Mathematical+Reflections,+p.+36

February 27, 2009 LH Comparing and Scaling Big Idea Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them. Investigation 3: Comparing by Using Ratios Essential Question: What methods are there for comparing things?

1. Explain How to form a ratio and how ratios can be used to compare two numbers. Use examples to help explain your thinking.

To form a ratio and compare two, first you would need the data. Maybe there were 5 swimmers and 2 runners in a class. Then the ratio would be 5swimmers:2runners or 5 swimmers to 2 runners.

2. What strategy can you use to compare two ratios? Your strategy should allow you tell whether the two ratios are the same or different. Make a problem that can be solved with your strategy.

Then if you want to compare two ratios there are many ways. I’ll share two. One way is to turn the fractions into decimals. 5:7 = 0.71 < 7:10 = 0.7. Another way would be the LCM method.

3. The percent of orange concentrate in a juice mix is 60%. What is the ratio of concentrate to water in the mix?

6 concentrate: 4 juice 100-60= 40 ÷ 100 = 0.4 = 4 water: 10 cups, 6concentrate: 10cups 4. The ratio of concentrate to water in a juice mix is 3 to 5. What percent of the mix is concentrate?

40% of the mix is concentrate, because 3÷5 =0.6, so its 60% water which means the other 40% is concentrate. Summary

In this investigation, we focused mainly on ratios. We learned how to form them and how they can be used to compare two quantities.