Math Medic logo
  • Lesson Plans
    • Algebra 1
    • Geometry
    • Algebra 2
    • Precalculus
    +
  • Workshops
  • Blog
  • About
  • Contact
  • Resources
  • Signup / Login
Precalculus>Prerequisites>Linear Relationships

Linear Relationships (Lesson 0.4 Day 1)

Learning TargetsLesson HandoutsExperience FirstFormalize Later
  • 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/ActivityTime
Activity20 minutes
Debrief Activity10 minutes
Important Ideas5 minutes
Check Your Understanding15 minutes

Activity: How Much Does Coldstone Charge?

Lesson Handouts

Login to view contentpdf
Media Locked
You must be logged in to access this content.
Login to view contentdocx
Media Locked
You must be logged in to access this content.

Answer Key

Login to view contentpdf
Media Locked
You must be logged in to access this content.

Our Teaching Philosophy:

Experience First,
Formalize Later
(EFFL)

Learn More

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.

+
Banner Home
Math Medic logo

©2021 - Math Medic | All rights reserved

All lesson handouts are under this Creative Commons license.

Terms of Use  |  Privacy Policy

​
  • Lesson Plans
  • Workshops
  • Blog
  • About
  • Contact
  • Resources
Login

Having trouble?

Register Now.

Create an account for access to all our lesson plans and activity downloads.

Sign up
Math Medic Help
Send a message directly to our support, please be as descriptive as possible. Thanks!