Chapter 5 Ratios and Proportion

1. Chapter 5Ratios and Proportion MH101 Spring 2013 J. Menghini Class 1

2. 5.1Ratios

3. Relevant Vocabulary • Ratio • Fractional notation 1/2 • Colon notation 1:2 • Simplest form

4. Application 1 (p.323 #1-12) 2 to 3 7 to 12 5 to 91 3 to 4 ½ 789 to 1000 6.9 to 3.2 5 91 2 3 7 12 789 1000 3 4 1/2 6.9 3.2

5. Application 2 (p. 323 # 13-34) 12 to 24 9 to 81 150 to 200 1.2 to 2.4 $52 to $54 1’ to 32”

6. What is a ratio? • A ratio is a fraction with a notation other than fractional notation. • Based on parts of a whole theory. • A good relationship is each partner giving 100% • That is 200% possible • Partner 1 gives 100% (100:200) or ½ of the effort • Partner 2 gives 100% (100:200) or ½ of the effort • Together they give 200:200

7. Class Discussion 1 • Explore your thoughts…. Examples of “things” that can be measured by numbers. • Example on next slides

8. Visual Examples

9. Visual Examples

10. Visual Examples

11. Class Discussion 2 • Make a connection with a ratio • 4/7 - There are 4 boys to 7 girls in a class • Elaborate…..

12. Application 3 (p.324 #35-50) This year I have the privilege of working with 42 students. In September, 7 students were proficient on their standardized test. In April, for their most recent testing, 40 students were proficient. Find the ratio of proficient students in September to all students this year. 1 ------ 6

13. BREAK TIME: Take a 10 min break

14. 5.2Rates

15. Relevant Vocabulary • Unit rate • Per • Unit price

16. Application 1 (p.331 #1-12) 2 apples every 3 feet 5 laps in 91seconds 3” of snow in 4 ½ days 6.9 to 3 5 laps 91seconds 2 apples 3 feet 3inches 4 ½ days 6.9 miles 3 min

17. Lets turn the word RATE into easy English… Rates are used to compare different kinds of quantities. ex: *miles a runner can run in per minute *gallons of gas consumption per mile *price of an item per unit (oz, lb, item) Its time to look at fractions like division problems…

18. Fractions as division problems 3 3 72 = 1.5 = 0.75 = 8 • 4 9 = 15)345 = 345 15 miles per gallon

19. Application 2 2 apples every 3 feet 5 laps in 91seconds 3” of snow in 4 ½ days 6.9 to 3 2 apples 3 feet 5 laps 91seconds 3 inches 4 ½ days 6.9 miles 3 min

20. Real life application… If I use 15 gallons of gas to travel 345 miles, how many miles per gallon does my car use? p.331-334 #13-50 23 mpg

21. Class Discussion / Task • Develop a situation or example in which you could use rates to determine relative price or price per unit. You may connect it to you r prospective career or everyday life. • Create an equation to represent your situation.

22. B R E A K10 mins

23. 5.3Proportions

24. Proportion • A proportion is a statement that two ratios or rates are equal……. EQUIVALENT FRACTIONS!

25. How to read a proportion… 3 apples 6 oranges 12 trees 24 trees 3 apples is to 12 trees as 6 oranges is to 24 trees. =

26. Application 1 3 apples is to 12 trees as 6 oranges is to 24 trees. p. 343 # 1-10

27. True or False….. • We determine true and false proportions by determining if they are equal. • We most efficiently compare fractions by cross multiplying. • We don’t always have to cross multiply.

28. How do we cross multiply? 72 72 This is an equal proportion!

29. On your own… • Page 344 # 11-36 THEN Page 344 # 37 - 44 • Ask if you need help

30. REVIEW • What is a ratio? • a fraction with a notation other than fractional notation • What are rates used for? • to compare different kinds of quantities • What is a proportion? • a statement that two ratios or rates are equal

31. Homework Your syllabus states that for this chapter you should have a minimum of 11-13 hours of homework. • At some time in between tonight and next class, please complete “Chapter 5 PreTest-Form B” as a review and in preparation for the last lesson of Chapter 5 next class. • There will be an assessment next class. This will be turned completed next class and graded. • Watch relevant DVD lectures for Chapter 5 & Chapter 6. • Do not hesitate to email me at any time with questions or concerns, however, don’t wait until Tuesday night or Wednesday morning to email for an extra example….its a little too late then!

32. Project / Portfolio Submission It is the hope and desire of McCann School of Business & Technology as well as myself, that you gain real-life practical use of the material taught in this class. In order to be successful in your career, you need to be a reflective practitioner, meaning, always thing about what you are doing , how you are doing it and adjusting as necessary.

33. Project / Portfolio Submission With that being said, you need to think about and decide on a topic for your portfolio. I am going to want to see you use each “idea”learned/discussed in class and relate it to your real life future career in some way shape or form. The more practical and real life it is, the more impressed I will be and the higher the score you will receive.

34. Project / Portfolio Submission You already have 3 ideas that you will need to incorporate intoyour project/portfolio: Ratio, Rate, and Proportion. During this week and/or over the weekend, I need to submit to me your theoretical framework for your MH 101 portfolio project. Explain to me in your submission, how you will organize your project. How you will collect real-life data, and how you will present and submit it to me.

35. Project / Portfolio Submission This portfolio project is to be a culmination of everything learned in MH 101 and how it relates to your field of study/career. This portfolio project should be something you may potentially bring with you to future interviews to show your research and dedication to your career and the learning process that brought you there. This will account for 20% of your grade.