
Linear Relationships (Lesson 0.4 Day 1)
Unit 0: Prerequisites
Day 1: The Cartesian Plane
Day 2: Equations of Circles
Day 3: Solving Equations in Multiple Representations
Day 4: Reasoning with Formulas
Day 5: Linear Relationships
Day 6: Linear Relationships (Reasoning with Slope)
Day 7: Set Notation and Interval Notation
Day 8: Unit 0 Review
Day 9: Unit 0 Test
Unit 1: Functions
Day 1: Functions and Function Notation
Day 2: Domain and Range
Day 3: Rates of Change and Graph Behavior
Day 4: Parent Functions
Day 5: Transformations of Functions
Day 6: Transformations of Functions
Day 7: Even and Odd Functions
Day 8: Quiz (Sections 1.1-1.6)
Day 9: Combinations of Functions
Day 10: Composition of Functions
Day 11: Inverse Functions
Day 12: Inverse Functions
Day 13: Piecewise Functions
Day 14: Unit 1 Review
Day 15: Unit 1 Test
Unit 2: Polynomial and Rational Functions
Day 1: Connecting Quadratics
Day 2: Completing the Square
Day 3: Polynomials in the Short Run
Day 4: Polynomials in the Long Run
Day 5: Review 2.1-2.4
Day 6: Factor and Remainder Theorem
Day 7: Factor and Remainder Theorem
Day 8: Complex Zeros
Day 9: Connecting Zeros Across Multiple Representations
Day 10: Quiz (Sections 2.3-2.5)
Day 11: Intro to Rational Functions
Day 12: Rational Functions: Zeros, Holes, and Vertical Asymptotes
Day 13: Unit 2 Review
Day 14: Unit 2 Test
Unit 3: Exponential and Logarithmic Functions
Day 1: Exponential Functions
Day 2: Graphs of Exponential Functions
Day 3: Compound Interest and an Introduction to "e"
Day 4: Quiz (Sections 3.1-3.3)
Day 5: Logarithmic Functions
Day 6: Graphs of Logarithmic Functions
Day 7: Logarithm Properties
Day 8: Solving Exponential and Logarithmic Equations
Day 9: Exponential and Logarithmic Models
Day 10: Unit 3 Review
Day 11: Unit 3 Test
Unit 4: Trigonometric Functions
Day 1: Right Triangle Trigonometry
Day 2: Inverse Trig Ratios
Day 3: Radians and Degrees
Day 4: The Unit Circle
Day 5: The Unit Circle
Day 6: Other Trig Functions
Day 7: Quiz (Sections 4.1-4.4)
Day 8: Graphs of Sine and Cosine
Day 9: Transformations of Sine and Cosine
Day 10: Graphing Secant and Cosecant
Day 11: Graphing Tangent and Cotangent
Day 12: Quiz (Sections 4.5-4.6)
Day 13: Inverse Trig Functions
Day 14: Trigonometric Modeling
Day 15: Trigonometric Identities
Day 16: Unit 4 Review
Day 17: Unit 4 Review
Day 18: Unit 4 Test
Unit 5: Applications of Trigonometry
Day 1: Law of Sines
Day 2: The Ambiguous Case (SSA)
Day 3: Law of Cosines
Day 4: Area and Applications of Laws
Day 5: Vectors
Day 6: Review
Day 7: Quiz (Sections 5.1-5.4)
Day 8: Polar Coordinates
Day 9: Equations in Polar and Cartesian Form
Day 10: Polar Graphs
Day 11: Polar Graphs
Day 12: Checkpoint Review
Day 13: Checkpoint (Sections 5.5-5.7)
Day 14: Parametric Equations
Day 15: Parametric Equations (With Trig)
Day 16: Unit 5 Review
Day 17: Unit 5 Test
Unit 6: Systems of Equations
Day 1: What is a Solution?
