# Expanding and Simplifying Algebraic Expressions

This week, my 8th grade Algebra class will be having their first test.  Two topics that I want to review with them again before the test are the distributive property and combining like terms.  Jacquie of Mathematters has a great cutout activity that I use with my 8th grade pre-algebra class.  However, I wanted something that would take less time but still have the students engaged.  Also, I wanted the activities to make their thinking visible.  So I made a handout using the same idea, but students have to draw arrows to the correct corresponding step instead of cutting and glueing the pieces in the proper order.

Here is an example of a student’s work:

I was able to go around the room to see that students were showing their work with the distributive property and then circling and boxing in like terms to get the final answer.

After that, students worked in groups to figure out the errors in this free handout from Secondary Math Solutions.

Students had to locate the mistake, as well as explain how to correct the mistake using complete sentences.

In both activities, students needed to either show their steps or write out the process to complete the problems.  Both activities allowed me to see who understood the problems and who needed more direction.  Now for the test…

# Discovering the Pattern of Multiplying Negative Numbers

After reading Making Thinking Visible by Ron Ritchhart this summer, I knew I wanted to get students more engaged in the learning process.  I need to start talking less and have students discovering and writing more.  To be honest, this will be a challenge, so I will be taking small steps this year to accomplish this goal.

In a previous blog, I mentioned that I was making changes to my 7th grade math curriculum.  However, I noticed a spot in my 8th grade Pre-Algebra lesson plans where I could easily make a small inquiry-based task to get rid of direct instruction.  This week my 8th grade Algebra students were reviewing how to multiply real numbers.  In 7th grade we dealt mostly with multiplying only two numbers so my 8th graders were familiar with the rules that if two numbers had the same sign, their product was positive and if two numbers had different signs, their product was negative.  However, in 8th grade Pre-Algebra, this concept is extended to multiplying more than two numbers.  I wanted them to see that there is a pattern to multiplying with negative numbers. Rather than just tell them that the product of an even number of negative numbers is positive and the product of an odd number of negative numbers is negative, I wanted students to discover the pattern.  I made this handout for the students to help them come to that conclusion on their own.

Students were given 5 minutes to work independently.  Then they got in groups of 4 and discussed their answers for another 3 – 4 minutes.  Finally, we met as a whole class, at which point we could write out the rules in our notebook.

It didn’t take a lot longer for students to work through the handout, but I know that the extra time was worth it because all students were working to find the answers, rather than just copying what I wrote down on the board.

Like I said, small steps, but with each step I hope my students will have greater understanding.