Saturday, March 30, 2013

Notable Equations

Again focusing on identifying and understanding components of Algebra, I decided to discuss the parts of these two notable equations.



My students overall liked this page because they now understand what the letters represent in the equations. I heard a lot of "Well, that makes since" and "Now, I see the point".

I was impressed with their overall prior knowledge that they related to me during this lesson. It was refreshing.


My Tool for Finding Slope & Slope Scrabble

Before our test, I decided to review finding slope with the two methods we had studied.

1. Counting Slope on a Graph

2. Slope Formula

Several of my Geometry students used a method earlier in the year that I thought Algebra 1 might appreciate.

  • Positive: rise over run
  • Negative: fall over crawl


We also discussed the staircase within a staircase.

Then we moved over to the slope formula. We also discussed the relationship between coordinate values and slope values of horizontal and vertical lines.


SLOPE SCRABBLE! Not as exciting as it sounds right now. We tried this but it was difficult to get the idea across to my students.

They had an excellent time finding slope for all of the problems cards I gave them. I even set up a table with all the solutions laid out so that they could match them.

The idea of slope scrabble is to begin at the origin and, using slope, make your way to the far blue dot in the corner to win. All of the other dots are things like double your slope, draw again, etc. There was some success with my students that have to patience to solve puzzles. Other students wanted to match slope again.

My students have an excellent understanding of slope.

I just wish I could troubleshoot the process and get this game going for them.


X and Y Intercepts

We touched on how to identify the x and y intercepts of a linear function.



My students were quick to identify the inverse relationships of the intercepts.


Solving Equations is Like Wrapping Presents!

For my first year of teaching Algebra 1, I have made a lot of mistakes. These mistakes all revolve around an assumption. I assume that my students already know this and that. This comes from my experience in state testing remediation for 11th graders for the past three years. I now have realized that I have a chance to teach students to understand Algebra 1 from the beginning. I decided to review solving equations with my students, since this was a nightmare at the beginning of the year. I decided to teach them to understand each component of the process and what solving meant.

Step 1: "Unwrapping Your Solution"

I love reading educational material and Danika McKellar is one of my preferred authors. I remember her referencing gift-wrapping as a metaphor for solving equations. The idea of operations applied to a solution is similar to wrapping an object to hide its identity. To reveal the item, one has to reverse the process of wrapping, which is similar to finding a solution by reversing the applied operations.

It didn't turn out as spectacular as I would have preferred. However, this was a day well spent because my students no longer feared equations (for the most part).

First we started with x=3. Next, the students selected different operations and values to "wrap it up". Then in order to solve we reversed to process. When finished, we a concluded that solving is reversing the original operations. Hooray!!


Step 2: Properties Used to Solve

We identified the most common properties used in solving equations. Within the notes, we used the same equation to demonstrate how similar operations can be applied to acquire the desired result.

Step 3: How to Solve Those Equations

With the use of multi-door flap foldables, students identified each step in solving an equation by technical property and then by general vocabulary accumulated by the class. This step was critical in building their fluency in solving equations. Even lower level students that were hesitant in the process could solve.

Example1: We always started with the inside process.

Then finish by summing up with general words to help them identify the steps.

Example 2:

Step 4:
We moved from the in-depth process to identifying the general steps. By now, my students were using the vocabulary-properties, names of terms, quick steps, etc.

Step 5:

We reviewed with the giant Sorry board game. During this step, students started with a given equation including the solution and focused on the solving process.

Step 6:

TEST: I gave them a test in standardized format and received outstanding results! :)


Algebra 1 Journal Pages Continued... HOY VUX!

You know, I might have approached or pronounced this incorrectly. My students appreciated the idea, but loved the fact that I introduced them to a new word say in class-"Holy Vux!" Oh, what fun...

We did do two journal pages over HOY VUX because I wanted to examine the idea of horizontal and vertical lines on the coordinate plane. This helped to tie in the understanding of slope and the ordered pairs.

The two statements were what I had the students generate as their conclusion of the significance of identifying the ordered pairs of these two lines.

My favorite part of journaling is having students reflect and draw conclusions about the significance of what we have done. I feel that I do not do this enough. It has proven to produce some of the best and surprising knowledge of the day.


Slope Dude.... Win!

Slope Dude followed Pedro the Penguin in our journal. Pedro the Penguin was a great story that gave the students a visual to relate the idea of slope to. I also use the fact that we read a book from left to right means we also read a graph from left to right.

After building an internal understanding of slope, I wanted to provide the students with a memorable visual that my students could easily draw to reference. They love slope dude. I made sure to explain each component of his face as the students named each type of slope. It made slope dude all the more important.

Then I decided to take it one step further and go over what these slopes look like on a grid. I noticed that even though they knew the types, some of my students had trouble transferring the concept to a grid.

And I was right. As they graphed examples, I provided verbal guidance and feedback on their examples.

They were retested with a test previously given in the first semester and I had a significant increase in recognition and understanding on the concept of slope thanks to slope dude and the next few journal pages...


My first comment!

Hooray! My first comment! Thank you so much Marcy Murphy. Your comment is exactly what I am hoping to get out of this blog-ideas, feedback, collaboration, etc from others. I plan on using this strategy on our next assessment. Anymore ideas out there to get my students thinking, talking, justifying, etc. ?


Making a Change in Algebra 1

I just want to say thank you to all of you out there for your great ideas and passion for teaching. I feel rejuvenated and my Algebra 1 class is full of energy. Let me share some of the chaos as of late...


My students were having a hard time connecting the description of slopes with the actual graphs. While I was tutoring several students from other schools, one student shared an idea he learned of a skiing penguin for slope. My mind exploded with a story-Pedro the Penguin. I googled a skiing penguin as my inspiration to illustrate the rest of the story and my Algebra 1 girls wrote the story! We have no idea where the name Pedro came from.




We were solving equations and it came down to the day before the test. My students tell me that they do better solving on the marker boards, one question at a time, and with some sort of an engaging, high energy activity. Of course, right?!

Again, my brain goes into overdrive and out pops this insane idea of a giant board game.

I assigned the task to my geometry students and they succeeded. They put my tables into a closed rectangle, unrolled white poster paper all the way around, and taped it together. They finished by cutting and pasting colored squares for the track, circle for the start, mini squares for the safe zone, and a pentagon for home.

They decided to construct cubes of different colors for the playing pieces.

I googled sorry game cards and found some vintage printable cards.

Then, it was up to me to figure out how to use this for a review. Since I didn't assign a specific math concept to the game, I can reuse the board game for a multitude of activities (hopefully). I printed and pasted differing levels of equations on different colored index cards. I sat in the middle of the tables and rotated clockwise. On the first rotation, each student drew an equation and solved; and the second rotation was to verify solution and allow them to draw a sorry game card. (Idea: Have a leading student be the monkey in the middle.)

Troubleshooting: We quickly realized that the teacher looking up solutions took too long.

Solution: Each solution is written below the equation. Thus the solution was no longer the focus. The solving process became the focus of our time. WOW! You wouldn't believe the results. That small change resulted in student teaching students, collaboration, and justification of the process to me!

(Rule of Ms. Haley's class: Oral explanations only! You cannot write on others' marker boards/sheet protectors or touch others' calculators. All explanations and directions are to be given orally; therefore, students are putting any process into words.)