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!!

 

 

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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!

 

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Geometry: Finding Distance, and Applying Coordinate Geometry to Quadrilaterals

Pg 10. Finding the Distance

 

 

This is a foldable that I wrote as a template.

Pg 11. Rectangle Analysis

FAVORITE: This is an individual project that we paced ourselves through as a class.

GEOGEBRA: We used Geogebra to graph a rectangle. This required students to be able to enter in two sets of parallel lines perpendicular to adjacent sides. Each student was required to create their own individual rectangle (no two projects were alike). This required some thinking and reworking. Once graphed, printed, and pasted, students had to justify that the shape is a rectangle. On page one, they listed the equations, intersections/ordered pairs, slopes, y-intercepts, and the parallel/perpendicular relationships.

We discussed the other critical attributes needed to justify the rectangle; they came up with midsegments and lengths of each side.

I tried my best to focus on notation, and I wish that we had written a final summary justifying the rectangle. Writing is an important component on math.

This kind of activity allows students to collaborate without copying another's work. They see multiple rectangles and help others troubleshoot.

 

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What happened??!?!?

"What happened?" is the question that just seems to resonate in my brain. My Algebra 1 kids bombed their test. I had such high expectations. All I want to do is cry....

A few tears later...

Alright, I will figure this out and we will come back stronger and better.

Game plan:

1. I gridded student responses (right/wrong) against names.
2. We have tutorials 7:30 am to 8 am and 3:35 pm to 4 pm. Starting tomorrow afternoon, I will have students that missed certain questions attend tutorials on a certain day. Example: All students that missed number one will attend morning tutorials Thursday. A revised question will be a half credit towards the original test grade.
3. I plan on the students completing an in depth revision for each question by identifying properties, writing explanations, and justifying their solution. I use the Cornell notes systems as a guide for organizing the process.
4. During class I will give what I call quiz strips. These consist of two to three problems. I create two to three sets of differing questions. Purpose: Students cannot cheat, but they can collaborate and teach each other about the concept.
5. I will administer accumulative quizzes. These quizzes focus on several concepts at once with a few questions.
6. We will retest. This method of repetitive practice and accumulation has proven true with my juniors in Algebra 2. There's not a function that they cannot transform or a transformation they cannot read. They love transformations of functions.
7. OVERALL: I am focusing on my level of questioning. I have several versions of Bloom's Taxonomy printed and posted around my classroom to help prompt and remind me of the higher level of vocabulary to use.

Looking for...

I am looking for strategies in Algebra 1 to build fluency in the foundational skills. Game ideas, practice methods, anything???

 

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My method is not alone...

I had a parent ask me if their child ever has homework. I thought about it and answered "rarely." This year I have adapted a new method in practice and grading. I discovered that the battle of homework with today's students uses more energy than it is worth. Therefore I make homework 15%, quizzes 25%, and assessments 60%. Students quickly learn that they need to understand the material because I give a lot of quizzes and many differing forms of assessments.

I introduce a concept and put it to practice with five to ten problems that I monitor and grade the instant a student is finished- problem to problem or overall. I call this a double check process. If a student misses the problem I circle it and have them correct it. If and when I catch a student copying, I tell them to think for themselves and I closely monitor their work. If I think a student may have copied an answer; because I see no evidence of an attempt to solve, I ask the student how they got it. Most of the time, I am surprised. I learn a new method to solve that does not involve my extensively written out process. Sometimes I ask to see how they think. I love to learn and understand their methods.

They only receive partial credit for the corrected answer; however, I deduct four to six points per incorrect/corrected problem.

Why?

• This method provides a student with instant feedback and a chance to learn from their mistakes and get the correct answer.
• All of my papers are graded on the spot. I don't spend hours grading hundreds of papers later.
• Problems instantly correlate with a specific concept.
• My students confidence goes up with a since of ownership in the process. They love to know how they did and calculate their grade in the process.

Quizzes are where concepts accumulate and I incorporate what I have been told is a "spiral review." A quiz will consist of several questions that span differing concepts requiring my students to pull together their knowledge and skills. These also are a double check. I am more specific on the double check and points here. I use the quizzes to build my students towards confidence in their independence. Then the exams are a one time try just like the EOC. I grade them straight forward without curves. My students panic at first until I remind them that their Journal is there as a major grade in case of a low test grade.

 

The only area that I really struggle with is how to do test corrections/revisions. I want to develop a method that is thorough and worth the time. Suggestions would be appreciated.

 

I have noticed my students confidence has gone up and they take pride in their hard work in my class. They walk in, grab their journals, and are ready to go before me. I feel that my students are learning very well.

This topic was spurred on by a blog i have read recently by Math = Love.

Math = Love: A Very Good Day :)

 

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