Download CIC scheme

First Year Maths
Year Plan 2015/2016
Ter
Textbook:
Morris O.D., Cooke P., Behan P. Project Maths Text & Tests 1. The Celtic
Press, Common introductory course for first year maths.
Time Frame
September
Topic
Sets
Natural Numbers
Integers
Duration
1 week
1 week
2 weeks
October
Fractions
Decimals
Percentages
Ratio & Proportion
Algebra
Equations
Statistics – collecting data
Presenting Data
Geometry – Points, angles, lines
Geometry – Co-ordinates
Geometric constructions
Probability
Revision/Exam prep
2 weeks
2 weeks
2 week
2 weeks
3 weeks
3 weeks
2 weeks
3 weeks
1 week
1 Week
1 Week
2 Weeks
1 Week
November
December
January
February
April
May
Scheme of Work for 1st year 2015/16
Textbook:
Morris O.D., Cooke P., Behan P. Project Maths Text & Tests 1. The Celtic
Press, Common introductory course for first year maths.
SEPTEMBER
Topic 1
Sets {Strand 3: Number}
Chapter 5 (1week)
Students learn the concept of a set as being a collection of well-defined objects or elements.
They are introduced to the concept of the universal set, null set, sub-set; the union and
intersection operators and to Venn diagrams: simple closed bounded curves that contain the
elements of a set. They investigate the properties of arithmetic as related to sets and solve
problems involving sets.
Students should be able to:
 list elements of a set
 describe the rule that defines a set
 consolidate the idea that equality is a relationship in which two equal sets have the
same elements
 use the cardinal number terminology when referring to set membership
 perform the operations of intersection, union (for two sets)
 investigate the commutative property for intersection and union
 illustrate sets using Venn diagrams
Topic 2
Natural Numbers {Strand 3: Number}
Chapter 1 (1week)
Students should be able to:
 identify elements of N
 understand notation such as
N
 identify what a prime number is
 find the prime factors of a number
 express a number as a product of its prime factors
 find the highest common factor
 find the lowest common multiple
Order of Operations Students should be able to:
 understand and apply the operations of addition, subtraction, multiplication and
division in N where the answer is in N
 understand the meaning of an
 investigate the commutative, associative and distributive properties of number
operations and the relationship between operations

perform operations in their order, including brackets
Topic 3
Integers {Strand 3: Number}
Chapter 2 (2 Weeks)
Students should be able to:
 identify elements of Z
 understand the notation Z
 explain the difference between Z and N
 investigate models such as the number line to illustrate the operations of addition,
subtraction, multiplication and division in Z
 relate the use of integers to real life situations
OCTOBER & NOVEMBER
Topic 4
Number systems {Strand 3: Number}
Chapter 3, Fractions (2 weeks)
Chapter 4, Decimals (2 weeks)
Chapter 7, Percentages (2 weeks)
Chapter 11, Ratio & Proportion (2 weeks)
Students should be able to:
 identify elements of Q
 understand the notation Q
 investigate models to help think about the operations of
addition, subtraction, multiplication and division of rational numbers
 use the equivalence of fractions in solving problems
 consolidate the idea that equality is a relationship in which two mathematical
expressions have the same value
 analyse solution strategies to problems
 begin to look at the idea of mathematical proof
 calculate percentages
 use the equivalence of fractions, decimals and percentages to compare proportions
 consolidate their understanding of factors, multiples, prime numbers in N
 consolidate their understanding of the relationship between ratio and proportion
 check a result by considering whether it is of the right order of magnitude and by
working the problem backwards
 make and justify estimates and approximations of calculations
JANUARY (Commencing 9th)
Topic 5
Algebra {Strand 4}: 4.1 Generating arithmetic expressions from repeating patterns
Chapter 6, Algebra (3 weeks)
Chapter 14, Equations (3 Weeks)
Students examine patterns and the rules that govern them and so construct an understanding
of a relationship as that which involves a set of inputs, a set of outputs and a correspondence
from each input to each output.
Students should be able to:
 use tables to represent a repeating-pattern situation
 generalise and explain patterns and relationships in words and numbers
 write arithmetic expressions for particular terms in a sequence
 use simple graphs as a tool for analysing relations
 develop and use their own mathematical strategies and ideas and consider those of
others
 present and interpret solutions, explaining and justifying methods, inferences and
reasoning.
FEBRUARY (Commencing on the 20th ) & MARCH
Topic 6
Statistics {Strand 1}
Chapter 12, Collecting Data, (2 Weeks)
Chapter 16, Presenting Data (3 Weeks)
Students should be able to:
 engage in discussions about the purpose of statistics and recognise
Misconceptions and misuses of statistics
 work with different types of data (categorical/numerical/nominal/ordinal,
discrete/continuous) in order to clarify the problem at hand
 evaluate reliability of data and data sources
 Identify primary and secondary data
 discuss methods of gathering data
 Identify Populations and Samples
 Identify good questions/problems with questions on a questionnaire
 understand the effects of bias on data
 Tally data
 Complete a frequency distribution table


