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 = $\pi&space;\times&space;d&space;=&space;2\pi&space;r$ · Area of circle = $\pi&space;r^2$ · 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 $L&space;=&space;3.28l$ 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 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 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 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 $L$ = 3.28$l$  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 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.