Ireland · NCCA Curriculum Specifications
1st Class Foundations of Mathematical Thinking
This course develops first class students' fluency with numbers up to 100 while fostering spatial reasoning and data literacy. Students engage in hands-on exploration to build a deep conceptual understanding of how mathematics describes the world around them.
01Counting and Numbers to 100
Students explore the structure of the base ten system and develop strategies for counting and comparing numbers up to 100.
Examine different historical number systems and compare their efficiency to the base-10 system.
Investigate how the position of a digit determines its value in multi-digit numbers.
Explore various ways to represent rational numbers, including fractions, decimals, and percentages, and their interconversions.
Develop strategies for estimating quantities and checking the reasonableness of estimates.
Use comparison symbols and strategies to order integers, fractions, decimals, and numbers in scientific notation from least to greatest and vice versa.
Learn to round numbers to a specified number of decimal places and significant figures, understanding its practical applications and impact on precision.
Identify and extend arithmetic and geometric sequences, and express the general term (nth term) for simple linear patterns.
Explore the concept of negative numbers in real-world contexts like temperature and debt.
02Addition of Numbers to 20
Moving beyond rote memorization to understand the relationship between addition and subtraction.
Explore addition of positive and negative integers, fractions, and decimals, using various models and strategies.
Investigate subtraction of positive and negative integers, fractions, and decimals, using various methods and understanding 'subtracting a negative'.
Understand the inverse relationship between operations to solve linear algebraic equations involving one variable.
Develop a repertoire of mental strategies for addition and subtraction of larger numbers, decimals, and simple fractions.
Practice mental multiplication and division using strategies like doubling and halving, factorisation, and estimation for larger numbers and decimals.
Understand multiplication of integers, fractions, and decimals, including the rules for signs and multiplying by powers of ten.
Explore division of integers, fractions, and decimals, including understanding remainders, dividing by powers of ten, and the concept of reciprocals.
Apply addition and subtraction skills to solve multi-step word problems.
Use symbols to represent unknown quantities in simple equations and number sentences.
03Exploring 2D Shapes
Investigating the properties of 2D and 3D shapes and how they fit together in space.
Identify, describe, and classify polygons and quadrilaterals based on their specific properties (sides, angles, diagonals, parallel/perpendicular lines).
Explore lines of symmetry (axial symmetry) and rotational symmetry in various 2D shapes and identify symmetrical objects in the environment.
Examine the characteristics of three-dimensional objects and calculate their surface area, focusing on cubes, cuboids, and cylinders.
Investigate how 2D nets fold to form 3D shapes and design nets for simple solids.
Use the Cartesian coordinate system to plot points, identify coordinates, and perform basic transformations (translation, reflection, rotation).
Measure angles using a protractor, classify angles (acute, obtuse, right, reflex, straight), and understand angles on a straight line and around a point.
Investigate shapes that can tessellate (tile a surface without gaps) and create tessellating patterns.
04Measuring with Non-Standard Units
Using non-standard and standard units to quantify length, weight, capacity, and time.
Understand the concepts of precision and accuracy in measurement, and the impact of estimation and rounding on results.
Convert between different standard units of length (mm, cm, m, km), area (cm², m², km²), and volume (cm³, m³).
Explore concepts of mass and density, using standard units (grams, kilograms) and performing calculations involving mass, volume, and density.
Investigate the volume of various 3D solids, including cubes, cuboids, and cylinders, using appropriate formulas and units (litres, millilitres, cm³, m³).
Read and convert between 12-hour and 24-hour time, and solve problems involving time zones and international time differences.
Measure and compare the duration of various activities, including calculations involving different units (seconds, minutes, hours, days) and across dates.
Explore concepts of personal finance, including creating a budget, understanding income and expenditure, and the importance of saving.
Apply percentages to solve real-world problems involving discounts, sales tax, simple interest, and financial calculations.
05Sorting and Collecting Data
Collecting information and representing it visually to answer questions and make predictions.
Gather and organize data into frequency tables, including grouped data, and understand the importance of appropriate intervals.
Create and interpret bar charts and line plots to represent discrete and continuous data, understanding appropriate scales and labels.
Construct and interpret pie charts to represent proportional data, calculating angles and percentages for each sector.
Calculate and interpret the mean, median, mode, and range for a given set of data, understanding their strengths and weaknesses.
Calculate the theoretical probability of simple events as fractions, decimals, and percentages, understanding sample spaces and mutually exclusive events.
Perform simple experiments, record outcomes, and calculate experimental probability (relative frequency), comparing it to theoretical probability.
Explore the concept of fairness in games of chance based on calculated probabilities and introduce the idea of expected value.