# Lesson: Understanding Ratios

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### Lesson Objective

We will be able to write fractions as ratios in simplest form. We will be able to determine equivalent ratios.

### Lesson Plan

Do Now: (5 minutes)

1) Mr. Crane’s farm was 45 acres. He fenced â…– of the acres for his cows, then rented â…“ of the remaining acreage to his neighbor. What fractional part of the farm did he rent to his neighbor?

2) Compare: 3/25 to 7/30

3) Solve and graph:
|2x + 5 | > 9

Direct Instruction: (20 minutes)

As you start to think about high schools that you would like to go to, one of the things that you will hear about is the student/teacher ratio at the school. Who knows that the student/teacher ratio tells us? For example, one school may have a student/teacher ratio of 400:50. What does this mean? KEY Academy has a student/teacher ratio of approximately 320:30. Where do these numbers come from? How can we use this ratio to help us learn about the school? Is there another way to write this ratio? Why would an equivalent ratio to this one be more useful?

Ex. What is the student to teacher ratio at KEY Academy if there are 320 students and 30 teachers?

Ratios that express the same relationship between two quantities are equivalent ratios.

Review the three ways to write a ratio.
Ex. Are 250 miles in 4 hours and 500 miles in 8 hours equivalent ratios?
How can we determine if ratios are equivalent?

Equivalent ratios:
-          Are compared like fractions- use cross multiplication
-          The same units are in the denominators and numerators

Guided Practice: (10 minutes)
Ex. Derek Jeter of the New York Yankees had 32 hits out of 93 times at bat. Jorge Posada had 11 hits out of 31 times at bat. Are these ratios equivalent? Justify your answer.

Ex. A community pool requires there to be at least 3 lifeguards for every 20 swimmers.  There are 60 swimmers and 90 lifeguards.  Is this the correct number of lifeguards based on the requirements above? Justify your answer.

Ex. Determine if the two ratios are equivalent:
12 out of 20 doctors agree
10 out of 6 doctors agree

Assessment: (10 minutes)
Ratios work-out

### Lesson Resources

 ratios and rates work out   Assessment 2,578