I am a firm believer that students need to practice math concepts again and again for them to become proficient. Some students may need more practice than others, but everyone benefits from the review. Worksheets are good when there is not a lot of time, but they can be quite boring! However, give a student a pair of scissors and some glue and now they are engaged. That is what I like about Jacquie’s Expanding and Simplifying Card Sort. There are six problems for students to simplify using the distributive property and combining like terms. The problems are similar enough that you must do the work to figure out the answers. I wanted the pieces to be bigger so I retyped the problems in Keynote and put a border around each expression. (Don’t worry, I first purchased Jacquie’s set and I am not looking to sell my version.)
I thought this would be a great activity on a day that I wouldn’t be at school. I gave instructions for the substitute teacher to read to the students, along with all of the materials. Unfortunately, students seemed to glue pieces in random order. By just looking at the papers and not knowing what went on while I was away, I’m not sure if the students did not fully understand the directions or they just didn’t want to do the work. I do not fault the substitute teacher or the students. Rather it got me to thinking, what could I do better to keep all students accountable for actually doing the problems and for me to see the students thinking?
So, I re-ordered the cards on the handout so that the problems were in the first two rows, the middle steps were in the next two rows, and the final expressions were in the last two rows.
Instead of giving students all of the pieces at the start, they would only be given the initial problems to cut out and glue on their paper. Then they would have to work out the distributing and show me their work before getting the next set of cards. Students would be able to check their answers when they cut and glued these cards underneath their work. Finally, they would combine like terms and show me their final expressions before getting the last of the cards.
In the end, students still get to use the scissors and the glue. However, I can quickly glance at each student’s work to see who understands the concepts and if not, where they are making mistakes.
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…
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.