# All Lessons

## Simplify Radical Expressions

HSN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = (5^(1/3))^3 to hold, so (5^(1/3))^3 must equal 5.

HSN.RN.2HSN.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

This number sense lesson focuses on simplifying radical expressions. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the radical expression and identify the radicand. Then, they find the prime factors of the radical expression and rewrite it as the product of prime factors of the radicand. Finally, they simplify the radical expression and interpret the solution. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

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## Graph Linear Inequalities (Slope-Intercept Form)

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## Determine How Many Times the Graph of a Quadratic Function Intersects the X-Axis

HSA.REI.4 Solve quadratic equations in one variable.

HSA.REI.4.BHSA.REI.4.B 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 Â± bi for real numbers a and b.

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## Solve Equations with Unknown Coefficients

(A) Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

A1.12.E(E) Solve mathematic and scientific formulas, and other literal equations, for a specified variable.

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## Simplify Expressions with Roots

(10) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

A1.10.A(A) Add and subtract polynomials of degree one and degree two

A1.10.B(B) Multiply polynomials of degree one and degree two

A1.10.C(C) Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend

A1.10.D(D) Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

A1.10.E(E) Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

A1.10.F(F) Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

A1.11(11) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

A1.11.A(A) Simplify numerical radical expressions involving square roots

A1.11.B(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that âˆš2 is irrational.

HSN.RN.1HSN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = (5^(1/3))^3 to hold, so (5^(1/3))^3 must equal 5.

HSN.RN.2HSN.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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## Solve Multi-Step Linear Inequalities

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## Factor Quadratic Expressions - Part 1

(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

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## Factor Quadratic Expressions - Part 2

(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

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## Solve Exponential Equations

(C) Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

A2.5.D(D) Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions

PCAL.5.I(I) Generate and solve exponential equations in mathematical and real-world problems