1. Directions: 1. Circle ALL crayons. 2. Determine how many crayons you have. 3. Determine how many markers you have. There are crayons for every markers. Now, write your ratio in lowest terms below. Write your ratio in at least two different ways. COMMON CORE Unit 2: Ratios and Proportional Relationships CCSS 7.RP.1 Students will find Unit Rates and determine if ratios are equivalent.. CCSS 7.RP.2 Students will determine if two quantities are proportional. 7.RP.2a Students will interpret tables and graphs. 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, diagrams, and verbal descriptions of proportional relationships. What are we going to do? We will ________________ ______________________ ______________________. CFU 1 1 equivalent ratios Vocabulary We will solve problems involving proportions 1. Learning Objective Activate Prior Knowledge A ratio is a relationship between two quantities. A ratio can be written with words or numbers. Name: ______________________ Period: ___Monday, October 19, 2015 Write a ratio (crayons & markers) What two quantities are being compared in the problem to the left? CFU 2 Write your ratio as a fraction Write your ratio as using “TO” TO 84 21 2 1 2 If there are 8 crayons for every 4 markers, what is the unit rate (per one marker)? CFU 3 1

2. Concept Development Finding Proportional Relationship In your own words, what is a proportion? CFU 1 Create two proportional statements using any of the numbers below : When creating a proportion, what mistake was made below? CFU 2 1 2 3 4 Find a Proportion

3. Concept Development We will create Ordered Pairs from an Experiment. Directions: You will receive one sheet of paper. Fold when directed by Mr. Pearson. Converting From Tables, Create Ordered Pairs, Then Graph (Coordinate Plane) ORDERED PAIRS (x,y) (# of Folds, # of Sections) Fill in your ordered pairs ( 1, ) ( 2, ) (, ) Number of Sections Formed on Paper ( y ) Plot the ordered (x,y) pairs to the right. Number of Folds on Sheet of Paper ( x ) 1 2 3 4 5 6 7 8 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 24 2 4 8163264 3 8 4 16 5 32 6 64 xyxy How many points can you plot in the space provided? Connect each point in your graph.

4. Read the problem carefully. Identify what two quantities are being compared. Identify the given ordered pairs. What does each ordered pair tell you? Do the ordered pairs represent equivalent ratios? When graphed, in order to be a proportion, the graph must pass two tests: 1. Line Must Be Straight 2. Line must intersect at ORIGIN (0,0) Determine if the graph shows a proportion. We will determine if a graph shows a proportion. 1 2 3 4 a b How did I/you identify information about the given ordered pairs? How did I/you if the ratios given are equivalent? How did I/you determine whether the graph shows a proportion? CFU 3 1 2 Skill Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Human hair grows, on average, at a rate of ½ inch per month. We can represent this information in a graph. What does the ordered pair (3, 1.5) represent?___________________________________________ What does the ordered pair (6, 3) represent?___________________________________________ Are the ordered pairs (3, 1.5) and (6, 3) proportional?___________________________________________ It takes 3 months for hair to grow 1.5 inches It takes 6 months for hair to grow 3 inches Yes, both pairs are equivalent ratios.

5. RULES: Ratios are Equivalent Line Passes through the Origin (0,0) Line is straight and passes through all Ordered Pairs in graph How did I/you identify information about the given ordered pairs? How did I/you if the ratios given are equivalent? How did I/you determine whether graphs shows a proportional relationship? CFU 3 1 2 Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers.

6. Read each statement carefully. Determine quantities being compared. Identify whether the monthly rates remains the same month to month. Identify the unit rate and compare it to the monthly rate. Determine if each monthly rate shows an equivalent ratio. We will determine proportions in Tables. 1 2 a b How did I/you determine if the ratios are equivalent? How did I/you identify whether the ratios are proportional? CFU 1 2 Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. C3 Fitness Gym is a new and exciting Gym Coming to Redwood City in 2015. As an introductory offer, they will allow new members to sign up at the following rates listed below. The YMCA has over 30 locations in the San Francisco Bay area.. There is a sale price allowing new members to try a membership for five months. New members will pay the following rates listed below. $50 $90 $120 $140 $150 $15 $30 $45 $60 $75 Equivalent ratios? YES or NO Proportional? YES or NO

7. Skill Development/Guided Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Stage Toothpicks Read the problem carefully. Identify what quantities are being compared. Fill in the values for each Stage in the table. Do the ordered pairs (x,y) in the table represent equivalent ratios? Determine if the relationship in the graph is proportional. Finding Proportions in a table. 1 2 3 a b Fill in the table below. Equivalent ratios YES or NO Proportional? YES or NO Equivalent ratios? YES or NO Proportional? YES or NO 1 2 3 1 2 3 3 5 7 3 6 9

8. Skill Development / Guided Practice We will create Tables and Graphs from a Pattern. STAGE 1 Create the following ratios from STAGES 1-3 above: Each stage continues to grow. Are the Pumpkins proportional to the stage number? Create Ordered Pairs (x,y) (, ) (Stage Number, Pumpkins) Number of Pumpkins ( y ) STAGE Number ( x ) STAGE 2 STAGE 3 1 st 2 nd 3 rd 123 369 1 3 2 63 9 xyxy

