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Problem-Solving Pupils’ Version Bridging the Gap What Will You Learn ? 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 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) 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 … Form 6A has 30 pupils: Form 6B has 18 pupils: 10 Rovers fans 9 Rovers fans 20 United fans 9 United fans You’re a Rovers fan. Which class would you rather be in? Discuss and take a class vote. 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? 6A: 10 + 20 = 30 6B: 9 + 9 = 18 2 to fans picked 6B: - But other red Rovers 1 third and half is a ratio MARTIN SAYS 1 out of 3 are fractions is a “I’m not going to 6A - I’d be outnumbered 2 United proportion to every 1 Rovers fan!” BECKY SAYS: “Only one third HANNAH SAYS: of 6A Rovers “6A only has 10 out fans. It’s one of 30 Rovers fans. half in 6B. That’s 1 out of 3.” Who is different All answers are correct! But - 3right? sorts of answer. Discuss and take a class vote! Which do you prefer? Why? Recap – 3 Ways to Compare Numbers Which question “6A only has 10 out is a … of 30 Rovers fans. That’s 1 out of 3.” Fraction? “I’m not going to 6A. Ratio? I’d be outnumbered 2 to every 1.” Proportion? “Only one third of 6A Rovers fans. It’s one half in 6B.” What’s the Difference - Summing Up: . 3 different ways to 3 different ways to say the same thing compare numbers Ratios compare “1 to every 2” is a Ratio PART WITH “1 Rovers fan to every 2 United fans” PART “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 Proportions “1 out of every 3 fans is a Rovers fan” compare PART “The proportion of Rover fans is 1 out of 3” WITH WHOLE Fractions “One third” is a Fraction compare PART “One third of all fans are Rovers fans WITH WHOLE “1/3 of all fans are Rovers fans” using shorthand such as 1/3 So comparing totals isn’t the only way to look at these numbers… Form 6A has 30 pupils: Form 6B has 18 pupils: 10 Rovers fans 9 Rovers fans 20 United fans 9 United fans …You can compare part with part using RATIO Eg: Rovers : United = 1 to every 2 = 1:2 …You can compare part with whole using 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 two fifths This is a … proportion This is a … fraction four tenths four to every ten This is a … fraction ten to every four This is a … ratio four out of ten This is a … ratio 4/10 This is a … proportion This is a … fraction 4:10 This is a … 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 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 4 girls to every 8 boys The dinner queue girls : boys = 4 : 8 Ratio of girls But the simplest ratio is still 1 : 2 to boys? 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 8 boys to every 4 girls The dinner queue boys : girls = 8 : 4 Ratio of boys But the simplest ratio is still 2 : 1 to girls? 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 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 ? The dinner queue 4 girls out of 12 Simplest proportion of girls What is still 1 out of 3 proportion 3 girls out of 9 is girls? 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 The dinner queue 8 boys out boys? Proportion of of 12 Simplest proportion of Simplest proportion of What boys? boys is still 2 out of 3 proportion 6 boys out of 9 Proportion of boys? is boys? Simplest proportion of Simplest proportion of boys is still 2 out of 3 boys? 4 boys out of 6 Proportion of boys? Simplest proportion of Simplest proportion of boys is still 2 out of 3 boys? Proportion of boys? 2 boys out of 3 Simplest proportion of boys? This is the simplest proportion of boys = 2 out of 3 What fraction is girls? 