Problem-Solving Pupils’ Version Revising Ratio and Proportion . Bridging the Gap Revising Ratio and Proportion . L3 L4 to

What Will You Learn ? If you work through this slideshow, Never heard of ratio before? How exactly do you keep numbers in proportion? What’s the difference between ratio, proportion and fractions? If you work through this slideshow, you will find out that: Ratio and proportion are EASY! Fractions will make more sense too You can work out most of the maths in your head!

How to use this resource You can control how fast or slow you go using: FORWARD: OR OR Enter OR Left-hand mouse BACK: OR OR Back Space TO START POWERPOINT: F5 OR Slide Show > View Show TO RETURN TO MENU: Escape

Contents (TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE) Slides 5 – 16: Part 1: Ratio, Proportion & Fractions What is ratio? What is proportion? What’s the connection? Where do fractions fit in? Slides 17 – 26 Part 2: Simplest Ratios and Proportions Equivalent ratios. Simplest ratios. Equivalent proportion. Simplest proportions. Slides 27 – 44 Part 3: Recipes & Proportion How to scale a recipe for 10 people down to 4 people without disaster. (TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE) TEACHING NOTES The terms ‘ratio’, ‘proportion’ and ‘fractions’. The language associated with each one The connection between the three: - Ratio, proportion and percentage are 3 different ways of looking at different sets of numbers and comparing them - Ratio, proportion and percentage are 3 different ways of saying the same thing. TEACHER NOTES “We’re used to comparing totals of numbers only. The examples show that this isn’t always the most useful way…”

DO’s and DON’Ts Working Through DO go as fast or as slow as you like! You can use the mouse or arrow keys to control the speed of the slideshow. DON’T try to do it all in one go – there’s loads of stuff. Working Out You can work a lot of the questions out in your head, -but keep a pen and paper handy.! To START, press F5 To STOP, press ESC

First Thoughts … There’s lots of differences between the classes in your school – … Some have more boys than girls … Less United fans than Rovers fans … More cat-lovers than dog-lovers … Less pizza-munchers than chicken-dippers

First Thoughts … 10 Rovers fans 20 United fans 9 Rovers fans Form 6A has 30 pupils: 10 Rovers fans 20 United fans Form 6B has 18 pupils: 9 Rovers fans 9 United fans You’re a Rovers fan. Which class would you rather be in? Discuss and take a class vote.

so there’s more Rovers fans in 6A than 6B. Did You Pick 6A? 6A: 10 + 20 = 30 6B: 9 + 9 = 18 – Rani, a mad Rovers fan, picked 6A: “10 is bigger than 9, so there’s more Rovers fans in 6A than 6B. Yey!”

Did You Pick 6B? Who is right? Discuss and take a class vote! 6A: 10 + 20 = 30 6B: 9 + 9 = 18 - But other red Rovers fans picked 6B: 2 to 1 is a ratio 1 out of 3 is a proportion third and half are fractions MARTIN SAYS “I’m not going to 6A - I’d be outnumbered 2 United to every 1 Rovers fan!” BECKY SAYS: “Only one third of 6A Rovers fans. It’s one half in 6B. HANNAH SAYS: “6A only has 10 out of 30 Rovers fans. That’s 1 out of 3.” All answers are correct! But - 3 different sorts of answer. Which do you prefer? Why? Who is right? Discuss and take a class vote!

Recap – 3 Ways to Compare Numbers Which question is a … “6A only has 10 out of 30 Rovers fans. That’s 1 out of 3.” Fraction? “I’m not going to 6A. I’d be outnumbered 2 to every 1.” Ratio? Proportion? “Only one third of 6A Rovers fans. It’s one half in 6B.”

What’s the Difference - Summing Up: . 3 different ways to say the same thing 3 different ways to compare numbers Ratios compare PART WITH PART “1 to every 2” is a Ratio “1 Rovers fan to every 2 United fans” “The ratio of Rovers to United fans is 1 to 2” “The ratio of United to Rovers fans is 2 to 1” “1 out of 3” is a Proportion “1 out of every 3 fans is a Rovers fan” “The proportion of Rover fans is 1 out of 3” “One third” is a Fraction “One third of all fans are Rovers fans “1/3 of all fans are Rovers fans” Proportions compare PART WITH WHOLE Fractions compare PART WITH WHOLE using shorthand such as 1/3