use bar charts and line plots to display data
Analyse data presented graphically
APRIL (Commencing 16th)
Topic 7
Geometry {Strand 2}: 2.1 Synthetic Geometry (see Appendix 1)
Chapter 10, Geometry 1: Points – Angles –Lines (1 week)
The geometrical results should be first encountered through discovery and investigation
Students should be able to:
 convince themselves through investigation that theorems 1-6 are true
 Complete the following constructions:
 the bisector of a given angle, using only compass and straight edge
 the perpendicular bisector of a segment, using only compass and straight edge
 a line perpendicular to a given line l, passing through a given point on l
 a line parallel to a given line l, through a given point
 divide a line segment into 2, 3 equal segments, without measuring it
 a line segment of given length on a given ray
Topic 8
Geometry {Strand 2} : 2.3 Co-ordinate geometry
Chapter 13, Coordinates (1 Week)
Students should be able to:
 coordinate the plane
 locate points on the plane using coordinates
MAY
Topic 9
Geometry {Strand 2}: 2.2 Transformation geometry
Chapter 18, transformations Geometry – Constructions (1 Week)
Students should be able to:
 use drawings to show central symmetry and axial symmetry
Topic 10
Probability {Strand 1}: 1.6 Concepts of probability
Chapter 8, Probability (2 Weeks)
It is expected that experiments (including simulations), both individually and in groups, will
form the primary vehicle through which the knowledge, understanding and skills in
probability are developed.
Students should be able to
 decide whether an everyday event is likely or unlikely to happen
 appreciate that probability is a quantity that gives a measure on a scale of 0 - 1 of how
likely an event is to occur
 connect with set theory; discuss experiments, outcomes, sample spaces
 use the fundamental principle of counting.
REVISION (1 Week)
Teaching and Learning Methods:










‘Chalk and Talk’
Whole class instruction and questioning
Co-operative learning
Pair work
Individual work
Written and oral work
Worksheets/Revision sheets
Data Projector
Discovery Learning
Use of computer software when possible
Interdisciplinary Links:








Geography: Surveying
Computers
English: relevance to use of statistics in Media
Business: Use of Statistics and Arithmetic
Economics: Statistical analysis
Accounting: Use of percentages and ratios
Design Communications Graphics: Constructions
Science: Use of percentages, balancing equations, statistical analysis
Resources:











Whiteboard and markers
Data Projector
Worksheets
Calculator
Active Maths
Concise Maths
Mathematical Tables
Computer Software- Geogebra
Internet
Graph paper
Construction Instruments


Standard Mathematical resources: Dice etc
Project Maths teaching and learning plans
Homework Policy:




Homework is to be assigned very night
Homework is to be written on board and transcribed to Students Journal.
Graded questions to consolidate learning
More difficult questions to be given to allow students to assimilate knowledge.
Pupil Assessment
a.
Link to Aims and Objectives





On Completion students should be able to:
Recall knowledge of syllabus content
Demonstrate ability to apply this knowledge to given situations
Demonstrate an understanding of terminology and vocabulary central to the syllabus
Make evaluative judgements









Teacher observation
Teacher questioning
Written observation
Pupil questioning
Peer to peer questioning
Activities
Homework
Diagnostic Tests
Testing (Formal Written Exam)
b.
List of Procedures Used
c.
Times for assessment





d.
Throughout the class for informal assessment
Written Assignments
Homework
Exam style Questions
Tests (Administered by higher diploma students and class teacher)
Criteria for judging progress/achievement


Checking that students have achieved aims and objectives as set out in scheme of
work
Performance of students in Tutorial if required to attend
Evaluation:
Student Appraisal



Examinations
Interim and end of year meetings with teachers involved in teaching the year.
Informal discussions with students
Self Appraisal
Post-Lesson


