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concepts and methodology in mathematics education - Nelson ...

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Irrational NumbersIrrational numbers are decimals that do not term<strong>in</strong>ate or recur. is probably the most famous of irrationalnumbers <strong>and</strong> is the ratio between the circumference <strong>and</strong> the diameter of a circle. Irrational numbers werecalled ‘<strong>in</strong>commensurable’, as they could not be found exactly nor could they be plotted on a number l<strong>in</strong>e.However Pythagoras’s theorem showed clearly that irrational numbers do have a specific size that can bedrawn accurately.Another way of show<strong>in</strong>g learners visually how different numbers fit together is to use concentric circles.Representation 3: Visual representation of types of numbers us<strong>in</strong>g concentric circlesReal Numbers:Rational <strong>and</strong> irrational numbersRational numbers:Integers <strong>and</strong> fractions3/5Integers:Whole numbers <strong>and</strong>negative numbers7/8120.345...½-3Wholenumbers:Naturalnumbers<strong>and</strong> zeroNaturalnumbers1, 2, 3, ...-120.6660-7-350.54-2/38Imag<strong>in</strong>arynumbers44

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