9. Guided Practice Creating Tables and Graphs from a Pattern. STAGE 1 Create the following ratios from STAGES 1-3 above: Patterns are comparing the number of STAGES to STARS (shown below) Create Ordered Pairs (x,y) (, ) (Stage Number, Stars) Number of Stars ( y ) STAGE Number ( x ) STAGE 2 STAGE 3 1 st 2 nd 3 rd 123 35 7 (, ) 1 3 2 5 3 7

10. Guided Practice Look at each pattern carefully. Identify what quantities are being compared. Fill in the table for each Stage. Write the values in the table as Ordered Pairs (x,y). Do the ordered pairs in the table represent equivalent ratios? Graph the ordered pairs, then determine if proportional. Solve problems involving proportional relationships. 1 2 3 4 a b How did you determine the values that go in the table? How do you use the values in the table to form ordered pairs? How can you tell from the table and graph whether the relationship is proportional? CFU 3 1 2 A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Stag e ( x ) Number of tiles ( y ) (, ) (, ) (, ) Proportional? YES or NO 4812 1 42 83 12

11. Stag e ( x ) Number of Tiles ( y ) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. These can be modeled in tables, graphs, etc. Proportional? YES or NO What did you learn today about solving problems involving proportional relationships? (Pair-Share) Use words / phrases from the word bank on the right. Summary Closure Word Bank Proportional Relationship Non-Proportional Equivalent Ratio Table / Graph Skill Closure Look at each pattern carefully. Identify what quantities are being compared. Complete the table below. Write the values in the table as Ordered Pairs (x,y). Graph the ordered pairs on the Coordinate Plane. Determine if proportional. Finding Proportions using Tables and Graphs. 1 2 3 4 a b Stag e 1 Stag e 2 (, ) (, ) (, ) Stag e 3 1. Fill in the table. 81216 1 82 12 3 16

12. Independent Practice Fill in the table below. Equivalent ratios? YES or NO Proportional? YES or NO Stage Toothpicks Fill in the table below. Number of Toothpicks ( y ) Stage ( x ) Number of Toothpicks ( y ) Stage Toothpicks Fill in the table below. Equivalent ratios? YES or NO Proportional? YES or NO 123123 5 10 15 123123 5 9 13

13. Tabl es ( x ) Number of chairs ( y ) SCENERIO (Restaurant A): A restaurant uses square tables. The tables can be pushed together in a row to seat large groups of people. The figure below shows the number of chairs (circles) that are needed for various numbers of tables (squares). Number of Tables (x) Number of Chairs (y) Independent Practice (Extension) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did you determine the values that go in the table? How do you use the values in the table to form ordered pairs? How can you tell from the table and graph whether the relationship is proportional? CFU 3 1 2 Look at each pattern carefully. Identify what quantities are being compared. Fill in the table for each Stage. Write the values in the table as Ordered Pairs (x,y). Do the ordered pairs in the table represent equivalent ratios? Hint: Multiply or divide by the same value. Graph the ordered pairs on the right, then interpret the graph. Solve problems involving proportional relationships. 1 2 3 4 a b Proportional? YES or NO

14. Tabl es ( x ) Number of chairs ( y ) SCENERIO (Restaurant B): A restaurant uses square tables. The tables can be pushed together in a row to seat large groups of people. The figure below shows the number of chairs (circles) that are needed for various numbers of tables (squares). Number of Tables (x) Number of Chairs (y) Independent Practice (Extension) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did you determine the values that go in the table? How do you use the values in the table to form ordered pairs? How can you tell from the table and graph whether the relationship is proportional? CFU 3 1 2 Look at each pattern carefully. Identify what quantities are being compared. Fill in the table for each Stage. Write the values in the table as Ordered Pairs (x,y). Do the ordered pairs in the table represent equivalent ratios? Hint: Multiply or divide by the same value. Graph the ordered pairs on the right, then interpret the graph. Solve problems involving proportional relationships. 1 2 3 4 a b Proportional? YES or NO

15. CLASSWORK 10.17.14 Look at each pattern carefully. Identify what quantities are being compared. Fill in the table for each Stage. Write the values in the table as Ordered Pairs (x,y). Do the ordered pairs in the table represent equivalent ratios? Graph the ordered pairs, then determine if proportional. Solve problems involving proportional relationships. 1 2 3 4 a b How did you determine the values that go in the table? How do you use the values in the table to form ordered pairs? How can you tell from the table and graph whether the relationship is proportional? CFU 3 1 2 A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Stag e ( x ) Number of tiles ( y ) (, ) (, ) (, ) Proportional? YES or NO

16. Review (Classwork) Fill in the missing values for each proportional relationship. 36918 4121628 1. 246814 52025 2. 142135 816404856 3. Determine how much the elevator moves in the specified time. Set up a proportion, then solve. Determine if the tables below represent a proportional relationship. The elevator travels up 5 stories every 6 seconds. How many floors does it rise in 24 seconds total? Number of Stories Time (seconds) Proportional? YES or NO Proportional? YES or NO Proportional? YES or NO Proportional? YES or NO The chart to the left shows prices paid for different quantities of Tickets. What is the unit rate (cost per Ticket)? Answer: ___________________________ Explain how you found the unit rate:__________________________________