Today's lesson has students engaged in solving two systems of equations: one comparing job offers from two different companies and the other comparing the cost of two different cell phones. The lesson has a strong focus on common core content standards, particularly around creating and solving systems of equations
I use language and writing as a tool to access the mathematical ideas in this lesson. The lesson has many different language components, asking students to not only to articulate their own reasoning, but compare and contrast their reasoning with those of their classmates, getting at the core of MP.3.
I want students to document their reasoning in mathematics through writing, and to do that I find it helpful to provide students the time and support to do this. If I do not value their writing through time and support then the class quickly reverts to "answer getting."
The intent of the Sentence Strip Activity is to persevere in problem solving and to focus on the organizational structure of a written response in mathematics. Students work in small groups to create a written response from the sentence strips.
The activity provides students with a scaffolded investigation into how to analyze and critique a real-life situation that shows the utility of creating and interpreting systems of equations. In this case, students "see" how an understanding of systems can help them make decisions about which cell phone plan to choose.
*Note: Prior to the lesson, it saves a lot of time if teachers cut the sentence strips. I like to have a class set of this activity and then collect the sentence strips at the conclusion of class so I can re-use them year after year.
If there is time in the lesson, I also have students review the model written response and compare and contrast it to both their groups' constructed sentence strip paragraph but also to their original response.
After the initial activity students complete Reflection: Sentence Strip Activity to process the activity and identify areas of learning as a result of working in groups on the sentence strips.
The objective of the Cell Phone Activity is for students to apply mathematics to real life situations and engage in modeling (MP.4).
An important element of the task is for students to express their thinking in writing. For the Cell Phone Problem, I intend for students to complete a think-pair-share as a way to hear other perspectives and begin the process of organizing their own ideas. The Think-Pair-Share gives students an opportunity to process and communicate their ideas and to listen to the ideas of their classmates.
I like to have students work in groups to understand the problem. Group work also provides a nice degree of scaffolding in the class, as students can rely on their peers for support in understanding and solving the problem.
With about 10-15 minutes left in the section, I cue students to begin working on the written response independently. During this time students complete the Idea Organizer (Student Work: Cell Phone Plan Idea Organizer)and also craft a well-developed written response (Student Work: Written Response Cell Phone Plans), using the Idea Organizer as a guide to their writing.
After completing the written response on the cell phone plan problem, I have students swap their responses with a peer from another group and complete the Peer Reflection: Cell Phone Plan Problem. Students then spend time reviewing the response of their peer and providing constructive feedback on the response. An example of student work is included as a resource in this section.
This exercise gets at Math Practice 3 (MP.3) as students get to think about the problem they just solved from the perspective of one of their classmates.
The reflection activities in this section sets up students to think about how to communicate their thoughts.
The first time students complete an activity like this can be a difficult process. For example, the Student Work: Peer Reflection is a good initial attempt at completing the peer reflection exercise.
I have found that if I adjust my goals and have the expectation that students will understand the process and try providing feedback to a peer, then the first-run of the activity has been a success.
Over time, like many routines (Turn and Talk, Think-Pair-Share, Entry and Exit Tickets, etc.), peer and self reflections become more automatic and part of the regular routine.
To conclude class I have a class wide discussion on lessons learned from the two main activities of the day. The class brainstorms different lessons learned and we work on identifying areas the class did well on as well as concepts that the class would benefit from additional review.
I also like having a class wide discussion so I can check in on students and provide a lot of positive reinforcement. Writing is a very personal activity and I want to congratulate and praise students for not only writing, but allowing a peer to provide feedback on their writing.
For homework students complete the Homework Self Reflection Cell Phone Plan Problem on the cell phone writing activity. I want students to take the time at home to independently think about the strengths and weaknesses of two main components: 1. writing about math and 2. their understanding of working with systems to make decisions.