Unit 2 - Quadratic and Rational Functions
Global Context
Key Concept
Form
The shape and underlying
structure of an entity or piece
of work, including it's
organization, essential nature,
and external appearance.
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Scientific and
Technical
Innovation
Related Concepts
Patterns, Space,
Equivalence
Patterns: Sets of numbers or objects that follow a specific pattern or rule.
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Space: The frame of geometrical dimensions describing an entity.
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Equivalence: The state of being equal to or identically interchangeable, applied to statements, quantities, or expressions.
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Learning Objectives
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Factorizing quadratic expressions, where the coefficient of x^2 is 1, including the difference of squares
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Factoring quadratic expressions where the coefficient of x^2 is not 1
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Finding the axis of symmetry and vertex of a quadratic function
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Expression a quadratic function in three different forms: standard, vertex, and factored
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Finding a quadratic function given three distinct points on its graph
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Finding a function to model a real-life parabola
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Solving quadratic equations algebraically and graphically
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Solving real life problems by creating and using quadratic models
Statement of Inquiry
Representing patterns with equivalent forms can lead to better systems, models and methods.
Inquiry Questions
Factual
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What does "expanding brackets" mean?
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What does "factorize a quadratic expression" mean?
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What shape is the graph of a quadratic equation?
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How do the parameters of a quadratic function affect the shape of the graph?
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What is the null factor law?
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How do you solve a quadratic equation in factorized form?
Conceptual
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How do patterns in expanding brackets help you factor quadratic expressions?
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How can you express a quadratic function in three different ways?
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What are the advantages of each form of a quadratic equation?
Debatable
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Can everything be written in a different form?
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What makes one quadratic form better than another one?
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Do systems, models, and methods solve problems or create them?
Unit Discussion
Questions & Suggestions
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Begin a discussion thread by adding a specific question under a Lesson heading.
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Suggest links to videos and websites that have helped you in your learning.
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Learn
Lesson 1:
Review of
Expansion Laws
Take notes and discuss this
presentation.
+ Notes Page
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Bonus Problem Set
Collaborate
Criterion C:
Communicate mathematically. .
.None today.
Criterion D:
Real world mathematics.
.None today.
Reflect
Lesson 2:
Factoring GCFs and
Difference of Squares
Criterion C:
Communicate mathematically. .
Complete this TASK.
Criterion D:
Real world mathematics.
None today.
Reflect
Lesson 3:
Factoring Quadratic
Trinomials
Video Lesson 1
+ Notes Page
Video Lesson 2
+ Notes Page
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in our Unit Discussion.
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Learn
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
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Reflect
Lesson 4:
Factoring Review
Criterion C:
Communicate mathematically. .
Complete THIS task.
Criterion D:
Real world mathematics.
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Reflect
Lesson 5:
Solving Quadratic
Equations
If you haven't finished:
Challenge Problem Video
Video Lesson
Practice Assignment
Ask your questions
in our Unit Discussion.
Learn
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Complete STEP 1 today.
Reflect
Lesson 6:
Solving Quadratic
Equations 2
In Class Video Lesson
(Quadratic Word Prb.)
.More Challenge
Problems
Need More? (go HERE)
Collaborate
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
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Reflect
Lesson 7:
Effects of Changing
Quadratic Parameters
Some collaborative
activities will be
shared during the lesson.
Collaborate
Additional Resources:
More on the Effects of Changing a, b, and c
Get Inspired !
The Bubble that Breaks Maths !
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Explore
Lesson 8:
Graphing Standard
Form Quadratics
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Continue STEP 1 today.
Reflect
Lesson 9:
Intercept and Vertex
Form Quadratics
Lesson 10:
Completing
the Square
Did you complete the "Applied Problems" from Lesson 8 ?
What about the extra word problems in Lesson 6?
Ask your questions
in our Unit Discussion.
Learn
Investigation 1:
Vertex Form Quadratics
Video Notes Page
Investigation 2:
Intercept Form Quadratics
Video Notes Page
Collaborate
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Continue STEP 1 today.
Reflect
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Continue STEP 2 today.
Reflect
Lesson 11:
Area Maximization
Problems
Make Corrections
to the Bouncing Ball Task
Continue STEP 2 of the
Criterion D Unit Project.
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Learn
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Continue STEP 2 today.
Reflect
Lesson 12:
Solving by
Completing
the Square
Video Lesson
Practice
Also: did you try Problem 4 in the class word problems? You should!
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Unit Discussion Padlet.
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Learn
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Continue STEP 2 today.
Reflect
Explore
Lesson 13:
Applying the
Discriminant
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Criterion D:
Real world mathematics.
Continue STEP 3 today.
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Lesson 14:
Final Quadratic
Word Problems
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Complete Step 3.
Reflect
Lesson 15:
Creating Quadratic
Models
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
Complete the project today.
Step 4.
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Explore
Lesson 16:
Simplifying
Rationals
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Communicate mathematically. .
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Criterion D:
Real world mathematics.
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Lesson 17:
Adding and
Subtracting
Rationals
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Communicate mathematically. .
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Criterion D:
Real world mathematics.
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Lesson 18:
Solving Rational
Equations
Criterion C:
Communicate mathematically. .
Complete THIS task.
Criterion D:
Real world mathematics.
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Reflect
Lesson 19:
Applied Problems
and Review
...
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Unit Discussion Padlet.
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Learn
Criterion C:
Communicate mathematically. .
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Criterion D:
Real world mathematics.
None today.