4 / 12 The dinner queue Simplest proportion girls Simplest fraction of of is still 1 / 3 girls? What fraction is 3 9 What fraction /is girls? girls? Simplest fraction girls? Simplestfraction ofof girls is still 1 / 3 2 6 What fraction /is girls? Simplest fraction of girls is Simplest fraction of girls? still 1 / 3 1 3 What fraction /is girls? This is the simplest Simplest fraction of girls? fraction of girls = 1 / 3 The dinner queue What fraction is boys? 8 / 12 Simplest proportion of Simplest fraction of boys is What boys? still 2 / 3 fraction is 6 9 What fraction /is boys? boys? Simplest fraction of boys is Simplest fraction of still 2 / 3 boys? 4 6 What fraction /is boys? Simplest fraction of boys is Simplest fraction of still 2 / 3 boys? 2 3 What fraction /is boys? Simplest fraction of This is the simplest boys? fraction of boys = 2 / 3 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 Click to check your answer girls : boys = 2 : 1 means 2 girls to every boy ORDER MATTERS! Be careful what you write! True or Not 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 .. 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 … 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? 4 eggs ? + 2 tsp of butter = 2 omelettes ? ? 6 eggs + ? 3 tsp of butter = 3 omelettes ? 8 eggs + ? 4 tsp of butter = 4 omelettes ? eggs 10 eggs ++ ? 5 tsp of butter = 5 omelettes 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 10 eggs + ? ? 5 tsp of butter = 5 omelettes ? eggs 20 eggs 10 tsp of butter = ? omelettes ++ 10 tsp of butter = 10 omelettes ? eggs 22 eggs + 11 tsp of butter = ? omelettes + 11 tsp of butter = 11 omelettes STEP 1: CHOOSE the maths! RECAP x you ? How did or ÷work these out? BIGGER AMOUNTS mean X SMALLER AMOUNTS mean ÷ 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 is the recipemaths! This 1: Choose the for 20 STEP 3: recipe for 10? biscuits. Can you scale down theCHECK the maths! x or ÷ ? - using ratio. BIGGER means X Eg: The weight of the butter STEP 2: Do the maths! – if you halve the sugar, Remember to keep your recipe in proportion is always 2 times the weight SMALLER means ÷ halve the rest asX or ÷or it won’t tastethe sugar. remember to DO THE SAME well to of good! ALL ingredients 20 400g + 400g + 200g + 200g = flour butter sugar semolina biscuits ÷?2 ÷?2 ÷?2 ÷? 2 ÷?2 10 200g + 200g + 100g + 100g = flour butter sugar semolina biscuits STEP 1: CHOOSE the maths! 3 Steps for Scaling CHOOSE FROM x or ÷ RECAP BIGGER means X … … SMALLER means ÷ 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 Mistake in STEP 1: Choose the maths! Nirmal Check x ÷ CHOOSE FROM + - his for 2 biscuits, scaled down the recipe working out but they don’t taste right! BIGGER means X SMALLER means ÷ Did BUT… Nirmal did X 10 instead of ÷ 10 he scale down correctly and keep the recipe in proportion? Then click to see if you’re right 20 20 400g + 400g + 200g + 200g = flour sugar semolina biscuits biscuits butter ÷ ? 10 x10 ÷ x? 10 10 ÷ x? 10 10 ÷ x? 10 10 x?10 ÷ 10 20 g 2 WHAT 40 g 4000 g + 4000 g + 2000 g + 2000 g 40 g 20 g = 200 DIFFERENCE flour butter sugar semolina biscuits BISCUITS DID THE INSTEAD OF MISTAKE 2! MAKE? STEP 1: CHOOSE the maths! 3 Steps for Scaling CHOOSE FROM x or ÷ RECAP BIGGER means X … … SMALLER means ÷ 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 Check her Do biscuits, Liana scaled down the recipe2:working outbut they don’t taste right! Mistake in STEP for 5the maths! DO THE SAME X or ÷ to ALL ingredients BUT …Liana did not do ÷ 2 to the sugar. Then click to see if keep the recipe Did she scale down correctly and you’re right in proportion? 