GCSE Maths - Higher Lesson 5

GCSE Maths - Higher Lesson 5
Ratio and proportion – and finishing off fractions, decimals and percentages from last week

Factors multiples puzzle

Answers

Moodle vs

Homework last week Mr Corbett’s real life negative number questions
3 fraction questions Equivalences The next 2 slides – negative numbers Bidmas matching Look at mathsgenie website

The number in the centre equals = -5 + -3
The number that goes in the top right box is 5 less than -5 The number in the bottom left is -3 x -3 The number in the top left is the number in the centre x -1 add -13 The number in the middle of the bottom row is 6 less than the number above it There is a number 6 in one of the middle row boxes There is a number equal to -4 x -5 next to the box containing -5 When you add up the numbers in the right hand column you get -27 The number below -5 is -6-10

Copy & Complete; subtract the right hand square from the left to get the square below...
5 3 -1 6 4 2 4 -9 -33

A fraction problem to solve together
Anna, Bobby and Cheryl order a large 24 piece pizza. Anna eats 1/6 of the pizza. Bobby has 5 pieces and Cheryl eats a quarter. What fraction of the pizza is left? 3/8 is the answer

Another fraction problem – “The builder’s day”
A builder works for of a day. If he sleeps 7 ½ hours per day what fraction of the day does he have left ? 13/48

Yet another – “The TV Programme”
A TV programme lasting an hour has ⅖ of it dedicated to adverts. The rest of the programme is split equally between current affairs and sport. How long is spent on Sport ? 18 minutes

Please can you complete the equivalencies table showing the fraction, decimal and percentage for each amount.

What did we do last week? Squares, cubes and roots – this week we’re going to estimate them Fractions x ÷ this week we’re going to use whole numbers – and put fractions in order using the common denominator Percentages – this week we’re going to look at reverse percentages and compound interest

For higher, you may need to estimate the values of powers and roots.

Estimate the square root of 43
Between which two integers does the square root of 150 lie? Between which two integers does the cube root of 100 lie? Estimate the value of Estimate the value of Estimate the value of 2x = 40

+, -, x and ÷ top heavy fractions and mixed numbers

Finally - ordering fractions (together)
We use equivalent fractions to put fractions in order: We find the common denominator and use it to place the fractions in order, smallest to largest

Your turn Using the common denominator place the fractions in order, smallest to largest.

(A percentage is a fraction out of 100)

Percentage increase and decrease – how would you do that?

My monthly gas bill of £64 is going up by 15% - what is the new price
My monthly gas bill of £64 is going up by 15% - what is the new price? The value of my car which I bought new for £3,600 has gone down by 35% - what is the new value?

Percentage Profit/Loss (another form of percentage increase/decrease)
If a value has increased or decreased by an amount and the question asks what this would be as a percentage, this is how you would work it out: actual increase/decrease x 100 original amount

Example

Your turn

Reverse Percentages

There is a 20% sale on in Topshop. The bag I want is now £60.
What was the original cost of my bag? % 60

In a sale, everything is reduced by 30%
In a sale, everything is reduced by 30%. If an armchair costs £175 in the sale, how much did it cost before the sale? % 175

A mouse increases its body weight by 15%
A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse’s original weight? % 368

Compound Interest

Definition

£2000 earning Compound Interest at 5% per year for 3 years
Original Amount = 100% Compound Interest = 5% 100% + 5% = 105% = 1.05 3 £2000 x 105% 1.05 = £ This is the total amount including interest: £

Mathswatch clip 137 This is based on the method on the previous slide

Compound Interest Questions
£10,000 earning Compound Interest at 1% per year for 3 years £8,650 earning Compound Interest at 2% per year for 5 years £5,000 earning Compound Interest at 0.5% per year for 4 years £10,000 earning Compound Interest at 1.5% per year for 6 years £8,000 earning Compound Interest at 3% per year for 7 years

The formula to calculate compound interest is:
A = P x (1 + i)n

For after the break

Next – new topic – ratio & proportion
Use ratio notation Simplify ratios Divide a given quantity into parts Find amounts given parts of a ratio Proportion Understand and use proportion Solve problems involving proportion Ratio, Proportion, Fractions, Decimals and Percentages Link ratio, proportion, fractions, decimals and percentages

What is ratio? Ratio is a way of comparing amounts of something.
It shows how much bigger one thing is than another.

How is ratio written? 4 : 1 This ratio has 5 parts altogether as = 5. This will be important a bit later on!

Simplifying Ratios The ratio of yellow to green blocks is
yellow : green = 4 : 2 Which can be simplified to: 4 : 2 ÷2 ÷2 2 : 1

1 : 2 2 : 3 1 : 3 1 : 2 2 : 9 1 : 2 7 : 5 2 : 3 1 : 2 4 : 5 2 : 5

Copyright © AQA and its licensors. All rights reserved.
Think Write the ratios in their simplest form (a) 1mm : 5cm (b) £3.50 : 70p (c) 15 mins : hour (d) 2mm : 10mm (e) 5.2 litres : 300cl Copyright © AQA and its licensors. All rights reserved. Version 2.0

Sharing in Ratio

Share €10 between Mandy and Lara in the ratio 3 : 2
Number of equal parts = = 5 2 2 2 2 2 2 2 2 2 2 Amount in 1 part = 10 ÷ 5 = € 2 Mandy gets = € 2  3 = € 6 Lara gets = € 2  2 = € 4

