Draft Mathematics Module Descriptor

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Draft Mathematics Module Descriptor ...






    Level 1 C10139

    Support Notes

    February 2001

    Clarification of Module Descriptor

     Guidelines for Delivery and Assessment

     Sample Assessment Material

    Interpreting Section 11 and 12





    3.1 Unit 1 Arithmetic

    3.2 Unit 2 Finance

    3.3 Unit 3 Algebra

    3.4 Unit 4 Data Handling

    3.5 Unit 5 Co-ordinate Geometry

    3.6 Unit 6 Geometry


    4.1 Examples of practical situations from which material can be drawn

    4.2 Exemplar Problems

    4.3 Exemplar Assignments

    4.4 Exemplar Written Examination Questions


    5.1 Interpreting Section 11 and 12

    5.2 Written Examination

    5.3 Marking

    5.4 Grading




These support notes have been developed to help the tutor interpret the standards set out in the

    module. The content and recommendations are not mandatory, but aim to provide guidance

    about the intentions, scope and objectives of the standard laid down in the module descriptor.

The notes include suggestions about delivery approaches and recommendations for instruments

    of assessment including many examples of assignments.

Note: Additional exemplar material will be circulated to all centres for inclusion in this pack

    as it becomes available.


    ECTION 1.I


One of the primary goals of mathematics education is to inculcate a positive attitude to

    mathematics so that the pupil will be willing to apply his or her knowledge as needed.

    This module has been designed to encourage tutors and candidates to deliver mathematics in an

    active and innovative way. Tutors should encourage their learners to use mathematical skills in

    everyday contexts and provide candidates with an opportunity to create a base from which they

    can develop their mathematical knowledge and skill and provide motivation to attempt further


    Several approaches are possible depending on the availability of resources, expertise of the tutor

    and the type of candidate group. These may involve individualised learning, groupwork or class

    work and should include a combination of the following techniques:1

    ? Exposition (teacher talk)

    ? Problem solving and applications

    ? Practice and consolidation

    ? Practical work

    ? Investigational work

    ? Discussion (teacher/pupil and pupil/pupil)

The module descriptor lists discrete specific learning outcomes, but the approach to delivery

    adapted by a tutor may change the order or integrate the outcomes as appropriate.

At level 1 problems and assignments should be set in a variety of vocational contexts. The

    emphasis should not be on memorising formulas, but on using whatever aids are available, e.g.

    calculators, computers and tables, to solve real mathematical problems. Thus, learners can

    expect to be supplied with mathematical tables and a centre devised list of formulas for use

    during assignments and examinations.

    Using learned mathematics in real contexts or learning mathematics in real context is likely to

    involve several competencies at the same time. For that reason tutors should expect to assess

    SLOs in clusters rather than in isolation. This will mean that specific skills will be assessed on

    many occasions consolidating the learners’ achievements over time.


    ECTION 2.I

1 Cockroft, W H (1982) Mathematics Counts, HMSO, London


3.1 Corresponding to Unit 1: Arithmetic

    This unit outlines key arithmetic skills that underpin this level of mathematics. It is intended that

    these skills should be developed and assessed as an integral part of all the units of the module.

3.2 Corresponding to Unit 2: Finance

    This unit selects a number of sample areas that will provide the learner with opportunities to

    develop confidence in dealing with money on a personal level. While learning certain mathematical

    techniques such as percentage, compound interest, etc. learners have to be able to identify when

    these skills can be used to solve problems related to their personal finance.

3.3 Corresponding to Unit 3: Algebra

    In this unit, formulas and equations are derived from practical situations, and are written using

    mathematical symbols including letters. When symbols are used in this way to represent problem

    situations, they can be manipulated by applying the usual laws of arithmetic. By doing algebra in

    this way practical problems can be solved.

