1

Chapter 5Ratios and Proportion

MH101Spring 2013J. MenghiniClass 1

2

5.1

Ratios

3

Relevant Vocabulary

•Ratio

•Fractional notation1/2

•Colon notation1:2

•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 3.2 789

1000

7 12

5 91

3 4 1/2

2 3

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

5.2

Rates

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

3inches

4 ½ days

2 apples

3 feet

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 2 4 9

= 15)345 =

345 15

miles

gallon

per

Application 2

2 apples every 3 feet 5 laps in 91seconds

3” of snow in 4 ½ days 6.9 to 3

19

5 laps

91seconds

3 inches

4 ½ days

2 apples

3 feet

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

1. 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.

2. Create an equation to represent your situation.

22

B R E A K

10 mins

23

5.3

Proportions

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?

7272

This is an equal proportion!

29

On your own…

•Page 344 # 11-36THEN

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

HomeworkYour 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 into your 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.