Mathematics Learning Journey
Junior Cycle Mathematics encourages students to develop the following five interconnected and interwoven components:
- conceptual understanding—comprehension of mathematical concepts, operations, and relations
- procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
- strategic competence—ability to formulate, represent, and solve mathematical problems in both familiar and unfamiliar contexts
- adaptive reasoning—capacity for logical thought, reflection, explanation, justification and communication
- productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence, perseverance and one’s own efficacy.
This strand permeates all of the contextual strands and is composed of the six elements of the specification : Building Blocks, Representation, Connections, Problem Solving, Generalisation and Proof, and Communication.
There is no specific content linked to this strand; rather, its learning outcomes underpin the rest of the specification. Each learning outcome in this strand is applicable to all of the activities and content of the other four strands—for example, students should be able to draw on all of their mathematical knowledge and skills to solve a problem or to communicate mathematics.
Furthermore, the elements of this strand are interdependent, so that students should develop the different skills associated with each element in tandem rather than in isolation – for example, engaging in problem-solving can help students improve their understanding of building blocks and their ability to make connections within mathematics.
This strand focuses on different aspects of number, laying the groundwork for the transition from arithmetic to algebra. Learners explore different representations of numbers and the connections between them, as well as the properties and relationships of binary operations. They investigate number patterns, and use ratio and proportionality to solve a variety of problems in numerous contexts. Learners are expected to be able to use calculators appropriately and accurately, as well as to carry out calculations by hand and mentally. They appreciate when it is appropriate to use estimation and approximation, including to check the reasonableness of results.
Geometry and Trigonometry Strand
This strand focuses on analysing characteristics and properties of two- and three-dimensional geometric shapes. Learners use geometry and trigonometry to model and solve problems involving area, length, volume, and angle measure. They develop mathematical arguments about geometric relationships and explore the concept of formal proof, using deduction to establish the validity of certain geometric conjectures and critiquing the arguments of others.
Algebra and Functions Strand
This strand focuses on representing and analysing patterns and relationships found in numbers. Building on their work in the Number strand, learners generalise their observations, expressing,
interpreting, and justifying general mathematical statements in words and in symbolic notation. They use the idea of equality to form and interpret equations, and the syntactic rules of algebra to transform expressions and solve equations. Learners explore and analyse the relationships between tables, diagrams, graphs, words, and algebraic expressions as representations of functions.
Statistics and Probability Strand
This strand focuses on determining probability from random events and generating and investigating data. Students explore the relationship between experimental and theoretical probability as well as completing a data investigation; from formulating a question and designing the investigation through to interpreting their results in context and communicating their findings. Learners use graphical and numerical tools, including summary statistics and the concepts and processes of probability, to explore and analyse patterns in data.
Assessment for the Junior Cycle Profile of Achievement
The assessment of mathematics for the purposes of the Junior Cycle Profile of Achievement (JCPA) will comprise two Classroom-Based Assessments: CBA 1; and CBA 2. In addition, the second Classroom-Based Assessment will have a written Assessment Task that will be marked, along with a final examination, by the State Examinations Commission.
Classroom Based Assessment 1
End of Second Year
Students will, over a three-week period, follow the Problem-solving cycle to investigate a mathematical problem.
Define a problem; decompose it into manageable parts and/or simplify it using appropriate assumptions; translate the problem to mathematics if necessary; engage with the problem and solve it if possible; interpret any findings in the context of the original
Classroom Based Assessment 2
End of First Term of Second Year
Students will, over a three-week period; follow the Statistical enquiry cycle.
Statistical enquiry cycle:
Formulate a question; plan and collect
unbiased, representative data; organise and manage the data; explore and analyse the data using appropriate displays and numerical
summaries and answer the original question giving reasons based on the analysis section.
The Assessment Task is a written task completed by students during class time, which is not marked by the class teacher, but is sent to the State Examinations Commission for marking. It will be allocated 10% of the marks used to determine the grade awarded by the SEC. The Assessment Task is specified by the NCCA and is related to the learning outcomes on which the second Classroom-Based Assessment is based. The content and format of the Assessment Task may vary from year to year.
There will be two examination papers, one at Ordinary and one at Higher level, set and marked by the State Examinations Commission (SEC). The examination will be two hours in duration and will take place in June of third year. The number of questions on the examination papers may vary from year to year. In any year, the learning outcomes to be assessed will constitute a sample of the relevant outcomes from the tables of learning outcomes.
Learning maths is fun
Pizza is divided into 8 portions. Where has 1/8th gone??
What is the most popular colour?
Why did the m&m go to school? To beome a smartie!!!
Maths Week in Dominican College
Maths Week in Dominican College aims to raise awareness, appreciation and understanding of mathematics for all. Maths is needed in today's world and those people with poor proficiency in Maths will be disadvantaged in life. In addition we need to encourage more young people to work harder at Maths in school to progress on to areas such as Maths itself,
engineering, science, accountancy etc. All too common we hear people say "I can't do Maths" and this leads to an idea that you have to be hardwired for Maths. Of course, not everyone will become a top mathematician but everyone can do better than they do and many could learn to enjoy Maths if we can break this "cycle of fear". The events of Maths Week are designed to present Maths as interesting, challenging and yet rewarding - and yes, even fun! Link : www.mathsweek.ie
Why study Mathematics?
Mathematics is about developing an understanding of numbers and measuring. It helps to prepare for many practical aspects of day-to-day living. It enables the learner to think logically and solve problems, which are skills for life. Engineering, computing, architecture, business and, in fact, every possible career choice will involve one or more aspects of Mathematics. Without Maths, we would not have the technology to surf the Internet, build a bridge, weigh ourselves, design or manufacture a car, fly an aeroplane, use a mobile phone…
What is the best way to study Mathematics?
A common problem faced by students of Mathematics is that when presented with a Maths problem, it can be hard to establish a correct starting point. When prompted in class by a teacher or fellow student, they know how to complete the task but without that assistance at home can feel very lost. It is essential to take useful notes and tips from class, which can easily be understood later. This will prove invaluable when studying at home.
How should Maths be studied at home?
Revise the material learned in class that day. This should include:
1. Mathematical concepts.
2. new Mathematical terms/vocabulary.
3. working through examples shown in class.
Use examples from the textbook and class to help you but make every effort to understand them instead of just trying to make your exercises look like the examples.
Answer the homework questions by showing the methodology used as well as the answers. When a question is completed, always ensure that the answer makes sense. Eg. Make sure that a table that you should calculate to be 2m in length is not found to be 2cm or 20m!
The best way to study Mathematics is to actually work out questions for yourself.
Useful Websites for Mathematics
A very comprehensive gateway site (a site that categorises and links to lots of other sites). It contains sections on:
General Topics, Geometry, Fractals, History of Mathematics and Mathematical Software
Some fun numeracy games here can be played online. A good way to practise against the clock!
This is part of one of the most famous sites for mathematics education: the Maths Forum at Swarthmore. There are many categorised links to other pages.
This is a search engine and yields Yahoo's categorisation of many mathematical sites.
This site is loaded with problems and games for both teachers and students. It is definitely worth a look!
This site contains multiple levels of games for any age group. All are colourful and easy to follow.