3.4 Corresponding to Unit 4: Data Handling

    This unit is designed to enable learners to acquire skills in collecting, organising, processing,

    presenting and interpreting presented data. It is intended that the learners will be introduced to

    the concepts of data handling by working with data that they themselves collect, as well as by

    interpreting data presented in graphical or tabular form in newspapers, brochures etc. These are

    particularly important skills in the context of the modern world where so much information is

    presented in tabular and graphical form. There are two assignments based on this unit. The first, Assignment 3, aims to help the learner

    to become familiar with handling given data and calculating mean, mode, and the range of the


    To successfully complete Assignment 4 the learner must complete a small project e.g. car

    occupancy, traffic flow or any topic of vocational/local interest to the learner.

3.5 Corresponding to Unit 5: Co-ordinate Geometry

    This unit is designed to introduce the concept of function, which is central to mathematics and

    applications of mathematics. Through the study of functions, learners will be able to represent a

    variety of real situations, plot graphs, compute values for and use functions to model and solve

    practical problems.

    In this unit the learner should be introduced to the concept of a function through a practical

    activity of gathering sets of ordered pairs. The dependent and independent variables should be


    identified. The learner would then plot a graph using appropriate scales (e.g. distance walked v

    time, volume filled v time). The co-ordinate plane is thus introduced through representing real-

    life situations. Learners then proceed to understand the significance of, and to be able to

    calculate the slope of, a straight line graph and to interpret functional relationships between two

variables when the relationship is represented by a table. Learners must also be able to graph the

    function and formulate the relationship in algebraic terms

3.6 Corresponding to Unit 5: Geometry

    This unit includes the study of angles, shapes and related concepts such as perimeter, area, volume

    and capacity. These concepts are embedded in many aspects of society and social interaction such

    as everyday living, work and communication. An ability to use systems of measurements in common

    use to make unit conversions is very important for modern living.

3.7 Integration

Tutors are encouraged to integrate assignments and delivery with other level 1 modules when

    possible e.g. Personal Effectiveness module (Level 1) and Communications (Level 1).




4.1 Examples of practical situations from which material can be drawn:

    Unit 2:

    ? In calculations in relation to payslips, learners can either:

    ? complete a blank payslip given information related to total earnings, tax rates, tax-free

    allowances and PRSI.

    ? explain how the various deductions were calculated in sample payslips.

    ? Complete a personal tax form correctly given the required information. ? Check bills and invoices for accuracy of VAT and totals, e.g., electricity bills, phone bills,

    invoices for goods.

    ? Use advertisements in newspapers and elsewhere to calculate discounts. ? Calculate savings for buying in bulk, e.g. are larger packets of cereal better value than smaller


    ? Calculate the percentage profit made on goods by a retailer (cost price v selling price).

    ? Compare the cost of goods bought for cash with the same goods bought under hire purchase,

    e.g. using information from advertisements.

    ? Convert from Irish punts into other currencies and convert from other currencies into Irish

    punts using today's currency exchange rates as found in the daily newspapers or the local bank.

    ? Compound interest could be calculated using the example of credit card repayments where

    interest is charged.

Unit 3:

    Identify some of the variables in each of the following situations and identify the dependant and

    independent variable:

    ??the amount of money a person spends on cigarettes

    ??the distance covered by a long distance runner

    ??the amount of money a driver spends on petrol in a week

    ??the amount of milk a cylindrical jug can hold

    ??the cost of an ESB bill

    ??the amount of foreign currency you can get for ?100

    SECTION 4.1.I

??the amount of oil used in heating a building in a month

    ??the time taken for an ice cube to melt

    ??the time taken to fill a bath with water

    ??the amount of interest a person gets on money invested

    ??the amount of tax a person pays

Unit 4:

    ? Interpret simple statistical tables and graphs for example newspaper surveys, opinion polls,

    and soccer result tables as presented in the media, identifying important features and trends

    and introducing statistical terms.

    ? The concept of ‘scale’ should be introduced in a number of contexts e.g. scale of maps, scale

    drawings of rooms, houses, scale models. The relationship between scale and direct

    proportion should be discussed. The significance of scale in presenting data, e.g., in trend

    graphs, should be explored.

