Ireland · NCCA Curriculum Specifications
Junior Infants Foundations of Mathematical Thinking
This course introduces Junior Infants to the fundamental concepts of number, shape, and logic through hands-on exploration. Students develop early numeracy skills and spatial awareness by engaging with concrete materials and collaborative problem solving activities.
01Number Systems and Operations
This unit delves into the structure of number systems, focusing on integers, rational numbers, and fundamental operations. Students will develop fluency in arithmetic and problem-solving strategies.
Students will represent and order integers on a number line, understanding their relative values and real-world applications.
Students will perform addition and subtraction of integers, using various models and understanding the concept of absolute value.
Students will explore the rules for multiplying and dividing integers, applying them to solve contextual problems.
Students will understand equivalent fractions, simplify fractions to their lowest terms, and compare their values.
Students will add and subtract fractions with like and unlike denominators, including mixed numbers.
Students will multiply and divide fractions, including mixed numbers, and solve related word problems.
Students will understand decimal place value, convert between fractions and decimals, and order decimals.
Students will perform addition, subtraction, multiplication, and division with decimals, including real-world applications.
Students will convert between fractions, decimals, and percentages, and calculate percentages of quantities.
Students will understand ratios and proportions, solve problems involving direct proportion, and apply them to scale and rates.
Students will apply the order of operations to simplify numerical expressions involving various operations and grouping symbols.
Students will identify prime and composite numbers, understand prime factorization, and find the greatest common factor (GCF) and least common multiple (LCM).
Students will understand exponents as repeated multiplication, evaluate expressions with exponents, and apply basic exponent rules.
Students will identify perfect squares and their square roots, and estimate non-perfect square roots.
Students will learn basic budgeting concepts, including income, expenses, and saving, through practical examples.
02Algebraic Thinking and Expressions
This unit introduces students to fundamental algebraic concepts, including variables, expressions, and basic equations. They will learn to translate between verbal and algebraic representations and solve simple linear equations.
Students will define variables, identify terms, coefficients, and constants, and write algebraic expressions from verbal phrases.
Students will substitute numerical values into algebraic expressions and evaluate them using the order of operations.
Students will identify and apply the commutative, associative, and distributive properties to simplify algebraic expressions.
Students will identify like terms and combine them to simplify algebraic expressions.
Students will define equations and inequalities, understand the concept of a solution, and represent them verbally and symbolically.
Students will solve one-step linear equations involving addition and subtraction using inverse operations.
Students will solve one-step linear equations involving multiplication and division using inverse operations.
Students will solve two-step linear equations by applying inverse operations in the correct order.
Students will understand the coordinate plane, plot points, and begin to graph simple linear equations by plotting points.
Students will identify patterns in input-output tables, determine the rule, and express it as an algebraic equation.
Students will identify arithmetic sequences, find the common difference, and determine subsequent terms.
Students will identify monomials and binomials, understand their components, and perform basic addition and subtraction.
Students will translate word problems into algebraic equations and solve them using learned techniques.
Students will write, graph, and solve one-step linear inequalities, understanding the implications of inequality symbols.
Students will explore simple algebraic proofs and justify their steps in solving equations and simplifying expressions.
03Geometry and Measurement Fundamentals
This unit covers foundational concepts in geometry, including properties of 2D and 3D shapes, transformations, and measurement of perimeter, area, and volume.
Students will define and identify fundamental geometric terms such as points, lines, planes, segments, and rays.
Students will classify angles (acute, obtuse, right, straight, reflex) and measure them using a protractor.
Students will identify and calculate complementary and supplementary angles, and angles formed by intersecting lines.
Students will define and identify parallel and perpendicular lines, and angles formed by transversals.
Students will classify polygons based on the number of sides, identifying regular and irregular polygons.
Students will classify triangles by sides and angles, and understand that the sum of angles in a triangle is 180 degrees.
Students will identify and classify quadrilaterals (e.g., squares, rectangles, parallelograms, trapezoids) based on their properties.
Students will calculate the perimeter of various polygons, including composite shapes, and solve real-world problems.
Students will calculate the area of rectangles and triangles, understanding the formulas and their derivations.
Students will calculate the area of parallelograms and trapezoids, understanding the formulas and their derivations.
Students will understand pi, calculate the circumference and area of circles, and solve related problems.
Students will identify and describe properties of common 3D shapes, including prisms and pyramids.
Students will calculate the surface area of rectangular and triangular prisms using nets and formulas.
Students will calculate the volume of rectangular and triangular prisms, understanding the concept of cubic units.
Students will perform and describe translations, reflections, and rotations of 2D shapes on a coordinate plane.
04Data Analysis and Probability
This unit introduces students to collecting, organizing, representing, and interpreting data. It also covers fundamental concepts of probability and chance.
Students will learn various methods for collecting data (surveys, observations) and organize it using tally charts and frequency tables.
Students will construct and interpret bar graphs and pictograms, understanding their components and appropriate uses.
Students will construct and interpret line plots and stem-and-leaf plots for numerical data.
Students will calculate and interpret the mean, median, and mode of a data set, understanding their differences.
Students will calculate and interpret the range of a data set as a measure of data spread.
Students will interpret information presented in various data displays, drawing conclusions and making predictions.
Students will understand the concept of probability, describe the likelihood of events using terms like impossible, unlikely, equally likely, likely, and certain.
Students will calculate the probability of simple events as fractions, decimals, and percentages.
Students will conduct simple probability experiments, compare experimental results to theoretical probabilities, and understand the law of large numbers.
Students will identify the sample space for simple events and use tree diagrams to list all possible outcomes for compound events.
Students will calculate the probability of independent compound events.
Students will use probability to make predictions about future events and evaluate the reasonableness of those predictions.
Students will identify common ways statistics and graphs can be misleading and learn to critically evaluate data presentations.
Students will convert between different units of time (seconds, minutes, hours, days, weeks, months, years) and solve problems involving time.