##
* *Reflection: Student Self-Assessment
Algebraic Structures Review - Section 3: Wrap it Up

I expected most of the students to write something about not understanding geometric series because they had to memorize those formulas, but only one person had that as an area for further study. I'm intrigued to see how many actually get those problems correct on tomorrow's exam. I also expected most of the students to feel pretty confident about polynomials but to say they needed to study rational expressions more, because most students I've worked with are less sure of themselves when working with fractions so any kind of rational problems is a challenge. I was correct in these assumptions as you can see from the "study more" and "good at" notecards of students A and B so now we will have to see if the exam supports their confidence.

*Student Self-Assessment: What do they think they know?*

# Algebraic Structures Review

Lesson 10 of 11

## Objective: SWBAT demonstrate understanding of basic algebraic structure through review activities.

## Big Idea: Notes, notes, notes...NOT. Show your students that review is not just about taking and organizing pages of notes.

*55 minutes*

#### Set the Stage

*5 min*

I always tell my students in advance what kind of assessment I'm using so that they can tailor their studying appropriately. This time it will be an individual assessment with a mix of skills and application. Rather than a whole-class review I help my students focus on organizing their notes, practicing their skills on previous assignments, and by challenging each other. I assure them that they do not need to memorize anything except the formulas for the sum of a finite or infinite series. I don't favor memorization as a rule because I believe that most of what my students need to know they will learn through usage or they will look it up. However, there are some things we just have to memorize, at least initially, like phone numbers, addresses, and the meaning of numeric and alphabetical symbols. My decision to have my students memorize these two formulas is based on the idea that some memorization is helpful for building that skill and also on the fact that there are really only two things to memorize. Before turning my students loose to review I ask for a quick recap of what we've covered, having volunteers come to the board to write up key topics and vocabulary words/phrases. By having my students do this rather than simply giving them a list of what to study, I get a chance to see what things they consider important from the unit. It also gives them ownership of the material so that I hear far fewer complaints like "You didn't tell us to study that." or "You didn't put that word on the board during review." My students know that they are responsible for the material we've covered in the unit whether they specifically list it on the board or not.

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#### Put it into Action

*45 min*

For the major portion of today's lesson my students will be working either independently or in small groups while I circulate and assist as needed. I explain my expectation that each student will be working appropriately and will be courteous of other students who are also trying to prepare for tomorrow's exam. I have several graphic organizers for students to use if they choose as well as lined and unlined paper. This is an opportunity for each student to determine which study aids and methods work best for him/her. **(MP5) **There are a few students who insist that they do not need to study, will study in the evening, or never do well on tests and studying doesn't help. To those in the first category I pose a few challenge questions and if they truly know the material then I encourage them to help their classmates review. (I remind them that the best way to truly understand something is to try to teach it to someone else.) For those in the second category, I commend their enthusiasm for so much study and repeat my expectation that they use class time to prepare and allow that they can also study in the evening if they wish. It is students in the final group that are most difficult for me because I know that underlying their comments are feelings of being unable to "get" math. I try to work with these students individually to help them identify which parts of the material from the unit they understand and which parts they need to work on. Sometimes just recognizing that they actually do understand some of what we've covered helps them to persevere, but sometimes it takes more than one review and assessment to overcome years of negative expectations. As the end of class approaches I remind my students that they can check with me before and after school and during lunch if they have additional questions.

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#### Wrap it Up

*5 min*

To close out our day of review I give each student a notecard and ask him/her to write three things on the front that they feel very confident about and then put two things on the back that they will study more before the assessment. These notecards combined with the test results give interesting insight into whether my students actually know what they think they know. They also give me a check for how well I'm doing as I explain in my Review video.

#### Resources

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Whatchamacallit
- LESSON 2: Puzzle it Out
- LESSON 3: Polynomial Rewrite
- LESSON 4: More Puzzles
- LESSON 5: Rational Rewriting
- LESSON 6: Formula 1
- LESSON 7: Geometric Series Formula, Too
- LESSON 8: Working the Formula
- LESSON 9: Infinity and Beyond!
- LESSON 10: Algebraic Structures Review
- LESSON 11: Summative Assessment