit some sections.  If your students are studying Level 2 Algebra and graphs you will be able to omit the algebra sections, but will need to include extra work depending on which other FSMQ you are using.

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 AQA assessment of this core unit.  Also note that the AMP activities were not written specifically for this core unit and may include some work beyond what is needed.

Work Scheme A       

Use this scheme of work if your students are also studying Money management and Using 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

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.

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).

Convert measurements
(4 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
(2 hours)

Measure angles in degrees. 

 

Angles  
Presentation and activity measuring and classifying angles.

Calculate perimeters and areas of 2D shapes
(8 hours)

Use measurements of length, in both metric and imperial units, to calculate:

· Perimeters

· Circumference of circle = \pi \times d = 2\pi r

· Area of circle = \pi r^2

· Area of rectangle = length x width

· Area of triangle = ( 1/2  base x perpendicular height)

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  
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 5 people which can be extended for use by 8/10 people.

 

Topic area

Content

Nuffield resource

Calculate surface area and volume of 3D shapes
(5 hours)

Find surface areas and volumes of cuboids and prisms (including triangular), using volume formula:

· volume = area of cross-section \times length

and giving values in correct units.

Volume 
Students find the volume of a variety of cuboids in real life contexts.

Solve problems
(6 hours)

Solve problems involving lengths and angles, deciding on the correct arithmetic to use (adding, subtracting, multiplying, dividing)

Use similarity in terms of scale factors.

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.

Recognise and classify plane shapes
(4 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 your own shapes in Word   
Activity showing students how to draw their own shapes in Word, with and without gridlines.

Tessellations in Word    
Activity showing students how to draw tessellations in Word, with and without gridlines.

Tessellation shapes   
Collection of shapes to print on card and laminate.

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 lines by eye as an approximate fit when appropriate and discuss ideas of positive and negative correlation. Identify errors in data by inspection and graphical means.

Discuss gradients and intercepts of graphs with the axes and where appropriate understand their physical significance.

Road test  
Use data from a road test on a sports car for practice in drawing and interpreting graphs.  Optional use of spreadsheet.

 

Topic area

Content

Nuffield resource

Proportional and linear graphs
(6 hours)

Use functions to find data pairs of the form  (y = mx + c), including functions in terms of variables other than y and x. Use tables to display results.

Look for patterns that data fitting proportional (y = mx), and linear (y = mx + c) models have.

Consider the main features of proportional and linear graphs and their differences.

Use graphs to find the values of functions and to solve linear equations.

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.

Substitution into formulae
(4 hours)

Substitute data into formulae and functions using BIDMAS to find secondary data (including formulae with multiples and fractions of linear terms).

Use formulae to convert units
e.g. using L = 3.28l to convert  l metres to L feet.

Use substitution of values into a given expression for a model (y = mx + c, y = kx2 + c) to find unknown constants

Formulae   
Presentation, notes and exercise including a range of formulae involving areas and volumes, interest calculations, temperature conversion and equations of motion.

Non-linear graphs    
Draw graphs from data and formulae then use them to solve problems in real contexts.  Includes presentation.

Solve equations
(4 hours)

Form and solve exactly simple equations where there is only one unknown e.g. 2x = 1.5x + 4

 

Revision
(10 hours)

Revise topics across the whole core content (including money 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 Money management and Using spatial techniques.

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 statistical diagrams) are similar to those in the Money Management content. You may wish to extend the work done for Money Management to include these rather than studying them separately.

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 resource

Collecting and organising data
(5 hours)

Collect and record data using an appropriate degree of accuracy (include significant figures & decimal places).  Include the use of tally charts.  Organise data on paper and spreadsheets (compare different ways of doing this). 

 

Statistical measures
(8 hours)

Find sum, mean, mode, median and range of data with and without a calculator.  (Include use of the calculator’s memory.)

Use a spreadsheet to sort data and find the sum, mean, median, mode and range.

Print out spreadsheet formulae.

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 charts (8 hours)

Revision of drawing pictograms, bar charts and pie charts (also included in 'Money management' allowing possible combination of work).  Use words to describe what statistical diagrams indicate about the situations they represent.

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  
Data sheets about eclipses, discussion sheet and exercise involving interpretation of statistical diagrams.

Election results   
Spreadsheet containing the 2005 and 2010 General Election results. Select local data for practice in drawing charts, finding %, and so on.

 

Topic area

Content

Nuffield resource

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. 

Discuss accuracy of data and how it affects its subsequent use.

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.  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).

Outdoor gig   
Students use weather data to consider which month would be the best to hold an outdoor gig. (Calculator and spreadsheet versions.)

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 resource

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 lines by eye as an approximate fit when appropriate and discuss ideas of positive and negative correlation.  Identify errors in data by inspection and graphical means.

