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Ratios Continued

This guide explores the concept of ratios, focusing on comparing quantities, finding equivalent ratios, and converting them into percentages. For example, the ratio of buttons to paper clips is analyzed in multiple ways, demonstrating how equivalent ratios work. You'll learn how to derive percentages from fractions and vice versa. Engage in collaborative activities like a game of "I Spy" with ratios to reinforce your understanding of the topic. Finally, a transition into independent learning with ST.Math's unit on ratios will enhance your skills.

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Ratios Continued

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  1. Ratios Continued

  2. What is the ratio of buttons to paper clips? • This means that there are 6 buttons and 4 paper clips. • But is there another way to compare the numbers of buttons and paper clips?

  3. By dividing the objects into two equal groups, we see that every time there are 3 buttons, there are 2 paper clips. • Therefore, another way to write the ratio of buttons to paper clips would be

  4. What if we doubled the amount of each object? • Now there are 12 buttons and 8 paper clips. Would the ratio be equivalent to the ratio ?

  5. Yes, whenever there are 6 buttons there are 4 paper clips. So is equivalent to

  6. We have shown that , , and are all equivalent ratios. • What do they have in common?

  7. Just like with fractions, we are allowed to multiply or divide both parts by the same number. • How can ratios be changed? • There are 18 bats and 15 frogs. What is the ratio of bats to frogs?

  8. There are 10 bottles and 5 cans. Write the ratio of cans to bottles in 3 different ways. (Don’t write the same ratio in 3 forms, write different ratios with different numbers)

  9. Out of 100. • Find an equivalent fraction with a denominator of 100. The numerator will be the percent. • What does percent mean? • What is 87% as a fraction? • How can we easily turn some fractions into percents?

  10. 56% • Convert into percent

  11. 42% • 30% • 60% • Convert into percent • Convert into percent • Convert into percent

  12. Direct Station • We will do ratio and percent word problems.

  13. Collaborative Station • We will be playing a ratio version of I Spy. • There will be a picture with many different objects in it. • Partner A picks two objects and says their ratio. “I spy two objects with a ratio of 2 to 1.” • Partner B (and C) try to guess what two objects Partner A was thinking of. • Once the objects are correctly guessed, write down the ratio on your work paper and have the next person pick two objects.

  14. Collaborative Station Example • Partner A: “I spy two objects with a ratio of 3 to 1.” • Partner B: “Is it the ratio of candles to snowmen?” • Partner A: “No, even though that ratio is also 3 to 1, I was thinking of different objects.” • Partner B: “Is it the ratio of gingerbread men to snowmen?” • Partner A: “Yes!” • Everyone writes down “The ratio of gingerbread men to snowmen is 3 to 1.” on their papers. • Now it’s Partner B’s turn to pick.

  15. Independent Station • We will now switch to ST Math’s unit on Ratios

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