So comparing totals isn’t the only way to look at these numbers… Form 6A has 30 pupils: 10 Rovers fans 20 United fans Form 6B has 18 pupils: 9 Rovers fans 9 United fans …You can compare part with part using RATIO …You can compare part with whole using Eg: Rovers : United = 1 to every 2 = 1:2 PROPORTIONS or FRACTIONS Eg: 1 out of 3 are Rovers fans Eg: 1/3 are Rovers fans

Ratio, Proportion or Fraction? two out of five This is a … two fifths This is a … proportion fraction four tenths This is a … four to every ten This is a … fraction ratio ten to every four This is a … four out of ten This is a … ratio proportion 4/10 This is a … 4:10 This is a … fraction ratio

Ratio, Proportion or Fraction? 3 United fans to every 2 Rangers fans This is a … ratio 9 girls out of 10 use soap This is a … proportion 3 boys out of 10 use deodorant This is a … proportion

Ratio, Proportion or Fraction? 3 out of 4 pizza-munchers love olives This is a … proportion Half of all girls in 6D love History This is a … fraction One third of all road accidents involve drinking This is a … fraction

Ratio, Proportion or Fraction? 3 out of 4 drivers speed at some time This is a … proportion Three quarters of drivers speed This is a … fraction 3 drivers speed to every 1 which does not This is a … ratio

Ratio and Proportion: Different Words! Ratio: “to every” 1 Rovers fan to every 2 United fans Proportion: “out of” 1 out of 3 football fans is a Rovers fan

PART 2: Simplest Ratios and Proportions

The dinner queue Ratio of girls to boys? 4 girls to every 8 boys girls : boys = 4 : 8 Ratio of girls to boys? But the simplest ratio is still 1 : 2 3 girls to every 6 boys girls : boys = 3 : 6 But the simplest ratio is still 1 : 2 2 girls to every 4 boys girls : boys = 2 : 4 But the simplest ratio is still 1 : 2 1 girl to every 2 boys girls : boys = 1 : 2 This is the simplest ratio is 1 : 2

The dinner queue Ratio of boys to girls? 8 boys to every 4 girls boys : girls = 8 : 4 Ratio of boys to girls? But the simplest ratio is still 2 : 1 6 boys to every 3 girls boys : girls = 6 : 3 But the simplest ratio is still 2 : 1 4 boys to every 2 girls boys : girls = 4 : 2 But the simplest ratio is still 2 : 1 2 boys to every 1 girl boys : girls = 2 : 1 This is the simplest ratio is 2 : 1

2 : 1 is a simpler ratio than 4 : 2 Simplest ratios 2 : 1 is a simpler ratio than 4 : 2 but They both mean the same 2 : 1 = 4 : 2 Can you explain why 2 : 1 = 6 : 3 ? 2 : 1 = 8 : 4 ? 2 : 1 = 100 : 50 ?

What proportion is girls? The dinner queue 4 girls out of 12 Simplest proportion of girls is still 1 out of 3 What proportion is girls? 3 girls out of 9 Simplest proportion of girls is still 1 out of 3 2 girls out of 6 Simplest proportion of girls is still 1 out of 3 1 girl out of 3 This is the simplest proportion of girls = 1 out of 3

What proportion is boys? The dinner queue 8 boys out of 12 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? What proportion is boys? 6 boys out of 9 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 4 boys out of 6 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 2 boys out of 3 Proportion of boys? Simplest proportion of boys? This is the simplest proportion of boys = 2 out of 3

The dinner queue What fraction is girls? 4 / 12 What fraction is girls? The dinner queue Simplest fraction of girls is still 1 / 3 Simplest proportion of girls? What fraction is girls? 3 / 9 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? 2 / 6 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? 1 / 3 What fraction is girls? This is the simplest fraction of girls = 1 / 3 Simplest fraction of girls?

The dinner queue What fraction is boys? 8 / 12 What fraction is boys? Simplest proportion of boys? Simplest fraction of boys is still 2 / 3 What fraction is boys? 6 / 9 What fraction is boys? Simplest fraction of boys? Simplest fraction of boys is still 2 / 3 4 / 6 What fraction is boys? Simplest fraction of boys is still 2 / 3 Simplest fraction of boys? 2 / 3 What fraction is boys? This is the simplest fraction of boys = 2 / 3 Simplest fraction of boys?

Does order matter? There are 20 boys and 10 girls in 6D. Which of these are correct? b) girls : boys = 2 : 1 a) boys : girls = 2 : 1 c) boys : girls = 1 : 2 boys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy Click to check your answer ORDER MATTERS! Be careful what you write!

