COMHAIRLE NÁISIÚNTA NA
NATIONAL COUNCIL FOR
Level 1 C10139
Clarification of Module Descriptor
Guidelines for Delivery and Assessment
Sample Assessment Material
Interpreting Section 11 and 12
SECTION 1: INTRODUCTION
SECTION 2: APPROACHES TO GENERATING EVIDENCE
SECTION 3: CONTENT/CONTEXT
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
SECTION 4: EXEMPLARS
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
SECTION 5: ASSESSMENT PROCEDURES
5.1 Interpreting Section 11 and 12
5.2 Written Examination
SECTION 6: MODULE DESCRIPTOR – ERRATA SHEET
SECTION 7: POTENTIAL RESOURCE MATERIAL
SECTION 1: INTRODUCTION
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.
SECTION 2 APPROACHES TO GENERATING EVIDENCE
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.
1 Cockroft, W H (1982) Mathematics Counts, HMSO, London
SECTION 3 CONTENT/CONTEXT
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
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.
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).
SECTION 4: EXEMPLARS
4.1 Examples of practical situations from which material can be drawn:
? 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.
Identify some of the variables in each of the following situations and identify the dependant and
??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
??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
? 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.
? 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.
4.2 Exemplar Problems
Example 1 THE FOLLOWING IS THE WEEKLY TIMESHEET OF JOHN MURPHY FOR A PARTICULAR
Monday Tuesday Wednesday Thursday Friday Saturday
9.am- 5.30pm 9.am- 6pm 9.am- 7.30pm 9.am- 6pm 8.am- 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.
GROSS PAY ANALYSIS Deductions
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
Example 2: THIS IS SAM MCCARTHY’S TIME CARD FOR WEEK NO. 6
EMPLOYEE DAY IN OUT TOTAL ASIC VERTIME OMMENTS BOCWEEK NO. HOURS HOURS HOURS
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
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
ECTION 4.2 II