For the last part of the year we are focused on operations and algebraic expressions. In order to build a good understanding of how algebra works, we started with the pan balance approach. The purpose of this is to show students that we have to keep both sides of the equations balanced. Students need to eventually generate numerical patterns to create ordered pairs that will be graphed on a coordinate plane.
Generate two numerical patterns using two given rules. Identify apparent relationships between cooresponding terms. Form ordered pairs consistenting of cooresponding terms from the two patterns and graph the ordered pairs on a coordinate plane.
The essential question I started with in order to get to the standard was... How do I solved simple equations?
I felt if students could demonstrate knowledge of this questions they would be ready to move on to the 2 pattern rules.
I started the unit with a claim-support-question activity. This task was given to them before we had any knowledge about pan balances. The students had to work independently for the first try on a Monday. I then taught them about pan balances. The students were given a blank copy of the question from Monday on the following Friday. Many of the students (event he higher thinkers) struggled with the pan balnce problem on Monday. However, many of them were able to complete the task on Friday. In both cases they had to explain their thinking. Below are the examples of their work.
The first 3 are Monday thinking. The last 2 are Friday thinking.