I just wanted to say thank you to all of those who have been reading my blog and to those of you who have emailed with me. I only started doing this in February and I get great pleasure out of keeping up with this blog. I actually search to find things to post sometimes just because of how good I feel after a post. So thank you, to those of you who read this because I passed 1,000 pageviews today and already passed the amount of views since last month, and it's not even over yet!

Keep reading and keep commenting because I know I love to hear your thoughts as well!

## Sunday, May 20, 2012

### End of the Year Projects

As many of us know, the end of the school year is upon us. For my school district, we are done this week with Monday being the last day of having a full day of classes followed by three days of exams. It is a really bitter sweet time for me because unlike many of my counterparts in the program, I stayed in my student teaching placement rather than receiving an additional placement. Because of this, I had the privilege of being with some of my students for half of the school year. After these last couple months, I have grown to appreciate each student for their uniqueness and have continued to grow in my own ability learning what not to do along with what I should do.

With the end of the year came my decision to provide my students with a final project (they still take a final exam and typically my mentor teacher gives out a project, as well). Rather than sticking to a project that my mentor typically does, I decided to give a very open ended project to my students.

Below is the handout that I gave to my students but I'll give you the jist of it here. Basically, I told my kids to pick a topic that was covered in the recent semester. Their job was to find a way to present the material that they could also have fun with. I gave some ideas such as art (if you can't tell, I love this option), music videos, games, books, etc. I really emphasized though that it was their time to find a way to bring their talents and interests into the math classroom and have some fun beginning to review for their finals. Now of course, the open endedness of this project was a little difficult for students to grasp as many times, they are given a project where they must discuss this and this and this and blah blah blah. It was also rather difficult to grade because of how different most of them were based upon the broad grading criteria that I gave. A bulk of the points was for "content" where I looked at the depth, accuracy, whether it helped them review, as well as having all components of their project.

Each student gave me a proposal where they discussed what they wanted to accomplish and create in the project and I provided feedback based upon their proposal. Proposals that I didn't approve and had the students redo were basically "poster" ideas where they would write examples, definitions, and theorems. One critique that I did have for myself was the timing of when I gave the students the project guidelines. Next time, I would give the project guidelines out sooner so the proposals and acceptances could be received sooner that way students would have more time to work on their projects (the videos would benefit from this).

This project reaffirmed to me how wonderfully talented my students are and I am so incredibly proud of all of them. About half of the projects that I got back were games (be it gameboards or Smart board games) and the other half were a variety of creations ranging from art to movies to books. I've included a few pictures of some of the wonderful projects that I had the privilege of grading this past weekend.

With the end of the year came my decision to provide my students with a final project (they still take a final exam and typically my mentor teacher gives out a project, as well). Rather than sticking to a project that my mentor typically does, I decided to give a very open ended project to my students.

Below is the handout that I gave to my students but I'll give you the jist of it here. Basically, I told my kids to pick a topic that was covered in the recent semester. Their job was to find a way to present the material that they could also have fun with. I gave some ideas such as art (if you can't tell, I love this option), music videos, games, books, etc. I really emphasized though that it was their time to find a way to bring their talents and interests into the math classroom and have some fun beginning to review for their finals. Now of course, the open endedness of this project was a little difficult for students to grasp as many times, they are given a project where they must discuss this and this and this and blah blah blah. It was also rather difficult to grade because of how different most of them were based upon the broad grading criteria that I gave. A bulk of the points was for "content" where I looked at the depth, accuracy, whether it helped them review, as well as having all components of their project.

Each student gave me a proposal where they discussed what they wanted to accomplish and create in the project and I provided feedback based upon their proposal. Proposals that I didn't approve and had the students redo were basically "poster" ideas where they would write examples, definitions, and theorems. One critique that I did have for myself was the timing of when I gave the students the project guidelines. Next time, I would give the project guidelines out sooner so the proposals and acceptances could be received sooner that way students would have more time to work on their projects (the videos would benefit from this).

This project reaffirmed to me how wonderfully talented my students are and I am so incredibly proud of all of them. About half of the projects that I got back were games (be it gameboards or Smart board games) and the other half were a variety of creations ranging from art to movies to books. I've included a few pictures of some of the wonderful projects that I had the privilege of grading this past weekend.

The game of Trig-Pop! This was a very unique game where the students placed balloons on various spots of the sine and cosine graphs. Players were to pop the balloons with darts giving them a number associated with a particular question. I had informed the group as well as all groups making games that they needed to have all parts of a game (aka instructions, a box, all necessary pieces) and this group did a great job of including extra balloons, darts, tape for the balloons, and instructions that were on paper such that it looked as if it were straight out of a real game box. Hasbro, look out!

