Types of Number – Squares, Cubes and their Roots Mathematics Types of Number – Squares, Cubes and their Roots

Aims of the Lesson To learn about square numbers, square roots and their link to the shape. To learn about cube numbers, cube roots and their link to the shape. To learn about triangle numbers.

Square Numbers – linked to shape Imagine a square tile. Its side lengths are always equal. Now imagine you have lots of these square tiles and you use them to make bigger squares… The number of tiles you need is a ‘square’ number!

Square Numbers – linked to shape The 1st square number = 1 (tile) The 2nd square number = 4 (tiles) The 3rd square number = 9 (tiles) and so on…

Square Numbers – linked to area The ‘area’ of the square is the ‘square’ number. Area is found by multiplying the length by the width and as these are equal, you are multiplying the same number by itself. So…

Square Numbers – linked to area 1st square number = 1 × 1 = 1 2nd square number = 2 × 2 = 4 3rd square number = 3 × 3 = 9 and so on…

Square Numbers – linked to odd no.s You can also find square numbers by adding consecutive odd numbers together… 1st square number = 1 2nd square number = 1 + 3 = 4 3rd square number = 1 + 3 + 5 = 9 and so on…

Task Find the 5th square number by… 1) Drawing a square grid 5 by 5 - count the number of squares in the grid. 2) Calculating the area of a 5 by 5 square 3) Adding the first 5 odd numbers together

Answers 1) Here is a 5 by 5 grid. It contains 25 tiles. 2) Area = length × width so… Area = 5 × 5 = 25 3) Add the 1st 5 consecutive odd numbers… 1 + 3 + 5 + 7 + 9 = 25

Squaring & Rooting Squaring means multiplying a value by itself. Its symbol is: 2 E.g. 122 means 12 × 12 = 144 The opposite of squaring is square-rooting. It’s symbol is: √ or 2√ You have to find the original number that multiplied itself to get the value being rooted.

Tasks What does 72 mean? What is the value of 72? What is the square root of 81? Calculate √64.

Answers 2) What is the value of 72? 7 × 7 = 49 1) What does 72 mean? It means 7 × 7 4) Calculate √64. 64 is made from 8 x 8, so √64 = 8 3) What is the square root of 81? In other words, what number when it is multiplied by itself makes 81? OR If the area of a square is 81, what is the length of its side? 81 is made from 9 x 9, so √81 = 9

What next? Work through the MyMaths lesson (and then its online homework) called: Number > Powers and Roots > Squares and Triangles Make a note of how triangle numbers are formed. Now move on to ‘cubes’ on the next slide…

Cube Numbers – linked to 3D shape Imagine a multilink cube. All of its dimensions are always equal. Now imagine you have lots of these multilink cubes and you use them to make bigger cubes… The number of cubes you need is a ‘cube’ number!

Cube Numbers – linked to 3D shape The 1st cube number = 1 (cube) The 2nd cube number = 8 (cubes) The 3rd cube number = 27 (cubes) and so on…

Cube Numbers – linked to volume The ‘volume’ of the cube is the ‘cube’ number. Volume is found by multiplying the length by the width by the height and as these are equal, you are multiplying the same number by itself three times (but NOT by the number three!!!). So…

Cube Numbers – linked to volume 1st cube number = 1 × 1 × 1 = 1 2nd cube number = 2 × 2 × 2 = 8 3rd cube number = 3 × 3 × 3 = 27 and so on…

Cubing & Cube-Rooting Cubing means multiplying a value by itself three times. Its symbol is: 3 E.g. 123 means 12 × 12 × 12 = 1728 The opposite of cubing is cube-rooting. It’s symbol is: 3√ You have to find the original number that kept multiplying itself to get the value being rooted.

Tasks What does 53 mean? What is the value of 63? What is the cube root of 512? Calculate 3√729.

Answers 1) 5³ means 5 × 5 × 5 2) 6³ = 6 × 6 × 6 = 216 3) 512 is made from 8 x 8 x 8 so the cube root of 512 = 8 4) 729 is made from 9 x 9 x 9 so 3√729 = 9 Remember that if you are given the volume of a cube and asked for its side length, you need to find the cube root of the volume! (You do NOT divide by 3!)

What next? Work through the MyMaths lesson (and then its online homework) called: Number > Powers and Roots > Squares and Cubes Work through the MyMaths game called: Number > Powers and Roots > Squares and Cubes Pairs 1 Save and complete worksheet: SqCuRt-S1.xlsx