Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Saturday, January 18, 2014

Kindergarten? No, I Teach High School Math!

Ok, so, funny story. My students love telling this one to newbies. We were running out of glue. (I store glue in a detergent bottle with one of those neat little spouts that make refilling glue pretty easy. However, from experience, I would invest into one of those hand pumps that screw onto the Elmer's gallon of glue. Much easier.)

 

I went to Office Depot and grabbed my usual bottle of glue and snagged 12 packages of giant white construction paper on clearance for $1.64 each. Awesome find!

I am checking out and the cashier stares at my selection and says, "Man, you do a lot in kindergarten."

Awkward pause. I reply, "I teach high school math."

His eyes widen and he then calls me "Bizarre."

Not the first time I have been called this. I just smile and say thank you!

 

Sunday, January 12, 2014

Success!!! Simplifying Algebraic Expressions

I have found that I have success in teaching when I am able to present a concept properly to the students with full definitions, correct vocabulary, and examples outlined with strategy. I leave nothing questionable or allow something to be called "that thing". I have also learned that if a strategy, method, object, concept, term etc., has a name, students learn, relate, retain, and apply them more.

This technique is very easy for me in Geometry. Geometry is my specialty to teach; however, Algebra 1 has been a nightmare.

Key problem: I teach kids how to do the math and then they ask me WHY?

And I can't answer them because sometimes I don't know why. I never questioned what I was taught; it's just how you do the math. This needs to change.

My goal this year has been to raise my skill level in teaching Algebra 1 to my skill level of teaching Geometry. It has been slow. I am extremely behind. There's no excuse. And I'm freaking out! But there are positive results. My students understand and use what I have taught them. Some of the most difficult concepts for me to teach, have become easier and more approachable. I'm beginning to see the flow of Algebra 1 and how it builds upon each concept. With Geometry, it just clicked. The struggle I've had with Algebra 1 has been the sequence. I've asked, and I couldn't find an answer. This year, I decided to pick up the textbook as my core resource pulling in CSCOPE materials, EOC prep materials, and other supplemental materials.

This is a look at our journal for the first semester. We haven't even made it half way through the journal!

Here's one area that has kicked my tush every time I try to teach it: Simplifying Algebraic Expressions. When it arrived on the horizon, I spent a large amount of time researching other teachers' strategies. I typed up my journal page pulling information from the textbook along with thoughts found on Math=Love. I liked how she took the time to define each part and show how the term can be expanded and seen in different ways. This made a difference, and answered several questions from students throughout the unit. The definition of combining like terms was referenced multiple time. For instance, a student wanted to change the exponent when adding x and x to x squared. I refered the student to the definition followed by guiding questions.

Another strategy/activity I loved was "Sorting Like Terms". A colleague of mine writes pairs of terms on cards and students have to decide on Like or Unlike and justify.

Here's my journal page on Simplifying Algebraic Expressions.

 

When we got to the example adding distribution into the mix, we discuss the operations behind distribution and combining like terms and then determine the proper order based on GEMDAS.

And I love when some student says "you do the parenthesis first". That drives me crazy!!!!! We analyze that comment and what it really means in relation to GEMDAS and what operation distribution represents.

Instead of dropping one practice assignment on my students, I have three different assignments spread out over a week that we keep going back to. This helps them review and retain the skills of combining like terms. I want them comfortable and confident with this skill. Kuta Software has multiple practice pages and at different levels. There skills are improving!!

 

 

Tuesday, January 7, 2014

Distributive Property

We had reviewed the Distributive property earlier in the year.

My students love distributing the b and making "ba+by" and distributing the c to make "ac+dc".

Another part of the distributive property is reviewing its use in mental math. Some of my students have fun using the strategy throughout the year to beat others that use a calculator.

 

Tuesday, August 13, 2013

First Day of School Journal Page

As I was putting my classroom in order, I ran across an old notebook from one of my first journaling workshops. I found a neat idea for the first day of school and will try it out this year. The presenter had created a set of classroom expectations that were cut up into a tangram for the students to put together.