This group created a town using various 3-d objects. Their job was also to find the volume, surface areas, and lateral areas of these objects. One things that I would have suggested to a group doing a mock town would be to use an inspiration such as New York where the students can incorporate scales into their work.

This one and the next one are two of the art projects that I received. This one is from my honors algebra 2 class where the students took the various conics that they studied and created paintings of the topics. On the back, they put examples and various equations used in the sections. My mentor teacher and I both wanted to keep this set..... we shall see who keeps them....

No matter what, I'm keeping these two paintings and I've already let the artists know. Two of my geometry students painted a night and day painting where they found surface area, volume, and lateral area of the various objects in their paintings. I can't wait to hang these up in my future classroom!

These were three of the books that I received. One of them (the harder to see one) was a graphic novel style story where the students used their classmates and isms from our class to frame how they retaught volume and surface area. The other book, the circus theme, featured several bits of info from the circle chapter in a circus style example book. Lastly, the Max book was a short story featuring several word problems throughout for the reader to solve. They were all very creative and fun to read!

Of the board games that I received, several were very original ideas. In this one, the student created a race car theme, "The Winner's Circle," and had the whole box for the game with cars and instructions. It was very original and it was for this originality that I really appreciated it.

This game was a graphing trig functions game where the students created graphing boards for students to use during a jeopardy style game. Originally, they had talked about creating boards with nails and rubberbands for students to adjust based upon the given graph.

Another original board game that was themed around baseball and even had handmade baseball pieces to play with.

I received several games that had the theme of CandyLand but this one was by far the best. The student recreated the several characters of CandyLand to feature different math characters such as Mr. Pascal. It was adorable. Even their instructions were well done as the student took a picture of the different landing spaces to refer to when describing the game.

Another well done game, the student created a matching game where the students would slide the card into a created hole in the board based upon the space that it matched. You can't see it, but it actually makes a smiley face once completed.

This book looks deceiving but it is filled with tons of wonderful math applications based upon the content in chapter 9 (Conics). The student researched the various areas of the world such as our eye sight and roller coasters that dealt with the conics that the students studied. The students were in awe with this project.

This PacMan themed project dealt with the circle unit done in the Geometry classes where the students found the measure of the arc and arc length for PacMan as well as did a tangent line problem using PacMan and the food he eats.

As I said earlier, I received many wonderful projects from my students further showing me how talented they all are. Some of the projects, however, I couldn't post on here. I had students playing music in the classroom on the violin after discussing the applications of sine and cosine with music. I had students create music videos for the unit circle, one of which will be uploaded to YouTube tomorrow that I will later post the link to!! I also had a ClayMation movie done by students, which if you don't know requires over 1000 pictures to be taken to piece together. I have another SlowMation video being shown to me on Monday due to other technologic difficulties. Two of my Geometry students did a live performance of their version of "Red Solo Cup" where they described how to find the volume of a cylinder and cube (ice). I had a Law and Order: SVU themed informational video as well as a survival in the wilderness video describing the Midpoint and Distance formulas. I also can't show the wonderful calculator programs that my students designed. One program helped students solve trigonometric identities/inverses, two topics that my kids didn't really care for.

After all of this, my mentor and I talked about what I would do differently and here was what I decided.... I would have a Midterm and a Final project so that they could review for both. As well, I would have 4 categories of Project: Games / Videos / Art / Books. I would pair these categories and one pair would be offered as a Midterm Project and the other pair as a Final Project. Of course, I could always create the rubrics for all of these options and have the kids receive the various rubrics so that they can continue to choose freely.... I'm very torn by this just because I so much value of the differentiated focus that the project offered.

So the next time you debate doing a project with your students, I challenge you to leave it open ended so that your students can showcase their ability because you really will see students actively engaged who typically wouldn't be as interested in math.

Final Project
## Wednesday, May 16, 2012

### Who Has? Reading/Writing Expressions and Equations

The game of Who Has? It's a fairly common game that can be played in many different ways. In my fall placement, I played the game when teaching students how to read and write various expressions and equations. After going through the lesson with students where we developed a list of words that described the various operations as well as going through a couple of examples, we played the game.

Students were each given a card. On one side of the card, students had a question such as "Who has a number added to 7?" and on the other side had "5/(x+8)." Basically, we started out the game by reading the "Who Has?" card and whoever had the card, would continue by reading the expression again and then reading their own "Who Has?" question. The game went around in a circle and it fit perfectly. Many students wanted to have multiple cards, and they were given them because I made extra, and each student had to participate. It was important for students to listen closely and it was amusing because students often got annoyed when their peers weren't paying attention bringing the game to a halt.

Now, I don't have the cards with the examples I did on them to upload because I'd have to upload nearly 40 sides but I can tell you that I used a series of examples from my textbook and had to create the cards such that I ensured there would be a circle of problems. But I did provide the general game instructions below. Originally, it was a document but I just copied and pasted below.

