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Create Learning Experience · Mathematics

CONTENT STUDIO PREVIEW

1. Official curriculum anchor

GT.3 · Geometry and trigonometry · Geometrical proof

investigate the concept of proof through their engagement with geometry so that they can: perform specified constructions; recall and use specified concepts, axioms, theorems, corollaries and converses; use and explain the terms theorem, proof, axiom, corollary, converse and implies; create and evaluate proofs of geometrical propositions; and display understanding of the specified proofs and corollaries

Ordinary and Higher; official source specifies additional Higher-level constructions, theorems and corollaries · Junior Cycle Mathematics current specification

2. Original iLEARN experience

  1. Learning intention: work directly toward GT.3.
  2. Entry: short original explanation plus key vocabulary.
  3. Active task: use one of the recommended formats below.
  4. Check: learner explains, applies or demonstrates the outcome.
  5. Improve: feedback then retry/redraft.
  6. Evidence: save the improved response against MATH-JC-GT-03.

3. Recommended content formats

  • Investigation / experiment — question · hypothesis · method · variables/safety · evidence table · reflection
  • Interactive model — interactive brief · prediction · manipulation · observation · explain-back
  • Project brief — authentic brief · constraints · milestones · evidence checklist · reflection
  • Audio lesson — original script · transcript · pause-and-think prompts · vocabulary support

Originality rule: new wording, examples, questions, datasets, diagrams and sequences. Publisher material is not copied or stored.

4. Required learner variants

Easy English · Standard English · Exam/subject language

Easy / Standard / Exam English · Read aloud · Reduced motion · Chunked instructions · Voice or typed response · Vocabulary support · Non-visual / non-drag alternative when needed

5. Teacher control

The authenticated Content Studio backend now supports preview → save draft → teacher edit → approve. Nothing becomes learner-visible by default.

