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Bridging the Gap Problem-Solving

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First Thoughts … Form 5A has 30 pupils: 10 Rovers fans 20 United fans Form 5B has 18 pupils: 9 Rovers fans 9 United fans You’re a Rovers fan. Which class would you rather be in?

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Did You Pick 6A? 5A: 10 + 20 = 30 5B: 9 + 9 = 18 – Rani, a mad Rovers fan, picked 5A: “10 is bigger than 9, so there’s more Rovers fans in 5A than 5B. Yey!”

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Did You Pick 6B? 5A: 10 + 20 = 30 5B: 9 + 9 = 18 - But other red Rovers fans picked 5B: MARTIN SAYS “I’m not going to 5A - I’d be outnumbered 2 United to every 1 Rovers fan!” BECKY SAYS: “Only one third of 5A Rovers fans. It’s one half in 5B. HANNAH SAYS: has 10 out of 30 Rovers “5A only has 10 out of 30 Rovers fans. That’s 1 out of 3.” 2 to 1 is a ratio third and half are fractions 1 out of 3 is a proportion All answers are correct! But - 3 different sorts of answer.

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Recap – 3 Ways to Compare Numbers Fraction? Proportion? Ratio? Which question is a … has 10 out of 30 Rovers “5A only has 10 out of 30 Rovers fans. That’s 1 out of 3.” “Only one third of 5A Rovers fans. It’s one half in 5B.” “I’m not going to 5A. I’d be outnumbered 2 to every 1.”

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What’s the Difference - Summing Up:. “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” Ratios compare PART WITH PART Proportions compare PART WITH WHOLE Fractions compare PART WITH WHOLE using shorthand such as 1/3 3 different ways to say the same thing 3 different ways to compare numbers

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So comparing totals isn’t the only way to look at these numbers… Form 5A has 30 pupils: 10 Rovers fans 20 United fans Form 5B has 18 pupils: 9 Rovers fans 9 United fans …You can compare part with part using RATIO …You can compare part with whole using PROPORTIONSor FRACTIONS Eg: 1/3 are Rovers fans Eg: 1 out of 3 are Rovers fans Eg: Rovers : United = 1 to every 2 = 1:2

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

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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

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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

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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

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

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

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

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

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

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

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