Friday, November 29, 2013

Cartesian Coordinate Plane Again

My journal pages are now working towards a compilation of foldables within a larger foldable. I try to devote a page to a concept with a combination of approaches-definition, strategies, manipulatives, etc.

For Algebra, I wanted to review to coordinate plane. I used a half page overall and divided into sections. One section was for definitions.

The second was for the foldable that diagramed the components.

The third section is on the back side of the second and is used for a check for understanding

Students liked this page because we stepped outside my traditional boring half page book.


M.I.A for how long? And what for?

I've been told that I have a very limited attention span, but there are times when I will dedicate hours to a specific activity.

Who knows!?

One reason for my absence is PUPPIES. My beautiful golden red retriever had puppies. This is a blessed event to behold. Watching their eyes open, their first steps, and every new experience. She had nine puppies, all lived, and all found wonderful homes including the runt (I kept the beautiful little fart!). Her name is Penny Blossom. Yes, her name is from the Big Bang Theory.

Penny was cute and cuddly one morning.
Our first visit to the vet. Penny is on the left. And I love the puppy's face to the right. Her name was Vanilla Ella and she was a quirky puppy. We nicknamed them to tell them apart and for the vet. We had Chuncky Monkey, Rocky, Cocoa, Bernie, Cooper, Penny, Vanilla Bean, Blonde Baby 1, and Blonde Baby 2. So much fun!!

What a crazy eight weeks!

I have also been asked to head up U.I.L. Academics this year. This is where students compete academically across the state of Texas. Of course, I want to make the most of it!

The competition is held in the spring. I have some ideas on how to get students more involved. After last year's spring competition, I had many students upset because they didn't know what it was and wanted to participate. This year is going to be different.

We are hosting what I'm calling a Campus Competition. We spent several weeks practicing. I required every student to select two or more events to participate in. Technically, everything I ask of them is a choice-academic fun day or beautify campus day.

Our academic fun day will consist of Uil events, movie marathon, and concession stand.

No, it has not been easy. You always have those terribly negative kiddos. However, I continually remind myself that the focus of the campus competition is to broaden the awareness of Uil Academics. I do have some positive results already. Students that would have never given Uil Academics a second thought are practicing and studying on their own time! They are proud of what they have done and are confident in placing.

I'm psyched! We have some bright and talented students. Our campus competition will be held December 4th. I hope all goes as planned!


Thursday, November 28, 2013

My Classroom: Organized Choas

Another teacher refers to my organized chaos as "controlled clutter".

Students that I don't have will walk by and say they couldn't handle the chaos. The kids I teach say they can't learn without it!

Here's my door. It's a little beat up, but I love it. My students decorated it last year and I added the Mathematician thing.

M ake inquiries

A ttack problems

T ranslate knowledge

H ypothesize phenomenons

E levate cognizance

M ake observations

A nalyze data

T heorize suppositions

I mplement strategies

C reate graphicorganizers

I llustrate ideas

A ssess comprehension

N avigate mathematics

S ummarize findings


This is as you walk through my door. My teacher zone is across the way and designated by red duct tape on the floor. I just have to have a little personal space.

My teaching area/power zone faces the students. I use my document camera mostly and I have it positioned where I face the kids. I don't worry about not being able to see what is displayed. I have a general idea and if I'm ever off, they let me know. I cannot stand to have my back to my entire class.

After working through college in retail, I prefer to stand at a desk at counter level. It blows the students mind that I don't have an official teacher's desk.

This is as you scan the room to the left. I have six giant whiteboards hanging around my room. Anytime a student asks me a question, I have someplace to demonstrate. There's lots of space for students to demonstrate their knowledge and then compare what they see. When I'm gone, my instructions are written there for the students to see. Sometimes I teach lessons on both the whiteboards and Promethean just to mobilize my power zone and draw more focus.

Standing directly in front of the Promethean board.

There's stuff everywhere. Sometimes we play I Spy for kicks.
To the right and left of the Promethean board are giant bulletin boards made from painted ceiling tiles! Love these!! The ceiling tiles cost me $40 for ten. Painted them black and hung them using liquid nail.
On the right side of my Promethean board, I have designated a portion of my bulletin board for the 'Since You've Been Gone' board. When a student is absent, their table mates write the absent student's name on any papers handed out, and these papers are pinned to that board. Therefore, the responsibility of pinning papers is the table mates and the responsibility of obtaining missed papers is the absent student's. So far, this has worked out very well.
I have used various arrangements of my tables in the past. This arrangement works out best. On the first day of school, I have colored dots on the table that show students where to sit. I don't have students sit with their back to me or the Promethean board.
These are the supplies that are always on the table. Surprisingly, they stay very organized. At the beginning of the year, I did teach the behavior and procedure I expect to see with supplies.