Who Has…?

The students will be given cards that have an expression or
equation as well as a question asking who has a certain representation of a
phrase. Students will be translating these phrases mentally in order to compare
their particular expressions or equations.

**Materials:**

- Deck of

**Cards (20 cards)***Who Has…?*#
**Game:**

Pass out the entire deck to the class. There may
be extras; in this case, give some students an extra card or evaluate these
cards on your own. Any student may begin
by reading his or her card aloud. The
student with the answer responds by reading his/her card. Play continues until all cards are used.

## Monday, May 7, 2012

### 3-D Object Project UPDATE

As I promised, I would be receiving the three dimensional objects from my children today and this was what I had to carry to my car and up three flights of stairs into my apartment. The project was due today so I received several well-constructed and several not-so-well constructed objects with calculations.

My children were "assigned" a three-dimensional object that they could then trade with someone in their group. Some students had the easy way out with cubes or rectangular prism while others had a more difficult task of doing a cylinder or a cone or something with a base with more than 4 sides. Most difficult of all could be a composite figure.

Anyways, the project was pretty straight forward. My students got points for their object (also for doing an object that was either a prism, cylinder, etc), turning in the rubric with calculations, drawings of both the net and 3-D object, finding the surface area and volume.

I just started grading tonight and have had the good, the bad, and the ugly. I figured I'd share some of their creations.

A composite figure that the student designed to be a cat. This composite figure had the most objects combined to make a composite figure. As well, this student is infamously my student who did the circle project with 133 circles. Another great reason why I enjoy differentiating and finding activities that my students will enjoy.

Another composite figure. This was one of the first that I got back and it definitely took her and I extra time to work on.

As you can see, I was quite proud of the composite figures. This one was made of cardboard whereas most of the other ones were made of cardstock. I would highly recommend doing this project and having students use more sturdy material.

A beautiful triangular prism that had great detailed work.

One of my artists created a cereal box. I, of course, greatly enjoyed the math jokes on the back. It was another job well done.

Now this composite figure got mucho extra credit as he did two figures that had bases with 6 sides. It was again, a great job. Students who did bases with sides more than 4 discovered that they had to account for other calculations when creating their objects.

This one was just so pretty. Her mother got carried away with the bow apparently.....

This was just a very well constructed pyramid. The material was very sturdy and it held together very well.

Lastly, one student created a triangular prism that was a bird house. Rather than placing his in the box with the rest of them, this one was hanging in my room until I left for the day.

Well, these were some highlights from my grading this evening. Of course, I am very well aware that with projects comes extremely long and tedious grading. For this project, I'm having to check a lot of calculations to ensure that the object is within the dimension. My mentor and I decided that it'd be nice to have two prototypes that show what your object should be between, size wise.

Another con to this project that I am discovering is students not following the rubric completely..... If you want to see the rubric again, it is on the original post for the 3-D Object Project.

However, I stand by my decision to this project as I believe that it was a great way to get students thinking outside of the formulas that they were taught. These students are, after all, the future engineers and architects and I would like to see the creativity and ingenuity that we have to look forward to in our future.

So I challenge you. Do a project. Spend lot's of time grading. But find a way to challenge your students to think outside of the formulas.

Enjoy!

## Saturday, May 5, 2012

### Connect the Dots: Trigonometric Identities

This past quarter, one of the units that I taught to my Honors Algebra 2 course was all about the trigonometric identities. Now, if you've ever taught the course, you will recognize that identities/proofs/teenagers, well they don't really mix. The unit was rather difficult, especially if the students didn't have a firm grasp on the unit circle or the identities.

When it came time to prove an identity, it was hard for students to see where an identity could fit or how they could change an identity so that they could substitute it into the proof. Prior to proving identities with my students, I gave them a connect the dots. Now, the one that I used in the class was one that I had found online. After using it, I decided that I didn't like it and it didn't have what I wanted my students to see so that they could "connect the dots". My mentor teacher had told me that I could create my own but I wasn't sure at the moment how I would or what I would want to change.

After completing the unit, I finally realized what I would change, now I just had to figure out how I could change it..... Part of proofs and eventually trigonometric inverses is figuring out how you can adjust the Pythagorean Identities. Often times, students don't see where identities come from once they are changed. Therefore, I wanted to create a Connect the Dots that featured some of these tweaks so I did! Below, you will find my handwritten version of the worksheet as well as what I created after my connections are drawn.

Connect the Dots: Trigonometric Identities

When it came time to prove an identity, it was hard for students to see where an identity could fit or how they could change an identity so that they could substitute it into the proof. Prior to proving identities with my students, I gave them a connect the dots. Now, the one that I used in the class was one that I had found online. After using it, I decided that I didn't like it and it didn't have what I wanted my students to see so that they could "connect the dots". My mentor teacher had told me that I could create my own but I wasn't sure at the moment how I would or what I would want to change.

