Introduction to Ratios and Proportional Relationships

1. 11.07.2017 Agenda Ticket in the Door X+1+4≤9 5k-2k>-9 • Ticket in the door • Ticket in the door review • Current lesson: Introduction to unit 3 Ratios and proportional relationships, Cornell notes on unit 2 Vocabulary . • Wrap up

2. Unit 3 Ratios and Proportional Relationships

3. Standards MCC7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½mile in each ¼ hour, compute the unit rate as the complex fraction (½ · ¼ ) miles per hour, equivalently 2 miles per hour.

4. Standards 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. MGSE7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.Show details MGSE7.RP.2. Recognize and represent proportional relationships between quantities. MGSE7.RP.2a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

5. Standards MGSE7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. MGSE7.RP.2c. Represent proportional relationships by equations.Show details MGSE7.RP.2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. MGSE7.RP.3. Use proportional relationships to solve multistep ratio and percent problems

6. Essential Questions What information do I get when I compare two numbers using a ratio? What kinds of problems can I solve by using ratios? How do I compute unit rate in tables, graphs, equations and diagrams? How do I compute unit rate in real-world problems? How do I use ratios and their relationships to solve real world problems? How do I recognize and represent proportional relationships between quantities?

7. Essential Questions How do I solve multistep ratio and percent problems using proportional relationships? How do I represent proportional relationships by equations? How do I solve problems involving scale drawings of geometric figures? How do I compute actual lengths and areas from a scale drawing? How do I reproduce a scale drawing at a different scale?

8. Vocabulary Fraction: A number expressed in the form a/b where a is a whole number and b is a positive whole number. Multiplicative inverse: Two numbers whose product = 1. Percent rate of change: A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by (5/50) = 10% per year.

9. Vocabulary Ratio: A comparison of two numbers using division. The ratio of a to b (where b ≠ 0) can be written as a to b, as a/b , or as a:b. Proportion: An equation stating that two ratios are equivalent. Scale factor: A ratio between two sets of measurements.

10. Vocabulary Rate of Change:

11. Vocabulary Similar Figures:

12. Vocabulary Equivalent Fractions

13. A number expressed in the form a/b where a is a whole number and b is a positive whole number.

14. Fraction

15. Two numbers whose product = 1.

16. Multiplicative inverse

17. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by (5/50) = 10% per year.

18. Percent rate of change

19. A comparison of two numbers using division. The ratio of a to b (where b ≠ 0) can be written as a to b, as a/b , or as a:b. Blue to Red

20. Ratio

21. An equation stating that two ratios are equivalent.

22. Proportion

23. A ratio between two sets of measurements.

24. Scale factor