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!!

 

 

Posted with Blogsy

Geometry: Non-Central Angles, Interior and Exterior Angles, and Secant and Tangent Relationships of Circles

Pg 5. Non-Central Angles (Need to rethink the title now that I think about it.)

This page consists of a half page fold of two pages glued together with four half page folds on each page. This entire page is pulled from the CSCOPE curriculum and tweaked just a bit.

First, we completed a page/lesson using paper folding and making conclusion based on what we know. When complete, the students would make a conclusion based on the evidence. We wrote that on the front off that page. After we completed all four pages, we went to the front and wrote three summarizing conclusions. I think it went pretty well and soundly build and understanding.

First section:

Left side:

I drew up a general diagram for the following three pages. We then completed the lesson with the same diagrams.

Right side:

Second Section:

Left side:

Right side:

 

Pg 6. Circles, Lines, and Angles

I want to find a better way to present and organize the following two pages. My students understood, but it didn't make a lasting impact.

 

 

 

Pg 7. Secant and Tangent Relationships

 

 

 

Posted with Blogsy

Geometry: Pythagorean Theorem

Pg 6. Right Triangle Basics (Optional - Used this my second year, but not my third.)

 

Pg 7. Pythagorean Theorem

LEFT: We took a square piece of paper and folded it until the entire square is made up of small right triangles. We then selected a right triangle and the three surrounding squares to demonstrate the Pythagorean Theorem.

RIGHT: Another time, we selected, drew, and then cut out the diagram to demonstrate the Pythagorean Theorem.

I have seen other diagrams using all the pieces to make a square, but I have yet to understand them or see the purpose. Any suggestions for enlightening resources?

Pg 8. Pythagorean Theorem and It's Converse

This next year, I will use Anglegs and worksheet to introduce and classify triangles.

My students came with excellent prior knowledge of the Pythagorean Theorem.

Pg 9. Multistep Pythagorean Theorem

 

 

Posted with Blogsy

Geometry: Parallel and Perpendicular Lines

I have struggled with this unit for the past three years. I do a great job with the geometry side, but the algebra is really tough to handle. I'm not sure what skills my students have coming in from Algebra 1 and in my first two years I ended up bogged down reteaching. My third year, I set a schedule and limited myself to a set number of days and pushed through. I made my primary focus applying geometry on the grid and tried to make the algebra as logical and visual as possible.

These journal pages are from my second year of teaching.

Pg 1. Unit 2 Coordinate Geometry

Pg 2. Types of Slopes

 

My first attempt at teaching slope with a foldable.

Pg 3. Slope - Intercept Form

I now like to pair rise over run with fall over crawl.

 

 

Pg 4. Parallel vs. Perpendicular

 

 

 

Posted with Blogsy

Supplies... Key to Journaling!

SUGGESTIONS?!? Anyone?

For some reason, I cannot type in the reply comment box through my iPad and my iPad is all I have to work with.

A fellow expert in her field added a comment:

Jessica MonahanJune 26, 2013 at 5:42 PM

"I decided to try journals with my kids this year. It lasted about two weeks before all of the scissors, glue, markers, etc that I had bought for the "supply" baskets disappeared. I had spent hundreds of dollars and wasn't replacing it so the journals went away. I explained to the kids that these weren't for the taking but they disregarded me. Any ideas for solving this problem? I am an old teacher. I'm very comfortable being the sage on the stage so out of the box thinking is very new for me and everything I try, blows up. I work with VERY inner city kids who do not bring their own supplies...ever."

I wish that I had all the answers. All I can do is share some thoughts and reflections.

I purchased supply 'caddies' from Dollar Tree for $1 EACH. I have seen them elsewhere such as K-mart, Wal-mart, Target, etc. These helped me to organize and quickly count supplies before dismissing class.

Each caddy consists of three

• bottles of glue (always liquid, it's cheaper and holds better)
• small safety scissors (They may be highschool students, but I found that the smaller the scissors, the less time the scissors spend in their hands.)
• highlighters
• ultraflex rulers
• safety compass
• mini protractors

The following images are ones that I pulled from a google image search and do not reflect what my baskets consist of. My baskets remain on my classroom tables where the students sit.

Thought the above image was a neat idea for storing the baskets. The teacher used 3m plastic hooks.

IDEAS:

My second year students purchased one supply of their choice to contribute. This sort of brought out some ownership from them and they didn't disappear.

STAPLES: My first year, Staples had amazing sales and as a teacher they would let you get 15 to 30 of penny/quarter items instead of a limit of one. (Must have evidence that you are a teacher.)

The caddies made a difference in organization and counting of supplies.

I am extremely particular when it comes to objects in my class. My saying: "Don't jack with my stuff!" I watch students like hawk. Supplies stay in the basket until needed. If I see one out or used without need, I tell the student to put it back and continue teaching without pause.

Modifying behavior: I start day one with what is supposed to be in the basket and before they leave each day we make sure everything is put up and accounted for.

For middle school and freshmen, a colleague of mine assigned supply managers every other week. The supply manager was in charge of getting the basket and accounting for the supplies for each table when class was dismissed.

Journaling is a daily event of my class. The only day the journals are not used is on testing days. The journals are turned in for a major grade.

 

If anyone has strategies, advice, and/or success stories, please share!

 

Posted with Blogsy

Constructions!

I LOVE CONSTRUCTIONS! I plan on teaching them as an ongoing concept.

Last summer, I was introduced to them at a workshop. I was never taught constructions when I was in high school or college. This was brand new. I went home and completed a detailed step by step and guideline for myself. I will share this. If it doesn't make since or you have another way or constructive criticism, please let me know. I did teach some this past year and the experience went really well. The students loved them and it helped build a stronger connection and understanding amoung the fundamental concepts of Geometry.

 

I begin constructions with a diagram and a few 'rules' or guidelines for myself and my students.

I couldn't tell you how I folded and glued these ten pages togther, but this is the coolest document that I think I've ever done. It is front and back and about 9 feet long.

One side is my initial attempt and additional practice. The other side is my detailed steps and constructions. I hope that these make sense, and if not, you can find a lot of great videos on youtube!

 

 

 

 

 

 

 

 

This last one is a confusing combination of my discovery and the presenter's approach. I always knew that SSA was not a postulate/theorem of triangle congruency. How? "Because you don't say ASS in class!" is what my high school teacher told me. It wasn't until my third year of teaching that I figured it out. I actually learned this through Khan Academy and of course put it to paper. The way the presenter approached it, you would never have a problem with the 'a-word' in class, but I couldn't tell you what or how she said it.

 

Posted with Blogsy