Alphabet Slope

by: Algebra Funsheets - March 12th, 2012   Add Comment

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???

by: Algebra Funsheets - January 20th, 2012   Add Comment


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

by: Algebra Funsheets - January 12th, 2012   Add Comment

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

by: Algebra Funsheets - November 29th, 2011   Add Comment

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.

Tracing
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.

Verbal
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

by: Algebra Funsheets - November 26th, 2011   Add Comment

For the classroom

Graphing Point-Slope
IXL
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 and Forensics – Activity or Project

by: Algebra Funsheets - November 18th, 2011   Add Comment

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).

World’s Largest …

by: Algebra Funsheets - November 8th, 2011   Add Comment

coffee
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?

Proportions:
- 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.


burger
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

Patterns, Linear Equations and Toothpicks

by: Algebra Funsheets - October 28th, 2011   Add Comment

toothpicks
Toothpicks are a great tool for exploring patterns. Add mini marshmallows and now they take on a new dimension (just make sure to dry out the marshmallows for a day or so before using). An obvious use is to make those 3D shapes for geometry, but for the Algebra class, it’s a great way to introduce students to linear equations:

Toothpick patterns and linear equations
-Create a triangle using three toothpicks. Then add a second triangle next to it (which requires 2 more toothpicks). The second triangle should be upside down so that the two triangles together look like a parallelogram with a diagonal. Continue the pattern, keeping track of the number of triangles vs. number of toothpicks needed, plot the data and come up with the equation that models the data. Calculate how many toothpicks it would take to make 100 triangles, or 1000 triangles.

-Create a square using four toothpicks. Then create a second square next to it (which requires 3 more toothpicks). Then continue the pattern, keeping track of the number of squares and number of toothpicks. Plot the data, come up with an equation that models that data, use that equation to figure out how many toothpicks it would take to make 100 squares, etc.

-If you add marshmallows, you can now also create cubes or tetrahedrons, and follow the same sequence as above to explore more equations.

Options
-To add even more graphs to explore, or if your students are advanced, keep track of the number of toothpicks vs. the perimeter or area or volume (using toothpicks as the unit, of course).
-If you use marshmallows, keep track of marshmallows vs. perimeter or marshmallows vs. toothpicks, etc. There are too many variations, which is why I don’t have a student guide to go along with this.

Notes
I love any hands on activity that allows students to explore things on their own. This activity (or activities like this) gives students a foundation from which I can help build the meaning of “rate of change.” Unfortunately, the y-intercept portion does not work out too well, as 0 triangles should require 0 toothpicks, but the equation comes out to 1 toothpick. Regardless, since I use this as an exploratory activity, before any “lecture” on linear equations, then students never know to look for this. Plus the lowest value they graph is 1. And the point is to experience gathering data, graphing lines, figuring out how to come up with the equation and to see how the rate of change differs for each pattern.

Online Activity for Slope and Slope-Intercept Linear Equations

by: Algebra Funsheets - November 22nd, 2008   2 Comments

roachlinearEqns
The other day, my students spent the day in the computer lab and explored the myriad of web sites on line that let them explore linear equations. I directed them to some fairly decent tutorials, and various online tools that allowed them to physically move lines to explore the effect it had on slope and equations. It was the first time I took them to the lab this year, and thought they would thoroughly enjoy this hands on opportunity. But they blandly went through the tutorials, and some even complained that they would prefer next time to stay in the class room, because it’s more interesting when I explain things to them.

However, the last 15-20 minutes of the day, I directed them to the website below. The student loved it. Many students who struggled with rate of change/slope and writing slope-intercept equations were proficient by the end of class. Unlike most other math “games,” the graphics on this are excellent and students actually enjoy the concept of the game, which is rather strange (which is why they liked it). There are roaches that traverse the coordinate plane at a particular line, for which the students must identify the slope or slope-intercept equation that will exterminate the roaches. They can even choose the method of exterminating the roaches (fumigator, shoe …).

Linear equations game

If you don’t have the time to do this during a class period, show the students the site and they will go there on their own time. Many of my students asked me to send them the link at their home address so they could play at home!

Teaching Slope of Horizontal and Vertical Lines.

by: Algebra Funsheets - November 19th, 2008   10 Comments

lines
I’ve arrived at that one frustrating point in teaching Algebra – teaching linear equations. I don’t know why the concepts are so difficult for students to grasp. I’ve tried teaching it a myriad of ways, and have yet to discover the best method for teaching this section. It takes me nearly a month to teach all the things that go with slope, slope-intercept and standard form equations. And those are just the basic concepts of linear equations. (After the tortuous month is over, something kicks in and they finally get it and claim it’s SO easy).

And why it is difficult for students to remember that horizontal lines have a slope of zero and vertical lines have undefined slopes is beyond me.

I always start by trying to show them how to arrive at that conclusion using the slope formula. Since vertical lines invariably end up having zero in the denominator – which is THE big mathematical no-no – then their slope is undefined. They insist on calling it zero.

I resort to making them actually divide by zero on the calculator (after having arrived at some vertical line ratio using their slope formula), because it gives them “ERROR” since dividing by zero is a big mathematical no-no. And even though it says ERROR on their calculator, they still want to call it zero. The few who can actually remember that it’s undefined don’t want to call it undefined – they call it unfined, unrefined, or unidentified …

We analyze how linear equations with positive slopes increase or rise (from left to right) and how equations with negative slopes decrease or fall. Then we contrast that with a horizontal line, which neither rises or falls – and since it does “nothing” then it is “nothing” (0). But with a vertical line, you can’t tell if it is rising or falling; therefore since you can’t DEFINE which way the line is going, it is UNdefined.

Then I get desperate and resort to telling them that hOrizOntal has O’s in it, which looks like zeroes, because horizontal lines have a slope of zero. And that Vertical starts with a V, which strongly resembles the U in Undefined.

…that horiZontal has the letter Z in it, just like Zero …
…that Zero starts with a letter Z which actually has not one, but two horizontal lines ….