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Thursday, October 16, 2014 Name: ______________________ Period: ___ Learning Objective We will solve problems involving proportions1 . What are we going to do? We will ________________ ______________________ ______________________. CFU 1 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. 1 equivalent ratios Vocabulary What two quantities are being compared in the problem to the left? CFU 2 Activate Prior Knowledge A ratio is a relationship between two quantities. • A ratio can be written with words or numbers. If there are 8 crayons for every 4 markers, what is the unit rate (per one marker)? CFU 3 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. 8 4 8 8 4 8 4 4 TO Write a ratio (crayons & markers) Write your ratio as using “TO” Write your ratio as a fraction

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**1 2 3 4 Find a Proportion Finding Proportional Relationship**

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

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**Connect each point in your graph.**

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) x y Number Folds 1 2 3 4 5 6 Number of Sections 2 4 8 16 32 64 ORDERED PAIRS (x,y) (# of Folds, # of Sections) Fill in your ordered pairs ( 1, ) ( 2, ) ( , ) ( , ) 20 19 18 17 16 15 14 Plot the ordered (x,y) pairs to the right. 2 4 13 12 11 10 9 8 7 6 3 8 How many points can you plot in the space provided? Number of Sections Formed on Paper (y) 4 16 5 32 5 4 3 2 1 6 64 Connect each point in your graph. Number of Folds on Sheet of Paper (x)

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Skill Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. 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 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 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 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 ra It takes 6 months for hair to grow 3 inches Yes, both pairs are equivalent ratios.

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**Proportion? Yes or No Proportion? Yes or No**

Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. 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 RULES: Ratios are Equivalent Line Passes through the Origin (0,0) Line is straight and passes through all Ordered Pairs in graph Proportion? Yes or No Proportion? Yes or No

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**Equivalent ratios? YES or NO Proportional? YES or NO**

Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. How did I/you determine if the ratios are equivalent? How did I/you identify whether the ratios are proportional? CFU 1 2 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 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. $ $ $ $ $150 Equivalent ratios? YES or NO Proportional? YES or NO C3 Fitness Gym is a new and exciting Gym Coming to Redwood City in As an introductory offer, they will allow new members to sign up at the following rates listed below. $ $ $ $ $75 Equivalent ratios? YES or NO Proportional? YES or NO

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**1 3 2 5 3 7 1 3 2 6 3 9 Fill in the table below. Stage Toothpicks**

Skill Development/Guided Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. 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. Stage Toothpicks 1 3 2 5 3 7 Equivalent ratios? YES or NO Proportional? YES or NO Fill in the table below. Stage Toothpicks 1 3 2 6 3 9 Equivalent ratios YES or NO Proportional? YES or NO

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**Create the following ratios from**

Skill Development / Guided Practice We will create Tables and Graphs from a Pattern. Each stage continues to grow. Are the Pumpkins proportional to the stage number? STAGE 1 Number of Pumpkins (y) STAGE 2 STAGE 3 Create the following ratios from STAGES 1-3 above: STAGE Number (x) 1 2 3 x y Create Ordered Pairs (x,y) STAGE Number Pumpkins 3 6 9 (Stage Number, Pumpkins) ( , ) 1 3 ( , ) 2 6 ( , ) 3 9 1st nd rd

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**Create the following ratios from**

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

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**4 8 12 1 4 2 8 3 12 Number of tiles (y) Stage (x) ( , ) ( , ) ( , )**

Guided Practice 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? Graph the ordered pairs, then determine if proportional. Solve problems involving proportional relationships. 1 2 3 4 a b Number of tiles (y) 4 8 12 Stage (x) 1 4 2 8 3 12 ( , ) ( , ) ( , ) Proportional? YES or NO

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**Proportional Relationship**

Skill Closure 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. 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 Number of Tiles (y) 1. Fill in the table. 8 12 16 Stage (x) Stage 1 Stage 2 Word Bank Proportional Relationship Non-Proportional Equivalent Ratio Table / Graph Stage 3 ( , ) ( , ) ( , ) 1 8 2 12 3 16 Proportional? YES or NO Summary Closure What did you learn today about solving problems involving proportional relationships? (Pair-Share) Use words / phrases from the word bank on the right.

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**1 2 3 5 10 15 1 2 3 5 9 13 Fill in the table below. Stage Toothpicks**

Independent Practice Fill in the table below. Stage Toothpicks 1 2 3 5 10 15 Number of Toothpicks (y) Equivalent ratios? YES or NO Proportional? YES or NO Stage (x) Fill in the table below. Stage Toothpicks 1 2 3 5 9 13 Fill in the table below. Number of Toothpicks (y) Equivalent ratios? YES or NO Proportional? YES or NO Stage (x)

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