Linear Relationships and the Slope Through Two Points

For the last couple of weeks we have been working on Finding the Slope of a Line and the Rate of Change in Linear Relationships.  I have been "Tweeting" about my method of using a "Mini Table" to find the Slope of a Line.

Here is a wall chart that explains the method that I use with my students.

The students practiced finding the slope of a line and comparing functions using my "Mini Table" method and my dry erase "Mini Table" Mat.

My "Mini Table" Mat

Feel free to download and use my "Mini Table" Mat:     Download: PDF File

I also did a really cool "Solve It, Post It" Collaborative Group Warm-up to solidify what the students have been learning.

Here is the "Solve It, Post It" Warm-up:

Each "Team" was given a different card with a pair of points.  Teams were to discuss and find the slope of the line through their two points using the "Mini Table" method.

Here are the cards. Each "Team" received one card.

After each "Team" solved their problem.  They "Posted" their answer by putting their "Team" whiteboard on the board in front of their "Team" number. (Boards are turned so that the answers are not showing).

After all of the "Teams" had "Posted" their answers, I put up a slide with a graphed line with color-coded points. I told the students that each of their set of points were represented on this line.  (It was color-coded to match the teams).

I asked the students, "Now knowing that all of the points that each of the "Teams" used to find the slope are on the same line, what should we see when I turn the boards around?"

It took some discussion and some good answers such as they should all be negative, but they finally determined that the slope on each of the boards should be the same.

I turned the boards around and....

They were all the same.... The students we super excited that it worked and all of the "Teams" had done it correctly.  :o)

This was a good lesson to help solidify the concept that I have been working on with the students.

Feel free to download my files and use in your classroom.... :o)

"Solve It, Post It" Warm-up Prompt  ~ Download:    PDF File  -  PNG File

 Cards with Two Points  ~ Download:    PDF File  

 Color-coded Graphed Line  ~ Download:    PDF File  -  PNG File

Thanks for stopping by and checking out my blog.  I hope you were inspired.... :o)

8th Grade Math - Unit 1a: Linear Equations and Solutions

A New Year and a New Schedule
Last year I taught 8th Grade Math and Math Support with 1:1 iPads. This year I am not teaching Math Support.  All math classes have gone to a block schedule. I have decided to merge my Math 8 structure with my Math Support structure from last year for the structure of my blocked math periods for this year.  The first half of the math block is called Math 8 which is centered on guided instruction and collaborative teams. The second half of the math block is iMath which is centered on independent (self-paced) lessons.

Unit 1a: Solving Linear Equations
We have finished our first unit on Linear Equations and Solutions to Linear Equations so I thought I would blog about my lessons in this unit and hopefully give some inspiration.

Last year the pacing on this unit was very short because we had 10 less school days.  This year I added back some time to this unit to give the students a good foundation for solving equations.  This unit was very hard for majority of my students because they came in extremely low and without background knowledge on the basics of solving equations such as integer rules, inverse operations, and the distributive property.

I kept pushing through the unit, forcing the collaboration and discussion because I knew that it would help make the concepts stick. Because I can't go back and reteach everything the students didn't have coming in, I gave them some resources for their math notebooks. I gave the students an integer rule graphic organizer and a multiplication table through 25.  They are finally starting to use them and realizing what a difference it makes in their attention to precision. :o)

This year in this unit I put an emphasis on solving multi-step equations with variables on both sides and simplifying both sides of a multi-step equation to analyze the type of solution the equation will have.

Students Interactive Math Notebooks
It's been a rough start and the beginning of the year is always exhausting because of the constant repetition of routines and procedures. We started with the expectations of their Math Vocabulary Book and the expectations and procedures for their Interactive Math Notebooks.

One of my classroom non-negotiables is my IMN expectations for my students.  The students are finally able to follow along and color-code their notes effectively and are finding the value in the connections they can see when they use their notes as a learning resource. And most importantly they are finally learning to keep their Interactive Math Notebooks in order and free of clutter.

Here is what the students Interactive Math Notebooks look like for Unit 1a.

My Collaborative Team Structure
Teaching my students my expectations and procedures for my collaborative team structure is also very exhausting. But I know that it will pay off and be conducive to the learning in my classroom when it all comes together.

The students have got the collaborative team "Resource Monitor" role down which is saves so much time. We are now focusing on the other roles in the collaborative teams.  They are doing so much better after a few weeks of Recorder/Reporter and my collaborative team "Solve It, PROVE It" Daily Warm-up.

I love this activity because it involves a lot of math discussion and collaboration.  I am able to check for understanding and clear up misconceptions as I facilitate.  Because we are on a block schedule, I now have every team share out their reasoning and justification.  In the future I am going to add a collaborative agree or disagree and why to this.  But for now I am just getting the students comfortable with the collaboration and sharing out to the class.

Here is some examples of my Collaborative Team "Solve It, PROVE It" Daily Warm-ups.

Although most of my collaborative team structure is done "Recorder/Reporter" style with a team whiteboard, I also create Collaborative Team Tasks that include the role of Task Manager and Team Mathematician.

Here are some examples of my students working on a Collaborative Team Task on Solutions to Equations.

iMath and Unit 1a: Solutions to Linear Equations
This have revamped a lot of my 1:1 self-paced lessons.  I know that I need to increase the rigor if I want my students to be successful this year. The foundation of my iMath is my favorite app Showbie. If you have read my blog before you know that I absolutely am in love with Showbie's Platform. This year I have the honor of being a Showbie Champion Teacher.  :o)

Here are some of the great things that can be done with Showbie.  I love that you can create assignments, students can comment in the assignments and you now grade assignments.

I  also love, love, love Showbie because I can create "Paperless" assignments and the students can annotate and leave typed responses on the assignment.  I can look at these assignments and grade and comment from my iPad. :o)

Here are some of my "paperless" assignments from Unit 1a in Showbie.

One of my other favorite apps is Socrative.  I use this platform to create (self-paced) "Digital Task Cards".  My students love these assignments because they are fun.  I love the fact that I can see real time data on how they are doing as they progress through the assignment. :o)

Here are some examples of my students doing my Socrative "Digital Task Cards".

I also tried my 1st Google Forms Formative Assessment on Linear Equations (SBAC Style).

Thanks for stopping by and checking out my blog. I hope you were inspired... :o)