Online Activity for Slope and Slope-Intercept Linear Equations

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!

Slide and Divide Method of Factoring Trinomials

FactoringTri
Someone asked about how to teach factoring trinomials where the leading coefficient is not 1, so I thought I would post it here as well.

The best method I’ve found is often referred to as the slide and divide method, for trinomials of the type ax^2 + bx + c

Anyways, take the trinomial 3x^2 + x – 10.
(Always ensure to pull out any common factors before continuing with this method).
First you slide the leading coefficient to the end and multiply it by the constant:
You get x^2 + x – 30
Then factor like normal
(x + 6)(x – 5)
You have to “put back” the number you slid out, so to speak. You do this by dividing the constant in each factor by the leading coefficient you “slid” out of the way.
(x + 6/3)(x – 5/3)
Simplify the fractional terms you end up with.
(x + 2)(x – 5/3)
Once it’s simplified, if there’s a fraction left, the denominator becomes the coefficient of the variable term.
ANSWER: (x + 2)(3x – 5)

Here’s another example without the explanations:

2x^2 – 7x + 5
x^2 – 7x + 10
(x – 5)(x – 2)
(x – 5/2)(x – 2/2)
(x – 5/2)(x – 1)
ANSWER: (2x – 5)(x – 1)

Finally, an example where you have to pull out a common factor first:
12x^10 + 42x^9 + 18x^8
6x^8(2x^2 + 7x + 3)
6x^8(x^2 + 7x + 6)
6x^8(x + 6)(x + 1)
6x^8(x + 6/2)(x + 1/2)
6x^8(x + 3)(x + 1/2)
6x^8(x + 3)(2x + 1)