# Algebraic Thinking

This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any unforeseen events that may occur during the semester.

### 1:

### Tues/Wed Class: Introductions #. assign groups #. introductions and [syllabus scavenger hunt](handouts/syllabus-game.html) #. [Jinx puzzle](handouts/jinx-puzzle.html) → Excel → strips → algebra #. Q&A After class - [WeBWorK: Review](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Thursday Before class - prepare math questions for instructor, "why" questions recommended Class: Optional Q&A #. instructor answers questions prepared by students After class - [WeBWorK: Review](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 2:

### Mon/Tues Before class - take notes on Numerical expressions (Chapter 9.1) Class: Expressions and order of operations #. "expression" vs. "equation" #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9A.1-5 #. PEMDAS issues (see facebook "math") #. GEMA (groups, exponents, multiplication, addition) #. finish Class Activity After class - take notes on Nix the Tricks: Nix: PEMDAS, BIDMAS - [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9C (15; 20,100)
### Wed/Thurs Before class - take notes on Commutative Property of Multiplication (Chapter 4.3) Class: Factor out a one #. unpack $$\frac{31}{67} \cdot \frac{4}{31}$$ using commutative property and multiplication identity #. be careful with "cancel", instead "factor a one" #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9F After class - take notes on Nix the Tricks: Nix: Cancel - [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9D.1-4 (4, 9, 16, …; square numbers; $$100^2$$; $$50^2$$)

### 3:

### Mon/Tues Before class - take notes on Associative Property of Addition (Chapter 3.2) - take notes on Distributive Property (Chapter 4.4, no FOIL) - take formative quiz Class: Discuss quiz Class: Associative and distributive properties #. discuss Properties of Operations After class - take notes on Nix the Tricks: Nix: FOIL - [WeBWorK: Expressions](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - finish Properties of Operations - take formative quiz Class: Discuss quiz Class: Story problems (pre-variables) #. CGI problem types #. summarize addition and subtraction by grade level : CCSS, WI After class - [WeBWorK: Story problems](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 4:

### Mon/Tues Before class - take notes on Expressions with variables (Chapter 9.2) - prepare for summative quiz Class: Summative quiz 1 Class: Expressions with variables #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9G, 9H.1-3 #. revisit [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9A.6 After class - [WeBWorK: Variables](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - try practice exercises 9.2.3, 9.2.4 - general expression for [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9A.6 Class: Discuss quiz Class: Equivalent expressions #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9I After class - try sidewalk multiplication (answers)

### 5:

### Mon/Tues Before class - take notes on Solving Equations (9.4) - take formative quiz Class: Discuss quiz Class: Solving equations #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9S #. revisit [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9Q, informally and formally After class - take notes on Equations for Different Purposes (9.3)
### Wed/Thurs Before class - take notes on Strip Diagrams (Chapter 9.5) - take formative quiz Class: Discuss quiz Class: Solving algebra word problems #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9U, 9V.1, 9W After class - read Using a model approach to enhance algebraic thinking in elementary (Ferrucci, et al., 2008) - [WeBWorK: Equations](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 6:

### Mon/Tues Before class - take formative quiz Class: Discuss quiz Class: Solving algebra word problems, continued #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9U, 9V.1, 9W After class - [WeBWorK: Equations](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - prepare for summative quiz Class: Summative quiz 2 Class: Solving algebra word problems, continued #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9U, 9V.1, 9W After class - [WeBWorK: Equations](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 7:

### Mon/Tues Before class - prepare note sheet Class: Discuss quiz, clean out folders Class: Review #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9U, 9V.1, 9W (answers) #. [review topics](handouts/review.html) #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9P.2 (on separate piece of paper; exchange) After class - [WeBWorK: Midterm review](https://uweau.instructure.com/courses/493418/assignments/4742218): Midterm review (0 pts)
### Wed/Thurs Before class - prepare note sheet Class: Exam I - allowed: one page notes (1-sided, handwritten) - allowed: calculator After class - n/a

