Getting Creative with Systems of Equations A Cinematic Lesson - - PowerPoint PPT Presentation

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Getting Creative with Systems of Equations A Cinematic Lesson - - PowerPoint PPT Presentation

May 25, 2023 136 likes •581 views

Getting Creative with Systems of Equations A Cinematic Lesson Samuel Otten & Zandra de Araujo University of Missouri at Columbia www.TwoMinuteTeachersGuide.com 1 @2minteachguide Overview Cinematic Lesson Structure One-Page Lesson

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Getting Creative with Systems of Equations

Samuel Otten & Zandra de Araujo University of Missouri at Columbia

www.TwoMinuteTeachersGuide.com @2minteachguide

A Cinematic Lesson

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Overview

  • Cinematic Lesson Structure
  • One-Page Lesson Plan
  • Sample Lesson – Selecting Systems of Linear Equations
  • Debrief
  • Q&A

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Pixar Animation Studios

  • Toy Story – favorite toy replaced by new model
  • Monsters, Inc – monsters are deathly afraid of kids but
  • ne sneaks into their world
  • Finding Nemo – overprotective father loses his son
  • Wall-E – a lone robot on desolate Earth is suddenly

visited by a beautiful new robot from outer space

  • Inside Out – fun and happy adolescent girl has to move

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Inciting Incidents in Film & Literature

  • Major event that propels action and characters forward,

setting the story into motion.

  • Should…

○ Happen within the first 25% of the story ○ Directly involve the protagonist (or require them to act/respond) ○ Set the stage for revelation or growth for the protagonist ○ Hook the reader and spur questions

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Some Types of Inciting Incidents

  • Leaving home (“Hero’s Journey”)
  • Life interrupted (a big change to self or circumstances)
  • Scary discovery (or learning a dark secret)
  • I need to help (but there will be personal cost)
  • Joining a coveted group or institution
  • Whodunnit?
  • Howcatchem?

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How can we use inciting incidents in math lessons?

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Introduction to Quadratic Functions (Non-inciting)

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Introduction to Quadratic Functions (Non-inciting)

Quadratic equations are second-order polynomials, and have the form Their graphs make a shape called a parabola.

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Introduction to Quadratic Functions (Inciting)

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Introduction to Quadratic Functions (Inciting)

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Introduction to Quadratic Functions

QUADRATIC FUNCTIONS NOT QUADRATIC FUNCTIONS

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Graphing a Polynomial (Non-inciting)

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Graphing a Polynomial (Non-inciting)

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Graphing a Polynomial (Inciting)

HOW???

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Some Types of Inciting Incidents in Math Lessons

  • Guess the rule (e.g., quadratics vs. non-quadratics)
  • Gain an insight (e.g., polynomial graphs)
  • Throw a wrench in it (e.g., systems of equations, coming soon)
  • Can we extend it?
  • Can we predict it?
  • Does it always work?
  • Are they the same?

Examples of these? Or others categories?

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Inciting Incidents in Math Lessons

RECALL

  • Major event that propels action and characters forward, setting the story into motion.
  • Should…

○ Happen within the first 25% of the story ○ Directly involve the protagonist (or require them to act/respond) ○ Set the stage for revelation or growth for the protagonist ○ Hook the reader and spur questions

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Inciting Incidents in Math Lessons

Foster curiosity Focus on mathematical ideas (the protagonist!) Provide a rationale and motivation for the lesson Is a good inciting incident just an inciting incident, or does it influence the remainder of the lesson?

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Thinking about Full Lesson Plans

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Cinematic Storytelling Structure

○ Setup ○ Inciting Incident ○ Rising Action ○ Climax ○ Resolution (what was learned, new normal, sequel?)

  • “Show, don’t tell.”

Snyder “Save the Cat”; Dietiker (2013)

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Cinematic Structure

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  • Rear Window – a homebound photograph snoops on his

neighbors and notices what might be a domestic murder

  • Shrek – a reclusive ogre finds his swamp invaded
  • Toy Story – favorite toy replaced by new model
  • Finding Nemo – overprotective father loses his son
  • Wall-E – a lone robot on desolate Earth is suddenly

visited by a beautiful new robot from outer space

  • Inside Out – fun and happy adolescent girl has to move

Setup

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  • Setting
  • Main character (mathematical object or phenomenon)
  • Something to be learned

In service of the inciting incident. Some setups can be very short, some a bit more involved. Remember 25% guideline.

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Setups

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Setups

QUADRATIC FUNCTIONS NOT QUADRATIC FUNCTIONS

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Setups

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One-Page Lesson Plan https://tinyurl.com/1pagesystems

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TITLE Goal(s) Standard(s) Setup Inciting Incident Rising Action Climax Resolution

https://tinyurl.com/1pagesystems

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Selecting Systems of Equations

https://tinyurl.com/1pagesystems

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Otten & Otten (2017)

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Systems of Equations

Solution Methods

  • Substitution
  • Elimination/Combination
  • Graphing
  • Inspection

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https://tinyurl.com/1pagesystems

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Systems of Equations

Thus far, you’ve been given systems to solve.

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https://tinyurl.com/1pagesystems

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Systems of Equations

What sort of variety do you see in these equations?

Today you get linear equations.

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https://tinyurl.com/1pagesystems

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Systems of Equations What would you look for if you got to pick which equations go together into a system?

Today you get linear equations.

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https://tinyurl.com/1pagesystems

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  • Pick 2 equations for substitution and solve
  • Pick 2 equations for elimination/combination and solve
  • Pick 2 equations for graphing and solve
  • You can only use an equation once, so be strategic!

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https://tinyurl.com/1pagesystems

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What did you look for when choosing?

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Solution Methods

  • Substitution – solved for a variable; same term in two equations
  • Elimination/Combination – multiple of one term appears in another

equation (they cancel); standard form preferred but not required

  • Graphing – equations easy to graph (slope-intercept form,

horizontal or vertical)

https://tinyurl.com/1pagesystems

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  • Is there a pair that you could solve in your head?
  • Do any pairs of lines have no solution? How do you know?
  • Is it possible to have a solution to a system with three equations?

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https://tinyurl.com/1pagesystems

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Exit Slip

Which 2 equations would you choose for your system if you had to solve it by the substitution method? Why would you choose those 2? Note: You don’t have to solve the system.

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  • A. 𝑧 + 5𝑦 = 2
  • B. 5𝑦 = 2𝑧 +11
  • C. -7𝑦 + 3𝑧 = 3

https://tinyurl.com/1pagesystems

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Lesson Debrief

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Lesson Debrief

  • “Throw a wrench in it” – pick equations instead of pick

the solution method

  • Forces conversation to be about the structure of the

equations and flexibility in solution processes, not about steps to follow or answers.

  • No single “right” answer, but there are more or less

strategic ones.

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https://tinyurl.com/1pagesystems

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Cinematic Lesson Structure

  • Setup
  • Inciting Incident
  • Rising Action
  • Climax
  • Resolution

Overall thoughts? Questions?

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https://tinyurl.com/1pagesystems

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Q&A

  • ttensa@missouri.edu

www.TwoMinuteTeachersGuide.com @2minteachguide

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