This is my second classroom, and so far it is my favorite.


Rigor, Rigor, Rigor: How many of you hate that word?

I was apart of a book study today over the book titled: The Fundamental Five

I have always disliked the word rigor and I think, like my students, it is due to the fact that no one would define it for me.

Revelation: In the book, it states: "The concept of rigor, or the level of cognition, as described by Dr. Benjamin Bloom in his now famous taxonomy, is almost universally recognized by teachers."

Another words: Rigor is the level of cognition. The level of cognition going on in the classroom can be determined using Bloom's Taxonomy.

Profound realization for me. I love Bloom's taxonomy and can easily relate the idea of rigor to it.

I am coming around to the word!!!


My Adventures in Summer School...a delayed review!

My small rural school needed someone to do summer school for elementary math.

So I volunteered. I teach high school. How hard could it be? We split the large group of 16 into a junior high group and elementary group. Summer school would consist of 8 days total, split into two weeks, Monday through Thursday from 8:30 to 11:30. The idea is that the students would complete their previous grade level using Study Island. Study Island is a great website that would provide an individualized curriculum and pacing for each student.


Day 1:

After day one, I was going out of my mind with boredom. I went around and helped a few that had questions and observed many that chose not ask questions and just guess. This was dissapointing. Not only were they bored and discouraged, but I was not seeing the type of learning I love-engagement, confidence, enthusiasm.

I decided that the next day, I would break up the monotony with some activities. I stopped by HEB and purchased two plastic balls, six foam noodles, and giant markers. When I have fun, I like to go big!

Day 2:

Taking one of the plastic balls I wrote the numbers one through twelve all over it. As a warm-up game, the students and I would get in a circle (harder than I thought it would be) and bounce the ball to each other. When the student catches the ball they would read off the two numbers that their thumbs were on as a multiplication fact and then the answer aloud.


After the multiplication fact warm-up, I had the students go online to Study Island. While they worked, I wrote the numbers 0 to 50 on sheets of colored paper. I laid them on the floor in order and in rows of ten (exception of the first row).

After about twenty minutes on the computers, I called for a break and transision.

We began 'Prime and Composite Exploration'

Phase 1

Initial layout of values 0 to 50.

I want to share the conversation that I had with the students. This is my favorite part of teaching-listening to what the students think. (I think that's what drove me crazy the first day-no interaction.)


T: What do you notice about the values you see?

S: The numbers are between zero and fifty.

T: What else do you notice?

S: They are in rows of ten.

T: Elaborate.

S: Five rows of ten except for the first which includes zero.

T: What else do you notice about the values that you wouldn't notice if I had tossed them on the floor?

S: Order

Phase 2

T: The following value exist between which two values?

S: Zero and fifty

T: Select a value for me.

S: Fifty

T: What are the fact pairs of fifty? (we elaborated a little on the difference between factor and fact pairs)

S: Five times ten, fifty times one, twenty-five times two.

T: Are you sure?

S: (Thinking. When you ask if they are sure, they start thinking and exploring) ten times five, one times fifty, and two times twenty-five

T: Are you sure? Do you think it makes a difference?

S: No, not really.

T: Does anyone know the name of that property ten times five and five times ten?

S: (Uncertain)

T: Commutative Property

S: (Recognition)

T: Now, select a value and list the fact pairs for that value.

Phase 3

I laid out their selected values

(There was one incorrect factor pair-twelve times three for sixteen)

T: What do you notice about the values?

S: They are between four and thrity-six.

T: What else do you observe about the following values? What do they have in common?

S: They all have a factor of two.

T: What do you know about numbers that contain a factor of two?

S: Even?!?

T: Are you sure?

S: (Pause)... Yes!

(Process is repeated. Students are this time asked to select an odd value as their second number and list the factor pairs. One student selected zero. ;) I love when this happens. Oh, the conversations to come.)

(The student that selected zero realized that his list of math fact pairs of multiplication wasn't going to stop. He asked me if he could just list what he had. I told him a mathematician never leaves something unfinished. They, at the very least, summarize with a hypothesis and then give it up to peer review. He liked the idea. He did pretty well: "everything times zero is zero!")

T: The following numbers exist between what values?

S: Zero and forty-nine. (I need to expect complete sentences now that I reflect upon this lesson.)

T: Take thirty seconds to make an observation of the following values. ... Share your conclusion with your neighbor. ... Who would like to share?

S: They're all odd.

T: What indicates an even number?

