Sunday, April 29, 2012

Quadratic Equations & Aliens

As I've mentioned before, my roommate Heidi is also a secondary math teacher currently doing the same Masters program. One of the great perks of living with her, there are many, is that we can bounce ideas off of one another for our lessons. So Heidi is currently teaching algebra 1 at one of the local high schools and needed to teach the topic of quadratic equations. Rather than doing a standard lecture on the equations, she did a 3 lesson where students researched the quadratic equation and taught themselves. It was a true example of a flipped classroom. She sent the students to this website: http://smithalgebra.wikispaces.com/Home+Page and they were to develop a presentation on how they would teach an alien how to do the quadratic equation. Students created poems and songs and they had a great couple of days presenting what they had learned.

Yes, it's a short post but I really wanted to give a shout out to her awesome idea!! One day, I'm totally stealing this. Because hey, as I keep saying, stealing is one of the great perks to this profession.

Monday, April 23, 2012

Discovering Special Right Triangles

Phew, needless to say, it has been a very hectic last couple days/week. Last week, we had a job fair to attend, which took a bit of priority in my life preparing for. Hopefully I can soon have a post where I announce that I have a job :)

Anyways, the point of this post is to talk about this activity that I did earlier in the year with Geometry classes. Rather than giving my students the side to side ratios for special right triangles (45-45-90 / 20-60-90), I wanted them to discover the ratios on their own using prior knowledge (Pythagorean Theorem). Now, as this was early on in my student teaching at the placement, they were VERY resistant to not being told what to do or just being told the formula. However, I am a huge fan of discovery/inquiry based teaching methods and this was a great version of this. Basically, I gave my students these packets (one triangle on each day) where they developed a conjecture about the side ratios for each triangle. For the most part, it is now firmly placed in their minds. Anyways, I have a few screen shots of the worksheets just for your reference.


Basically, the 45-45-90 triangles were slightly easier, thus why we started with these first, but the the students struggle with radicals. Overall, they can see that the sides will be the same (because of the angles) and then they find the ratio. I would have added something about how to go backwards more firmly as this was a struggle.

Starting with an equilateral triangle, you can draw a bisector to create a 30-60-90 triangle. The short and hypotenuse are very easy to see for the students, but again, the radical throws students for a loop. Again, I would also emphasize how to go backwards after deriving this.

But again, I truly love discovery and the students are super proud of themselves after they notice the property. So good luck using discovery/inquiry in your classroom but it really does make a world of difference, especially with common core coming into play :)

Wednesday, April 11, 2012

Mosaics with Percents/Decimals/Fractions UPDATED

Despite having an extremely long day today (oh about a 15 hour day), I'm sitting here wide awake. I've been meaning to make post for a while now about a lesson that I did back in the fall when my student teaching placement was in a middle school. At this placement, I taught 7th grade math to a group of inner city children. One of the lessons that I taught was about converting between percents, decimals, and fractions. For the first part of the lesson, I created a Smart Notebook file that I based upon something I found on Smart Exchange (a wonderful resource that I highly recommend). It proved to be a very wonderful lesson that broke down the three topics very well starting with a 10 by 10 square shading leading to different and more complex fractions that my students solved. If you are interested, I'd be happy to post a few of the slides but for now, I want to focus on what I had my students do after the lesson.

I'm a huge fan of incorporating outside skills and subjects into my classroom. Before I wanted to be a math teacher, I grew up wanting to be an art teacher (I really wasn't that great) but it was something I loved. Because of this, I always look for ways to incorporate art into my classroom. Can you tell? Did you read my post about graphing circle artwork?

Anyways, with my 7th graders, I based their assignment off of an article I read somewhere (I can't find it anymore) about creating a mosaic or a quilt where students must develop the percent, decimal, and fraction for their design. Each student was given a 10 by 10 square that they were to color using at least 4 colors. For my advanced classes, I had them exclude the outside rows (making it an 8 by 8 square) to create more difficult fractions. This also required them to think about what the new dimensions would be. A problem on its' own. The back side of the worksheet was an additional chart that had certain values included such as a percent and they had to find the fraction and decimal as well as a column for the dollar amount. Sometimes, they'd be given a fraction or maybe a decimal and so forth.

Basically, my kids were super pumped to be coloring in a math class. Especially in my inner city placement where many of my students went home and weren't allowed to be kids. Warning for some of you, some of your students might not have coloring utensils at home and because of this, they don't end up doing their homework.... But here are a few that I got back :)


 This is an example of one of the differentiated mosaics.

The back side of the worksheet.

Hopefully, this gives you some ideas on how you can use art when teaching the fraction, decimal, percent conversion. Let me know, if I can send you or post any of my documents, I've included the link to the front side of the worksheet where students can color on scribd :)



Warm Regards!

P.S. Update (1/21/13) Wow! This post has been popular! Thank you to everyone who has pinned this and helped create traffic to my blog! I realized that i never gave credit to the article that inspired this lesson so I wanted to add it! Masterpieces to Mathematics

Percents Decimals Fractions Mosaic

Sunday, April 8, 2012

Unit Circle Plate


The unit circle plate is a concept that I got from my mom. When I was in high school, learning about trig, which I hated by the way, my mom had us create a plate with all the radians, degrees, and trig values (we added those after I made my plate). So I decided to do this with my students.

