A slippery SLOPE
Slope -- this has been mentioned a few times in our class and I just don't think I have a strong enough grasp on it and want to dive a little deeper into the subject.
From what I can find slope is par to the 8th grade curriculum which is beyond what I will teach but I think it is still important for me to get a better understanding.
These are the standards in relation to slope that I could find:
CC.8.EE.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CC.8.EE.6
Use 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; 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.
DEFINITION:
Slope is a number that describes the steepness of the line, represents the unit rate of change as it applies to the data that generates the graph
Slope is represented by "M" in equations and the equation for it is:
M=vertical change/horizontal change
This is often said as RISE (the vertical change) over RUN the horizontal change)
Dr. Moldovan once said a good way to remind kids of the order is that if you hear the fire drill you have to RISE up from your chair and then RUN, you can't really run before you get out of your chair!!
From what I can find slope is par to the 8th grade curriculum which is beyond what I will teach but I think it is still important for me to get a better understanding.
These are the standards in relation to slope that I could find:
CC.8.EE.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CC.8.EE.6
Use 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; 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.
DEFINITION:
Slope is a number that describes the steepness of the line, represents the unit rate of change as it applies to the data that generates the graph
Slope is represented by "M" in equations and the equation for it is:
M=vertical change/horizontal change
This is often said as RISE (the vertical change) over RUN the horizontal change)
Dr. Moldovan once said a good way to remind kids of the order is that if you hear the fire drill you have to RISE up from your chair and then RUN, you can't really run before you get out of your chair!!
So, thinking about this in an equation:
A few things to remember though when it comes to negatives!
UP is a positive movement
RIGHT is a positive movement
DOWN is a NEGATIVE movement
LEFT is a NEGATIVE movement
Also interesting...a line has the same slope everywhere...WHAT!?!?! Yes, that is right.
You can choose any 2 points to calculate the slope (makes sense because you can reduce a fraction and it still equals the same thing!) Also, you can check your work by just taking two other points on the same line, the slope should be the same!
I found this little worksheet to be helpful:
A few things you can keep in mind if teaching this to make it a little more fun...Running up or down a hill, skiing, bike riding. As the slope changes going up or down, does it get easier or harder? Do you go faster or slower? Asking the kids questions and having them think about steepness of slope before the lesson is a good way to get them thinking logically before getting into the equations. Even a field trip to a few hills cold be fun!
It is also fun to do a little project with beads and anything with a slope (maybe even the classroom floor??)
I have attached a quiz and the answer key. admittedly I got a lot of them wrong when I took it the first time but I am improving!
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