True or Not True? Ratio of teachers to pupils = 30 : 1 GUESS! TRUE! Ratio of teachers to pupils = 30 : 1 Ratio of fans to players = 1 : 1000 This would mean all the players would be sitting in the stadium! Ratio of weekdays to weekend days = 2 : 5 You wish! Ratio of porridge lovers to pizza guzzlers = 100 : 1 - Not until they invent Porridge Takeaways .. TRUE! TRUE! TRUE!

PART 3: Recipes and Proportion How to scale a recipe for 10 people down to 4 people without disaster!

Biscuits and Bananas Skins Enjoy cooking? Check out these fantastic recipes! Some of them need changing to suit the number of people, - But remember to keep them in proportion, - And watch out for the or else … Whoops !

It’s supper time! You make a simple omelette like this: + = 2 eggs + 1 teaspoon of butter = 1 omelette Your omelette tastes amazing! - So of course your mates start turning up. Can you scale up your ingredients to feed them all? ? eggs + ? tsp of butter = 2 omelettes 4 eggs + 2 tsp of butter = 2 omelettes ? eggs + ? tsp of butter = 3 omelettes 6 eggs + 3 tsp of butter = 3 omelettes 8 eggs + 4 tsp of butter = 4 omelettes ? eggs + ? tsp of butter = 4 omelettes 10 eggs + 5 tsp of butter = 5 omelettes ? eggs + ? tsp of butter = 5 omelettes

2 eggs + 1 teaspoon of butter = 1 omelette And the next week … + = 2 eggs + 1 teaspoon of butter = 1 omelette … word’s getting around and more mates turn up the next day. Can you scale up your ingredients to feed them? 4 eggs + 2 tsp of butter = 2 omelettes 4 eggs + ? tsp of butter = ? omelettes 10 eggs + 5 tsp of butter = 5 omelettes 10 eggs + ? tsp of butter = ? omelettes 20 eggs + 10 tsp of butter = 10 omelettes ? eggs + 10 tsp of butter = ? omelettes 22 eggs + 11 tsp of butter = 11 omelettes ? eggs + 11 tsp of butter = ? omelettes

RECAP How did you work these out? STEP 1: CHOOSE the maths! x or ÷ ? BIGGER AMOUNTS mean X SMALLER AMOUNTS mean ÷ RECAP How did you work these out? STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients (This is called ‘keeping it in proportion’) STEP 3: CHECK the maths! - using ratio ! Eg: If there are 2 eggs to every 1 tsp butter, the ‘eggs number’ is ALWAYS twice the ‘butter number’. Hungry for more? Try these recipes … REMEMBER THE 3 STEPS

Recipe for Shortbread Biscuits Makes 20 shortbread biscuits Ingredients 200g butter 200g plain flour 100g golden caster sugar 100g fine semolina Pre-heat the oven to gas mark 2, 300°F (150°C). You will also need an 8 in (20 cm) diameter fluted flan tin, 1¼ in (3 cm) deep with a loose base.

10 Mouth-watering Shortbread Biscuits! STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ This is the recipe for 20 biscuits. Can you scale down the recipe for 10? Remember to keep your recipe in proportion – if you halve the sugar, remember to halve the rest as well or it won’t taste good! STEP 3: CHECK the maths! - using ratio. Eg: The weight of the butter is always 2 times the weight of the sugar. STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients + + + = 400g flour 400g butter 200g sugar 200g semolina 20 biscuits ÷ 2 ? ÷ 2 ? ÷ 2 ? ÷ 2 ? ÷ 2 ? + + + = 200g flour 200g butter 100g sugar 100g semolina 10 biscuits

3 Steps for Scaling RECAP STEP 1: CHOOSE the maths! CHOOSE FROM x or ÷ … BIGGER means X … SMALLER means ÷ RECAP STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients STEP 3: CHECK the maths! - using ratio. Eg: If the weight of the butter is always 2 times the weight of the sugar…

… Nirmal makes 2 shortbread biscuits Whoops ! … Nirmal makes 2 shortbread biscuits Mistake in STEP 1: Choose the maths! CHOOSE FROM + - x ÷ BIGGER means X SMALLER means ÷ BUT… Nirmal did X 10 instead of ÷ 10 Nirmal scaled down the recipe for 2 biscuits, but they don’t taste right! Did he scale down correctly and keep the recipe in proportion? Check his working out Then click to see if you’re right + + + = 20 biscuits 400g flour butter 200g sugar semolina 20 biscuits ÷ 10 ÷ 10 ÷ 10 ÷ 10 x10 ? x 10 ? x 10 x 10 ? x 10 ? ? ÷ 10 WHAT DIFFERENCE DID THE MISTAKE MAKE? 200 BISCUITS INSTEAD OF 2! + + + = 4000 g flour 40 g flour 40 g butter 4000 g butter 2000 g sugar 20 g sugar 2000 g semolina 20 g semolina 2 biscuits