S: A factor of two. ... Wait, so, zero isn't odd? (Interesting result.)

T: What do you think?

(I love these moments because students begin to think and share. After a few minutes of good spirited debate between the students, I shared my brief research on the number. Some people consider it even for certain reasons, others consider it neither even nor odd, and some consider it both. I told the students to be objective.)

(For my younger group of 2nd through 4th grade, they were not as quick to see even and odd numbers. I was surprised and figured it was due to my type of questioning and vocabulary. So, I took their stack of selected values and split them into to two seperate circles for a Venn diagram. (I created two circles out of pool foam noodles with bright blue duct tape.) I used a think pair share strategy and finally aquired the conclusion of even and odd from them. I asked them why and they described the value of the ones place as the determining factor for even or odd. I then had them label to two circles of the Venn diagram as Even and Odd.)

Day 3:

We continued a combination of computer work, listing factor pairs, and multiplication fact practice.

Day 4:

My classroom is ready for my return!!! I couldn't wait to get into my teaching grove. I'll admit that over the past year, I have gotten further away from integrating technology into my classroom. My first two years, my students each had a laptop and the integration of technology was a breeze. From Khan Academy to My Big Campus to Survey Monkey, class work was full of technology usage.

The kids were intrigued when they found out we were going to my classroom. If I could make so much out of a computer lab, what would my classroom be like? (I will share it later :) )

They were not dissappointed, and I was instantly back in my groove.

Today's Lesson: Pentominoes into Probability!!

I started with something familiar to most - a domino.

I asked what shape they saw. The answer I sometimes get and am always concerned about is "It's a square." No matter what, I have to have the square to rectangle to rhombus conversation. I feel that it's too important to leave out.

I tried several strategies. My first was to draw some rectangles and squares on my document camera. I asked what they saw and how they knew. Still, no connection to side lengths and angle measures. I pulled out the Anglegs. I asked what they thought the different colors indicated of each stick. They were quick to know same length for same colors. Then, I asked them to make a square. I watched as most chose four of the same color and a few chose pairs of different lengths that were close to congruent. I chose some for presentation and finally, the students came to understand the similarities and differences between, rectangles, squares, and rhombi.

Then, we went back to the domino. How many squares make up a domino? So, if 'do' could stand for two, then what could pentomino represent? Students were unsure until I boxed 'Pent' asked them what they knew. Instantly, a student would blurt out 'pentagon'. Ok, what is a pentagon? They knew it to be a shape with five sides. So, what would be a Pentomino? Loved this response: "An omino with five squares!"

From a box of tiles, I showed how two squares make a domino and then made a pentomino. We went over the facts of a pentomino - tiles connected with full sides, no overlapping, etc. I provided each table with a box of tiles and challenged them to find as many different pentominoes as they could.

Then came another great conversation. Is it the same pentomino if the pattern is flipped, turned, etc. So, I used myself as an example. Who am I? Ok, when I turn around, who am I? Am I still the same person? Ok, is it still the same pentomino? Yes!


After I had passed out the materials to make our summer school mini interactive books, I asked the students how many pentominoes they had and provided them with the goal of twelve pentominoes. Once, each table had discovered twelve, I asked each group to rotate to the next table and check the previous group's work.

After checking and modifying, they pushed the pentominoes aside. It was time to create our mini interactive books.

How to make a 'No Staples, Glue, or Tape Needed' Booklet:

For simple usage and to start with, you only need two pieces of paper and a pair of scissors.


1. Fold both sheets in half.

2. Taking one folded sheet of paper, measure appoximately an inch along the folded side from both edges and mark it. Do the same to the other folded sheet of paper.

3. Taking the scissors and one of the folded sheets and trim just a hair off the folded edge rom the edge to the marked spot on both sides. We will call this sheet A.

4. Taking the scissors and the other folded sheet, trim a hair off the folded side between the two markings. We will call this sheet B. The trimmings should be opposites - one inside and the other outside the markings.

5. Unfold sheet A. Bend and hold sheet A long ways and so that it resembles the shape of a taco.

6. Take sheet A and slip it through sheet B's slit, unfolding sheet A so that it locks into place.

7. Fold it over to finish making a booklet.

Kids are amazed! So simple, yet tricky. I also use this to represent intersecting planes in geometry!

After creating our mini books, we turned to page one and wrote the title - "Pentominoes"

On a gridded marker board displayed by the document camera, I had each student come up and draw one pentomino until we had all twelve displayed. After we finished copying down all pentominoes, I asked them a question.

How many total squares/tiles are on the table?

Most students thought about it and concluded to sixty.

