Topic Four (1.4): Powers and Roots

Introduction Icon.png Introduction

First, we are going to look at square numbers. When you multiply a number by itself, for example, 3×3, you calculate a square number. Next you will study how to take a square number and calculate which number produced it. This is called ‘finding the square root’. For example, the square root of 16 is 4, because 4×4=16.

So, when you multiply an integer by itself, the result is called a square number. When you multiply that integer by itself again, the result is called a cube number. We can also work backwards to find the cubed root. This topic is about square and cube numbers and how they can be written with an index number.

Consolidate Icon.png Warm Up

First complete the skill checker on page 76.

Interact Icon.png Working through the coursebook

  • Start by watching these four short videos, which introduce the topic nicely:

                         What is a square number:                                                                                     What is a cubed number:

                           

                             What is a square root:                                                                                         What is a cubed root:

                           

  • Read and make notes on pages 76-77, copying out the worked examples, if you think it will help you. Now see if you can answer the Band 2, questions 6-10 on page 78. 
  • If you would like more practice, then work through these lessons on the MyMaths website: 

EXPLORE - Squares and cubes (MyMaths) Links to an external site. [Not available on sample course]

  • You may also want to watch the following Corbettmaths videos on square and cube numbers:  

                           

Optional Activities Icon.png Plenary

You have a choice: you can end this lesson by playing a maths game, or watching a video (or even both, if you have time!)

Game-time!

Try this loop card game on squares and cubes on slide 4: 

PLAY - Squares and cubes: Loop Card Game (MyMaths) (slide 4 only) Links to an external site. [Not available on sample course]

Video

This is a video about the legend of the inventor who asked to be given grains of rice for each square of a chess board, but on an exponential basis. It shows how powerful powers can actually be! 

WATCH - The Emperor's Chess Board (Twig) [Not available on sample course] 

Bridge Icon.png Support activities for this topic 

The Band 1, questions 1-5 on page 78 will help build your skills on this topic. 

Stretch Icon.png Extension activities for this topic 

If you would like more of a challenge on this topic, go to page 78 and attempt Band 3, question 11.