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Proportional Reasoning

Proportional Reasoning. Secondary Numeracy Project In-school Facilitator Training February 2007. 4. 5. Language. Proportion, Fraction, Ratio, Rate 4 times as many red stars as there are yellow ones Ratio of red stars to yellow stars is 4:1 4 red stars to every yellow star

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Proportional Reasoning

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  1. Proportional Reasoning Secondary Numeracy Project In-school Facilitator TrainingFebruary 2007

  2. 4 5 Language • Proportion, Fraction, Ratio, Rate • 4 times as many red stars as there are yellow ones • Ratio of red stars to yellow stars is 4:1 • 4 red stars to every yellow star • of the stars are red

  3. Quantities change together • To understand a ratio or a rate you must distinguish a relationship that remains constant when two linked quantities are changing together • The constant relationship is not directly observable

  4. 2 3 AP Strategy learning outcomes • Find equivalent ratios It takes 10 balls of wool to make 15 beanies. How many balls of wool does it take to make 6 beanies? • Convert from ratios to proportions and visa versa 2:3 = …

  5. Solve problems with rates 40 km in 80 minutes is how far in an hour? • Find amounts in given ratios Four grey garden tiles are used to every three red ones. If you use 210 tiles altogether how many are grey and how many are red. • Solve problems with inverse rates If 4 people can build a house in 9 days, how long will 3 people take to do it?

  6. Ratio using Fruit Cards • Knowledge recap • Materials • Imaging • Number Properties

  7. Knowledge recap Fraction versus a Ratio • What fraction of the group is the pear? the lemons? • What fraction of the group are bananas?, apples? • How many bananas compared to the apples in the group? • What is the ratio of lemons to pears?, lemons to bananas?

  8. Fruit Bowl Problems Apples and Oranges There are 3 oranges to every one apple in the bowl. How many oranges will there be if there are 5 apples?

  9. Fruit Bowl Problems contd. Apples and Oranges There are 3 oranges to every one apple in the bowl. How many apples if there are 12 oranges? How many apples and how many oranges, if thereare 20 pieces of fruit in the bowl?

  10. Jelly Bean Mix In a bag of Otago mix jellybeans there are 6 blue and 4 yellow jellybeans. • How many jellybeans of each colour in 3 packets? Answer • A box contains 80 jellybeans. How many packets in the box? • How many yellow jellybeans in the box? • How many yellow jellybeans if there are 48 blue ones?

  11. Multilock block models Paint mixes Which is the stronger shade of green? • 2 parts blue with 3 parts yellow • 3 parts blue with 5 parts yellow

  12. Adding doesn’t work! ‘Green’ paint is made by mixing blue and yellow paint in the ratio 1:2.

  13. Making Bread 40 loaves of bread can be made from 6 kg of flour. How many loaves can be made from 15 kg of flour? How did you work it out?

  14. Within measures M1 M2 Weight Cooking Time .5 10 2.5 ? Cooking a chicken takes 10 minutes for every 500g. How long to cook a 2.5kg chook. 1:5 Or x5 1:5 Or x5

  15. Between measures Cooking a chicken takes 10 minutes for every 500g. How long to cook a 2.5kg chook? M1 M2 Weight Cooking Time .5 10 2.5 ? 1:20 1:20

  16. Unit Rate Cooking a chicken takes 10 minutes for every 500g. How long will it take to cook a 2.5kg chook? Weight Cooking Time 0.5 10 1 20 2.5 20 x 2.5 = 50

  17. Ratio Table Cooking a chicken takes 10 minutes for every 500g. How long will it take to cook a 2.5kg chook?

  18. Double Number Lines It takes Cara 8 hours to groom 12 cars. Each car takes the same time. How long will it take her to groom 21 cars? Hours 0 8 ? 12 0 21 Cars

  19. Look-alike rectangles • Group the rectangles into three groups of four rectangles and an odd one out. • Discuss reasons for groupings. • Measure and record the sides of each rectangle, calculate ratios for short to long sides for each one. • Draw a graph plotting length against width.

  20. Look-alike rectangles • Describe relationship of length to width • Reinforce adding doesn’t work • Place rectangles on top of one another and draw diagonals • A line drawn through all the rectangles in a set goes through the origin • Make predictions – given the width of a rectangle in the set, what is its length

  21. Look-alike rectangles graph

  22. back

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