Building Quadratic Functions from Geometric Patterns

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

Earlier in this video series, students reasoned about visual patterns using different representations and wrote expressions to describe the patterns. In this lesson, they continue to work with patterns but begin to see these relationships as quadratic functions and write equations to define them.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.15

Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

UP:MA19.A1.15

Vocabulary

  • Domain
  • Range
  • Function
  • Relation
  • Function notation
  • Set notation

Knowledge

Students know:
  • Distinguishing characteristics of functions.
  • Conventions of function notation.
  • In graphing functions the ordered pairs are (x,f(x)) and the graph is y = f(x).

Skills

Students are able to:
  • Evaluate functions for inputs in their domains.
  • Interpret statements that use function notation in terms of context.
  • Accurately graph functions when given function notation.
  • Accurately determine domain and range values from function notation.

Understanding

Students understand that:
  • A function is a mapping of the domain to the rangeFunction notation is useful in contextual situations to see the relationship between two variables when the unique output for each input relation is satisfied.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.25

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

UP:MA19.A1.25

Vocabulary

  • Arithmetic and geometric sequences
  • Arithmetic sequence
  • Geometric sequence
  • Exponential function

Knowledge

Students know:
  • That linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
  • Properties of arithmetic and geometric sequences.

Skills

Students are able to:
  • Accurately recognize relationships within data and use that relationship to create a linear or exponential function to model the data of a contextual situation.

Understanding

Students understand that:
  • Linear and exponential functions may be used to model data that is presented as a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.13

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

UP:MA19.A2.13

Vocabulary

  • Polynomial Functions
  • Exponential Functions
  • Logarithmic Functions
  • Radical Functions
  • Trigonometric Functions
  • Reciprocal Functions
  • Piecewise Functions

Knowledge

Students know:

  • When a particular two variable equation accurately models the situation presented in a contextual problem.

Skills

Students are able to:

  • Write equations in two variables that accurately model contextual situations.
  • Graph equations involving two variables on coordinate axes with appropriate scales and labels, using it to make predictions.

Understanding

Students understand that:

  • There are relationships among features of a contextual problem, a created mathematical model for that problem, and a graph of that relationship which is useful in making predictions.

Body

  1. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.13

Use the recursive process and difference equations to create fractals, population growth models, sequences, and series.

UP:MA19.FM.13

Vocabulary

  • Difference equation
  • Recursive process
  • Recursive formula
  • Fractals
  • Population growth models
  • Sequences
  • Series

Knowledge

Students know:

  • How to recognize a pattern.

Skills

Students are able to:

  • Apply recursive formulas in real-world contexts.

Understanding

Students understand that:

  • Models such as population growth should be recognized as recursively developed models.
  • The recursion process can be applied to many situations.
  • A sequence lists the solutions of a set of related problems.

Body

  1. Use the recursive process and difference equations to create fractals, population growth models, sequences, and series.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
https://aptv.pbslearningmedia.org/resource/im20-math-ep3-63/building-quadratic-…

Comments or Notes

This resource contains student practice problems and student task statements.

Approved Date

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