Day 2: Proportions Notes

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Presentation transcript:

Day 2: Proportions Notes Module 3: Proportional Reasoning

Review Key Vocabulary Proportional – when two quantities simplify to the same ratio. Constant – a quantity having a value that does not change or vary. Constant of Proportionality - a constant value of the ratio of two proportional quantities.

Review As stated yesterday, a proportion is two ratios/fractions equal to each other. You created equivalent fractions yesterday. A proportion allows you to create equivalent ratios using algebra. You need to be able to solve one-step equations in order to solve proportions. Solve the following equations: 1. 3x = 9 2. 12x = 60 3. 2x = 10 4. 4x = 14

Exercise: Babysitting You have been hired by your neighbors to babysit their children on Friday night. You are paid $8 per hour. Complete the table relating your pay to the number of hours you worked. Hours Worked Pay ($) 1 2 3 4 4.5 5 6 6.5

Example 2 x Number of Days y Cost 6 2 9 3 24 8 1 Determine if y is proportional to x. Justify your answer. The table below shows the relationship between cost of renting a movie to the number of days on rent. x Number of Days y Cost 6 2 9 3 24 8 1

Example 3 Determine if y is proportional to x. Justify your answer. The table below shows the relationship between the amount of candy (pounds) bought and the total cost. x Pounds y Cost 5 10 4 8 6 12 16 20

Creating Proportions When creating proportions, you can set up your proportion in several ways. The key to creating them is always match up corresponding parts or wholes. Example: In a Valentine's Day bouquet, 2 out of every 5 roses are pink. If there are 6 pink roses, how many total roses are in the bouquet?

Practice 1. Rita made 12 pairs of earrings in 2 hours. How many pairs of earrings could she make in 3 hours?

Practice 2. Perry earned $96 shoveling snow from 8 driveways. How much would Perry have earned if he had shoveled 10 driveways?

Practice 3. Marlene is planning a trip. She knows that her car gets 38 miles to the gallon on the highway. If her trip is going to be 274 miles and one gallon of gas is $2.30, how much should she expect to pay for gas?

Multi-Step with proportions 1. For every 3 boys at soccer camp, there are 2 girls. If there are 20 children at soccer camp, how many are girls?

Multi-Step with proportions 2. It takes Ryan about 8 minutes to type a 500 word document. How long will it take him to type a 12 page essay with 275 words per page?