Week 3 Understanding and using numbers MATHS Week 3 Understanding and using numbers

To warm up……. Can you answer all 10 questions on this weeks number?

What are we going to do today? Recap from last week Understand and use very large numbers Use and calculate with the 4 operations - +, -, x and ÷ Identify Prime numbers Factors Multiples Powers and roots – squares, cubes, square roots, cube roots Highest common factor Lowest common multiple from lists of numbers Follow BIDMAS – the order of operations

For today…

What did we do last week?

Why are they misleading? Misleading graphs Why are they misleading?

True or False: Sales are rising rapidly! 4370 4360 4350 4340 Sales 4330 4320 The graph is misleading because it suggests that sales have increased significantly over a five year period. In reality they have only increased by 70 units, which is not much given that they are selling thousands. 4310 4300 2000 2001 2002 2003 2004 2005 Year

This may help to explain the previous slide

Although the vertical scale starts at 0, it does not go up in even steps. This distorts the graph, and makes it look as though the biggest jump is between 1 and 2, rather than 3 and 4. Also, there are no labels on the axes, so we have no idea what this graph represents!

On this pictogram, there is no category for people who do not own a pet. The pictures are different sizes, and it appears that more people own a horse than any other animal. An improvement would be to redraw the pictogram, with each of the animals the same size and aligned with one another.

True or False: There are more 15 year old boys than girls. 18 year olds 18 year olds 15 year olds 15 year olds 17 year olds 17 year olds 16 year olds False. We cannot make this conclusion from these graphs because we don’t know the totals. There might be 10 boys in total, making roughly 5 aged 15, but 100 girls, 30 of which are 15. It only tells us the proportion of 15 year olds. 16 year olds

Summary of points Scale doesn’t start at zero Scale made very small to make graph look very big Scale values or labels missing from the graph Information missing from a pie chart Incorrect scale placed on the graph Size of images used in pictograms are different for the different categories

Here are some annual salaries Here are some annual salaries. Write them out in order from largest to smallest. Can you say the figures in words? (talk about place value) £25,740,030 £51,931,640 £40,100,000 £51,750,000 £34,621,093 £9,600,000 £149,440 £143,789 £25,216,800 £27,847,401 £0 £43,500,000

The order should look like this: £51,931,640 £51,750,000 £43,500,00 £40,100,000 £34,621,093 £27,847,401 £25,740,030 £25,216,800 £9,600,000 £149,440 £143,789 £0

Who am I? Write down the name of the celebrity next to the amount of money you think they earn in a year. Good luck! (Source: www.wageindicator.co.uk)

Who am I? How much money do I earn per year? Usain Bolt

Who am I? How much money do I earn per year? Theresa May

Who am I? How much money do I earn per year? Boris Johnson

Who am I? How much money do I earn per year? Lewis Hamilton

Who am I? How much money do I earn per year? Adele

Who am I? How much money do I earn per year? Jeremy Clarkson

Who am I? How much money do I earn per year? Daniel Radcliffe

Who am I? How much money do I earn per year? Pope Francis

Who am I? How much money do I earn per year? Queen Elizabeth II

Who am I? How much money do I earn per year? Jose Mourinho

Who am I? How much money do I earn per year? Ed Sheeran

Who am I? How much money do I earn per year? Simon Cowell

The wealthiest is…. correct them as you go

The wealthiest is…. £51,931,640

Next wealthiest is…. £51,750,000

Next wealthiest is…. £43,500,000

Next wealthiest is…. £40,100,000

Next wealthiest is…. £34,621,093

Next wealthiest is.… £27,847,401

Next wealthiest is…. £25,740,030

Next wealthiest is…. £25,216,800

Next wealthiest is…. £9,600,000

Next wealthiest is…. £149,440

Next wealthiest is…. £143,789

And the least wealthy is…. £0

The order should look like this: Adele £51,931,640 Daniel Radcliffe £51,750,000 Simon Cowell £43,500,00 The Queen £40,100,000 Lewis Hamilton £34,621,093 Ed Sheeran £27,847,401 Usain Bolt £25,740,030 Jose Mourinho £25,216,800 Jeremy Clarkson £9,600,000 Theresa May £149,440 Boris Johnson £143,789 The Pope £0