I decided to add this to my course syllabus page that will be page one in our journals this next year.
Reason: When a students asks me a question about classroom policy, I will redirect them to the course syllabus.
Page 1:

I have typed up my course syllabus and crammed it into two pages.

We will take these two pages, fold them in half, and glue them together.
On the front will be where we glue the tangram classroom expectations. (Now, I didn't write these. I'm not sure if the presenter before me wrote them either. :) )

 

Sunday, August 4, 2013

Method to my madness!! Building Journal Pages:

Questions: How do you create a journal page or foldable? Where do you start? How do you come up with it?

I'm not sure if I've written about this yet, but it is definitely on my mind quite a bit. My second year co-teacher always asked, "How do you come up with this?"

The answer to that question has been on my mind all through my third year of teaching. So let me see if I can lay it all out.

Step 1: I start with a general objective, select an assignment, and check to see that it aligns with the quiz and unit assessment.

This strategy evolved from the curriculum director at my previous school. "Keep the end in mind." When planning you want to continually loop through and keep the assignment, quiz, and assessment in mind as you plan a journal page, lesson, activity, etc.

I have several EOC prep books that I use for quizzes and the CSCOPE curriculum for unit assessments. I always start by taking the quiz or assessment myself. I work each problem in as many different ways as I can and note each strategy used. The hardest strategy for me to see is always the logical approach. Usually, this method comes out during the lessons from my students. I know that this idea looks and feels like teaching towards a test, and it probably is, but I do what I can.

Step 2: Now that I know what we're working towards, I take the concept, topic, or objective and begin my research. I look online mostly, reference CSCOPE curriculum, Glencoe textbooks, EOC prep guides, colleagues, etc. I try to reference a minimum of four to make sure I have confirmed my findings.

Step 3: Time to organize. I look at the information that I want to convey to my students and begin to think about the method that would best fit this lesson.

  • Are we defining something?
  • Is this too much at one time?
  • Do I need to break this into mini lessons with guided and independent practice loops? (That's what I did for special right triangles this past year and it worked out great.)
  • What will this journal page or foldable contain?
  • Will it define and organize the concept, contain a reusable manipulative, be the result of a paper folding activity or lesson, a reference of guided practice, or all of the above?
  • What is the point of this journal page and how will it benefit my students?

Once I decide the purpose, I then begin to look for or create a foldable that will organize the information and lesson into sections.This is important to me. I like information to be organized, sectionalized, bolded, boxed, highlighted, etc. Kids tend to remember things like that. A lot of times, we'll end up with glued attachments here and there to accomodate new information or make a little more room.

I can't really explain how I come up with my lesson. I've been told that my wacky brain is hard to follow. Sometimes, the lessons are from colleagues, workshops, or previous experiences that I tweak to fit my agenda. My goal on each journal page is to take an overload of information, organize it, and make it relatable to my students. If you've read previous posts, you'll see where I ask for suggestions on how to make a journal page better.

I'll admit, I am not always this on top of my lessons. Sometimes, I walk in knowing what I need to teach, but not how. My go to "don't know where to start" strategy is to go with a blank white sheet of paper. My students know to use my go to short fold half page foldabable. It's boring but I can expand this, glue attachments, glue it like a pocket for additional stuff, and initially this simple foldable provides three sections for attempting to organize. I use this foldable alot, even if we're not writing much. I don't want to run out of room. (Occasionally, I come up with nothing. I turn to a printed paper lesson. We glue together like a book and then into our journals.)

During the past year, my geometry class actually wrote on a lined page in the journal.... twice maybe. There's never enough room and I like to contain a concept to one page. We actually used 90 of the 100 sheets in the composition book. I did only use the front side, but hope to use the back/opposing side as a reflection, sentence stem, summarizing, something page.

Step 4: Once I know how I want to organize and relate, I create a quick disposable mock up of what I plan the journal page to look like. I scribble an outline and notes to self. This is usually something that I use as a guide to keep me on track and throw away later.