Choose another Mathematics outcome

AF.1 · Algebra and functions — investigate patterns and relationships (linear, quadratic, doubling and tripling) in number, spatial patterns and real-world phenomena involving change so that they can: represent patterns and relationships in tables and graphs; generate generalised expressions for patterns; and categorise patterns using their defining characteristicsGT.1 · Geometry and trigonometry — calculate, interpret, and apply units of measure and timeN.1 · Number — investigate the representation of numbers and arithmetic operations so that they can: represent addition, subtraction, multiplication and division in ℕ, ℤ and ℚ using models; perform these operations and understand commutative, associative and distributive properties; explore numbers in index form and apply index laws; calculate and interpret factors, multiples and prime numbers; present numerical answers to a specified degree of accuracy; and convert numbers to the form a × 10^n where applicableSP.1 · Statistics and probability — investigate the outcomes of experiments so that they can: generate a sample space for an experiment in a systematic way, including tree diagrams for successive events and two-way tables for independent events; and use the fundamental principle of counting to solve authentic problemsU.1 · Unifying strand — recall and demonstrate understanding of the fundamental concepts and procedures that underpin each strandAF.2 · Algebra and functions — investigate situations in which letters stand for quantities that are variable so that they can: generate and interpret expressions in which letters stand for numbers; find the value of expressions given the value of variables; and use the concept of equality to generate and interpret equationsGT.2 · Geometry and trigonometry — investigate 2D shapes and 3D solids so that they can: draw and interpret scaled diagrams; draw and interpret nets of specified solids; find perimeter and area of plane figures made from combinations of discs, triangles and rectangles; find volumes of specified solids and combinations; and find surface area and curved surface area as appropriateN.2 · Number — investigate equivalent representations of rational numbers so that they can: flexibly convert between fractions, decimals and percentages; use and understand ratio and proportion; and solve money-related problems including bills, VAT, profit or loss, percentage profit or loss, cost price, selling price, compound interest, income tax, net pay, value for money, mark-up and margin as specified in the official outcomeSP.2 · Statistics and probability — investigate random events so that they can: demonstrate understanding that probability measures likelihood on a scale from 0 to 1; use the equally-likely-outcomes principle to calculate probability; and use relative frequency as an estimate of probability from experimental data, recognising that repeated experiments generally improve estimatesU.2 · Unifying strand — apply the procedures associated with each strand accurately, effectively, and appropriatelyAF.3 · Algebra and functions — investigate situations in which letters stand for quantities that are variable so that they can add, subtract and simplify specified expressions; multiply specified algebraic expressions; divide specified quadratic and cubic expressions by linear expressions; and flexibly convert between factorised and expanded forms of the specified algebraic expressionsGT.3 · Geometry and trigonometry — investigate the concept of proof through their engagement with geometry so that they can: perform specified constructions; recall and use specified concepts, axioms, theorems, corollaries and converses; use and explain the terms theorem, proof, axiom, corollary, converse and implies; create and evaluate proofs of geometrical propositions; and display understanding of the specified proofs and corollariesN.3 · Number — investigate situations involving proportionality so that they can: use absolute and relative comparison where appropriate; and solve problems involving proportionality including currency conversion and average speed, distance and timeSP.3 · Statistics and probability — carry out a statistical investigation which includes the ability to: generate a statistical question; plan and implement a method to generate and/or source unbiased, representative data and present it in a frequency table; classify data; select, draw and interpret appropriate graphical displays of univariate data; select, calculate and interpret appropriate summary statistics; evaluate graphical displays; discuss misconceptions and misuses of statistics; and discuss assumptions and limitations of conclusions drawn from sample data or graphical/numerical summariesU.3 · Unifying strand — recognise that equality is a relationship in which two mathematical expressions have the same valueAF.4 · Algebra and functions — select and use suitable strategies (graphic, numeric, algebraic, trial and improvement, working backwards) for finding solutions to linear equations in one variable; quadratic equations in one variable; simultaneous linear equations in two variables; and specified linear inequalities, within the number sets and coefficient conditions stated in the official outcomeGT.4 · Geometry and trigonometry — evaluate and use trigonometric ratios (sin, cos, and tan, defined in terms of right-angled triangles) and their inverses, involving angles between 0° and 90° at integer values and in decimal formN.4 · Number — analyse numerical patterns in different ways, including making out tables and graphs, and continue such patternsU.4 · Unifying strand — represent a mathematical situation in a variety of different ways, including: numerically, algebraically, graphically, physically, in words; and to interpret, analyse, and compare such representationsAF.5 · Algebra and functions — generate quadratic equations given integer rootsGT.5 · Geometry and trigonometry — investigate properties of points, lines and line segments in the co-ordinate plane so that they can: find and interpret distance, midpoint, slope, point of intersection and slopes of parallel and perpendicular lines; draw graphs of line segments and interpret them in context; and find and interpret equations of lines in the specified formsN.5 · Number — explore the concept of a set so that they can: understand a set as a well-defined collection of elements and set equality; define sets by listing elements or generating rules; use suitable set notation and terminology; perform intersection, union, difference and complement operations; and investigate whether intersection, union and difference are commutative and/or associativeU.5 · Unifying strand — make connections within and between strandsAF.6 · Algebra and functions — apply the relationship between operations and an understanding of the order of operations including brackets and exponents to change the subject of a formulaGT.6 · Geometry and trigonometry — investigate transformations of simple objects so that they can: recognise and draw the image of points and objects under translation, central symmetry, axial symmetry and rotation; and draw the axes of symmetry in shapesU.6 · Unifying strand — make connections between mathematics and the real worldAF.7 · Algebra and functions — investigate functions so that they can: demonstrate understanding of the concept of a function; represent and interpret functions in different ways using the language and notation of functions; use graphical methods to find and interpret approximate solutions of equations and inequalities; and make connections between the shape of a graph and the story of a phenomenon, including maximum and minimum pointsU.7 · Unifying strand — make sense of a given problem, and if necessary mathematise a situationU.8 · Unifying strand — apply their knowledge and skills to solve a problem, including decomposing it into manageable parts and/or simplifying it using appropriate assumptionsU.9 · Unifying strand — interpret their solution to a problem in terms of the original questionU.10 · Unifying strand — evaluate different possible solutions to a problem, including evaluating the reasonableness of the solutions, and exploring possible improvements and/or limitations of the solutions (if any)U.11 · Unifying strand — generate general mathematical statements or conjectures based on specific instancesU.12 · Unifying strand — generate and evaluate mathematical arguments and proofsU.13 · Unifying strand — communicate mathematics effectively: justify their reasoning, interpret their results, explain their conclusions, and use the language and notation of mathematics to express mathematical ideas precisely

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