Numbers and Their Operations — Real Numbers

About this lesson

This unit introduces the concept of real numbers, focusing on the distinction between rational and irrational numbers. It explains that irrational numbers cannot be expressed as a fraction of two integers and includes examples such as square roots of non-perfect squares, cube roots of non-perfect cubes, π, and the golden ratio. Students learn to estimate the approximate value of irrational numbers and locate them on a number line by identifying consecutive integers between which they lie. The unit also covers the set of real numbers as the union of rational and irrational sets, and includes exercises on classifying numbers, comparing and ordering real numbers, and solving equations involving squares and cubes within different number sets (Q, Q', R). Real-world contexts include the golden rectangle and its appearance in nature and art, such as the Mona Lisa and seashells.