Ireland

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Skills available for Ireland third-year maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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Y1-3.1 Statistics and Probability

Y1-3.1.1 Counting

Y1-3.1.1.1 Listing outcomes of experiments in a systematic way.

Y1-3.1.2 Concepts of probability

Y1-3.1.2.1 The probability of an event occurring: student progress from informal to formal descriptions of probability.

Y1-3.1.2.2 Predicting and determining probabilities.

Y1-3.1.2.3 Difference between experimental and theoretical probability.

Y1-3.1.3 Outcomes of simple random processes

Y1-3.1.3.1 Finding the probability of equally likely outcomes.

Y1-3.1.4 Statistical reasoning with an aim to becoming a statistically aware consumer

Y1-3.1.4.1 The use of statistics to gather information from a selection of the population with the intention of making generalisations about the whole population. They consider situations where statistics are misused and learn to evaluate the reliability and quality of data and data sources.

Y1-3.1.5 Finding, collecting and organising data

Y1-3.1.5.1 Formulating a statistics question based on data that vary allows for distinction between different types of data.

Y1-3.1.6 Representing data graphically and numerically

Y1-3.1.6.1 Methods of representing data. Students develop a sense that data can convey information and that organising data in different ways can help clarify what the data have to tell us. They see a data set as a whole and so are able to use fractions, quartiles and median to describe the data.

Y1-3.1.6.2 Mean of a grouped frequency distribution.

Y1-3.1.7 Analysing, interpreting and drawing conclusions from data

Y1-3.1.7.1 Drawing conclusions from data; limitations of conclusions.

Y1-3.1.8 Synthesis and problem-solving skills

Y1-3.1.8.1 explore patterns and formulate conjectures

Y1-3.1.8.2 explain findings

Y1-3.1.8.3 justify conclusions

Y1-3.1.8.4 communicate mathematics verbally and in written form

Y1-3.1.8.5 apply their knowledge and skills to solve problems in familiar and unfamiliar contexts

Y1-3.1.8.6 analyse information presented verbally and translate it into mathematical form

Y1-3.1.8.7 devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.

Y1-3.2 Geometry and Trigonometry

Y1-3.2.1 Synthetic Geometry

Y1-3.2.1.A Axioms

Y1-3.2.1.B Theorems

Y1-3.2.1.C Corollaries

Y1-3.2.1.D Constructions

Y1-3.2.2 Transformation Geometry

Y1-3.2.2.1 Translations, central symmetry and axial symmetry.

Y1-3.2.3 Co-ordinate Geometry

Y1-3.2.3.1 Co-ordinating the plane.

Y1-3.2.3.2 Properties of lines and line segments including midpoint, slope, distance and the equation of a line in the form: y - y1 = m(x - x1) y = mx + c; ax + by + c = 0 where a, b, c, are integers and m is the slope of the line

Y1-3.2.3.3 Intersection of lines.

Y1-3.2.3.4 Parallel and perpendicular lines and the relationships between the slopes.

Y1-3.2.4 Trigonometry

Y1-3.2.4.1 Right-angled triangles: theorem of Pythagoras.

Y1-3.2.4.2 Trigonometric ratios

Y1-3.2.4.3 Trigonometric ratios in surd form for angles of 30°, 45° and 60° Right-angled triangles

Y1-3.2.4.4 Decimal and DMS values of angles.

Y1-3.2.5 Synthesis and problem-solving skills

Y1-3.2.5.1 explore patterns and formulate conjectures

Y1-3.2.5.2 explain findings

Y1-3.2.5.3 justify conclusions

Y1-3.2.5.4 communicate mathematics verbally and in written form

Y1-3.2.5.5 apply their knowledge and skills to solve problems in familiar and unfamiliar contexts

Y1-3.2.5.6 analyse information presented verbally and translate it into mathematical form

Y1-3.2.5.7 devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.

Y1-3.3 Number

Y1-3.3.1 Number Systems; N: the set of natural numbers, N = {1,2,3,4...}; Z: the set of integers, including 0; Q: the set of rational numbers; R: the set of real numbers; R/Q: the set of irrational numbers

Y1-3.3.1.2 Students articulate the generalisation that underlies their strategy, firstly in the vernacular and then in symbolic language.

Y1-3.3.1.3 Problems set in context, using diagrams to solve the problems so they can appreciate how the mathematical concepts are related to real life. Algorithms used to solve problems involving fractional amounts.

Y1-3.3.2 Indices

Y1-3.3.2.1 Binary operations of addition, subtraction, multiplication and division in the context of numbers in index form.

Y1-3.3.3 Applied arithmetic

Y1-3.3.3.1 Solving problems involving, e.g., mobile phone tariffs, currency transactions, shopping, VAT and meter readings.

Y1-3.3.3.2 Making value for money calculations and judgments.

Y1-3.3.3.3 Using ratio and proportionality.

Y1-3.3.4 Applied measure

Y1-3.3.4.1 Measure and time.

Y1-3.3.4.2 2D shapes and 3D solids, including nets of solids (two-dimensional representations of three-dimensional objects).

Y1-3.3.4.3 Using nets to analyse figures and to distinguish between surface area and volume.

Y1-3.3.4.4 Problems involving surface area and volume.

Y1-3.3.4.5 Modelling real-world situations and solve a variety of problems (including multi-step problems) involving surface areas, and volumes of prisms and cylinders.

Y1-3.3.4.6 Students learn about the circle and develop an understanding of the relationship between its circumference, diameter and pi.

Y1-3.3.5 Sets

Y1-3.3.6 Synthesis and problem-solving skills

Y1-3.3.6.1 explore patterns and formulate conjectures

Y1-3.3.6.2 explain findings

Y1-3.3.6.3 justify conclusions

Y1-3.3.6.4 communicate mathematics verbally and in written form

Y1-3.3.6.5 apply their knowledge and skills to solve problems in familiar and unfamiliar contexts

Y1-3.3.6.6 analyse information presented verbally and translate it into mathematical form

Y1-3.2.3.2 Properties of lines and line segments including midpoint, slope, distance and the equation of a line in the form: y - y₁ = m(x - x₁) y = mx + c; ax + by + c = 0 where a, b, c, are integers and m is the slope of the line