(12) Algebra 2: Recursion & Linear Relations

Topic outline

• Essential Questions

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  1. When is recursion a good way to think about relationships? When are 2-variable relationships a better way? What are the strengths and weaknesses of each method?
  2. How do mathematicians represent the concept of change?
  3. How does knowing the definition of "solution" and "equation" help us in this unit?
  4. How does knowing math help make digital art?
  5. The most famous saying in statistics: "Correlation isn't causation." What does this mean? Why do we need statisticians to tell us this?

• Whole Course Resources

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• Lesson 1: Representing Recursion

  I will...

  1. Begin learning the coordinate plane with pencil-and-paper drills.
     1. Introduction to the Coordinate Plane
     2. Rational Numbers on the Coordinate Plane
  2. Do software activities on Desmos.
     1. Desmos: Turtle Crossing
     2. Desmos: The (Awesome) Coordinate Plane Activity [bullseyes]
     3. Desmos: Mini Golf Marbleslides
  3. Represent recursion in a variety of ways
     1. Linear Sequence & Relations Template
     2. Visual Patterns: #435, 436, 437 (dots)

   

  So I can...

  1. Use recursion in stories, tables, diagrams, and graphs to make predictions about linear relations.
  2. Translate among those representations fluently and explain in my own words how they model the same quantitative relationship.
  3. Name and use all components of the coordinate plane.

   

  As assessed by...

  [coming soon]

• Lesson 2: Types of Recursion

  I will...

  [coming soon]

   

  So I can...

  1. Recognize that “linear” means a constant rate of change and I can represent that in a variety of ways.
  2. Distinguish linear vs non-linear relations.
  3. Use a spreadsheet to create tables and visuals.

   

  As assessed by...

  [coming soon]

• Lesson 3: Rates of Change

  I will...

  [coming soon]

   

  So I can...

  1. Determine rates of change from data with non-unit gaps.
  2. Interpret this in context and determine whether relations are linear or not.
  3. Recognize and represent a rate of change in a variety of ways.
  4. Parse any linear relation in terms of input variable, output variable, rate of change, and "initial" value.

   

  As assessed by...

  [coming soon]

• Lesson 4: From Recursion to Relations

  I will...

  1. Reverse engineer and perform generalization Magic Tricks
  2. Crack the code (formula) on some VisualPatterns.org.
     1. Beginner patterns: #4, 7, 14, 17, 18, 435
     2. Example
     3. Blank Template
  3. Also make the leap from patterns to algebra with
     
     1. JUMP 8 Formulas, Tables, and Graphs
     2. Level 1 Example
     3. Level 1 Exercises
     4. Level 2 Exercises
     5. Level 2 Template . (Make your own!)
     6. Level 3 Exercises. Recompile to get new numbers.
     7. Generalizing Linear Patterns
  4. Crack the code (formula) on even HARDER VisualPatterns.org.
     1. Intermediate: #12, 32, 436, 437
     2. Advanced: 265, 269
     3. What do you most need to remember from each level of difficulty?
     4. Can you tell which are linear and which are not?
  5. Solve equations using inverse operations.
     1. JUMP 7.1 Solving by Inverse Operations
  6. Optional: Reasoning with Lengths

   

  So I can...

  1. Recognize situations in which recursion is tedious or inexact.
  2. View algebraic formulae as a generalized relationship, one that is verified when all the data are solutions. I know that the graph of an equation is the plot of the equation’s solutions.
  3. Understand letter variable as an abbreviation for a class of numbers rather than a fixed and known number.
     
     

  As assessed by...

  [coming soon]

• Lesson 5: Graphs

  I will...

  1. 1. JUMP 7.1 Creating and Using Algebraic Expressions & Equations
     2. Linear Structure Recognition
     3. Linear Relations Word Problems, Part 1
        1. Example
        2. Exercises
     4. Linear Relations Word Problems, Parts 2 & 3
     5. Complete the Graphs and Equations exercises.
     6. Determine Equation from Line
        1. Level 1 (only integers)
        2. Level 2 (some fractions)
     7. Desmos: Match My Line
     8. Desmos: Marbleslides - Lines
     9. Desmos: Land the Plane
     10. Tables to Equations
         1. Example
         2. Exercises
     11. From Equation to Parameters to Line (no tables)
     12. Visual Patterns: #435, 436, 437 (dots)

   

  So I can...

  1. 1. Translate between data, visuals, tables, equations, and graphs for all linear relations. I can explain in my own words how they all model the same logical relationship.
     2. Solve problems symbolically and graphically.
     3. Create art with points, lines, and restrictions in Desmos.

   

  As assessed by...

  [coming soon]

• Lesson 6: Intro to Statistics

  I will...

  1. Analyze the Sleep & Seizures case
  2. Analyze the International COVID case numbers.

   

  So I can...

  1. Sketch regression lines and estimate and interpret their equations.
  2. Generate multiple reasonable hypotheses for the relationship and propose ways to test (falsify) them.
  3. Generate practical examples of how correlation does not imply causation.

   

  As assessed by...

  [coming soon]