### 8:

### Mon/Tues Before class - n/a Class: Discuss exam Class: Coordinate points #. review coordinate graphs #. [secret message](handouts/secret-message.pdf) After class - (optional) make your own [secret message](https://www.worksheetworks.com/math/geometry/graphing.html) - check [answer](handouts/secret-message-2.pdf) - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - n/a Class: Linear equations #. [Is it linear?](https://www.icloud.com/keynote/0r3ZP1MCqXDm8DjbQgRzvDV8g#Math_302_-_lines) #. check with [Desmos](https://www.desmos.com/calculator) or graphing calculator After class - [Desmos formulas](https://www.desmos.com/calculator/rkcwillw0e) - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 9:

### Mon/Tues Before class - n/a Class: new groups Class: Graphing and solving equations #. [Desmos?](https://www.desmos.com/calculator) #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9T.1-4 (algebra & [graphing](https://www.desmos.com/calculator/t3nvidb9sc)) #. review [substitution and elimination](handouts/systems-eqn.html) #. if time, [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9T.5-6 After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - take notes on Functions (Chapter 9.7) - take formative quiz Class: Discuss quiz Class: Functions #. definition: a function is a rule that assigns one output to each input #. notation: name(input) = output #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9EE.2 #. plot Example 4 in [Desmos](https://www.desmos.com/calculator/dgyzummrz1) and vertical line test #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9FF.1 After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 10:

### Mon/Tues Before class - take notes on Linear Functions (Chapter 9.8) - take formative quiz Class: Discuss quiz Class: Non-linear functions #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9OO (which are linear? quadratic?) #. [elimination strategy for quadratics](handouts/finite-differences2.html) After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - take formative quiz Class: Discuss quiz Class: Non-linear functions (continued) #. practice [creating quadratic equations](handouts/finite-differences1.html) After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 11:

### Mon/Tues Before class - finish Function J and K on [functions from tables](handouts/finite-differences1.html) - take formative quiz Class: Discuss quiz & schedule Class: Non-linear functions (continued) #. finish [functions from tables](handouts/finite-differences1.html) #. [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9OO (Tables B-F) #. exponential functions, $$y = A \cdot B^x$$ #. inversely proportional functions, $$x \cdot y = C, x \neq 0$$ #. 1:linear, 2:quadratic, 3:exponential, 4:inversely proportional, 5:linear challenge, 6:free choice After class - [Desmos](https://www.desmos.com/calculator/ymla0htvms) results for [Class Activity](https://uweau.instructure.com/courses/493418/pages/class-activities-from-beckmann) 9OO - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - prepare for summative quiz Class: Summative quiz 3 After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 12:

### Mon/Tues Before class - n/a Class: Discuss quiz Class: Quadratic functions (table layout) #. tabular layout for [polynomial elimination](handouts/finite-differences2.html) #. random practice for [functions from tables](handouts/finite-differences1.html) Note: WeBWorK scores will be turned on in Canvas soon After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs #### No class for Thanksgiving break

### 13:

### Mon/Tues Before class - n/a Class: Reminder about webwork scores Class: Exponential functions #. derive [Compound interest](handouts/compound-interest.html) formula After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - take formative quiz Class: Discuss quiz Class: Set operations #. [Venn diagrams](handouts/set-ops.html) After class - [WeBWorK: Logic](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 14:

### Mon/Tues Before class - take formative quiz (posted soon) Class: Discuss quiz Class: Boolean logic #. and, or, not #. truth tables After class - [WeBWorK: Logic](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - prepare for summative quiz Class: Summative quiz 4 Class: Proof by contradiction #. Tic-Tac logic (aka. Kryssring puzzles) #. contradiction: make assumption, logic steps, contradiction implies incorrect assumption After class - (optional) read [12 Math Rules that Expire in the Middle Grades](https://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/2015/Vol21/Issue4/mtms2015-11-208a/) - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)

### 15:

### Mon/Tues Before class - take notes on "Irrationality of sqrt(2)" (Chapter 8.6, last section) Class: Discuss quiz Class: Proof by contradiction (continued) #. Irrationality of sqrt(2) #. Infinite prime numbers After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Wed/Thurs Before class - n/a Class: Review #. clean out folders #. [numberless problem banks](https://numberlesswp.com/problem-banks/) #. [review topics](handouts/review.html) After class - [WeBWorK](https://uweau.instructure.com/courses/493418/assignments/4742218)
### Final exam - [review topics](handouts/review.html) - one page of notes (one-sided, handwritten) - allowed: calculator