I Admit

To Be Honest

A former student posted this sweet message on my Facebook wall today.
I was tired at the end of the day. Then I wasn't! :D

Mnemonic Device for Euler's Formula

I introduced Euler's Formula to all my students today. Said formula states the relationship between the number of vertices (v) of a polyhedron, its number of edges (e) and its number of faces (f) as follows:

     v  -  e  +  f  =  2.

I thought about asking my second period class to come up with a mnemonic device that they can use to help them remember said formula. Adriana Garcia, a sophomore, quickly came up with one. 

"Victor eats fruits!" She shouted.

We settled with the following:
     Victor eats fruits 2 times a day.

The very first group of National Honor Society members of Achieve Early College High School

got inducted May 5, 2011. The induction ceremony was held at the Cooper Center of South Texas College.

These members include juniors and sophomores.

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Collaborative Group Work Lesson: Constructing Rectangular Prisms

CONSTRUCTING RECTANGULAR PRISMS

OBJECTIVES:

1.        To construct a rectangular prism.

2.        To determine the volume and total surface area of said prism.

3.        To find patterns in the changes in volume and total surface area when the dimensions are doubled, and tripled.

MATERIALS:  Paper, Pencil, Ruler, Scissors, Calculator

PROCEDURE:

STEP 1: Construct rectangular prisms using paper.

                                Student 1:  Construct a 2 ¼ in. by  3 ½ in.  by  4 3/8 in. rectangular prism.

                                Student 2:  Construct a second rectangular prism. Double the dimensions

used by Student 1. Are your dimensions correct?

                                 Student 3:  Construct a third rectangular prism. Triple the dimensions

used by Student 1. Are your dimensions correct?

STEP 2: Determine the different ways one may find the volume of your rectangular prism. Show complete work. Did the volume of the same rectangular prism change? Explain why each solution is different from the other/s.

STEP 3: Determine the different ways one may find the total surface area of your rectangular prism. Show complete work. Did the total surface area change? Why so?

STEP 4: Discuss the following with all other members of the group:

1.       What do you think happens to the volume of a rectangular prism when the dimensions are doubled? Tripled?

2.       What do you think happens to the total surface area of a rectangular prism when the dimensions are doubled? Tripled?

STEP 5: As a group, make a poster that reflects your group’s answers to the questions in Step 4.

STEP 6 (Final step): Gallery Walk & Classroom Talk. Compare your group’s findings to the findings of the other groups. Any similarity?

EXTENSION: Write a proof for each of the two cases: doubled dimensions and tripled dimensions.

(Lesson designed by R.E. Jope, Achieve Early College High School, McAllen, TX USA)

Taking the High Road

I like taking the high road.
On it the ride is so much more

peaceful and inspired.

Photosophics 1

"Even if it means finding myself
naked and exposed,
I would still choose to be right."

I wake up to this view from my apartment window everyday for a year now.
Photographed February 4, 2011. Location: Las Misiones Apartments, Mission, TX USA.

Age Doesn't Matter!

My friend Norma asked me a question last night via Facebook. For practical purposes, I am rephrasing her question as:

Why is the sum of the person's two-digit birth year and that person's age plus one always equal to 111?

Norma, who is now 34, was born in '76. She observed that 76 + 34 + 1 = 111.

I thought of Matty. He was born in '83. Last year, he turned 27.  Observe that 85 + 25 + 1 = 111.

My student Alisha, who was born in '96, celebrated her 14th birthday last year. Well, 96 + 14 + 1 = 111.

"So why does this work?," Norma insisted.

Readers, what do you think?


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SOLUTION:
When you say your birth year is 76, you actually mean 1976, which is 1900 + 76.

So if your birth year is X, then it is actually (1900 + X).

If you were born in the year (1900 + X), then in the year 2010, your age was [2010 - (1900 + X)] years old.

So your birth year plus your age plus one
= X + [2010 - (1900 + X)] + 1
= X + 2010 - 1900 - X + 1
= 111.

It doesn't matter how old the person is, the result will always be 111.


Norma's question reminded me of a similar problem. Last December, in a statewide conference I attended in Dallas, the following question (that I also rephrased) was raised for us to play with:

Add your age by the end of this year to the year you were born. What do you get?

Now your turn. Prove why it works.