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* *Reflection: Modeling
Review, Justification, and Critique - Section 2: Quiz: Critiquing and Justifying

This task is highly engaging for students, easy to implement, and it provides me with plenty useful information about what my students know and can explain about what they understand. It is also an activity that pushes students toward the skills of critique, feedback, and attention to detail that I think are such keys to success in any discipline.

All of that is to say that I've realized that this work should have started a little earlier in the year, and it should happen more often in a 9th Grade Algebra course. That's why I changed the end of this year's Linear Equation Project, which I reflected on a few weeks ago.

Moving forward, I want to continue to ask students to provide feedback to made-up solutions like these. I also want to be intentional about making the transition to having students provide structured feedback on the work of their classmates. It's a goal that I'll reflect upon more as the year continues - so I'll keep you posted!

*Developing Critique and Justification*

*Modeling: Developing Critique and Justification*

# Review, Justification, and Critique

Lesson 7 of 8

## Objective: SWBAT critique solutions to linear equations and justify the solutions to others.

As the week comes to a close, students should have completed the Creating Equations Problem Set. Their last chance to submit it is tomorrow, because that's the last day of the marking period. In any implementation of mastery-based grading, we can give the students as much time as possible to learn and to demonstrate mastery, but still, when grades are due, I have to use what I've got.

If that's done, which it is for about two thirds of my kids, then the focus is on preparing for tomorrow's exam by asking questions and making Cheat Sheets. I tell the class that in 15 minutes, we'll get started on today's Critique and Justification Quiz.

#### Resources

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This quiz is an assessment of **Mathematical Practice #3:**

**I can construct viable arguments and critique the reasoning of others. **

I want to assess this one more time, because I know that students are better at this than they've demonstrated on the Linear Equations Project. I want this to be separate from the exam. I don't frame like this for kids, but for me, the Unit 1 Exam really begins now, and this is like Part 1. Then, they can focus on the other SLTs tomorrow.

Because sometimes it's easier to write mathematics with pen and paper than on a computer, I use a document camera to post one task at a time, and for each task I give students a few minutes to work. I give them between 2 and 5 minutes, depending on the task.

First, I post these instructions. I tell students to look at their progress reports or to find on the walls of the classroom Mathematical Practice #3, and to copy it onto their papers. That's what I'll be grading them on when I look at these quizzes.

Then, for two to three minutes each, I post a selection of the following problems:

I may choose different problems for each class, depending on their different levels of skill, and for each class I do two or three of these. When I put up the first one, I say, "Here's what good critique sounds like: *I think you did a good job on blank and blank, and here's what I think you can improve...*"

After a few of those, we move on to the justification part of the quiz, which is identical to the Linear Equation Project, just on a much shorter timeframe. I ask students to do one or two of these, again, selected based upon how confident I know each class to be.

I time things so students can have the last 5-10 minutes of class to work on whatever problem comes last. Just before the bell rings I remind everyone of tomorrow's exam and to make great cheat sheets.

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- UNIT 1: Number Tricks, Patterns, and Abstractions
- UNIT 2: The Number Line Project
- UNIT 3: Solving Linear Equations
- UNIT 4: Creating Linear Equations
- UNIT 5: Statistics
- UNIT 6: Mini Unit: Patterns, Programs, and Math Without Words
- UNIT 7: Lines
- UNIT 8: Linear and Exponential Functions
- UNIT 9: Systems of Equations
- UNIT 10: Quadratic Functions
- UNIT 11: Functions and Modeling

- LESSON 1: Creating Linear Equations in One Variable
- LESSON 2: From Guess and Check to Creating Equations; From Equations to Inequalities
- LESSON 3: Problem Set: Creating Equations
- LESSON 4: Progress Reports and Closing Out
- LESSON 5: Guess and Check is a Bridge to Creating Equations
- LESSON 6: Review and Quality, Day 1
- LESSON 7: Review, Justification, and Critique
- LESSON 8: First Marking Period Exam