Day 2: Solving Systems with Substitution
Day 3: Solving Systems with Elimination
Day 4: Quiz (Sections 6.1-6.3)
Day 5: Solving Systems in Three Variables
Day 6: Solving Systems in Three Variables
Day 7: Partial Fractions
Day 8: Unit 6 Review
Day 9: Unit 6 Test
Unit 7: Sequences and Series
Day 1: Introducing Sequences
Day 2: Using Sequences and Series to Describe Patterns
Day 3: Arithmetic Sequences and Series
Day 4: Review
Day 5: Quiz (Sections 7.1-7.2)
Day 6: Geometric Sequences and Finite Series
Day 7: Infinite Geometric Sequences and Series
Day 8: Proof by Induction
Day 9: Proof by Induction
Day 10: Quiz (Sections 7.3-7.4)
Day 11: Review Unit 7
Day 12: Unit 7 Test
Unit 8: Limits
Day 1: What is a Limit?
Day 2: Evaluating Limits Graphically
Day 3: Evaluating Limits Analytically
Day 4: Evaluating Limits Analytically
Day 5: Evaluating Limits Analytically
Day 6: Review
Day 7: Quiz (Sections 8.1-8.2)
Day 8: Continuity
Day 9: Continuity
Day 10: Intermediate Value Theorem
Day 11: Intermediate Value Theorem
Day 12: Review
Day 13: Quiz (Sections 8.3-8.4)
Day 14: Limits at Infinity
Day 15: Review Unit 8
Day 16: Unit 8 Test
Unit 9: Derivatives
Day 1: Introduction to Derivatives
Day 2: Average versus Instantaneous Rates of Change
Day 3: Calculating Instantaneous Rate of Change
Day 4: Calculating Instantaneous Rate of Change
Day 5: The Derivative Function
Day 6: The Derivative Function
Day 7: Review
Day 8: Quiz (Sections 9.1-9.3)
Day 9: Derivative Shortcuts
Day 10: Differentiability
Day 11: Connecting f and f’
Day 12: Connecting f and f’
Day 13: Review
Day 14: Quiz (Sections 9.4-9.6)
Day 15: Derivatives of Sine and Cosine
Day 16: Product Rule
Day 17: The Quotient Rule
Day 18: Review
Day 19: Quiz (Sections 9.7-9.9)
Day 20: Unit 9 Review
Day 21: Unit 9 Test
Unit 10: (Optional) Conic Sections
Day 1: Intro to Conic Sections
Day 2: Parabolas
Day 3: Parabolas
Day 4: Quiz (Sections C.1-C.2)
Day 5: Ellipses
Day 6: Ellipses
Day 7: Hyperbolas
Day 8: Hyperbolas
Day 9: Unit C Review
Day 10: Unit C Test
Learning Targets
Identify situations with a constant rate of change as describing linear relationships
Interpret a y-intercept and slope in context
Write an equation of a line in slope-intercept and point-slope form
Tasks/Activity | Time |
---|---|
Activity | 20 minutes |
Debrief Activity | 10 minutes |
Important Ideas | 5 minutes |
Check Your Understanding | 15 minutes |
Activity: How Much Does Coldstone Charge?
Lesson Handouts
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Answer Key
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Experience First
Today students reason about linear relationships in the context of the cost of ice cream. The idea of the additional price in the larger size accounting for the additional toppings gives meaning to the slope formula of ∆y/∆x. When students graph in question 2, look for groups that use point-by-point graphing in contrast to groups that simply plot two points and “connect the dots”. For students who choose the latter, ask why this is allowed. For the former, ask how many points they need to find in order to be confident of their graph. Also push students to articulate what the $3.90 means and what it looks like on a graph. Students’ comfort with question 4 may vary depending on their experience with point slope form in previous classes. During the activity, try not to use this language unless students bring it up themselves.
Formalize Later
Although these topics are familiar to students, students may still struggle to interpret slopes and y-intercepts in context. Encourage language around “for each additional topping…” When debriefing question 3, make a VERY big deal about how students were able to find the 5-toping price without actually knowing the base price. For students using the expression “8.06+3(0.89)” in the second half of the question, push students to articulate where the 3 came from. (I thought it was 7 toppings!) In our experience, students love slope-intercept form and are not immediately hospitable to point-slope form. We hope that this activity invites students to see the usefulness of point-slope form as a way to predict values without actually knowing the y-intercept. We say that any point, not just the y-intercept, can be used as an anchor point, or point of reference.