3 Steps for Scaling RECAP STEP 1: CHOOSE the maths! CHOOSE FROM x or ÷ … BIGGER means X … SMALLER means ÷ RECAP STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients STEP 3: CHECK the maths! - using ratio. Eg: If the weight of the butter is always 2 times the weight of the sugar…

… Liana makes 5 shortbread biscuits Whoops ! … Liana makes 5 shortbread biscuits Mistake in STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients BUT …Liana did not do ÷ 2 to the sugar. Check her working out Then click to see if you’re right Liana scaled down the recipe for 5 biscuits, but they don’t taste right! Did she scale down correctly and keep the recipe in proportion? + + + = 20 biscuits 400g flour butter 200g sugar semolina ÷ 4 ÷ 4 ÷ 4 ÷ 2 ÷ 4 ÷ 4 ? THE BISCUITS WERE TOO SWEET! WHAT DIFFERENCE DID THE MISTAKE MAKE? + + + = 100 g flour 100 g butter 100 g sugar 50 g sugar 50 g semolina 5 biscuits

3 Steps for Scaling RECAP STEP 1: CHOOSE the maths! CHOOSE FROM x or ÷ … BIGGER means X … SMALLER means ÷ RECAP STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients STEP 3: CHECK the maths! - using ratio. Eg: If the weight of the butter is always 2 times the weight of the sugar…

Further Practical Examples Recipe No.1 Melon Merenga Serves 8 people Ingredients 300 g raspberries 200 g bananas 100 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour and serve with ice or ice-cream.

Can you work out the missing amounts? STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The bananas’ weight is ALWAYS twice the melons’ weight. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Melon Merenga for 8 600 g + + = 400 g 200 g Melon Merenga for 4 ? g + + = ? g ? g 300 g 200 g 100 g General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 2 people. 2) X 3 (easier than X6) Melon Merenga for 2 ? g + + = ? g ? g 150 g 100 g 50 g Melon Merenga for 1 You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? ? g + + = ? g ? g 75 g 50 g 25 g Melon Merenga for 6 ? g + + = ? g ? g 450 g 300 g 150 g

Further Practical Examples Recipe No Further Practical Examples Recipe No.2 Raspberry Fruitloop (Same ingredients. Different amounts) Serves 10 people Ingredients 500 g raspberries 250 g bananas 150 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour and serve with fresh raspberries

Can you work out the missing amounts? STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The raspberries’ weight is ALWAYS twice the melons’ weight. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Raspberry Fruitloop for 10 500 g + + = 250 g 150 g Raspberry Fruitloop for 5 ? g + + = General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it! (Easier than X8) 250 g ? g 125 g ? g 75 g Raspberry Fruitloop for 1 ? g + + = ? g ? g 50 g 25 g 15 g Raspberry Fruitloop for 4 You can work this out from the quantities for 1 person, BUT … Can you see any shortcuts? ? g + + = 200 g ? g 100 g ? g 60 g Raspberry Fruitloop for 8 ? g + + = 400 g ? g 200 g ? g 120 g

Further Practical Examples Recipe No Further Practical Examples Recipe No.3 Bombastic Banana Boat (Same ingredients. Different amounts) Serves 12 people Ingredients 120 g raspberries 600 g bananas 120 g melon Method Place ingredients in a juicer and switch on power for 30 seconds. Pour into a scooped out melon half . Serve with fresh raspberries

Can you work out the missing amounts? STEP 1: Choose the maths! x or ÷ ? BIGGER means X SMALLER means ÷ STEP 3: CHECK the maths! - using ratio. Eg: The weight of bananas is always 5 times the weight of the melon. Can you work out the missing amounts? STEP 2: Do the maths! DO THE SAME X or ÷ to ALL ingredients Banana Boat for 12 120 g + + = 600 g 120 g Banana Boat for 6 ? g + + = ? g ? g 60 g 300 g 60 g General Method: 1) Work out the recipe for 1. 2) Multiply by the number you need Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it! (Easier than X8) Banana Boat for 4 ? g + + = ? g ? g 40 g 200 g 40 g Banana Boat for 1 You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? ? g + + = ? g ? g 10 g 50 g 10 g Banana Boat for 8 ? g + + = ? g ? g 80 g 400 g 80 g

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