Intro to Proportions

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Intro to Proportions:

Intro to Proportions By: Marla Nevarez

Students will be able to…:

Students will be able to… Define, identify, and simplify proportions Learn how to cross multiply to solve proportions Use real-world scenarios to understand the importance of proportions

What is a Proportion?:

What is a Proportion? Based on the image, what do you think proportions are? Think about the numbers and how they are placed in the equation. What are they trying to say? Does it matter what order they are placed in?

Vocabulary Words:

Vocabulary Words Proportion: An equation stating that two ratios are equal Ratios: A comparison of two quantities Scale: The ratio of the size of a figure on a drawing to the actual size of the figure Rate: A ratio in which to units of measure are compared Unit Rate: The price for one unit of measure

Ratios:

Ratios A ratio compares two things: let’s compare the number of boys and girls in the class There are 12 boys and 15 girls There are 3 ways to show a ratio or 12:15 or 12 to 15 Remember to always write your answer in simplest form !!! ÷ 3 =  

Classroom Ratio:

Classroom Ratio Part-to- Part We already know that we have Part 1: # of boys Part 2: # of girls   Part-to- Whole What if we wanted to know how many boys there are in the entire class? Girls? or  

Unit Rates:

Unit Rates We can also compare two things to find the price of one Pam bought 6 boxes of pizza for $42 or This means that she bought each box of pizza for $7 When you reach the denominator of one, you found the unit rate . Discussion: How can we use unit rates to find the price of multiple items? What method should you use?  

Cross Multiply:

Cross Multiply When we want two compare to unknown things and we have one missing value, we can use the method of cross multiplying . Example: Jennie and Ray are both selling tickets for the Talent Show. For every two tickets that Jennie sold, Ray sold four tickets. If Jennie sold 30, how many tickets did Ray sell? = 2x = 120 x = 60 tickets; Ray sold 30 tickets.  

A Baker’s Dozen (Adapted by Meredith Beaton, https://www.ck12.org/algebra/dimensional-analysis/rwa/A-Bakers-Dozen/?referrer=concept_details ):

A Baker’s Dozen (Adapted by Meredith Beaton, https://www.ck12.org/algebra/dimensional-analysis/rwa/A-Bakers-Dozen/?referrer=concept_details ) To the right, is the recipe to make one dozen cookies, but the goal is to make 3 dozen cookies. Before we get started: How do you think we should go about making 3 dozen cookies? How can we convert these units using unit ratios?

How does it relate?:

How does it relate? By converting units, it makes it easier for a baker to quickly add the ingredients into the bowl. Create proportions to demonstrate how to convert the recipe for one dozen cookies to three. Think about how can you apply unit conversions in your daily life other than cooking/baking.

Video Recap:

Video Recap What two methods were used to find how many bananas were needed at the end? What strategy would you have used in order to ensure that you would have had enough for every chimp?

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