The Struggle of Learning Process

It might be my head-cold talking but this is a really good way of visualizing the learning process for kids and even adults.

You’re faced with a problem and a goal.
You have the capability to solve the problem but you don’t know it.
You try and you struggle;
You feel the difficulty push back until you try something new.
Now the problem is solved and goal is sweetened with the benefits.

What Do You Think?

earned_and_not_boughtI’m curious to see what you guys have to say.

5 x 5 Peg Lattice Board Answer

Answer:  50 Squares

Below are two animated .gifs of each square to be made on the lattice board.  If the images below are not moving, click on one to be directed to the original file of that image.

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Random Thought…

“I’ve just discovered I’m π-curious!”

Parametric Spiral Ball Animation with GeoGebra 5

This is that neat thing I said I was working on in GeoGebra 5.  I wanted to come up with a mathematical model that described this metal mixing ball. After playing around with some formulas and testing out properties, I chose some constants for a, n, and d for the base image.  For each frame p, GeoGebra took a “screen capture” of the curve after all t units in the domain [-π, π] were mapped.  This is the formula I came up with:

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How Many Squares Can You Make in a 5 x 5 Peg Lattice Board?

I’ve been wanting to post this problem for a long time.  I don’t know why I’m so lazy.

4 x 4 Unit Lattice Board

Suppose you have a 5 x 5 peg lattice board like one on the right:
Without injuring yourself or others, how many rubber band squares can you make on the board?
How many rubber band squares can you make on an N x N peg lattice board?

The picture above is a screenshot of the Geoboard app.
This app is a:
provided by The Math Learning Center.

Think About It: “If you could travel through time…”

spiral clockA lot of times I wonder what it would be like if a single person travelled to the past or to the future. What kind of questions would the time traveler ask the people of the of the culture at that time?

If a person travelled from the past to our time, do you think the traveler would ask if we’ve attained peace yet, as first of many questions?

Have we used our time wisely and efficiently enough to solve our problems?

Are we where we want to be as people? As a species?



I’m so excited to check out GeoGebra5. I just find it very ironic that the day it is released is the same day I’m admitted to the hospital.

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The Satisfaction of a Job Well Done

Cuuuurrrssee  yooooouuu maaaaaattthhh!!!!

A few days ago, I got a call from my uncle, Jerry, asking me if I could tutor his daughter, my cousin, Tayler.  Of course I agreed!  According to my uncle, my cousin was feeling very frustrated with the material in the classroom and more at home trying to understand.  So frustrated nearly to the point of tears.  So she took some time to cool off and clear her head for about an hour.

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Quadrilateral Properties Flowchart

I put this flowchart together years ago to help our students become familiar and identify quadrilaterals and their properties using side lengths and the slopes of the sides.  The information is usually gathered from a gridded Cartesian graph or sets of ordered pair vertices of the quadrilateral.

Click here for the Quadrilateral Properties Flowchart.pdf


Information Needed or to be Derived:

(x_1, y_1) \text{ and } (x_2, y_2)

Pythagorean Theorem:
\displaystyle c^2 = a^2 + b^2
\displaystyle \text{side length}=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}}
\displaystyle \text{side length} = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

m=\frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}

More handy documents can be found on my Printables page!