Lessons will be evaluated informally after classes
Student will be asked informally how they are coping with material do they
understand methods being used to explain material
Post-Topic
 Student homework and exams checked to see if learning has taken place
 Analysis of diagnostics tests
Mathematics department regularly review progress throughout the year
AI
6th year Ordinary Level Plan 2015-2016
Topic
Duration
Start
Finish
The Circle
3 weeks
31/08/15
18/09/15
Functions
1 Week
21/09/15
25/09/15
Graphing Functions
2 Weeks
28/09/15
9/10/15
Differentiation
2 Weeks
12/10/15
23/10/15
Statistics
4 Weeks
2/11/15
27/11/15
Revision
1 Week
30/11/15
4/12/15
Probability
3 Weeks
7/12/15
15/01/16
Junior Cert Geometry 1 Week
18/01/16
22/01/16
Geometry
2 Weeks
25/01/16
5/02/16
Complex Numbers
2 Weeks
8/02/16
19/02/16
Trigonometry
1 Week
29/02/16
4/03/12
Revision/Exam Prep
Mocks
Scheme of Work for 6th Year Ordinary Level 2015/2016
Textbook: Morris O.D., Text & Tests 3 Leaving Certificate Ordinary Level. The Celtic
Press.
September
Topic 1
Co Ordinate Geometry of the Circle
(3 weeks)
Students will learn how to represent and interpret circles given specific information. They
will also learn about the relationship between the circle and the line and the mathematical
importance of this relationship. They will be able to use the formulae provided in the log
tables to investigate a variety of different outcomes and conclusions.
Students should be able to:

Identify the centre and the radius of a given circle

Express the equation of a circle in the form ( x  h) 2  ( y  k ) 2  r 2

Use the Mid-Point, Distance and Slope formulae to find Points of Contact, Centres,
Diameters, Radii and Tangents

Investigate if a point is In, On or Outside a circle

Determine the Points of Intersection of a circle and a line

calculate the area of a triangle

recognise the fact that the relationships y= mx+c, y-y1 = m (x- x1) and ax + by + c =
0 are linear

solve problems involving slopes of lines

recognise that ( x  h) 2  ( y  k ) 2  r 2 represents the relationship between the x and y
coordinates of points on a circle centre (h, k) and radius r

solve problems involving a line and a circle with centre (0, 0)
Topic 2
Functions
(1 Week)
Students will learn about the relationship between numbers that are acted upon by the same
rule.
Students should be able to:

Use and understand terminology and notation used to identify and describe a function

Find missing Coefficients in a given function
October
Topic 3
Graphing Functions
(2 Weeks)
Students will learn how to represent a function in the form of a graph and use this visual
depiction to help ascertain a variety of outcomes.
Students should be able to:

Graph a linear, a quadratic and a cubic function

Use the graph to find a variety of information. E.g. values of x at a set point, max and
min points, points of intersection, positive and negative graphs

Read the period and range from a given graph of a periodic function
Topic 4
Differentiation
(3 weeks)
Students will learn that in a given function there exist a relationship between the x and the y
value. This change will help pupils to gain a greater understanding of what the function
means and what it represents.
Students should be able to:

Differentiate from first principles polynomials of degree < = 2.

Find First derivatives of polynomials and rational functions

Apply rules for differentiating sums, products, differences and quotients.

Use easy applications of the chain rule.

Apply their knowledge to problems of Rates of change, e.g. speed, acceleration
tangents.

Should be able to calculate the maximum and minimum points of quadratic and cubic
functions.
November/December
Topic 5
Statistics- Collecting and Representing data
(4 weeks)
Students will learn about the different types of data as well as the many way that we have to
represent this data. They will also learn how to analysis these graphs and draw conclusions
from them.
Students should be able to:

Work with different types of bivariate data

Discuss different types of studies e.g. sample surveys, observational studies and
designed experiments

Design a plan and collect data on the basis of above knowledge
Represent data both graphically and numerically
Using Graphical representation

Describe the sample (both univariate and bivariate data) by selecting appropriate
graphical or numerical methods

Explore the distribution of data, including concepts of symmetry and skewness

Compare data sets using back to back stem and leaf plots

Determine the relationship between variables using scatter plots

Recognise that correlation is a value from -1 to +1 and that it measures the extent of
linear relationship between two variables

Match correlation coefficient values to appropriate scatter plots
Using Numerical Representation

Recognise standard deviation as a measure of variability

Use a calculator to calculate standard deviation

Use a stem and leaf plot to calculate quartiles and the interquartile range

Interpret a histogram in terms of distribution of data

Make decisions based on the empirical rule

Explore patterns and formulate conjectures

Explain findings

Justify conclusions

Communicate mathematics verbally and in written form

Apply their knowledge and skills to solve problems in familiar and unfamiliar
contexts

Analyse information presented verbally and translate it into mathematical form

Devise, select and use appropriate mathematical models, formulae or techniques to
process information and to draw relevant conclusions.
Revision (4 classes)
During this week students will learn about the way specific questions are structured and the
way in which questions may be asked. Particular attention will be paid to the topic covered at
the beginning of 6th year.
December/January
Topic 6
Probability
(3 Weeks)
Student will further extend their knowledge of Junior Cert. Probability and learn to use this
knowledge in problem solving situations.
Students should be able to:

List outcomes of an experiment

Apply the fundamental principle of counting

Count the arrangements of n distinct objects (n!)