I asked them how they figured it out. Some students showed that they counted each tile and others explained that twelve groups of five tiles yields a total of 60 tiles. Now, that was my wording. It took some guided questioning to get that final statement written with labels. They were proud of it!!

We turned to page two and labeled it probability.

Day 5:

While the students were creating pentominoes last Thursday, I observed that each tile was drawn at random and thought-"sweet, a transision into probability".

I asked students if they selected each color specifically for each pentomino. They said no, it was at random. I answered with "and that is probability. Now, lets take a look at our results."

I asked students what would be the best thing to do with the tiles to analyze our results. They instantly knew to group them by color.

We then defined probability using a simple shutter fold to identify the numerator and denominator. I have found that defining probability in the form of a fraction helps students connect the definition to a representation. After this we calculated the empirical probability of each color from our experiment. We finished by comparing the final empirical percentages to the theoretical probabilities and talked about which group was closest.

Day 6:

Yesterday, a student requested a review of subtracting fractions. This was tremendous action for this young lady, because on day one she would say one single word. I told her I would come up with something. Now, I couldn't come up with an interesting foldable or lesson and decided to consult the middle school math teacher. She gave me an excellent strategy that the students relate well to. It involves brownies. I was sold, who doesn't love brownies!? When subtracting fractions and you need to borrow from the whole number, she tells the students that it is like borrowing a pan of brownies from your neighbor. You borrow one whole pan and cut it up into the parts you need. Now you have so many brownies and can take away from it. It comes across much better when teaching kids. It worked great!!

Today, we began our exploration of prime an composite. We started by making two quarter page door flap foldables and titled the flaps prime and composite. I list several numbers for each side and asked the students for the math fact pairs. I asked them why I considered 2, 11, and 3 prime and 45 and 16 composite. We finally got down to the conclusion that prime has one math fact pair and composite has more than one math fact pair.

Venn Diagram: I then proposed the idea of categorizing the numbers from zero to fifty based on the knowledge we discussed. I held up two foam circles in the traditional overlapping Venn diagram and asked them what they saw. Most recognized the Venn diagram. I asked them if the circles always have to overlap. They were unsure. I gave each table a selection of their math fact pairs for the numbers zero through fifty. I laid the two circles on the floor and asked them what they think each circle should represent. They wrote title for the circles as prime and composite. After they categorized the numbers as prime or composite, we completed a true false flash card activity to check their selections. We found some mistakes and justified what it should be. They concluded that there was no need for the circles to overlap.

We finished the day with a ball bounce check. On the pink ball, I listed the numbers from zero to fifty and each student identified the number as prime or composite and why. What I found exhilarating was when the students started justifying without being prompted and prompted other to justify if they didn't.

Day 7:

We came back today with a ball bounce review. We then went back to our prime and composite foldable to write a formal definition. We googled several sites and I encourage the students to write one in their own words for the class.

I wanted to provide the students another way to look at prime and composite numbers in terms of multiples. We started with a hundreds chart that we cut down to one to fifty. We started with the first prime that they knew and looked at the multiples. They were quick to pick up that the first number is prime and the multiples are composite.

Day 8:

Last day! And some were actually sad a little bit.

I started by asking them to turn to the last page in our book. I told them that this was the most important page in our book. It is a way for the student to share their reflections over summer school.

Question: What did you enjoy most about summer school? Why?

I told them to keep this question in mind throughout our time today. We have a few more activities to do today. They could answer it along the way or make notes of activities they enjoyed and why.

I was surprised to see students actively writing during down time between activities. It was powerful to see students engaged in a strategy that most generally find dreadful.

This is my favorite response. This response comes from a student who is very low, shy, and quietly spoken. I quickly recognized this on day two and spent days breaking through her tough shell. I knew she was scared to be thought of as stupid. I never once let her feel stupid or like a failure. No matter what her answer was, I would take it and explain what her answer meant and ask another guiding question. No matter how long it took, we always got to the right answer.


Reflection from summer school: During summer school, I noticed that the writing with the lower level students was a much slower progression than the writing of the jr high and high school. I couldn't figure it out. I thought that it was just the grade level. The lower the grade, the slower they write and respond. I took my concern and uncertainty to the elementary couselor. She pulled out their data and as I observed the data I realized that this specific grade had a significant low writing score. Come to find out, they are not writing in the classroom. As a result, their scores are low and my approach to teach was a whole new experience! I went to the principle and shared my findings. I offered the advice and idea that journaling should be used in several subjects for these kids. I warned her that it would be tough and very slow, but the success will be tremendous in the end. I came close to begging to change grade levels just to see how much we could do for the kids. I love the challenge and more than anything, I want to see the kids become successful and empowered!!