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Lesson Video
Lesson Video
Focus Standards
Focus Standards
Learning Focus
Learning Focus
Additional Resources
Additional Resources
Lesson 1: The In-Betweeners
Lesson 1: The In-Betweeners
A Develop Understanding Task
Introduces rational exponents to describe the outputs of a continuous exponential function between the integer outputs. Introduces the connection between rational exponents and radicals.
NC.M2.N-RN.1
Explore the meaning of a fraction as an exponent.
How can you determine the values of an exponential function that occur between whole number inputs?
Since the domain of a continuous exponential function includes all rational numbers, how do we interpret a fraction as an exponent?
Lesson 2: Half Interested or More Interesting
Lesson 2: Half Interested or More Interesting
A Solidify Understanding Task
Verifies the properties of rational exponents within a real-world context.
Examine how the properties of exponents work with rational exponents.
Write equivalent exponential functions using different growth factors.
What do rational exponents and negative exponents mean in contexts?
Do the laws of exponents work with rational exponents?
How does the growth factor change if we focus on a month of exponential growth instead of a year?
Lesson 3: Radical Thinking
Lesson 3: Radical Thinking
A Develop Understanding Task
Uses rules of exponents to simplify radical and rational exponents.
Change the form of radical expressions using properties of exponents.
Which is a more efficient way to change the form of a radical expression: using radicals or using exponents?
How do the properties of exponents help explain methods for representing and manipulating radicals?
Lesson 4: All Things Being Equal
Lesson 4: All Things Being Equal
A Develop Understanding Task
Introduces solving quadratic equations graphically and by completing the square.
Solve quadratic equations graphically and algebraically.
Make connections between solving quadratic equations and graphing quadratic functions.
How can we use graphs to solve quadratic equations?
Lesson 5: Formula for Success
Lesson 5: Formula for Success
A Solidify Understanding Task
Derives the quadratic formula as a way to find x-intercepts and roots of quadratic functions by completing the square.
Understand and use a formula for solving quadratic equations.
Is there any method that works for solving all quadratic equations?
Lesson 6: Comparison Shopping
Lesson 6: Comparison Shopping
A Solidify Understanding Task
Builds strategic thinking, efficiency, and flexibility in solving quadratic equations.
Solve quadratic equations efficiently and accurately.
Solve systems of quadratic and linear equations.
How can you determine the most efficient strategy for solving any particular quadratic equation?
A Develop Understanding Task
Introduces the Fundamental Theorem of Algebra and surfaces the need for non-real numbers as solutions for some quadratic equations.
Write quadratic functions in vertex, factored, and standard form.
Find roots of a quadratic function.
Use the roots of a quadratic function to write the function in factored form.
Can every quadratic function be written in all three of the forms we have studied: standard, vertex, and factored form?
How do solutions of a quadratic relate to the factors of a quadratic function?
Do all quadratic functions have two roots?
Lesson 8: I May be Irrational, But You're Imaginary
Lesson 8: I May be Irrational, But You're Imaginary
A Solidify Understanding Task
Examines irrational numbers and introduces imaginary numbers and complex numbers.
Relate irrational numbers to physical quantities such as the hypotenuse of a right triangle.
Understand expressions that contain negative numbers inside a square root, like .
Add, subtract, and multiply complex numbers.
Can numbers like be rewritten?
What types of numbers make up the number system?
Lesson 9: iNumbers
Lesson 9: iNumbers
A Develop Understanding Task
Formalizes relationships between sets of numbers and considers whether number sets are closed under a given operation.
Support or challenge claims about different types of numbers and the result of adding, subtracting, multiplying, and dividing.
What are the similarities and differences between the arithmetic of integers, rational numbers, real numbers, and complex numbers?
A Practice Understanding Task
Extends work with solving quadratic equations to solving quadratic inequalities.
Solve quadratic inequalities both graphically and algebraically.
Interpret solutions to quadratic inequalities that arise from context.
How can we use our understanding of solving quadratic equations and graphing quadratic functions to solve quadratic inequalities?
What do our solutions mean in the context of the problem?
How do we identify and write all the solutions?
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