Year 8 Unit 1 4 and 1 5

Year 8 Unit 1. 4 and 1. 5 Power, Roots, BIDMAS

Lesson 1 1. 4 Review Squares and Cubes

Starter in back of books – Choose a column

Count the dots…. what kind of numbers are these?

Square. Numbers numbers Square numbers are called square numbers because you can make a square out of that number of smaller squares. I can make a large square out of 9 small squares like this:

But I can’t make a larger square out of 10 small squares, however hard I try!

Square Numbers 1 4 9 16 Square numbers are found by multiplying a number by itself (15² = 15 x 15 = 225) The first twelve square numbers are…

Date: 3. 12. 20 Title: Squares, Cubes, BIDMAS

Square numbers Copy and complete all of this in books 1² = 1 x 1 = 2²= 2 x 2 = 3²= 3 x 3 = 4²= 4 x 4 = 5²= 5 x 5 = 6²= 6 x 6 = 7²= 7 x 7 = 8²= 8 x 8 = 9²= 9 x 9 = 10²= 10 x 10 = 11²= 11 x 11 = 12²= 12 x 12 = Key Point: Square numbers are found by multiplying a number by itself

Check your answers 11²= 11 x 11 = 121 12²= 12 x 12 = 144

Square roots Copy and complete in books • The square root is a number that has been multiplied by itself to reach the target Ex: √ 100 √ 9 = 10 =3 as 10 x 10 = 100 as 3 x 3 = 9 You should be able to find the √ button on a calculator.

Square root Keywords Square √ 3 9 Square Root INVERSE

Keywords You try a few: √ 25 √ 9 √ 16 Questions and Answers in books:

Keywords You try a few: √ 25 √ 9 =5 =3 √ 16 =4 1 36 4 8 Mark in BLUE PEN: 16 144 25 10, 000

Introducing Cube Numbers They come, not surprisingly, from CUBES! (really they do). We shall now find the first 5 cube numbers. How many little cubes are there in each?

Introducing Cube Numbers And these are your cube numbers… They are the result of multiplying a whole number by itself and then by itself again. 1000 is the tenth cube number. We write

Introducing Cube Roots A cube root is the opposite of a cube. The little three makes it a cube root not a square root.

Cubes and Cube roots Copy in books

Cubes and Cube roots Copy in books Squared and Cubed Numbers: https: //www. youtube. com/watch? v=w 6 h 2 k. F Dly. CU&safe=true https: //www. youtube. com/watch? v=kq. Qk. UMKIhv. M &safe=true

You try a few:

Mark in BLUE PEN:

Lesson 2 1. 4 Review BIDMAS

Order of Operations Copy into books B I DM Then Indices (aka powers – squares/cubes/etc. ) AS Do adding and subtracting together at the end, going left to right Brackets first Do dividing and multiplying together, going left to right

Try these questions Questions AND Answers in books 2² + 1² 6² + 4² 3² + 2² 3² - √ 16 10² + 2² 10² + √ 9 2² - 1² √ 25 - 2² Always do the powers (or indices) BEFORE you do the 4 operations (add, subtract, multiply, divide)

Mark in BLUE PEN 6² + 4² 36 + 16 = 52 Always do the powers (or indices) BEFORE you do the 4 operations 10² + √ 9 100 + 4 = 103 (add, subtract, multiply, divide) 3² - √ 16 9 – 4 = 5 √ 25 - 2² 25 – 4 = 21

Try these questions Questions AND Answers in books

Mark in BLUE PEN 9 + 1 = 10 2 x 9 = 18 3 x 4 = 12 2 x 16 = 32 1 + 2 x 25 1 + 50 = 51

Lesson 3 Continue 1. 4 Review Powers and Roots Calculator work

Multiplying Negative Numbers Negative x Negative = Positive -6 x -3 = 18 It also works for square numbers…… -6 x -6 = 36 -9 x -9 = 81 Remember!!!!

The calculator x² Squares a number √ Square roots a number x³ Cubes a number (times by itself 3 times) Calculates a number to any power Use your calculator to work out 7 5 = 7⁵

Ext: Sheet (following slide)