(12) Algebra 2: Recursion & Linear Relations
Topic outline

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

[coming soon]

I will...
 Master the coordinate plane by:
 Do art with Desmos Graphing Calculator.
 Represent recursion in a variety of ways
So I can...
 Use recursion in stories, tables, diagrams, and graphs to make predictions about linear relations.
 Translate among those representations fluently and explain in my own words how they model the same quantitative relationship.
 Name and use all components of the coordinate plane.
As assessed by...
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I will...
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So I can...
 Recognize that “linear” means a constant rate of change and I can represent that in a variety of ways.
 Distinguish linear vs nonlinear relations.
 Use a spreadsheet to create tables and visuals.
As assessed by...
[coming soon]

I will...
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So I can...
 Determine rates of change from data with nonunit gaps.
 Interpret this in context and determine whether relations are linear or not.
 Recognize and represent a rate of change in a variety of ways.
 Parse any linear relation in terms of input variable, output variable, rate of change, and "initial" value.
As assessed by...
[coming soon]

I will...
 Reverse engineer and perform generalization Magic Tricks
 Crack the code (formula) on some VisualPatterns.org.
 Beginner patterns: #4, 7, 14, 17, 18, 435
 Example
 Blank Template
 Also make the leap from patterns to algebra with
 JUMP 8 Formulas, Tables, and Graphs
 Level 1 Example
 Level 1 Exercises
 Level 2 Exercises
 Level 2 Template . (Make your own!)
 Level 3 Exercises. Recompile to get new numbers.
 Generalizing Linear Patterns
 Crack the code (formula) on even HARDER VisualPatterns.org.
 Intermediate: #12, 32, 436, 437
 Advanced: 265, 269
 What do you most need to remember from each level of difficulty?
 Can you tell which are linear and which are not?
 Solve equations using inverse operations.
 Optional: Reasoning with Lengths
So I can...
 Recognize situations in which recursion is tedious or inexact.
 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.
 Understand letter variable as an abbreviation for a class of numbers rather than a fixed and known number.
As assessed by...
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I will...

 JUMP 7.1 Creating and Using Algebraic Expressions & Equations
 Linear Structure Recognition
 Linear Relations Word Problems, Part 1
 Linear Relations Word Problems, Parts 2 & 3
 Complete the Graphs and Equations exercises.
 Determine Equation from Line
 Desmos: Match My Line
 Desmos: Marbleslides  Lines
 Desmos: Land the Plane
 Tables to Equations
 From Equation to Parameters to Line (no tables)
 Visual Patterns: #435, 436, 437 (dots)
So I can...

 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.
 Solve problems symbolically and graphically.
 Create art with points, lines, and restrictions in Desmos.
As assessed by...
[coming soon]


I will...
 Analyze the Sleep & Seizures case
 Analyze the International COVID case numbers.
So I can...
 Sketch regression lines and estimate and interpret their equations.
 Generate multiple reasonable hypotheses for the relationship and propose ways to test (falsify) them.
 Generate practical examples of how correlation does not imply causation.
As assessed by...
[coming soon]