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# Fixed Perimeter and Constant Sums/Differences Assessment

Lesson 9 of 9

## Objective: SWBAT demonstrate their understanding of the big ideas of this unit and their mastery of the key skills of this unit.

*80 minutes*

#### Summative Assessment

*70 min*

There are actually 4 different levels of this assessment. I wrote the easiest level (Level E) after writing the rest of the assessment, and I told students that if they struggled with the first version of the test, I had an easier version prepared. My hope was the students would attempt a more challenging level and if they felt they were not able to show their learning on this level, the could opt for an easier level.

My primary goals were that students would be able to:

- Express relationships linear and quadratic relationships both numerically and algebraically.
- Determine whether a data table shows a linear or a quadratic relationship and find a function rule for the table.
- Express quadratic relationships in different forms.
- Find function rules for linear and quadratic functions given graphs.

After breaking down the learning goals this way, I can ask students to assess themselves in each category and use the different levels of the assessment to determine the appropriate level of challenge for them.

There are two different ways to administer this assessment. One way is to copy each level as a different packet. Then I can give each student the level that I think is right for them. I try to push them a bit—and I tell them that if they show good effort on this level and they want to work on an easier level they can. Typically students continue to work on the level that I give them, but I allow them to choose an easier or harder level after they try this one.

A different teacher at my school gives all students a packet with the problems at all levels, and the problems are grouped into categories (like the ones above). Within each category, she presents the problems from each level in order of difficulty. Students then choose the problems at one level in each category. I like this method better for some reasons (except that it uses a ton of paper!) because students can work on problems more flexibly.

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#### Closing

*10 min*

During the assessment, I wrote each student a paragraph of narrative feedback about their effort and participation in the class. These notes focus on specific pieces of positive feedback that I have for each student, along with questions or specific suggestions I have for how they could improve in the upcoming weeks, or how I could possibly make class work better for them.

For the lesson closing, I want students to reflect on whether they feel they are working at the right level of challenge and I also want their response to my note. My goals is to have the closing of the lesson focus on the big idea of the lesson—which was actually not the quadratic functions content, but actually self-assessment and participation in class. The closing of the unit is useful because it gives me information about whether the students mastered the content—and I also get information about how students feel about the content, the class and their ability to challenge themselves.

I just post the questions on the board and given students the last 5-10 minutes to respond. I encourage them to put time and thoughtfulness into their responses by telling them that I invested a significant amount of time into writing the different levels of the test, and writing their individual feedback notes. I also tell them that I actually use this information—that what the write helps me make decisions about the class. Whether the words I say matter or not, I do want to tell them explicitly about what I use this material for, and why it matters to me that they put time into it.

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Rectangles with Fixed Perimeters
- LESSON 2: Equivalent Expressions Rectangles with Fixed Perimeters
- LESSON 3: More Rectangles with Fixed Perimeters
- LESSON 4: Multiple Representations Fixed Perimeter Problems
- LESSON 5: Sums, Differences and Products
- LESSON 6: Equivalent Expressions Generalization Constant Sums and Differences
- LESSON 7: Multiple Representations Sums, Differences and Products
- LESSON 8: Review Session and Workshop
- LESSON 9: Fixed Perimeter and Constant Sums/Differences Assessment