Alphabet Slope

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.

Python Anyone???

If you are daring, try incorporating Computer Programming and Art with slope and linear equations! Don’t be fooled, it’s actually very easy and straightforward and the students will love it.

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!

Linear Equations – Webquest Project

Here is a Webquest project set where students can choose from 3 different topics:

Burning Calories
Buying a cell phone
NBA or WNBA Statistics

Students will gather data, write an equation and graph using EXCEL. Handouts and rubrics are included.

Teaching Slope

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.

Writing “slope”
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…

Linear Equations – Online Activities

For the classroom

Graphing Point-Slope
Given a point and slope, graph the line. Simple, clean graphing program good for student work on the board.

Identifying Slope-Intercept
Recognizing Slope and Y-Intercept
Identify slope and y-intercept from an equation. All in slope-intercept form. Good for a mini checkpoint quiz.

Slope Investigations
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.

For students

Writing slope-intercept equations
Line Gems
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.

Linear Equations – Slope Project

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.

Here’s the Sample Project word document in case you want to use it as an example or if you want to modify it. And here’s a Student Template.

Linear Equations and Forensics – Activity or Project

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
Leg bones
T = tibia (ankle to knee)
F = femur (thigh)
Arm bones
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).

Monopoly and Line of Best Fit

A good data set to explore linear regression is analyzing the relationship between the number of spaces a property is from GO and the cost of that property (on a classic Monopoly board). This is actually a TI-Nspire activity, which can be found here.

I don’t like it the way it is for three reasons. First, the worksheet gives students all the data in a pre-filled table. I think students are more invested in a problem if they do the “work” themselves to gather the data, even if it is just counting spaces from go.

Second, it ignores the utilities and the railroads which are good outliers.

Finally, I think this could be done by hand instead of on the calculator. Students could always compare their manual calculations with the calculator answer at the end if using the calculators is one of the objectives of this activity.

One option is to project a picture of the monopoly board on the screen so students could create a table, plot their data and calculate the line of best fit. Unfortunately, it was difficult to find a picture of a classic Monopoly board that wasn’t blurry or angled, so here‘s one I found if you need it.

I also made a one page student handout which has a picture of the Monopoly board, a graphing area and a table to fill in.

World’s Largest …

I’m a great fan of dy/dan’s philosophy of teaching math. But I’m also a fan of practical ideas to integrate into a lesson plan. Luckily, he provides wonderful resources in that regard.

He has “3 Act” lessons which are lessons that incorporate multimedia. This particular lesson, as the title states, is about the world’s largest coffee cup. Here’s his complete coffee cup lesson:

dy/dan’s World’s Largest Coffee Cup

I categorized this post in the “Volume and Surface Area,” “Proportions,” and “Linear equations” because I’m considering using it as a “visual word problem” for those units.

Volume and Surface Area
- It could be a simple question about volume and surface area. How much paint did they need to paint the outside of the cup? How much coffee did they need to fill up the cup?

- If the average person drinks x ounces of coffee, how many people will it take to drink all the coffee in the worlds largest coffee cup or
-If the average person is 69 inches tall, what size would a person have to be for this cup to be a “normal” cup for him/her. (The typical regular sized coffee mug is 3.5 to 4 inches tall, but I wouldn’t have to tell the students this. I have enough coffee mugs that I could just give them a mug and a ruler…)

Linear Equations
- Given a rate of flow (and assuming a constant rate), students could calculate and graph how long it took to fill up the cup, or given the time of how long it took to fill up the cup, students could calculate the rate of flow, etc.

For whatever reason, my laptop mini won’t play the videos from Dan’s links, but will play them directly from YouTube. Here’s two of the videos in the lesson that can be found on YouTube:

Intro to Problem
(The repetitive “music” gets annoying…)

Video with Numbers

I’d still encourage you to go to Dan’s site, maybe his video links will work for you. You’ll also need the other information, such as the picture that shows the dimensions of the cup, etc. Lastly, you’ll see the whole picture of what Dan’s lesson is really about, which is more than my currently watered down version.

Following the same concept is the world’s largest burger:
I’ll list some of the stats that can be molded into questions below, but you can find them and the accompanying video here.

1,375,000 calories
Over 600 pounds of beef
30 pounds of lettuce
12 pounds of pickles
20 pounds of onions
28 inch thick, 110 pound bun.
(That’s only a total of 772 pounds so when they say over 600 pounds of beef, I’ll assume they mean 605 pounds of beef).
14 hours to cook
3 ft thick, 5 ft in diameter

Graphing Calculator 3D


This is a wonderful free download: Runiter’s Graphing Calculator 3D.  (The “try online” version is not very good).

In middle school, there’s little need for 3D graphing, but sometimes it’s good to show students where they’re going and not simply where they are. It also has 2D capability which would be more useful in regards to graphing linear equations or quadratic equations for Algebra.

It took less than a minute to install, and if you’re familiar with graphing calculators at all, it’s fairly self explanatory. For the Algebra 1 classroom, the basic functions you would need to know are:

1) Input your equation(s) in the “y=” on the top left.
2) Click on the coordinate plane icon at the bottom left if you want to change the default 5×5 grid to 10×10.
3) The table icon near the top middle will hide/show data.

It doesn’t do too much more than the TI software your school might have except that it’s more colorful and requires no set-up. But one school I taught at had very little technology resources at all – I wish I had known about this back then.

There are a few bugs, nothing that will affect your computer and nothing really important. For instance, the “example” button will show you various graphs.  Each time you click this example button, a new graph appears. There’s only 10 or so that it cycles through but if you switch from 2D examples to 3D, then it’ll just stop graphing anything even though the data still appears to change. Well, like I said, this isn’t important.

Also, with this free version your capabilities are limited.  Many of the functions are disabled such as the ability to save, etc. The most annoying part about that is that if you accidentally click on an icon that has been disabled, it will ask you if you want to upgrade (pay about $50 for the real deal). Which I understand since this is a free version, and they’d prefer to sell their product. But I think this free version is all that you would need for a middle school class, though maybe it would be worth purchasing for Calculus or Statistics (they have an advanced Stats calculator).