1. How can you represent a relationship between two quantities?
Ratios – Day 1
How can you represent a relationship between two quantities?

2. Introduction

3. Activity 3

4. Activity 4

5. Free Throw Comparison Shots Made Shots Missed Total Number 21 35
Complete the chart and then complete the following statements.
- There were ______ shots made to ________ total number of shots.
There were ______ shots missed to _______ total number of shots.
There were ______ shots made to _______ shots missed.

6. You just wrote several ratios!
Ratio – Comparison of two quantities.
They can be part – to - part, part – to – whole, or whole – to – part.
Ratios can be written three ways and must be in simplest form.
Example
Ratio of orange to blue
Ratio of orange to all crayons
Ratio of all crayons to blue

7. Ratios with Money Write the following rations. Quarters to pennies
- Dimes to quarters
-Dimes to total number of coins
Quarters to total number of coins

8. Extension Activity
In the continental United States, the ratio of states that border the ocean to those that do not border an ocean is 7 : 9. How many of the states border an ocean?

9. Summary of Ratios - Put at the end of yesterday’s notes

10. How can you use rates to describe changes in real-life problems?

11. Complete Activities 1 and 2

12. Activity 2

13. Key Terms Rate – a ratio of two quantities using different units
Unit Rate - compares a quantity to one unit of another quantity
Common unit rates are miles per gallon, miles per hour, words per minute, $ per pound
Equivalent rates – rates that are the same

14. Unit Rates – rate for one unit
To find a unit rate, divide the first quantity by the second quantity.
a units : b units = a b

15. Find the unit rate $24 saved in 4 weeks 270 miles in 6 hours
880 calories in 8 servings
$12.50 for 5 ounces

16. Equivalent Rates How can you determine if two rates are equivalent?
See if the unit rates are the same.
24 laps in 6 minutes
72 laps in 18 minutes

17. Which bag of dog food is the better buy?
A 20 pound bag for $17.20 or a 30 pound bag for $ Work in groups for a few minutes to see if you can determine which bag is the better deal.

18. Independent Practice

19. Summary of Rates in your notes
Remember to answer the essential question.
How can you use rates to describe changes in real-life problems?

20. How can you find two ratios that describe the same relationship?
Ratio tables
How can you find two ratios that describe the same relationship?

21. Equivalent Ratios and Ratio Tables
Equivalent Ratios – Two ratios that describe the same relationship.
Equivalent ratios can be found by
adding and subtracting quantities in equivalent ratios
multiplying or dividing each quantity in the ratio by the same number.

22. 3 8 6 36
Hint: I find multiplying the easiest way to complete the ratio table. Think of it like finding equivalent fractions.

23. water 4 20
sugar 1

24. Practice with Ratio tables

25. Ratio tables

26. 19 and 20 answers
Basketball 7 28
Soccer 6 24
Pop 5 40
Rock 4 32

27. Using a ratio table
You mix 3 pints of yellow paint for every 4 pints of blue paint to make green paint. You use 12 pints of blue paint. How much green paint do you make?
yellow 3
blue 4 12
green

28. Summary – Put at the end of your notes
How can you find two ratios that describe the same relationship?

29. Using Ratio Tables to Solve Proportions
How can you complete ratio tables when there isn’t a pattern?

30. Activity
Work in groups to see if you can complete the two ratio tables.

31. How do you solve Proportions?
Ratio tables are actually proportions, two equivalent ratios.
Try solving by cross multiplying.
25 x 16 = 100 x ?
400 = 100 x ?
400 = 100 x 4 25
100 16 4 2 3
4.5 3
2 x 4.5 = 3 x ?
9 = 3 x 3

32. Practice with Proportions
= 7 𝑥
= 𝑥 35
2 10 = 𝑥 35

33. Word Problem with Proportions
6 girls
How many girls are in the group that has 12 boys?
8 girls

34. Practice With Proportions
8 9 = 40 𝑚
Answer your essential question. How you can you complete ratio tables or proportions when there isn’t a known pattern?