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

# FSMQ Level 2 Financial calculations scheme of work

Before starting this Higher (Level 2) FSMQ students must

• be able to order numbers (decimal, fractional, large, small and negative numbers),
• be familiar with the idea and basic use of percentages,
• be able to carry out basic calculations involving money
• be familiar with common units of time (such as 12 months in a year).

A suggested work scheme showing topic areas and methods to be covered is given below. This recommends a total of 60 guided learning hours which could be used in a variety of ways, such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, or 5 hours per week for 12 weeks. There is plenty of scope for varying the order and time allocation as many of the mathematical techniques can be introduced/revised in several different topic areas.

Some techniques should be introduced as soon as possible and used throughout the course:

• selecting information from text and tables (two-way and more complex) and using tables to record results
•  using a calculator effectively and efficiently to carry out appropriate mathematical methods
• writing out calculations clearly and logically, rounding the result to the most appropriate value (such as nearest pence, £, £100)
• writing brief comments to explain calculations and interpret the results
• checking calculations using estimates, inverse operations and alternative methods
• using appropriate statistical methods of displaying results, including the use of spreadsheets to display results in tables and statistical charts and graphs
• using spreadsheet formulae to carry out calculations, including the use of relative and absolute referencing cell references and the 'fill down' facility.

Although topic areas are listed separately below, students will probably find it more motivating if a thematic approach is used.  Possible themes include the financial implications of being a student, the management of predicted finances during a first year of work, the financial aspects of  running a home, business or club or investigating different ways of purchasing an expensive item such as a house or car.  At key points the thematic work could be supplemented with practice exercises when necessary.

Note that the assessment of this AQA FSMQ is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments which have not been updated. These are included for possible use as classroom activities but will not form part of the assessment of this FSMQ.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Money calculations involving fractions and percentages  (7 hours) Use interesting/relevant contexts to find out what students know about fractions and percentages.  Extension/revision where necessary to include the following: · expressing one quantity as a fraction or percentage of another · calculating fractional and percentage increases and decreases such as ‘mark-ups’ and discounts · finding VAT and final price. Carry out reverse calculations: · find initial value when given a fraction of this value · find original price when given the final price and the percentage (or fractional) change (such as find the price before VAT from the price which includes VAT). Use spreadsheet formulae as well as calculations done by hand. Include use of relative and absolute cell referencing as well as the ‘fill down’ facility. Work out VAT   Find VAT without a calculator and on a spreadsheet. Working with percentages  Discussion and worksheets supported by slideshow for discussion about the use of multipliers in real-life percentage problems.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Salary calculations   (8 hours) Carry out calculations related to earnings (by hand and using spreadsheet formulae). Include the use of such terms as wage, salary, overtime, commission (including monthly wage = annual salary ÷ 12).  Complete more complex calculations that include fixed and variable rates eg the calculation of income tax (using all tax rates current for income under £100 000 per year). Include use of the terms: income tax, PAYE (Pay As You Earn), national insurance, gross pay, net pay (= gross pay – deductions). Draw pie charts and bar charts (by hand and using spreadsheets) to illustrate results. Payslips   Data sheets including three simulated pay slips and related worksheet. Pay as you earn   Students work out how much income tax is paid on typical earnings for a variety of jobs. Income tax   Notes, examples and exercises based on rates for the current tax year. National Insurance Notes, examples and exercise based on rates for the current tax year. Ratios   (2 hours) Use interesting/relevant contexts to assess students' knowledge of ratios and extend where necessary to include: · expressing two quantities as a ratio · dividing a quantity in a ratio · using ratios to make comparisons. Ratios    Activities giving learners practice in simplifying ratios. Savings  (8 hours) Use terms related to saving – interest rates, compound interest, AER (Annual Equivalent Rate) and carry out related calculations including: · using percentage rates (including AER) to find interest on savings compounded over a number of stages (include use of given formulae) · use of formulae associated with compound interest, including: A = P(1 + R)n for the amount accruing when principal P earns compound interest at an annual rate R in n years $R&space;=&space;\sqrt[n]{A&space;\over&space;P}-1$     for the annual rate at which principal P would increase to an amount A after n years. (Rate R used as a decimal in formulae.) Draw line graphs (by hand and using spreadsheets) to illustrate results. Compare interest rates using AER. Savings and interest  Relatively straightforward worksheet to give students practice with working out interest and amounts in accounts after one year. Interest on savings   Notes, examples and exercises involving simple and compound interest. Comparison of different types of savings. Simple and compound interest  Spreadsheet giving examples and practice. Separate spreadsheet gives answers. Saving   Leaflet giving interest rates on three instant access savings accounts, exercise and sample examination questions based on the leaflet and an assignment. Exercise uses Excel spreadsheet. Savings facts and formulae Slide presentation, notes and practice in using formulae related to savings. Exchange rates  (2 hours) Use exchange rates (such as to find the price in £ of a jacket whose price is \$80) Convert currency Interactive spreadsheet for practice in converting between £ and euros and £ and dollars Insurance (5 hours) Use tables and carry out calculations to do with insurance (including the use of terms such as insurance tax). Estimate probabilities from real data using relative frequency. Understand numerical values of probabilities and use ideas of basic probability to help make decisions. Insurance rates  Students investigate the link between crime figures and the cost of vehicle and home insurance.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Loans  (8 hours) Use terms and carry out calculations related to borrowing – interest rates, compound interest, handling charges, commission, APR (Annual Percentage Rate). Use tables to find monthly repayments on loans, the total amount repaid and the percentage interest charged. Use percentage rates to find interest on loans compounded over a number of periods. Use APR to compare interest rates. Draw line graphs (by hand and using spreadsheets) to illustrate results. Credit cards   Notes and example including spreadsheet formulae. Short-term loans  Notes, examples and exercise. Requires information from building society or bank leaflets. Long-term loans  Notes, examples and exercise. Mortgages   Notes, examples and exercise. Upper and lower bounds  (2 hours) Calculate upper and lower bounds to problems involving the addition, subtraction and multiplication of amounts. Errors  Slide presentation showing errors in measurements and how errors accumulate in calculations involving measurements.  Accompanying notes and worksheets. Recording and illustrating accounts (9 hours) Record financial transactions, using columns to record credits, debits and running totals.  Include use of negative numbers to represent debts, debits, negative credit etc. and methods of checking (eg using balance carried forward + total credits + total debits = new balance) Use a line graph to illustrate results.  Use fractions, percentages, ratios, bar charts and pie charts to make comparisons. Keeping an account   Notes, example and exercise. Interpreting diagrams  (2 hours) Interpret statistical diagrams that give financial information and line graphs that show how a quantity varies with time. Include using graphs to make sense of rates of change (such as recognising when inflation is greatest from a graph of price against time). Examine such statistical diagrams with a questioning and critical approach. Suggest ways in which some graphs or charts may be misleading and suggest improvements. Revision (7 hours) Revise topics and try past papers. Discuss data sheet – make up and try questions based on it.

Page last updated on 11 October 2012