Discuss gradients and intercepts of graphs with the axes and where appropriate understand their physical significance.

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

Proportional and linear graphs
(6 hours)

Use functions to find data pairs of the form y = mx + c, including functions in terms of variables other than y and x. Use tables to display results.

Look for patterns that data fitting proportional (y = mx), and linear (y = mx + c) models have.

Consider the main features of proportional and linear graphs and their differences. 

Use graphs to find the values of functions and to solve linear equations.

Currency conversion     
Introduction to conversion graphs and direct proportionality in the context of currency conversion  Includes use of a spreadsheet.

Reaction rates   
Drawing and interpreting graphs using data provided from chemical reactions. Requires graphs to be drawn using spreadsheet and by hand.

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  from the gradient of a graph.

Linear graphs    
Presentation and activity to introduce linear graphs.

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    
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. Presentation to aid discussion (same graphs with titles and labels). 

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.

 

Topic area

Content

Nuffield Resource

Substitution into formulae
(4 hours)

Substitute data into formulae and functions using BIDMAS to find secondary data including formulae with multiples and fractions of linear terms.

Use formulae to convert units
e.g. using L = 3.28 l to convert l metres to L feet.

Use substitution of values into a given expression for a model (y = mx +c, y= kx2+c) to find unknown constants

Formulae    
Presentation, notes and exercise including a range of formulae involving areas and volumes, interest calculations, temperature conversion and equations of motion.

Non-linear graphs    
Draw graphs from data and formulae then use them to solve problems in real contexts.  Includes presentation.

Solve equations
(4 hours)

Form and solve exactly simple equations where there is only one unknown, such as 2x = 1.5x + 4

 

Revision
(10 hours)

Revise topics across the whole core content including money and shape & 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 Using spatial techniques and Using data.
In this case, for the core unit you will need to cover the topic areas listed below which involve money and algebra. Note that some of the money topics (eg those involving fractions, % and ratio) are similar to those in the Using Data content.  You may wish to extend the work done for Using Data to include the money calculations listed below rather than studying them separately.

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

  • Rounding values as appropriate (e.g. nearest pence, pound, £100 etc)
  • 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

Currency
(3 hours)

Use British coins and notes to make amounts and give change.

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 percentage

(9 hours)

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

Calculating VAT    
Worksheet to give students practice with working out 5% VAT on fuel bills.

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 4 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 1 year.

 

Topic area

Content

Nuffield resources

Best buys
(8 hours)

Use decimals to make comparisons (putting in order of size).  Use % 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.

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

The best buy (assignment) 
Students work out which are the best buys for items sold in different-sized packs at different price. Assignment with structured section on best buys followed by an extension giving students the opportunity of working independently.

Recording financial transactions
(9 hours)

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

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

Writing one quantity as a fraction or percentage of another.

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

 

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.

Create a bank statement   
Sheet of transactions to put in order to create a bank statement. 

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.

Every second counts (AMP activity)  
Learners use maps & timetables to find how far they could travel in 1 hour.

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 lines by eye as an approximate fit when appropriate and discuss ideas of positive and negative correlation. Identify errors in data by inspection and graphical means.

Discuss gradients and intercepts of graphs with the axes and where appropriate understand their physical significance.

Road test
Use data from a road test on a sports car for practice in drawing and interpreting graphs. Optional use of spreadsheet.

 

Topic area

Content

Nuffield resource

Proportional and linear graphs
(6 hours)

Use functions to find data pairs of the form y = mx + c, including functions in terms of variables other than y and x. (Use tables to display results.)

Look for patterns that data fitting proportional
(y = mx), and linear (y = mx + c) models have.

Consider the main features of proportional and linear graphs and their differences. 
Use graphs to find values of functions and to solve equations.

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.

 

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.

 

Substitution into formulae
(4 hours)

Substitute data into formulae and functions using BIDMAS to find secondary data including formulae with multiples and fractions of linear terms.

Use formulae to convert units
such as using L = 3.28l  to convert l metres to L  feet.

Use substitution of values into a given expression for a model (y = mx +c, y= kx2+c) to find unknown constants

Formulae   
Presentation, notes and exercise including a range of formulae involving areas and volumes, interest calculations, temperature conversion and equations of motion.

Non-linear graphs  
Draw graphs from data and formulae then use them to solve problems in real contexts.  Includes slide presentation.

 

Solve equations
(4 hours)

Form and solve exactly simple equations where there is only one unknown, such as  2x = 1.5x + 4

 

Revision
(12 hours)

Revise topics across the whole core content including shape and space and statistics topics.
Try specimen and past papers.

Discuss Data sheet – make up and try questions based on it.

 

 

 

Page last updated on 20 March 2012