Count the number of ways of arranging r objects from n distinct objects

Discuss basic rules of probability (AND/ OR, mutually exclusive) through the use of
Venn Diagrams

Calculate expected value and understand that this does not need to be one of the
outcomes

Recognise the role of expected value in decision making and explore the issue of fair
games

Find the probability those two independent events both occur

Apply an understanding of Bernoulli trials*

Solve problems involving up to 3 Bernoulli trials

Calculate the probability that the 1st success occurs on the nth Bernoulli trial where n
is specified
Revision of Junior Cert Geometry
(1 week)
Students should be able to:

Understand the basic concepts of geometry.

Use the following terms related to logic and deductive reasoning: axiom, theorem,
proof, corollary, and converse and implies.

Investigate theorems 1-12 and corollary 1 and use them to solve problems.

Understand congruent triangle conditions and use them to solve problems.
January/February
Topic 7
Geometry
(2weeks)
Students should be able to:

perform constructions 16,17 18, 19, 20, 21 (as set out in Geometry Course for Post
Primary School Mathematics) use the following terms related to logic and deductive
reasoning: theorem, proof, axiom, corollary, converse, implies

Investigate theorems 7, 8, 11, 12, 13, 16, 17, 18, 20, 21 and corollary 6 (as set out in
Geometry Course for Post Primary School Mathematics) and use them to solve
problems.
March
Topic 8
Complex Numbers
(2 weeks)
Students will pay particular attention to exam paper questions and the style and wording of
these questions.
Students should be able to:

Construct an Argand diagram

Calculate the modulus of a complex number

Find and use the complex conjugate.

Perform basic functions such as addition, subtraction, multiplication and division of
complex numbers
Topic 9
Revision of Trigonometry
(1Week)
Student should be able to:

Solve problems that involve finding heights and distances from right-angled triangles
(2D only)

Use of the theorem of Pythagoras to solve problems (2D only)

solve problems that involve calculating the cosine, sine and tangent of angles between
0˚ and 90˚

use trigonometry to calculate the area of a triangle

use the sine and cosine rules to solve problems (2D)

define sin θ and cos θ for all values of θ

define tan θ

calculate the area of a sector of a circle and the length of an arc and solve problems
involving these calculations
April/May
Revision and Exam Preparation
Teaching and Learning Methods:

‘Chalk and Talk’

Whole class instruction and questioning

Use of real life example where possible – statistics, probability, trigonometry, etc.

Co-operative learning

Pair work

Individual work

Written and oral work

Worksheets/Revision sheets

Data Projector

Discovery Learning

Use of computer software when possible e.g. Geogebra in co-ordinate geometry
Interdisciplinary Links:

Geography: Surveying

Computers

English: relevance to use of statistics in Media

Business: Use of Statistics and Arithmetic

Economics: Statistical analysis

Accounting: Use of percentages and ratios

Design Communications Graphics: Constructions

Science: Use of percentages, balancing equations, statistical analysis
Resources:

Exam papers

Whiteboard and markers

Data Projector

Worksheets

Calculator

Texts and Tests 3

New Concise Maths

Mathematical Tables

Revision Books

Computer Software- Geogebra

Internet

Graph paper

Construction Instruments

Standard Mathematical resources: Dice, cards, etc.
Homework Policy:

Homework is to be assigned every night

Homework is to be written on board and transcribed to Students Journal.

Graded questions to consolidate learning

More difficult questions to be given to allow students to assimilate knowledge.
Pupil Assessment
a.
Link to Aims and Objectives

On Completion students should be able to:

Recall knowledge of syllabus content

Demonstrate ability to apply this knowledge to given situations

Demonstrate an understanding of terminology and vocabulary central to the syllabus

Make evaluative judgements
b.
List of Procedures Used

Teacher observation

Teacher questioning

Written observation

Pupil questioning

Peer to peer questioning

Activities

Homework

Testing (Formal Written Exam)
c.
d.
Times for assessment

Throughout the class for informal assessment

Written Assignments

Homework

Exam style Questions

Tests
Criteria for judging progress/achievement

Checking that students have achieved aims and objectives as set out in scheme of
work

Performance of students in Tutorial if required to attend
Evaluation:
Student Appraisal

Examinations

Interim and end of year meetings with teachers involved in teaching the year.

Informal discussions with students
Self-Appraisal
Post-Lesson

Lessons will be evaluated informally after classes

Student will be asked informally how they are coping with material do they
understand methods being used to explain material
Post-Topic

Student homework and exams checked to see if learning has taken place
Mathematics department regularly review progress throughout the year