Proportions Math Notebook & pencil

What is a proportion?  Proportion says that two ratios (or fractions) are equal.ratios Why is 1/3 proportion to 2/6?

When something is in proportion  When things are "in proportion" then their relative sizes are the same.  Here you can see that the ratios of head length to body length are the same in both drawings.  So they are proportional.  Making the head too long or short would look bad!

Remember when working with percents?  A percent is actually a ratio! Saying "25%" is actually saying "25 per 100": 25% = 25 out of 100  We can use proportions to solve questions involving percents.  First, put what you know into this form:  Part over whole = percent out of 100

Example  Preston wants to know what 25% of 75 is.  What do we know about this problem?  Percent? ________________  Part or whole? ________________  What are we trying to figure out? Whole or Part?

Set it up  What is our equation to set up a proportion?

Example 2  Rhiannon wants to know what 34% of $45 would be?  What do we know?  What do we want to know?

Proportions ARE EVERYWHERE!  Carson has a triangle ABC, where the line segment A is 4in, line segment B is 3in and line segment C is 5 in.  Draw a triangle that is larger than triangle ABC but is in proportion to triangle ABC How would we draw a proportional triangle?

Ideas  I want you to turn your elbow partner  “What’s an elbow partner?” : The person you connect elbows with. If it’s a group of 3, just discuss together.  Question: “What could be some ways you could create a proportional triangle to triangle ABC?”

Creating a Proportional Triangle  Let’s look at some things we know about proportions We know about GCF (Greatest Common Fact). How would that work with creating a similar triangle? We know how to create fractions and ratios. How would that be beneficial for creating similar triangles? We know that our triangle has to be in proportion. What does proportion mean?

Making Similar Triangle

Constant Rate of Proportionality  Directly proportional: as one amount increases, another amount increases at the same rate.  The "constant of proportionality" is the value that relates the two amounts  Example: you are paid $20 an hour  The constant of proportionality is 20 because:  Earnings = 20 × Hours worked

How can I write this?  y = kx  Where k is the constant of proportionality  What does constant mean?

Example  y is directly proportional to x, and when x=4 then y=20. What is the constant of proportionality? They are directly proportional, so what is our formula? Y = kx Put in what we know What we know: (y=20 and x=4): 20 = k × 4

Solve:  What is K?  What times 4 gives us 20?  K =

Example Let’s try to find the rate of proportionality What do we know about this graph? I want you to list 3 things you know about this graph and chart by looking at it

What do we know? Let’s list things that we know: From what we know, how can we step up an equation to find the constant proportionality?

Setting It Up We know that “x” is the weight in pounds We know that “y” is the cost in dollars Do we know what “k” is? Equation: y = kx (pick a value for y that corresponds with x) Y = 2 when x = 6 6 = 2k What times 2 gives me 6?