Algebra How Toons

Check out all of the Algebra student's Howtoons!
These are the animated cartoon created on xtranormal.

And the HowToons created mostly with the website writecomics.com and Comic Life.

Where I Draw the Line!

"I'll do science, social studies, and English, but graphing is where I draw the line!"

Math humor.
It's the absolute best.

Students in my algebra class have been working on creating HowToons for solving systems of equations.
Using websites such as writecomics.com and xtranormal.com, students used humor to help engage students in the solving systems of equations either by graphing, substitution, or elimination.

Stay tuned for finished products.

Ariadne's String

The Pythagorean Theorem can be found in many places.  

Even in Greek mythology.

Theseus was going to slay the minotaur so Ariadne sent him with string to use so he could find his way back as we wove his way through the maze of columns.  

The challenge was that each time he went around a column, that length of string had to be greater than the time before.  How many pathways could he find?  Below is an example of 5 pathways that got longer with each turn.  

Students worked on this for the whole class period, finally finding that 8 pathways was the most that could be found in the 5x5 grid.

For those students with extra time, they worked on the 8x8 grid.  With this larger grid, they found that 14 pathways were possible.

We organized this data into a table of values and filled in the missing pieces.

We even connected it to Algebra and found the equation... 2g - 2 = p

Because of our limited time, I told the students that it would just take one counterexample to disprove our pattern.

Sure enough, today a student came in to class with 9 pathways.

Are 10 pathways possible?

So now, how many pathways could fit in the 8x8 grid?

Gotta love math!  

Graphing a Story

Video Productions for modeling mathematics in a graph.

We got the idea from this website.

Check out what our students created!!!!

They were busy working all week long.
Some chose the video option...

Some chose to work more directly with the content.

Making Sense of Exponents

Exponents are the little number "sitting on the shoulder" of the base number.

They basically tell how many times that base number needs to be multiplied by itself.

This week 8th graders explored various operations with exponents.

~ What happens when you multiply exponents?

~ What is the short cut when you divide exponents?

~ What do you do when you have to find powers of powers?

~ What does an exponent of zero mean?

~ Yikes!  You can have negative exponents???

They first found patterns and wrote hypotheses for what they thought the rule (we called it a shortcut) was.

Then the next day, we acted the problems out so we could actually make sense of what was going on!

a(to the 5th power) divided by a(to the 3rd power)

a(cubed)squared

By just playing around with the numbers, students came up with their own questions.  

Wondering outloud in math definitely moves our thinking!

~ When working with negative exponents, will the top numbers ALWAYS be a 1?

~ What happens when there is a negative exponent in the denominator of the fraction?

~ Does the rule still work if I use a negative exponent?

Students were using several math habits as they tried to decipher through the exponents.

1) Patterns

2) Finding structure

3) Wondering

4) Perseverance...there were four properties we had to get through!

More Spheres, Cones, and Cylinders

Besides finding the volumes of the Kansas sphere, cone, and cylinder,
A student traveled all the way to DisneyWorld and found another set containing a large sphere, cone, and cylinder.
Check it out!

What is the radius of this "cylinder"?

How was the volume found for Epcot?  What would the math look like?

How was the problem worked backwards to find the radius?
What information would you need to look up to be able to find the radius?
Find the volume of Mickey's Hat.

Figuring It Out

This last week, students spent their time in class attempting to answer the following questions.  It was exciting to see their minds at work!

1.  What is the linear dimensions of this gigantic ball of twine found in Cawker City?  

2.  How long would it take to fill up the hand dug well in Greensburg from a regular water hose?  

What would the equation look like?

3.  What would a graph look like if we were able to fill the TeePee in Lawrence to the top at a steady rate? 

Student examples...

Check out the following video for the 16 Habits...

1)  Did the student(s) show persistance in solving the problem?  How can you tell?

2)  Did the student strive for accuracy and precision?  What evidence shows this?

3)  How did the student communicate clearly?