Number of equal parts = 4 + 3 = 7
A 35 ml orange drink is made by mixing orange juice and water in the ratio 4 : 3. Number of equal parts = = 7 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Amount in 1 part = 35 ÷ 7 = 5 ml Orange Juice = 5  4 = 20 ml Water = 5  3 = 15 ml

Number of equal parts = 3 + 1 = 4
Uncle John wants to share €20 between Mark and Amy in the ratio 3 : 1. How much money will each get? Number of equal parts = = 4 5 5 5 5 5 5 5 5 Amount in 1 part = 20 ÷ 4 = € 5 Mark gets = 5  3 = € 15 Amy gets = 5  1 = € 5

Number of equal parts = 6 + 3 + 1 = 10
A recipe for pastry uses flour, margarine and water in the ratio 6 : 3 : 1. What weight of each is needed to make a mixture that weighs 300 g? Number of equal parts = = 10 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 Amount in 1 part = 300 ÷ 10 = 30 g Flour = 30  6 = 180 g Margarine = 30  3 = 90 g Water = 30  1 = 30 g

3:2 Keith Burnett, Sutton Coldfield College,

3:2 3 parts water Keith Burnett, Sutton Coldfield College,

3:2 2 parts orange juice 3 parts water
Keith Burnett, Sutton Coldfield College,

3:2 2 parts orange juice 3 parts water 3 + 2 = 5 equal parts…

Find value of one share if you know the value of the whole amount…

£350 £?? Keith Burnett, Sutton Coldfield College,

£350 £?? How did you work it out?

£350 £70 350 ÷ 5 = 70 Keith Burnett, Sutton Coldfield College,

£350 £70 £70 £70 Keith Burnett, Sutton Coldfield College,

£350 £70 £70 £70 3  70 = 210 Keith Burnett, Sutton Coldfield College,

£350 £210 Keith Burnett, Sutton Coldfield College,

£350 £210 £?? Keith Burnett, Sutton Coldfield College,

Find value of one share if you know the value of the other share…

£20 Keith Burnett, Sutton Coldfield College,

£20 ?? Keith Burnett, Sutton Coldfield College,

£20 £30 Keith Burnett, Sutton Coldfield College,

£20 £30 How did you work it out?

Try these problems, some in pictures and some in words…

Jim’s Jemima’s Write down the ratio using the colon notation…

£800 Jim’s Jemima’s Find the value of Jim and Jemima’s shares…

£?? £280 £?? Find the value of the whole amount and the missing share…

Write down the ratio using the smallest whole numbers you can…

6 balls and 3 bats Ratio Balls : Bats 6 3 Proportion 9 object altogether (a) What fraction are balls? (b) Can you simplify the fraction (c) What fraction are bats (d) Can you simplify the fraction Copyright © AQA and its licensors. All rights reserved. Version 2.0

6 balls and 3 bats Ratio Balls : Bats 6 3 This can be rewritten as 3 lots of 2 : 1 The ratio can be simplified by dividing into 3 groups Balls : Bats 2 1 For every 2 balls, there is 1 bat. Bats : Balls 1 2 For every 1 bat, there are 2 balls. What link can you see between the simplified ratios and the simplified fractions? Copyright © AQA and its licensors. All rights reserved. Version 2.0

x of x Version 3.0

From last week’s basic questions

Ratio, scale and proportions
Ten quick questions

1 James and Charles share £60 in the ratio of 3:1 How much does James get? a: £15 b: £20 c: £30 d: £45

2 a: 1:5 b: 1:20 c: 1:25 d: 1:125 The model car is 25 cm long.
The length of the real car is about 5 metres. What is the scale used? a: 1:5 b: 1:20 c: 1:25 d: 1:125

3 a: 10 cm b: 60 inches c: 360 cm d: 10 metres
Barbie is approximately on a scale of 1:6. A real cooker is 60 cm wide. How wide is Barbie’s cooker? 3 a: 10 cm b: 60 inches c: 360 cm d: 10 metres

4 The scale on the map is 1:12 000 1 cm on the map is how much in real life? a: 12 km b: 120 km c: 12 m d: cm

5 In this photograph, what is the ratio of women to men? a: 7:2 b: 5:2 c: 2:7 d: 2:5

6 In the picture, what is the ratio of pink to blue cubes, in its simplest form. a: 14:8 b: 6:8 c: 7:3 d: 4:3

7 A bhaji recipe uses 100 g of gram flour to 50 g of self-raising flour. How much self-raising should be used with 150 g of gram flour. a: 50 g b: 75 g c: 100 g d: 150 g

8 The wheels on my bike have a diameter (D) of 700 mm. C is about 3 x D Which of these is closest to the circumference (C)? a: 1400 mm b: 350 mm c: 2100 mm d: 7 m

9 a: £100 b: £5 c: £50 d: £200 The currency exchange is approximately
£1 = 2 Australian Dollars. 100 Australian dollars is roughly equal to: a: £100 b: £5 c: £50 d: £200

10 a: 2 litres b: 5 litres c: 6 litres d: 200 ml
The squash bottle says mix one part squash to five parts water. How much drink, in total, can I make with one litre of squash? a: 2 litres b: 5 litres c: 6 litres d: 200 ml