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- HSA-SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*
- HSA-SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.â

Polynomial Puzzles 3: Multiplying and Factoring Polynomials

Algebra I

Â» Unit:

Polynomial Expressions

Big Idea:This lesson will help students to see that multiplying and factoring trinomials are inverse operations

Finding Roots of All Sorts

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:In this fast-paced lesson, students are introduced to as many ideas as they can handle, while also being given space to make their own sense of those ideas.

Features of a Parabola

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:Students finish up the Quadratic Functions Gallery Walk and begin to spot connections between where the roots and where the vertex are located.

Can the Dog Reach the Bone? Determine whether a Point Lies within a Circle

12th Grade Math

Â» Unit:

Circles

Big Idea:Will the dog be able to reach its bone? Students apply the definition of a circle, along with a method for determining whether or not a point lies on a circle.

Standard Form of Circle Equations

12th Grade Math

Â» Unit:

Circles

Big Idea:How can I tell if this weird-looking equation will make a circle when I graph it? Students discover how to apply previous knowledge about completing the square to a new problem.

What if We Start With the Axis of Symmetry?

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:An investigation of the relationship between the discriminant and the axis of symmetry lays foundations for students to understand the quadratic formula.

Area Models for Multiplying Polynomials and Factoring Quadratic Expressions

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:This fast-paced lesson introduces multiplication of binomials and factoring of quadratic expressions for the first time, which sets students up to explore both in depth over the next few days.

Moving Toward Mastery: Completing the Square (Day 2)

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:Students will continue to see that graphing quadratic equations and solving them work in tandem: the better we understand one, the more sense the other will make!

Can You Factor It?

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:Students make a list of perfect squares before keep a close watch to see where these special numbers pop up!

Circle Lattice Points

12th Grade Math

Â» Unit:

Circles

Big Idea:Instead of telling students the equation for a circle, developing it themselves enables students to make the connection between circles and the Pythagorean Theorem.

Quadratic Functions in Three Forms

Algebra I

Â» Unit:

Quadratic Functions

Big Idea:An brief adventure in number theory provides some background knowledge for completing the square, then students get to practice manipulating quadratic expressions in different forms.

Comparing Investments

Algebra I

Â» Unit:

Exponential Functions

Big Idea:To guide students in practice to develop meaning for each variable in either formula in order to make correct substitutions and evaluations.

Connecting Expressions to Area

Algebra I

Â» Unit:

Understanding Equations

Big Idea:Students form a concept image by representing area as the product of binomial factors.

Writing Circle Equations

12th Grade Math

Â» Unit:

Circles

Big Idea:After thinking deeply about the Pythagorean Theorem and the key properties of circles, students are able to generate circle equations themselves.

Circle Review Session and Portfolio Workshop

12th Grade Math

Â» Unit:

Circles

Big Idea:When students design their own review session and their own portfolios, you have time to work with each individual student to ensure that they get the most out of this learning opportunity.

HSA-SSE.B.3a

Factor a quadratic expression to reveal the zeros of the function it defines.

HSA-SSE.B.3b

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

HSA-SSE.B.3c

Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15<sup>t</sup> can be rewritten as (1.15<sup>1/12</sup>)<sup>12t</sup> â 1.012<sup>12t</sup> to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.