8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
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8.EE.6Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
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Slope: Comparing Proportional Relationships (Unit Rates)
Pre-Test
Code 806783
Kobayashi vs Giant Bear
Mario's Example:
Mario even uses unit rate, constant of proportionality and our new word, slope in his adventures. Let's look at what he has to offer our journey into the world of slope. What is the slope of the line that represents the jump Mario would have to make to clear the bricks from the pipe?
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Another Example:
People Who Learn At Different Rates
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How to Determine Their Learning Rates
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What's in a Word?
As we move deeper into mathematics, we find new words to describe familiar concepts. Below you will find 3 ways to represent the same idea. As you review the examples of unit rate, constant of proportionality and slope, what do notice in all 3 concepts? Hint: What type of structures do you see?
If you noticed that all 3 use graphs, tables and equations, you would be right. We will be looking at graphs, tables, equations and points to determine the differences between them.
Practice: Finding unit rate/constant of proportionality/slope
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Code: 454178
Graphing/Comparing Proportional Relationships
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Slope Basics 101:
Types:
There are four types of slope: Positive, Negative, Zero and Undefined. Check out the video and charts to help you remember them.
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Behold Mr. Slope Man!
1.) Positive slope (eye brow above "+" eyeball. 2.) Negative slope (eye brow above "-" eyeball. 3.) Undefined slope (vertical line for the nose, "U" is for undefined at the bottom of the nose. 4.) Zero slope (horizontal line for the mouth, "o" at the ends of the mouth are zeroes. |
How many triangles can you fit on a straight line?
- an INFINITE amount Did you know that you can pick ANY 2 points on a line and create a right triangle? You can!! You can make more than one. Big ones, little ones, medium ones, gigantic ones, tiny ones.......as many as you want. No matter how many you make, they will ALWAYS reduce to the same small triangle!! Watch the video to see how. |
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