Inequality symbols An inequality shows that two values are not equal. A < B says that A is less than B A > B says that A is greater than B

Use your amounts of money and your T/F card True or False? Use your amounts of money and your T/F card

Usain Bolt’s salary > The Queen’s salary True or False? Usain Bolt’s salary > The Queen’s salary

Lewis Hamilton’s salary > Jeremy Clarkson’s salary True or False? Lewis Hamilton’s salary > Jeremy Clarkson’s salary

Theresa May’s salary > The Pope’s salary True or False? Theresa May’s salary > The Pope’s salary

Simon Cowell’s salary > Adele’s salary True or False? Simon Cowell’s salary > Adele’s salary

True or False? 574 > 121

True or False? 1249 < 578

Number of days in a week > Number of sides of a nonagon True or False? Number of days in a week > Number of sides of a nonagon

Number of days in February < Number of days in October True or False? Number of days in February < Number of days in October

Number of degrees in a circle < Number of months in a year True or False? Number of degrees in a circle < Number of months in a year

True or False? Number of planets in the solar system > Number of blind mice in the nursery rhyme

Number of Olympic rings > Number of days of Christmas True or False? Number of Olympic rings > Number of days of Christmas

Addition & Subtraction Do you all have a method for adding and subtraction WITHOUT a calculator?

Addition 97 + 96 157 + 368 875 + 326

Subtraction 76 – 23 102 – 78 1016 - 358

Multiplication Which method do you use?

3 x 7 12 x 7

45 x 7

468 x 8

39 x 47

156 x 17

41.9 x 8 41.9 x 0.8 41.9 x 0.08

2.5 x 4.5 Extension: 0.58 x 126

Division

375 ÷ 2

2793 ÷ 4

591623 ÷ 8

746 ÷ 3

Word of the day - integer What is an integer? An integer is a positive or negative whole number, including zero.

+, -, x, ÷ positive and negative integers

Multiplication 4 x 5 -4 x 5 -4 x -5

Divide 20 ÷ 5 20 ÷ -5 -20 ÷ -5

Addition 4 + -6 -4 + 6 -4 + -6

Subtraction 10 - -2 -10 – 2 -10 - -2

Negative Number BINGO

Put one number in each box Put one number in each box. Pick any numbers from the list but no repeats. 15 -10 3 -21 -13 17 -9 11 18 -12 -15 -2 -4 22 6 25 7 20 -5 24 16 14 8 -3

8 -12

10 - -12

- 2 + 8

20 - -5

- 1 +8

-2 x -10

-2 -3

20 - -4

- 4 x -4

15 + -1

9 – 1

7 -10

16 + -1

-40 ÷ 4

-9 ÷ -3

7 x -3

-26 ÷ 2

-17 x -1

3 x -3

12 + -1

15 - -3

6 x -2

- 20 + 5

10 - 12

What is the answer to this question? 2 + 3 x 4

3 + 7 x 6 – 5

Bidmas activity:

Factors, Multiples and Primes

What is a …….. Factor Multiple Prime

Prime Numbers A prime number has exactly two factors – one and itself One is not a prime number because it has only one factor – itself Two is the first prime number Two is the only even prime number

Give an example of as many of these as possible Give an example of as many of these as possible. Then put it away - we will revisit this before the end of the lesson. A factor of 24 A multiple of 5 A prime number A power of 2 A square number A cube number The square root of 100 The cube root of 27

http://www.visnos.com/demos/sieve-of-eratosthenes

On your number grid, cross out the 5 times table, apart from the number 5.

Cross out the 6 times table, apart from the number 6.

