Lesson 2: Illustrating Ratio and ProportionElicit

1. Express the following as ratios: (a) , (b) 2/5, (c) 5/62. In the following ratios, how many times is one value as large as the other?(a) 4 : 8 (b) 12 : 6 (c) 3 : 8

Reflect: How did you express fractions as ratios?Engage

Alfies marblesJacks marbles

What is the ratio of the number of white to the number of black marbles of Alfie? What about Jackie, what is the ratio of the number of white marbles to the number of black marbles?Are the ratios equal?

Reflect: What do you want to know about ratio and proportion?Explore

Look at the two fraction bars at the right. What fractions do their shaded parts show?Are the two fractions equal? How do we show that the two fractions are equal?

How do we express the fractions above in ratios? Are the two ratios equal? How do we express that two ratio are equal? and We use equal symbol or = also to show that two ratios are equal. The two equal ratios below show a proportion.

What ratio represents the number of circles and the number of diamonds in the first figure? How about in the second figure? Are the two ratios equal? How do we express two equal ratios?

One of the many uses of proportion is in baking or cooking a recipe. The table shows ratios of the amount of ingredients in a recipe.

What are the two quantities being compared? What happens to the ingredients as the number of serving increases? Is the number of eggs proportional to the number of cups of flour?

Explain

Below are the ideas you should have learned in this lesson. Can you explain each one of them with one of your classmates? Check those you understood well and cross out those where you need further explanation.1. A proportion is the equality of two ratios. When two ratios are equal, they are said to be proportional. 2. If two ratios are proportional, the number of times one value is as large as another is the same for the two ratios. For example, 3 : 6 = 12 : 24. In the first ratio, 6 is 2 times as large as 3 and in the second ratio, 24 is also 2 times as large as 12.3.

If the ratios are expressed as fractions, we can use the equal (=) symbol to indicate the proportion. For example, is a statement of proportion. We say that is proportional to 4/8. Recall that in the past lesson, we can check that two fractions are equal by getting the cross-products, that is, since 1 x 8 = 2 x 4, therefore the fractions are equal and the statement is proportional.4. If the ratios are expressed using the colon symbol (:), it is more appropriate to use the double colon (::) instead of the equal symbol. For example, can be also written as 1:2 :: 4:8. We read this as one is to two as to four is to eight. However, it is still correct to write the proportion as 1:2 = 4:8 which can be read as one is to two equal 4:8. These three representations of a proportion are all correct.5. We can represent a proportion with a figure. Using triangles and squares, we can draw the figure corresponding to the proportion 1:2 :: 2:4, as follows:

Elaborate

Answer the following.In your own words, explain what a proportion is.1. Given the ratio 2:3, find other ratios that form a proportion with it. Write the proportion in three different ways using symbols. Express the proportion in words.2. Why is the statement 3:5 :: 6:9 NOT a proportion. Change one element (or one of the numbers to make the proportion correct.3. Explain the statement: The amount of harvest in a mango farm is proportional to the number of mango trees.4. Give real-life example of a proportion. Evaluate

A. Do the following.1. Identify the ratio/s is/are NOT equal to 3:4?a. 15:20b. 6:8c. 12:18d. 18:24e. 30:402. Show whether or not the following is a proportion:a. 2:3 :: 4:6b. 2:7 = 6:21c. 5:9 :: 18:10d. 7:5 :: 21:153. Find three ratios that are proportional to 2:5.B. Answer the following. Explain your answers.1. How do we test whether two ratios are proportional?2. Why is 2:3 not proportional to 3:4?3. If two ratios are proportional to a third ratio, are the two ratios proportional? Give example.4. Michelle and her sister Khrizna sells avocados and santol. In the basket of Michelle, there are 3 avocados and 7 santols. In Khriznas basket, there are 12 avocados and 28 santols. Draw a figure to represent the situation. Are the numbers of avocado and santol in the baskets proportional? C. Sketch a figure that models the following proportion1. 4:5 = 8:102. 6:8 = 3:43. 1: 1 = 2:2D. Follow the directions to make a proportional size of the picture below. 1. Construct a 10 by 10 grid on a piece of paper whose interval is thrice as large as that of the grid of the picture. 2. Copy the picture of our national hero on the larger grid.a. Who is in the picture?b. Is the picture you drew proportional in size to that of the picture in the book? Explain or show proofs.Pause & Reflect

Are you happy with the result of your evaluation? Why?

What concepts are clear to you?

What concepts are still not clear to you?

What is the most desirable value or attitude that you have developed in this lesson?

Extend

Study the table on the right which shows the amount of gasoline for every kilometer distance traveled by a brand new car on break-in.a. What is the ratio of the amount of gasoline to the distance traveled? b. Is the distance traveled proportional to the amount of gas used? Why? Illustrate with examples by setting sets of proportion.

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