## U3 L9 Seeing Structure.jpg - Section 1: Opener: Two Review Problems

# Summary, Work Folders, and a Quiz

Lesson 9 of 10

## Objective: SWBAT demonstrate what they know about creating and using linear equations to model a trio of abstract representations they've seen over the last two weeks.

#### Opener: Two Review Problems

*10 min*

As this two-week mini-unit comes to a close, today is a day for students to summarize what they've learned so far and it's quiz day. It's also the second-to-last day of class for the calendar year, and with a uniquely non-academic class coming up tomorrow, today's lesson serves to close out what we've done so far in this class.

Here is today's opener, which is ready when students arrive. There are two review problems here, each of a sort students have seen over the last two weeks. I hope that they will recognize that they've gained confidence in solving problems like these.

I give students time to get started, and I try to say as little as possible. I want everyone to make of sense of these problems as much as they can. I take a lap through the room, encouraging everyone to get started, and to help each other if necessary. When it comes time to go over these problems, I'll ask for student volunteers to show their solutions on the board; as I circulate, I'm looking for good, interesting work that might be worth sharing.

This opener and the next section of the lesson blend together a bit. I'm most likely to distribute folders and explain what they're for while students are still working on the opener, then circle back to this to debrief in about ten minutes. When I do, one key point I'd like to hammer home one more time is how we can see structure in both visual and algebraic representations of a pattern. After students successful find the rule for the second problem, by whatever method they choose, I ask them to sketch the 1000th figure in this pattern. We then generalize to the ** nth** figure, and see how, by combining like terms, we can arrive at the same expression for the number of dots in that term.

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**Student Work Folders**

As students are working on the opener, I distribute letter-sized file folders to each of them. We're setting up work folders today, that I'll keep in a crate in the classroom. I tell students to write their name, class period, and mascot on their folder, and then to place any work they'd like in the folder. As they do that, I return a store of work that I've gathered and graded over the last several weeks.

This is something that I've had on my to-do list for weeks, but I feel fine about getting to it now. In my experience, it's better to get work folders started after there's work to put into them. That's why we didn't do this right away at the start of the year. And although it would have fit in late October or November, I prioritized other goals. By waiting until now, it feels like a nice way to tie up the calendar year, and kids feel proud of their accomplishments as they look at work that already feels like it happened a long time ago.

I tell students to include everything I return: in particular, I'm returning final submissions of their projects and the argumentative writing prompt from the end of our stats unit. As there will be more projects and more writing prompts, I want students to be able to compare this work to what's coming later in the year, and then to be able to reflect upon their growth.

I also allow kids to add any other work they'd like - so if anyone wants to clear some space in their binder, they can do that now. I tell students to pay particular attention to work that most challenged them or of which they are most proud. These are the categories of work that they will present at their Student Led Conferences, later in the Spring Semester.

**Gallery Walk and Solutions**

Students are filing their work and completing the opener. In addition, I've prepared a gallery walk on the back wall of the room and I've left this extension problem at the front of the room for anyone who wants to think about it. It's unlikely we'll have too much extra time before the quiz, but if we do, I'm excited to discuss either of these with kids.

The gallery includes solutions to the "Math Without Words" problems we worked on last week, student work from the "Make Your Own Dot Pattern" lesson, and solutions to the "Equivalent Line Segments" assignment.

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During the second half of class, students take this quiz, which surveys problems of the sorts we've been working on over the last two weeks. Students can use their notes and their work folders as they do this work, but I erase solutions to the opener from the front board.

This quiz serves two purposes. First, it allows me to assess what students can do on problems like these. Second, when I return it after winter break, it will jog student memories of what we'd been working on, and will allow us to hit the ground running in the new year.

I give students about 20 minutes - maybe a couple more - to complete the quiz. When class ends, I collect their quizzes and work folders in a pair of piles as they leave.

#### Resources

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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: "The Answer" vs. "The Problem"
- LESSON 2: Seeing Structure and Defining Problems
- LESSON 3: Hour of Code
- LESSON 4: Seeing Structure in Dot Patterns and Linear Functions
- LESSON 5: Make Your Own Dot Pattern
- LESSON 6: Function Diagrams
- LESSON 7: Equivalent Line Segments
- LESSON 8: Introduction to Desmos
- LESSON 9: Summary, Work Folders, and a Quiz
- LESSON 10: Building Towers