Step 5: (optional) Sometimes, I create a pre fab printable foldable template. This makes journaling go much faster and students are less likely to fall behind or make mistakes. I usually have one foldable completed to show students what we're trying to make. Some students are quick to figure it out and begin to help others. I use solid lines to indicate folds and dotted lines to indicate 'cut here'. This strategy can save time by having the students write less and provides structure to help them better organize the information. However, I am a huge advocate of students writing! I think my students have learned more this past year than the previous two because they wrote everything. I rarely printed definitions, diagrams, illustrations, proofs, etc. It was sometimes hard, but my students were better off. Watching them draw platonic solids and cross sections was entertaining, but extremely difficult. I did give in in the end and printed them off. However, anytime I print something off, I still require students to participate by highlighting, fill in the blank, notating, etc.

Step 6: I teach the lesson. I try to make every step of the process engaging and mathematical. I ask open ended guiding questions before, during, and after the creation of the journal page. (I have developed excellent wait time. It was hard, but I'm quite proud of that.)

Even the foldable itself is a mini math lesson. I try to use mathematical language when referencing folds. It took about half a year to come up with new terms for hot dog and hamburger fold. Actually, a student suggested long or short half fold and I've used it ever since.

One time in geometry, I needed the students to fold a blank piece of paper to get sixteen boxes. They recognized a pattern in the words I was using - one half, one fourth, one eighth, one sixteenth. It turned into a mini lesson on exponential functions.

Is this strategy full proof? Absolutely not! I usually change a journal page up year to year, class period to class period. My students are my guiding force, and they let me know what works. Someone once told me that you have to learn to teach students and not just teach a curriculum.

 

Saturday, July 20, 2013

Quadrilaterals Project From My Second Year

My secret.... Sometimes when I'm not sure where to start, I go to my students. My second year of teaching, I got to the unit of quadrilaterals and had no idea where to start. I decided to assign an exploratory based project to my honors class and see what turns up.

Objective: Students design and create a graphic organizer on the topic of quadrilaterals.

It began as a very open project and resulted in some unique results. I gave them several days to research, design, and produce their graphic organizer. We used a round robin strategy to evaluate and rate the graphic organizers on display. After this, the students were to choose a graphic organizer and complete one of their own for their journal containing the generalized information of the class.

 

The following are student products and may contain copyright violations and incorrect information.

1. Multi Shutter Fold within Large Shutter Fold

This was by far the most creative and the inspiration for the Properties of Quadrilaterals foldable I now use.

2. Basic Half Page Book Fold

3. Shutter Fold
4. Shutter Fold
5. Half Page Book with Post-it pop ups
This student is one that always makes me smile-unique, challenging, and brilliant. His graphic organizer turned into "what is not a quadrilateral" and I think he enjoyed exploring other shapes more. He used post-its to summarize/justify why the shape is not a quadrilateral.
6. Attribute Pop-up
This graphic organizer is great!! They drew individual quadrilaterals and added pop-ups for definitions. Not overly organized, but I still like it.
7. Trifold Computer Generated
8. Half Page Book
I don't know how I feel about the quadrilateral web, because it depicts a parallelogram as being a subcategory of a trapezoid. That was another gray area topic. It was a good conversation to listen to when the kids evaluated this graphic organizer.
9. Half Page Book
10. Layered Flip Book
 

I collected the above graphic organizers, combined some styles that I liked, and produced the following graphic organizer that I used this past year. I am always still working on facts and information. So if you have any critiques or suggestions, please comment.

 

 
 

The second half of the project consisted of an essay.

Options:

  • Write two full pages analyzing the attributes and relationships of quadrilaterals.
  • Depict the attributes and relationships of quadrilaterals using fiction.

I ended up with quite a bit of plagiarism which was a violation of the course syllabus and resulted in failing grades and reprimands.

However, the best result is the relationship a student told of a rectangle and a rhombus. "Rectangle and Rhombus stayed out late one night, and nine months later they had Square."

 

EXTRA: This is my first quadrilateral foldable experience from a journaling workshop.