20 400g + 400g + 200g + 200g = flour butter sugar semolina biscuits ÷4 ÷4 ÷4 ÷2 ÷4 ÷4 ? 50 g 5 WHAT 100 g + 100 g 50 g + 100g + = THE DIFFERENCE flour butter sugar semolina biscuits BISCUITS DID THE WERE TOO MISTAKE SWEET! MAKE? STEP 1: CHOOSE the maths! 3 Steps for Scaling CHOOSE FROM x or ÷ RECAP BIGGER means X … … SMALLER means ÷ 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. STEP 1: Choose the maths! STEP 3: CHECK the maths! x or ÷ ? - using ratio. BIGGER means X Can you work outSTEP 2:missing amounts? the Do the maths! Eg: The bananas’ weight is SMALLER means ÷ DO THE SAME X or ÷ to ALWAYS twice the melons’ ALL ingredients weight. Melon 600 g + 400 g + 200 g = Merenga for 8 Melon 300 g g + 200 g g + 100 g g = ? ? ? Merenga for 4 General Method: 1) Work out the recipe for 1. Melon 2) Multiply by the ? g g + 100 g g + 150 ? ? g 50 g = Merenga for 2 number you need Melon Shortcut: 75 gg + ? ? g 50 g + 25 g ? g = You can work this out Merenga for 1 1) Work out from the from the quantities quantities BUT for 1 person,for 2 … Can you people. see a Melon 2) X 3shortcut? 450 g g + 300 gg + 150 gg ? ? ? = Merenga for 6 (easier than X6) 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 STEP 1: Choose the maths! STEP 3: CHECK the maths! x or ÷ ? - using ratio. BIGGER means X Can you work outSTEP 2:missing amounts? the Do the maths! Eg: The raspberries’ weight SMALLER means ÷ DO THE SAME X or ÷ to is ALWAYS twice the melons’ ALL ingredients weight. Raspberry 500 g + 250 g + 150 g = Fruitloop for 10 Raspberry 250gg + ? 125gg ? + ? g 75 g = Fruitloop for 5 General Method: 1) Work out the recipe for 1. Raspberry 2) Multiply by the ? 50 g g + ? g 25 + ? g 15 = Fruitloop for 1 number you need Shortcut: ? gg + + = Raspberry You can out from 1) Workwork this out 200 ? 100gg ? g 60 g the quantities Fruitloop for 4 from the quantities for 4 people. for 1 person, BUT … Can you see any 2) Just double it! Raspberry shortcuts? ? gg + 400 ? 200gg + 120gg ? = (Easier than X8) Fruitloop for 8 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 STEP 1: Choose the maths! STEP 3: CHECK the maths! x or ÷ ? - using ratio. BIGGER means X Can you work outSTEP 2:missing amounts? the Do the maths! Eg: The weight of bananas is SMALLER means ÷ DO THE SAME X or ÷ to always 5 times the weight of ALL ingredients the melon. Banana Boat 120 g + 600 g + 120 g = for 12 Banana Boat ? g 60 g + ? g 300g + ? g 60 g = for 6 General Method: 1) Work out the Banana Boat recipe for 1. g ?40 g + 200g ? g + ? g 40 g = for 4 2) Multiply by the number you need Banana Boat Shortcut: ? g 10 g + ? g 50 g + ? g 10 g = You can work this out for 1 1) Work out from from the quantities for 1the quantities… person, BUT for 4 see a Can youpeople. Banana Boat shortcut? 2) Just double it! ? g 80 g + 400g ? g + ? g 80 g = for 8 (Easier than X8) Still not had enough? Why not try … THE SCHOOL CANTEEN? - for FRIENDLY PROBLEMS about Money THE HISTORY CLASSROOM? - for FRIENDLY PROBLEMS about Area and Perimeter THE SPANISH CLASSROOM? For FIENDISH PROBLEMS about Money with Area and Perimeter! Press Escape to return to main menu

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Placement Papers, she asked, L&T INFOTECH, Interview Questions, logical reasoning, aptitude test, yes mam, Patni computer Systems, compound interest, I dont remember

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posted: | 3/11/2010 |

language: | English |

pages: | 46 |

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