Wednesday, January 11, Name: Period: We will solve problems involving proportions 1.

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Wednesday, January, 07 Learning Objective Name: Period: We will solve problems involving proportions. CFU What are we going to do? We will. Vocabulary equivalent ratios Activate Prior Knowledge A ratio is a relationship between two quantities.

$Now, write your ratio in lowest terms below. Write your ratio in at least two different ways. Write a ratio (crayons & markers) Write your ratio as a fraction TO Write your ratio as using TO$

1 Wednesday, January, 07 Learning Objective Name: Period: We will solve problems involving proportions. CFU What are we going to do? We will. Vocabulary equivalent ratios Activate Prior Knowledge A ratio is a relationship between two quantities. A ratio can be written with words or numbers. Directions:. Circle ALL crayons.. Determine how many crayons you have.. Determine how many markers you have. CFU What two quantities are being compared in the problem to the left? CFU If there are 8 crayons for every 4 markers, what is the unit rate (per one marker)? There are crayons for every markers. Now, write your ratio in lowest terms below. Write your ratio in at least two different ways. Write a ratio (crayons & markers) Write your ratio as a fraction TO Write your ratio as using TO

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

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) x y ORDERED PAIRS (x,y) (# of Folds, # of Sections) Fill in your ordered pairs (, ) (, ) (, ) (, ) (, ) (, ) Plot the ordered (x,y) pairs to the right. How many points can you plot in the space provided? Connect each point in your graph. Number of Sections Formed on Paper (y) Number of Folds on Sheet of Paper (x)

Skill Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. We will determine if a graph shows a proportion.

4 Skill Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. We will determine if a graph shows a proportion. Read the problem carefully. a Identify what two quantities are being compared. Identify the given ordered pairs. What does each ordered pair tell you? b Do the ordered pairs represent equivalent ratios? CFU 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? 4 When graphed, in order to be a proportion, the graph must pass two tests:. Line Must Be Straight. Line must intersect at ORIGIN (0,0) Determine if the graph shows a proportion. 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 (,.5) represent? What does the ordered pair (6, ) represent? Are the ordered pairs (,.5) and (6, ) proportional?

Skill Development (Continued) A proportional relationship is a set of

RULES: Ratios are Equivalent Line Passes through the Origin (0,0) Line is

identify information about the given ordered pairs?

5 Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. RULES: Ratios are Equivalent Line Passes through the Origin (0,0) Line is straight and passes through all Ordered Pairs in graph CFU 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?

Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. We will determine proportions in Tables.

Determine if each monthly rate shows an equivalent ratio. CFU How did I/you determine if the ratios are equivalent? How did I/you identify whether the ratios are proportional?

6 Skill Development (Continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. We will determine proportions in Tables. Read each statement carefully. Determine quantities being compared. a Identify whether the monthly rates remains the same month to month. b Identify the unit rate and compare it to the monthly rate. Determine if each monthly rate shows an equivalent ratio. CFU How did I/you determine if the ratios are equivalent? How did I/you identify whether the ratios are proportional? The YMCA has over 0 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. Equivalent ratios? YES or NO $50 $90 $0 $40 $50 C Fitness Gym is a new and exciting Gym Coming to Redwood City in 05. As an introductory offer, they will allow new members to sign up at the following rates listed below. $5 $0 $45 $60 $75 Equivalent ratios? 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. Finding Proportions in a table. Read the problem carefully. a b 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. Equivalent ratios? YES or NO Equivalent ratios YES or NO Fill in the table below. Stage Stage Toothpicks Fill in the table below. Toothpicks

STAGE STAGE Number of Pumpkins (y) x y STAGE Create the following ratios from STAGES -

8 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 STAGE Number of Pumpkins (y) x y STAGE Create the following ratios from STAGES - above: st nd rd STAGE Number (x) Create Ordered Pairs (x,y) (Stage Number, Pumpkins) (, ) (, ) (, )

9 Guided Practice Creating Tables and Graphs from a Pattern. Patterns are observed by comparing the number of STAGES to STARS. STAGE STAGE Number of Stars (y) STAGE Create the following ratios from STAGES - above: STAGE Number (x) Create Ordered Pairs (x,y) (Stage Number, Stars) (, ) st nd (, ) (, ) rd

10 Guided Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Solve problems involving proportional relationships. Look at each pattern carefully. a Identify what quantities are being compared. b Fill in the table for each Stage. 4 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. CFU 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? Number of tiles (y) Stage (x) (, ) (, ) (, )

Skill Closure A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers.

a Identify what quantities are being compared. b Complete the table below. Write the values in the table as Ordered Pairs (x,y).

Number of Tiles (y) Stage Stage Stage Stage (x) Word Bank Proportional Relationship Summary Closure (, ) (, ) (, ) What did you

11 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. Finding Proportions using Tables and Graphs. 4 Look at each pattern carefully. a Identify what quantities are being compared. b 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.. Fill in the table. Number of Tiles (y) Stage Stage Stage Stage (x) Word Bank Proportional Relationship 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. Non-Proportional Equivalent Ratio Table / Graph

12 Independent Practice Fill in the table below. Stage Toothpicks Number of Toothpicks (y) Equivalent ratios? YES or NO Stage (x) Fill in the table below. Stage Toothpicks Number of Toothpicks (y) Fill in the table below. Equivalent ratios? YES or NO Stage (x)

A unit rate shows the relationship between a quantity and one unit of another quantity.

Learning Objective We will compute unit rates. CFU What are we going to do? What does compute mean? Compute means. Vocabular y calculate Activate Prior Knowledge A unit rate shows the relationship between