After completing the unit, I finally realized what I would change, now I just had to figure out how I could change it..... Part of proofs and eventually trigonometric inverses is figuring out how you can adjust the Pythagorean Identities. Often times, students don't see where identities come from once they are changed. Therefore, I wanted to create a Connect the Dots that featured some of these tweaks so I did! Below, you will find my handwritten version of the worksheet as well as what I created after my connections are drawn.

Connect the Dots: Trigonometric Identities

Let it be known, this is a flower and the caterpillar type thing was me struggling how I could fit a "four connected dot" object onto the paper. I would have loved to have another "three connected dot" to make a petal but I didn't have any more identities left.

Any critique would be appreciated on this! And I would love to hear other topics that would work with a Connect the Dot style approach. I found this to be very visual and students were able to see more connections after doing this.

## Thursday, May 3, 2012

### You know how you're supposed to write down those little things.....

One of the great bits of advice that I was told was to write down every funny thing that your students do. I also like to keep notes that they pass or notes that they give me. Now, you don't have to keep doing this for all the good things. Of course, you have to do this for the bad things as well.

Since I don't have a book deal or anything in the works, I figured I would share on this!

Yesterday, mid lesson, all of a sudden what do I hear?

"Is that smoke?"

"You're burning my arm!"

Of course, I have to turn around to figure out why there is burning occurring in my math classroom....

A student of mine decided that she wanted to burn the arm hair off of her neighbor so she took her lighter and started to burn his arm hair.

I agree, an incredibly wise idea........

Since I don't have a book deal or anything in the works, I figured I would share on this!

Yesterday, mid lesson, all of a sudden what do I hear?

"Is that smoke?"

"You're burning my arm!"

Of course, I have to turn around to figure out why there is burning occurring in my math classroom....

A student of mine decided that she wanted to burn the arm hair off of her neighbor so she took her lighter and started to burn his arm hair.

I agree, an incredibly wise idea........

## Wednesday, May 2, 2012

### 3-D Object Project

I'm currently teaching the Volume / Surface Area unit in my geometry class (10th graders) and for the most part, they have all been pretty convinced that it is easy (being that they have so many formulas). Therefore, I wanted to have my students thinking about the topic in a reverse way. I got this idea from something I saw on pinterest where someone had their students create a "pokey wall" by having each student make a pyramid. And I was further convinced that my students needed to improve their ability to go behind formulas based on a question I gave on their last test on the Area / Perimeter unit (Draw and label a trapezoid with area of 100). The question had about a 50% success rate with many students unsure as to how they could pick and choose various heights and base lengths.

Anyways, I gave my kids two days in class to work on this project. On the first day, I had students randomly draw (from my hand) what their 3-d object would be [I did this so I wouldn't get all cubes]. I did allow for students to trade with one another as certain objects had possibilities for extra credit. I informed the students that because of the size restrictions (the base area and volume had specific limits), they should spend the day figuring out side/radius/slant height values so that they could start building the next day. Many students struggled with the concept that they could assign random values to meet the size requirements. Also, students who chose more complex bases, realized that they had a few more calculations to solve before being able to construct anything. On the second day, a few students began their constructions with me (the cones were rather hard for students to grasp) while others continued to work on their calculations.

The project isn't due until next Monday but I have so far gotten back a few projects and they are looking great! So far, I've gotten a rectangular prism decorated to be a present (bow and wrapping paper included) as well as a Captain Crunch box. I've also gotten some very well done pyramids and cylinders. When I get the lot of them (30 students in one class and 22 in the other), I'll take some pictures and upload.

Until then, enjoy the rubric below!

3-d Object Project

Anyways, I gave my kids two days in class to work on this project. On the first day, I had students randomly draw (from my hand) what their 3-d object would be [I did this so I wouldn't get all cubes]. I did allow for students to trade with one another as certain objects had possibilities for extra credit. I informed the students that because of the size restrictions (the base area and volume had specific limits), they should spend the day figuring out side/radius/slant height values so that they could start building the next day. Many students struggled with the concept that they could assign random values to meet the size requirements. Also, students who chose more complex bases, realized that they had a few more calculations to solve before being able to construct anything. On the second day, a few students began their constructions with me (the cones were rather hard for students to grasp) while others continued to work on their calculations.

The project isn't due until next Monday but I have so far gotten back a few projects and they are looking great! So far, I've gotten a rectangular prism decorated to be a present (bow and wrapping paper included) as well as a Captain Crunch box. I've also gotten some very well done pyramids and cylinders. When I get the lot of them (30 students in one class and 22 in the other), I'll take some pictures and upload.

Until then, enjoy the rubric below!

3-d Object Project

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