3.+Expressions+and+Equations

Standards
A.SSE.1. Interpret expressions that represent a quantity in terms of its context. ⋆
 * 1) Interpret parts of an expression, such as terms, factors, and coefficients.
 * 2) Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

A.SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x^4−y^4 as (x^2)^2−(y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2−y^2)(x^2+y^2).

A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ⋆
 * 1) Factor a quadratic expression to reveal the zeros of the function it defines.
 * 2) Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 * 3) Use the properties of exponents to transform expressions for exponential functions.

A.CED.1. Create equations and inequalities in one variable and use them to solve problems.Include equations arising from linear and quadratic functions, and simple rational and exponential functions. ⋆

A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ⋆

A.CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V=IR to highlight resistance R.   ⋆

A.REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.4. Solve quadratic equations in one variable.
 * 1) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x−p)^2=q that has the same solutions. Derive the quadratic formula from this form.
 * 2) Solve quadratic equations by inspection (e.g., for x^2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a±bi for real numbers a and b.

A.REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

N.CN.7. Solve quadratic equations with real coefficients that have complex solutions. N.CN.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2+4 as (x+2i)(x−2i). N.CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Examples of Learning Cycles and Tasks
==//**Quadratic equations **//(Murray CA, refers to A.CED.1) == ==//**Completing the square **//(Orem CA, refers to A.REI.4) ==

Interpret expressions (St. George CA, refers to A.SSE.1)
Quadratic Equivalent Expressions (Orem, UT refers to A.SSE.3)

Difference of Squares (Wasatch CA, refers to A.SSE.2)

Expressions&Equations (Salem Hills CA, refers to A.SSE.3)

Solve Systems of Linear and Quadratic Equations (Cedar City, UT, refers to A.REI.7)

Interpret and Write Quadratic Expressions (Richfield CA refers to A.SSE.1, A.CED.1, A.SSE.3, A.REI.4

Solving Quadratic Equations for Real World Scenarios (Cedar City CC Academy)

Solving Systems of Equations: Linear and Quadratic Functions (Richfield CA, refers to A.REI.7)