The alphabet provides plenty of practice in regards to slope. Printed letters can be created using lines – for example, an ‘A’ is just a positive, negative and zero slope line. Or ‘N’ is composed of two undefined slope lines and a negative slope line. A ‘C’ on the other hand would simply be made of a “non-linear” line. This is a great activity for students who need extra practice with the basics: positive, negative, undefined and zero slopes.
Below are the links for two handouts:
This handout is for students to simply identify the lines of letters as positive, negative, zero, undefined or non-linear.
This handout is where letters are described in slope and students decipher the message. This one could be done better, a la funsheets style, but I haven’t figured out how to attach documents to this blog that can actually open.
Just have your technology specialist download PYTHON on the students computers. Even if your students are not familiar with code (which is typically the case), they really only need to “copy” a few lines of code, changing only the parameters that indicate slope and intervals. Even so, students will love the results and this introduction to computer languages.
Here’s a slide show with example projects and directions. The project itself really won’t take two solid weeks, this teacher is integrating slope “lessons” with the actual project. In my experience, students need way more than two weeks on this subject anyways!
Here is a Webquest project set where students can choose from 3 different topics:
Buying a cell phone
NBA or WNBA Statistics
Students will gather data, write an equation and graph using EXCEL. Handouts and rubrics are included.
If there’s one thing I’ve figured out about teaching the basics of slope, it’s that there’s not one single method that will reach every single student. (This is true of any topic). However, it is still possible to reach every student since different methods work for different students. Here’s a few slope memory tricks that I’ve used when remediating students, if they just don’t get it after being shown the traditional ways:
Mr. Slope Guy
This was actually the favorite method of my below-level high school students. On every assessment relating to linear equations, the first thing most students did was sketch this on the top page as a guide. This isn’t my creation, but I can’t remember where and when I came across this to give the proper credit.
Since we write from left to write, people inherently will write the word “slope” from left to write, and this gives students a visual. Without moving the paper around, write the word “slope” on the line and if you find yourself writing upwards, it’s positive. Writing down is negative. Straight across is zero. And since there’s not really a place to write the word “slope” on a vertical line (without moving the paper), that’s undefined.
This only works for distinguishing positive from negative slopes, but simply tracing the line with a fingertip from left to right lets students physically feel the direction of the line as to whether it’s going up or down. I prefer that students write the word “slope” as mentioned above since writing is inherently left to right and tracing is not, but some students prefer this method.
One test asked “what is the slope of a horizontal line,” and a student told me that she couldn’t decide whether to write zero or undefined until she remembered that I had told them horiZontal has “z” for zero. Whatever works…
For the classroom
Given a point and slope, graph the line. Simple, clean graphing program good for student work on the board.
Recognizing Slope and Y-Intercept
Identify slope and y-intercept from an equation. All in slope-intercept form. Good for a mini checkpoint quiz.
Move the points around to see how the slope and graph of a line is affected. Mr. Kibbe’s Slope Demo
Slope and y-intercept Investigations
See how slope and y-intercept affect the graph of a line. Mr. Kibbe’s Slope and y-intercept demo.
Writing slope-intercept Equations
Kind of like Line Gems (for students), in that students write the equations that will go through the most points, but I like the cleaner look and feel of this one: Mr. Kibbe’s Slope Game.
Writing slope-intercept equations
Write the equation of the line that will go through the most gems.
Writing slope-intercept equations
Algebra vs. the Cockroach
Write the equation of the line that will exterminate the roaches.
I recently made a slope worksheet where I drew figures on a coordinate plane, and students had to state the slope of each of the sides of the figures. Then it occurred to me that this would make a really great slope project.
Students could create their own line design on a coordinate plane, and label the slopes of the lines they used. It doesn’t sound neat when stated like that, but here’s an example of what a final product might look like. (I only wrote the slope for six segments, but you get the idea).
Stained glass and linear equations (or inequalities) are fairly common, but I think keeping it just as slope might be better. Students don’t have to have lines running all across the coordinate plane since they only have state the slope for smaller line segments.
To ensure students don’t just draw a few squares, students should be given a list of criteria. For example, direct students that their design must include 6 negative sloped lines, 6 positive, 4 zero slope and 4 undefined slope lines. Or 5 pairs of parallel and 5 pairs of perpendicular lines, or some similar variation. That way students have to use different sloped lines in their designs, and it also gives them a finite number of segments they have to write the slope for. This way, they’re not penalized if they produce more complex designs.
There are a few standard linear equations which are often used to determine a person’s height if, for example, a human femur bone was found. Here’s an idea for a linear equation class activity or project about the relationship between the length of bones and a person’s height:
Information from bones (MALE)
h = 2.24F + 69.09
h = 2.39T + 81.68
h = 2.97H + 73.57
h = 3.65R + 80.41
Information from bones (FEMALE)
h = 2.23F + 61.41
h = 2.53T + 72.57
h = 3.14H + 64.98
h = 3.88R + 73.51
All measurements are in cm.
h = height
T = tibia (ankle to knee)
F = femur (thigh)
H = humerus (shoulder to elbow)
R = radius (forearm, elbow to base of thumb)
Instead of simply giving students the linear equations with numbers to plug in, I think a better idea is to have students measure the length of their own bones (and height), in centimeters. Collect the data sets (separating girls from boys) and see if they can come up with the linear equations themselves. I suppose this would be just another linear regression activity.
To turn it into a project, students can collect data from maybe 6-10 males and 6-10 females (siblings, parents, classmates, etc) and do this activity at home. This would probably be more interesting since students will all be working with different data sets. Students could then present their information on a poster, divided into four sections (one for each type of bone and linear equation).