lesson 49 Visualizing the ratio of 2 given numbers (2).ppt
- 1. Lesson 49: Visualizing the Ratio of 2 Given Numbers ANNALICE R. QUINAY MASTER TEACHER 1 SAN JOSE ES SAN PABLO CITY
- 2. Reduce the ff. fractions to lowest terms 12/15 4/5
- 3. Reduce the ff. fractions to lowest terms 10/55 2/11
- 4. Reduce the ff. fractions to lowest terms 18/50 9/25
- 5. Reduce the ff. fractions to lowest terms 35/50 7/10
- 6. Reduce the ff. fractions to lowest terms 35/50 7/10
- 7. Reduce the ff. fractions to lowest terms 14/42 1/3
- 8. Reduce the ff. fractions to lowest terms 21/84 1/4
- 9. Reduce the ff. fractions to lowest terms 9/81 1/9
- 10. Write the total number of male and female on the board.
- 11. What is the ratio of male to female? Female to male?
- 12. Male to total number of pupils? Female to the total number of pupils?
- 14. Mechanics: •Let the pupils count the number of girls and boys in their respective column. •Let the pupils write their answers on the board. •Tabulate the data on the board as follows:
- 15. Column number Number of Boys Numbe r of Girls Number of Pupils in a Column 1 12 6 18 2 10 5 15
- 16. •Ask the following questions: •How many pupils are there in each column? •How do you compare the number of boys to the number of girls in Column 1? Column 2?
- 17. Ratio is the comparison of two quantities.
- 18. Compare the number of boys in Rows 1 and 2. Compare the number of girls in Rows 3 and 4. Compare the number of pupils in Rows 1 and 5.
- 19. There are 7 boys and 8 girls playing volleyball. Problem Opener:
- 20. What is the ratio of boys to girls? What is the
- 21. What is the ratio of boys to players? What is the ratio of girls to players? How do we express ratio of 2 numbers?
- 22. Count the number of objects in each set and write your answers on the board.
- 23. Set 1 – 2 notebooks, 3 pencils Set 2 – 5 crayons, 10 sheets of paper
- 24. How will you compare the number of notebook with the number of pencils? What is the ratio of notebooks to pencils?
- 25. Crayons to sheets of paper? Define the ratio. Can we interchange the terms in ratio? Why or Why not? Write the ratios in two ways.
- 26. a. pencils to notebooks b. notebooks to pencils c. pencils to total numbers of things d. notebooks to total number of
- 27. a.eggs to baskets b.baskets to egg c.eggs to total number of things d.basket to total number of
- 29. Ratio A ratio compares the sizes of parts or quantities to each other. What is the ratio of red counters to blue counters? red : blue = 9 : 3 = 3 : 1 For every three red counters there is one blue counter.
- 30. What is the ratio of red counters to yellow counters to blue counters? Ratio red : yellow : blue = 12 : 4 : 8 = 3 : 1 : 2 For every three red counters there is one yellow counter and two blue counters.
- 31. Simplifying ratios Ratios can be simplified like fractions by dividing each part by the highest common factor. 21 : 35 = 3 : 5 ÷ 7 ÷ 7 For a three-part ratio all three parts must be divided by the same number. 6 : 12 : 9 = 2 : 4 : 3 ÷ 3 ÷ 3
- 32. Dividing in a given ratio A ratio is made up of parts. We can write the ratio 2 : 3 as: 2 parts : 3 parts The total number of parts is: 2 parts + 3 parts = 5 parts Divide £40 in the ratio 2 : 3. £40 ÷ 5 = £8 We need to divide £40 by the total number of parts.
- 33. Proportion There are many ways to express a proportion. We can express this proportion as: 12 out of 16 3 in every 4 3 4 0.75 or 75% Proportion compares the size of a part to the size of a whole. What proportion of these counters are red?
- 34. Direct proportion problems 3 packets of crisps weigh 90 g. How much do 6 packets weigh? 3 packets weigh 90 g. × 2 6 packets weigh × 2 180 g. If we double the number of packets then we double the weight. The number of packets and the weights are in direct proportion.
- 36. Answers: 1. 6:4 2. 16:4 3. 10:4 4. 18:6 5. 15:3 6. 16:12 7. 10:6 8. 50:20 9. 35:10 10. 50:40 11. 35:15 12. 33:44 13. 6:15 14. 16:24 15. 36:3 16. 8:8:4 17. 6:4:2 18. 25:20:5 19. 15:10:5 20. 15:9:3 21. 42:21:7 22. 56:24:16 23. 60:36:24 24. 35:28:21 25. 60:24:24 26. £80, £60 27. 6:9:12 28. 6:8:10 29. 60:150:210 30. 2.5:10:12.5
- 37. ANNALICE R. QUINAY Master Teacher 1
Editor's Notes
- #29: Talk through the points on the slide showing, with reference to the diagram, that the ratio 9 : 3 is equivalent to the ratio 3 : 1. State that this is the ratio in its simplest form. Compare this to simplifying fractions. Ask pupils what statements they can make about the number of red counters compared with the number of blue counters. For example, ‘the number of blue counters is a third of the number of red counters’ or ‘the number of red counters is three times the number of blue counters’. To distinguish between ratio and proportion you may wish to ask, What proportion of the counters are red? (three quarters) Emphasize that ratio compares the sizes of parts to each other while proportion compares the sizes of parts to the whole.
- #30: Show that ratios can compare more than two parts or quantities. Explain with reference to the diagram that 12 : 4 : 8 simplifies to 3 : 1 : 2. For every three red counters there is one yellow counter and two blue counters.
- #31: Discuss the simplification of ratios.
- #33: Discuss the various ways of expressing a proportion in words, as a fraction, as a decimal and as a percentage. Ask pupils to tell you what proportion of the counters are blue. Compare this slide to the ratio slide that shows the ratio of red counters to blue counters. Emphasize that ratio compares the sizes of parts or quantities to each other while proportion compares the size of a part to the size of the whole. Ratios can also be expressed as fractions, decimals and percentages and so pupils often confuse these two.
- #34: Establish that the number of packets of crisps and the weight of the packet are in direct proportion as long as the weight of each packet is the same. That means that if we double the number of packets, as in the example, we double the weight. If we half the number of packets, we half the weight, and so on. The number of packets and the weight of the packets are in direct proportion if the ratio of the number of packets : weight of packets is always the same.