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# Writing in Math Classroom, Part 2: Solving Equations & Inequalities in 2 Variables

Lesson 12 of 12

## Objective: SWBAT create viable arguments and critique the reasoning of others. SWBAT identify relative strengths and weaknesses in written explanations of math concepts and procedures.

## Big Idea: Students score sample MCAS open responses in groups as an entry point to understanding and reflecting on their own writing!

*90 minutes*

This lesson has a strong emphasis on writing. In what follows I provide some explicit instruction and practice for students to articulate their mathematical understanding through written language. Prior to this lesson students completed the **Q2 Algebra I Common Writing Prompt: Solving Equations and Inequalities in 2 Variables**. The common writing prompt is an open response item from a previous MCAS Assessment.

In terms of the mathematics of the lesson, students gain practice with solving systems of equations. At the same time, students gain experience with **Math Practice 4** in regards to modeling and applying systems of equations to solve real-world problems.

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#### Entry Ticket

*15 min*

To open the lesson, I have students complete the **Entry Ticket: Practice Creating Equations and Solving Systems. ** The included tasks review of creating equations and solving systems of equations.

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After reviewing the entry ticket, students begin working on the Q2 Common Writing Prompt. I have students complete the first section of the **Reflection on Writing and Developing a Writing Goal in Mathematics** in order to identify what they felt they did well on and what areas of the prompt was difficult for them.

The reason for completing this exercise is I want students to re-visit the prompt's content and questions they completed previously so they have a better context to the problem. I want students to re-activate their understanding of the problem because in the next section. I ask students to score other sample responses to the prompt.

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I now inform the students that they will each be scoring examples of student work on the writing task. As I make this announcement I hand out a copy of both the MCAS Scoring Rubric and my school's Short Response Rubric (see pages 3-5 of **Q2 Algebra I Common Writing Prompt: Solving Equations and Inequalities in 2 Variables**).

I ask students to silently read the rubrics and write down any questions they have. The class then has the opportunity to ask clarifying questions about the rubrics.

For this section of the lesson, students are grouped by how they, themselves, scored when they completed the writing prompt. Each group is handed an assortment of model student work from the MCAS public release database. Each group works together to score the responses based on the MCAS scoring rubric(s).

Each group also completes the **Reflection on Writing and Developing a Writing Goal in Mathematics** worksheet summarizing the reasoning behind their sorting method. The responses on this worksheet may vary considerably. Some students may say that they paid close attention to the rubric to score the responses. Other groups might say responses that scored higher tended to be writing that was more organized and/or used details to support their arguments.

I intentionally use the writing of others to begin this exercise because writing is so personal. Assessing the writing of another student can be easier than reflecting on your own writing. Using anonymous responses also allows me to have students talk about writing in groups. At this point in the school year, I would not have students peer edit in my own classes. I view this as an achievable goal, but I am not sure that my students are ready at this point.

**Differentiating the Lesson**: For some of my classes, I only hand out the MCAS scoring rubric and do not hand out my school's scoring rubric. I feel reviewing and using two rubrics for this first focus lesson on assessing writing can overwhelm some students. I would rather have students feel comfortable understanding the expectations, and being able to asses responses, of one rubric rather than partially understand two rubrics.

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After scoring the sample responses, I ask students to complete the independent work section of the * Reflection on Writing *worksheet.

The prompt asks students to reflect on the previous activity. Students are asked to identify relative areas of strength and weakness in their own writing. During the last few minutes of this section, students **Turn and Talk** with a partner summarizing their reflections. This partner sharing prepares students to share with the class.

This section of the lesson is all about giving students time to reflect on their writing, and * how to make it better*. I like to have students set personal goals. I have found that the process of setting goals, no matter how realistic those goals may be, supports improvement.

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#### Exit Ticket and Recap

*15 min*

To conclude this lesson I ask students to score their own written response AND create a plan on how they are going to improve upon their writing in mathematics (last section of the **Reflection on Writing and Developing a Writing Goal in Mathematics**

Last quarter I only had students assess the writing of others (sample student work from the MA DESE). Now that the class is in more of a routine and students are more comfortable with writing in math class, I ask them to shift the critical lens from assessing someone else's writing to assessing their own writing. I want students to think about what they are good at, what they need to work on, and perhaps most importantly HOW they can make a plan to make incremental improvements.

I remind students of the importance of writing in all classes. Students are also reminded that the next MCAS writing assessment will occur in a few months. Until then, we will continue practicing and working on writing in math class.

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
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- LESSON 1: Creating and Interpreting Equations to Solve Systems
- LESSON 2: Bring in the Sub!: Solving Systems of Equations in 2 Variables
- LESSON 3: The Whole is Greater than the Sum of Its Parts
- LESSON 4: Practice Session on Solving Systems
- LESSON 5: Graphing Systems of Equations
- LESSON 6: Solving Linear Equations in Two Variables
- LESSON 7: Solving Non-linear Systems of Equations
- LESSON 8: Graphing and Solving Systems of Inequalities
- LESSON 9: Job Offers and Cell Phone Plans: Making Informed Decisions with Mathematics
- LESSON 10: Study Session for Unit Test on Systems of Equations and Inequalities in 2 Variables
- LESSON 11: Unit Test: Systems of Equations and Inequalities in 2 Variables
- LESSON 12: Writing in Math Classroom, Part 2: Solving Equations & Inequalities in 2 Variables