Basically, we folded a plate in an honors class and used the concept of pie slices to figure out the radian fractions. The kids had already learned about degrees so this helped when relating trig values to radians. But basically, you can teach this lesson using the concept of how many pie slices do you need to make 120 degrees and relate it to the size of pie slice for 30 degrees. 

Oh, and it doesn't hurt to serve pie on this day :)

Graffiti Review

Prior to spring break, I had two days to review with my students for their terrible, awful, horrendous test on circles (it was really bad so they got the opportunity to do corrections and write a letter to me). One of the days of review, I played a game because I love playing games with my students. The other day, per their request, was a packet day, not so fun. However, I decided that before passing out the packet, I would do something a little more fun.

There are 4 white boards and 1 smart board in my class for a total of 5 boards. I explained that we would be doing something called Graffiti with our boards. Each group (I have the room divided into desk groups) was assigned a section that would be covered on the test and their job was to pick out the best theorems, definitions, examples that they think would help people study for their test. For the most part, the students enjoyed doing this, the Smart board group LOVED playing with the board. After drawing their graffiti, I had each group present their graffiti to the class. With today's technology, students were taking pictures of the graffiti with their phones to help them review. I, being without a smart phone, took pictures with my normal camera and here were the results!






Of course, the last picture, the group had a lot of fun drawing around the board afterwards but this didn't bother me as they did a great job showing the different cases of the theorems. I really liked this activity so students could explain what the theorems meant without huge language that they didn't understand. There were some negatives to the activity such as not having 30 markers so students couldn't all be participating plus some groups had a smaller work load than others so I had to encourage them to think about what else could help them. But overall, I loved it and would do it again. One student had asked if we could do this outside with chalk and I LOVED the idea and was sad I hadn't thought of it. Hopefully, I'll take my kids outside this week to do a different type of review.... details to come.

Happy Sunday!


Vista Print Shopping Spree UPDATE

Finally, a moment to breathe and a moment for me to post :) Per my usual Sundays, this is my day for lesson planning (in my program, lesson plans are due every Wednesday for the following week). Needless to say, my brain thinks that it's like April 20th because of the advanced planning. My roommate shocked me when she said it was only April 8th. Anyways, lessons planned, tomorrow is prepped so now I can post!

I just uploaded all my pictures from my Vista Print order and I was so excited!!!! Unfortunately, I did lose one soul to my anxious opening.... Warning to those who order from Vista Print, open carefully because you can tear things....


 Such cute stationary for thank you letters to students!!!


I've already used this notepad to leave notes for Heidi :) I also got cute sticky notes. I might use those for quick passes but it would have been wise to order a specific item from Vista Print just for hall passes.


PROPERTY OF MISS RUDOLPH :) I just taught my students what a kleptomaniac was. Ha, you can teach vocab in math :)


This is for my Cookie Challenge that I do with my students. I'll probably just put it on top of the score board.


My one and only class rule. It's a good reminder.


The signs you can make are really cute. I'll probably be revisiting this in the summer because it is so much more cost effective to make your own signs. Even Heidi thinks so :)


Door Sign! 


The one and only casualty :( I'm going to try and fix it with tape or lamination. Because it is far too cute and precious to dispose of. I had gotten this idea off of pinterest to make a letter/poster that shows my students that I care about them, as if they didn't already know... i mean i bake for them...

I feel like making another post..... so I probably will today..... but anyways. Here I am again saying... GO TO VISTAPRINT AND BE COST EFFECTIVE!!! It's really easy to use their free products to make awesome stuff for your classroom. And the posters aren't too bad either! Look out for coupons and gift certificates to make it even cheaper!

Happy shopping!

Sunday, April 1, 2012

Equations of Circles UPDATE

Sorry this has taken so long. We were on spring break this past week and well, I quite frankly didn't feel like grading homework/circle projects after their tests while I was vacationing with the family. I have a lot of posts that I need to do but I figured that I'd update you all, whoever you might be, on how the circle projects came out!!!

Here's a refresher: My students were asked to create a picture using at least 4 circles (if they did 8, they got extra points, and after their main 4, they could add on to it however they pleased) and then they had to label the equation, center, and radius for EACH circle. Lastly, I had students create a question that would be used for one of their circles. Below is a picture of the rubric that I gave to each student. They were then asked to staple this to their creations when they handed them in.
The pictures that I got back were for the most part, amazing!!! I had chosen to do this project because I was well aware that I had students who were very interested in art and I wanted to find a way to incorporate this into our class. Equations of circles was the perfect solution to this!! Although the students were only required to do 4, many did the 8 for extra credit and some students went above and beyond! Two students did more than 50 circles, one doing 56 and another doing 110!!!! My students and our youth are extremely talented. I find this to be sad, however, because the school district that I am in is losing their art classes next year due to budget cuts and a levy that hadn't passed in the fall. I'm uploading a few pictures of their creations. See for yourself!! Give your students the ability to draw in your math class instead of doing a worksheet (although some students did say to me that they would have preferred this, but they were a small portion). Please be reminded that these are samples of work from my students and all work has been de-identified and I do not take credit for their creative/artistic ability.









Phew, I've really been wanting to share all their beautiful work and the idea for teaching this lesson. Enjoy!!!

p.s. my vistaprint order came in... it's still in the box because I have been so busy with catching myself up for post spring break..... but I will repost about that soon!!!

UPDATE:


Here's a picture of all the pictures hanging up. The students and classes keep looking at their art work. My honors kids were rather jealous that "Geometry just colors."


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