Understanding Slope

I don’t know if I’ve ever mentioned this, but all 8th graders take Algebra at my school.  This often makes resource class interesting because my kiddos haven’t passed their standardized tests in past years so they have gaps – fractions, place value, decimals, 1-step equations.  My class becomes a weird balance of trying to fill in the gaps, but also trying to keep helping them with the Algebra (honestly, either side of the scale could have 100% of the year devoted to it).

Recently we’ve been working on fractions in resource.  In Algebra, they just began working on slope – finding it from a graph, from 2-points, and graphing slope-intercept form.  This week, I devoted a large chunk of time to helping them make the connection between fractions and graphing slope.

My room is a round-ish cinder block interior room.  To bring in some “natural light” part of the curved wall is made out of these really retro glass block cubes.  I LOVE using these cubes to make lessons more interactive.  We used them earlier in the year to talk about forming square roots.  This week we turned them into a coordinate plane (painter’s tape is definitely a must-have in my classroom)!

Most of my students really struggled with counting slope using the rise/run method.  I noticed they were really inaccurate with counting the squares and drawing in the “jumps” between each coordinate.  To make the graphs bigger we used the coordinate wall.  The student’s divided into two groups and we “raced” to see who could graph the slopes faster (instead of me giving them a graph and them finding the slope, I gave them the slope and they made the graph).  I told them they could place their first point wherever they wanted, but second point had to placed in such a way that the slope was shown in simplest form.  
The conversations that happened at that point were amazing.  I was astonished at how quickly they helped each other and how well they worked together (this class is not known for working well together or with others in general).  When one student tried to graph a 2/3 slope as a 3/2 slope, another student asked (didn’t tell!) him why he went up 3.  The next 2 minutes they had a really amazing conversation about how graphing slope was like graphing a coordinate but in the opposite order.  (For a coordinate you have movement in your x value, then your y value.  For a slope you have movement in your y-value then your x-value.)
We spent 2 days doing this activity.  The kiddos got really good at moving quickly and counting more accurately.
a positive two-thirds slope

an undefined slope 

a zero slope

a negative four-thirds slope

On the third day, we started working in graphing slope intercept form.  First we took time to just place points on the coordinate that represented x- and y- intercepts.  Once they had a pretty firm understanding of the y-intercept (and how it was different from the x-intercept) we started graphing in slope-intercept form.

y = mx + b
We talked about different strategies for graphing and how sometimes looking at an equation was very overwhelming.  However, once I broke down that the “b” was teh y-intercept and the “m” was teh slope, there was a bit of an “ah-ha” moment.  
Student: “Wait, Mrs. R, you mean we can just graph the slope like we’ve been graphing it, but this time the first point has to start in a special place?!”
Me: “You’ve got it!”
Student “Why didn’t our teacher say that in the first place?!”
Me: *giggles* “I’m sure they did, you just weren’t ready to hear it yet.”
From that point, they worked on “beginning with the B” and literally placed their circle B point first. Then they made their slope using the points A and C.  
y = -1x + 1
y = 2/3x
Categories: hands-on math, manipulatives, mental math, patterns, functions and algebra, and Uncategorized.


  1. I seriously LOVE my wall. It’s so great for graphing, perimeter and area, bar graphs… everything! The kiddos love that we continuously make it interactive. I really should take up stock in painter’s tape!

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