    ? The learner should also explore possible sources of error in the collection, analysis,

    presentation and interpretation of data, e.g. skewed samples, generalising, not considering all

    the variables, exaggeration due to incomplete scales, drawing unwarranted conclusions etc.

Unit 6:

    ? Recognise simple Pythagorean triplets, e.g. 3,4,5 or 5,12,13 and know their use in ‘squaring’ football fields, building sites, door frames etc

    ? Measure bearings on maps using a protractor or compass.

    ? Calculate perimeters and areas of table surfaces, floors, gardens, fields, etc.

    ? Measure and calculate surface areas for such purposes as:-

    ? calculating the area of sheet steel needed to construct a tank or the cost of painting the tank ? calculating the number of tiles needed to cover a floor

    2? calculating the cost of painting a room given coverage of paint in m per litre

    ? Calculate the capacities of tanks for such purposes as finding the cost of a tank full of oil. ? Compare dimensions of cylinders which have the same capacity, or where one has twice the capacity of another.

    ? Use conversion tables to change distances from kilometres into miles or from pounds into kilograms.

    ? Identify symmetry in nature and manufactured goods, e.g. leaves, buildings, plastic containers etc.

    SECTION 4.1.II

4.2 Exemplar Problems




    Monday Tuesday Wednesday Thursday Friday Saturday 5.30pm 6pm 7.30pm 6pm 4.30pm 10am- 12.30pm

    Q1. Calculate John’s gross pay using the following data:

    a) Lunch is from 12.30 p.m. and 1 p.m. and is not paid.

    b) The normal working week is 39 hours

    c) Weekday overtime ( Mon.- Fri.) is paid at time and a half

    d) Saturday mornings are paid at double time

    e) The rate of pay per hour is ? 4.

Q2. Calculate John’s net pay using the following data:

    a) His Tax Free Allowance is ?3900 per year.

    b) Tax is paid at a rate of 24%.

    c) PRSI is paid at a rate of 3% gross income.

Q3. Use the figures that you have generated to complete the following payslip.


     BASIC PAY _________ PAYE _________ O/T PAY _________

    HOURLY RATE _________ PRSI _________ HRS @ HR _________ HRS @ 1.25 _________

    HRS @ 1.5 _________

    HRS @ 2.0 _________

    Total Gross Pay __________ TOTAL DEDUCTIONS _________

     Net Pay _________

    SECTION 4.2 I



    MONDAY 08.00 17.01 980 6 9 8 1 T08.01 16.00 UESDAY

    07.59 16.30 WEDNESDAY

    07.57 16.00 THURSDAY

    08.00 15.00 FRIDAY

    08.00 13.00SATURDAY


    SHIFT TIME = 08.00 16.00

    BASIC HOURS = 8 hours per day Monday Thursday inclusive

    OVERTIME HOURS = Hours worked outside of basic hours

    Complete the Following

    I. Calculate Sam’s total hours.

    II. How many of Sam’s total hours were: basic hours? III. How many of Sam’s total hours were: overtime hours? IV. Sam is paid ?4.50p per basic hour. His overtime hourly rate is time and a half.

    V. Calculate Sam’s gross pay for week 6.

    VI. Sam has an annual tax free allowance of ?2800and he pays tax at 26% of his taxable


    a) How much tax will Sam pay in Week 6?

    b) What is Sam’s net pay per year (excluding overtime)? Example 3. A grocer buys a box of 48 apples for ?5.76. Four of the apples are bad and have to be thrown out. He sells the rest at 18p each. How much profit does he make?

    Example 4. A telephone bill, including VAT at 15% came to ?57.50. Calculate the bill without VAT. (encourage learners to look at a range of bills).

    Example 5. In a sale, an item is marked down to ?104.40 from ?120. What is the percentage discount?

    Example 6. A company uses 2500 litres of petrol each month at a cost of 60p per litre, less

    a discount of 3% for buying a large quantity. How much does the company pay for petrol in

    a month?


    ECTION 4.2 II

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