New Integer Strategy!

New Integer Strategy!

During CAMT 2016, I attended a session called "Access for all:  Collecting like terms and solving equations."

The presenters:

Drew Wyrick, Fort Worth ISD Colleen Eddy, University of North Texas

This session was AMAZING!!  The biggest take away from this session were these mats they use in the secondary classrooms to assist students dealing with positive and negative numbers.  I am NOT making any money off of this.

Algeblocks would be perfect for these mats; however, it is imperative that you have your students draw as well.  This will help your students gain a better tool for their tool belt.

Here is a link to a prezi presentation by the presenters; however, there is not an example provided showing the usage of these mats:

https://prezi.com/yxxrajr5stuk/access-for-all-1/

Here are the mats:

The students will write the problem at the top of the mat.  They will then draw circles/squares/something to represent 1 unit.  They can also draw rectangles to represent variables if you would like.

The students then combine like terms by matching zero pairs.  What was perfect for this mat is it is quick and easy to replicate for the students.

My example:

-3 + 5

Step 1:

In this example, I "drew" 3 negative circles and 5 positive circles.  Note that I did not have to put several negative or positive signs (Phew!).

Step 2:

I found a zero pair (AKA, a negative and a positive to cancel out).  I marked out one negative and one positive on each side.

Step 3:

I found 3 zero pairs and marked them out.  I found by marking out the zero pairs that I have exactly two circles left.  As they are in the "positive" section, I know my answer to -3 + 5 is a positive 2.

It's pretty simple, but it will definitely help fill in this gap for my students.  :) 

To take the mat further, you can use this below for equations and inequalities.  

Ok, when I first saw this, I was like "what the what?!"  After working with the great team that presented, I now feel comfortable implementing this into my classroom.

Step 1:

Solve 2x + 3 = 9

I wrote the problem on the line.  I then created the problem visually by drawing the left side of the equation on the left side and the right side of the equation on the right side of the mat.

Step 2

I need to cancel out my units as I cannot cancel multiplication while there is addition.  As such, I need to create a zero pair.  I do this by drawing 3 units (to match the 3 positive units) in the bottom left negative box.  This is equivalent to adding a -3 to the equation (or subtracting by 3 as some say).

Step 3:

If I add three negative units to one side of the mat, I must add three negative units to the right side of the mat.  It is an equation and must follow the rules of keeping the equation balanced.

Step 4: 

I then find zero pairs vertically (positive and negative on the left).  I cross them out.

Step 5:

I also complete this step on the right by finding zero pairs.

Step 6:

The most difficult step for our students is dividing.  For this instance, the students will need to count how many variables on the left and make exactly that many groups on the right.  In this case, it came out perfectly.  There are two variables, thus two groupings.  As there were six positive units on the right, I can make two groups of three.

Therefore:  x = 3.  I know 3 is positive as the units are all located in the positive section and my variables are in the positive section.

I do hope these mats help in your classroom.  Again, these are NOT my mats.  I am not making any money by sharing these mats.  I am sharing the knowledge I gained from the CAMT 2016 session.

Thanks!!