What are we left with? What about the number 1? Cross out the 2 times table, apart from the number 2. Cross out the 3 times table, apart from the number 3. What are we left with? What about the number 1?

What is a …….. Factor Multiple Prime

Question For each of these pairs of numbers, there is just one prime number that lies between them. In each case, write that prime number. a) 8 12 b) 14 18 c) 25 30 20 28 e) 32 40 f) 44 52 g) 54 60 h) 38 42

Factors multiples puzzle

Answers

From these numbers: 1 3 8 12 16 20 13 15 2 17 24 6 Write down 1 3 8 12 16 20 13 15 2 17 24 6 Write down 4 prime numbers all the factors of 6 any multiples of 4

Square numbers √ Square Square root Square Square root Area = 3 x 3 = 3² 3 9 =9 Square root √ Area = 4 x 4 Square = 4² 4 16 Square root = 16

cube numbers cube cube Cube root Cube root Volume = 3 x 3 x 3 Volume = = 3³ = 4³ cube = 27 cube = 64 4 64 3 27 Cube root Cube root

Can you answer these questions? What is the square of 5? What is the square root of 36? Is there another one? What is the cube of 2? What is the cube root of 125? What are the powers of 10?

From these numbers: 121 49 20 19 800 1000 5 Find two square numbers 121 49 20 19 800 1000 5 Find two square numbers a cube number the square root of 400 the cube root of 125

90 Prime factors Then with powers Over to you – prime factors of 84?

84

Finally - Factors, Multiples and Primes 8 quick questions Write down your answers

1 Which of the following numbers divides into 49, without remainder? Divisors a: 3 b: 4 c: 7 d: 9

2 Including one and itself, how many factors has the number 6? Factors a: 2 b: 3 c: 4 d: 6

3 Which of the following is a multiple of 6? Multiples a: 1 b: 3 c: 9 d: 12

4 Common Factors a: 2 b: 4 c: 8 d: 36 Which of the following is a common factor of 12 and 18? Common Factors a: 2 b: 4 c: 8 d: 36

5 Prime Numbers a: 2 b: 15 c: 17 d: 29 Which of the following is not a prime number? Prime Numbers a: 2 b: 15 c: 17 d: 29

6 Prime Numbers a: 51 b: 53 c: 55 d: 57 What is the next prime number after 47? Prime Numbers a: 51 b: 53 c: 55 d: 57

7 Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5 Which of the following shows the prime factors of 30? Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5

8 Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5 Which of the following shows the prime factors of 40 (with powers)? Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5 d: 4 x 10

Answers

1 Which of the following numbers divides into 49, without remainder? Divisors a: 3 b: 4 c: 7 d: 9

2 Including one and itself, how many factors has the number 6? Factors a: 2 b: 3 c: 4 d: 6

3 Which of the following is a multiple of 6? Multiples a: 1 b: 3 c: 9 d: 12

4 Common Factors a: 2 b: 4 c: 8 d: 36 Which of the following is a common factor of 12 and 18? Common Factors a: 2 b: 4 c: 8 d: 36

5 Prime Numbers a: 2 b: 15 c: 17 d: 29 Which of the following is not a prime number? Prime Numbers a: 2 b: 15 c: 17 d: 29

6 Prime Numbers a: 51 b: 53 c: 55 d: 57 What is the next prime number after 47? Prime Numbers a: 51 b: 53 c: 55 d: 57

7 Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5 Which of the following shows the prime factors of 30? Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5

8 Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5 Which of the following shows the prime factors of 40 (with powers)? Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5 d: 4 x 10

Add them up! 7 or 8? Brilliant 5 or 6? Jolly good show 3 or 4? Some good, but revision needed 1 or 2? Oh dear, have you been paying attention? 0 Whoops!

Plenary - revisit this: can you answer all these now? A factor of 24 A multiple of 5 A prime number A power of 2 A square number A cube number The square root of 100 The cube root of 27

Website of the week Help is at hand https://www.bbc.co.uk/education/examspecs/z8sg6fr

Homework AQA Number Homework sheet