Irrational Numbers & Roots

Irrational Numbers & Roots

Irrational Numbers and Roots explain to students how some numbers cannot be written as fractions and discuss the concept of roots. Through practice with these numbers, students develop the skills needed for higher mathematics like algebra, geometry and calculus. Math becomes useful for measuring things and performing calculations in science.

Square Roots

Students are taught to determine square roots of perfect squares and estimate the roots of other numbers. They examine how you can solve problems about squaring by using square roots and how square roots relate to area and geometric concepts. Being able to work with square roots allows you to solve equations and learn how numbers are related. Learning is more interactive when students use visual aids and practical examples.

Decimals

They look at irrational numbers that do not end or recur in decimal form, for example √2. They work with rational and irrational decimals to strengthen their grasp of numbers. When we use decimal approximations instead of exact values, we get sharper at guessing answers and making accurate calculations.

Pi (π)

The ratio of a circle’s circumference to its diameter is represented by the constant and irrational number π which students study. They are taught how π appears when working with circles and spheres and how to use rough decimal approximations to handle various calculations. Learning about π helps students understand how it is applied in engineering, physics and design.

Activity Idea

Pi Necklace - Use beads to make a necklace using the digits of pi (e.g., 3 red, 1 blue, 4 green…).

Entertainment Activities

1. Perfect Square Hunt - Find square numbers in household items (e.g., tile patterns).

2. Decimal Dice - Use dice to generate decimals and find their square roots.

3. Pi Measuring Circle - Wrap string around circles and divide by diameter to discover π.