Unit 2: Proportional Reasoning

1. Unit 2: Proportional Reasoning Learning Goal #1: Reason with Ratios and Proportions The students will know how to: Express ratios in different forms – using “to”, a colon, a fraction, and decimal form. Describe similarities and differences of rates and ratios. Describe similarities and differences of rates and unit rates. Describe similarities and differences of ratios and fractions. Identify and explain the two ratios used to create a proportion for a given situation. Generate ratios pertaining to real world situations (can include percents).

2. Unit 2: Proportional Reasoning Learning Goal #2: Computing Proportions The students will know how to: Simplify ratios and rates. Compute a unit rate. Set up and solve a proportion. Use cross products to test proportionality. Solve using cross products. Use proportions to find lengths of corresponding sides of similar figures. Solve problems using scale drawings. Determine ratios, rates, unit rates, similar figures, and proportions of real world applications. Check reasonableness of solutions using estimation.

3. Agenda Assignment: Page 280 (1 – 7 odds, 13 – 29 odd, 37, 38) Due: Nothing Bellwork Title your notes “Leaning Goal 1: Ratio’s and Proportions” On the left side of cornell note line write: Vocab Terms: -Write the definitions for each term listed in your notes. - Rate - Favorable outcome - Ratio - Unfavorable outcomes - Proportion - Possible outcome - Similar/similarity - Corresponding - Cross products - Scale - Variable - Estimation - Probability - Outcome

4. Learning Goal #1: Reason with Ratios and Proportions 1.) In 3 different ways write a ratio of students with a job to students without a job. 40 to 60 = 2 to 3, 40:60 = 2:3, 40/60 = 2/3 2.) In 3 different ways, write a ratio of students without a job to all students surveyed. 60 to 100 = 3 to 5, 60:100 = 3:5, 60/100 = 3/5 3.) Fraction form and colon form, write a ratio of students with a job to all students surveyed. 40/100 = 2/5, 40:100 = 2:5 Express ratios in different forms – using “to”, a colon, a fraction, and decimal form. Ratios have to be written in SIMPLEST FORM. - Ratios can be written in 3 different formats: a to b a:b a/b Students were surveyed and asked if they had a job.

5. Write a ratio in fraction form for the # of girls on Team A to # of girls on Team B: • 75/80 • 80/75 • 15/16 • 16/15 Female Student Per Team [Default] [MC Any] [MC All]

6. Write a ratio in colon form for the # of girls on Team A to the Total number of students on Team A. • 1:2 • 1 to 2 • 75 to 150 • 75:150 Female Student Per Team [Default] [MC Any] [MC All]

7. Write a ratio in both “to” form for the # Total number of students on A to the total number of students on B. • 80 to 145 • 150 to 145 • 30 to 29 • 29 to 30 Female Student Per Team [Default] [MC Any] [MC All]

8. Unit 2: Proportional Reasoning 2. Describe similarities and differences of rates and ratios. Ratio: comparison of two quantities by division Ex. 4 to 2, 4:2, 4/2 Notice there are no units (labels) Rate: ratio that compares quantities in different units 375 miles to 15 gallons of gas 375 miles:15 gallons of gas 375 miles/15 gallons of gas Unit Rate: a rate that has a denominator of 1 25 miles to 1 gallon of gas 25 miles:1 gallon of gas 25 miles/1 gallon of gas

9. Unit 2: Proportional Reasoning 2.) Describe similarities and differences of rates and ratios. Similarities between ratios and rates: Both compare numbers Both can be written in the same 3 ways: “to”, fraction, : Differences between ratios and rates: Ratio does NOT have a unit label, Rates HAVE to have a unit label

10. Unit 2: Proportional Reasoning 3.) Describe similarities and differences of rates and unit rates. Similarities between rates and unit rates: Both compare two different quantities Both can be written as a ratio in 3 different forms Differences between rates and unit rates: Unit rate HAS a denominator of 1, a rate does not

11. Unit 2: Proportional Reasoning 4.) Describe similarities and differences of ratios and fractions. Similarities between ratios and fractions: Both are written with a numerator over a denominator Both use the fraction bar as a sign of division Both can be written in simplest form or reduced Differences between ratios and fractions: Ratio uses division to compare two quantities Fraction uses division to represent part of a whole Fraction can be written as a percent when divided

12. Write the ratio as a fraction in simplest form: 12 to 8 • 2/3 • 6/4 • 3/2 [Default] [MC Any] [MC All]

13. Write the ratio as a fraction in simplest form: 2 to 18 • 1/9 • 2/9 • 1/8 [Default] [MC Any] [MC All]

14. Write the ratio as a fraction in simplest form: 100/1000 • 10/100 • 1/100 • 1/10 [Default] [MC Any] [MC All]

15. Write each situation as a ratio in simplest form: 3 out of 12 people live in a rural area. • 3/12 • 1/4 • 1/3 [Default] [MC Any] [MC All]

16. Write each situation as a ratio in simplest form: 98 homes in 100 have a tv. • 48/50 • 49/50 • 98/100 [Default] [MC Any] [MC All]

17. Is the following a ratio, rate, or unit rate? I drove 40 miles per hour • Ratio • Rate • Unit rate [Default] [MC Any] [MC All]

18. Is the following a ratio, rate, or unit rate? Last night it snowed 8 inches in 2 hours • Ratio • Rate • Unit rate [Default] [MC Any] [MC All]

19. Is the following a ratio, rate, or unit rate? 9 out of 15 girls like math. • Ratio • Rate • Unit rate [Default] [MC Any] [MC All]

20. Write the rate as a unit rate: 20 miles in 5 hours • 20 miles/5 hours • 4/1 • 4 miles/1 hour [Default] [MC Any] [MC All]

21. Write the rate as a unit rate: a fall of 144 feet in 3 seconds • 48 feet/1 second • 144 feet/ 3 seconds • 50 feet/ 1 second [Default] [MC Any] [MC All]