# All Lessons

## Simplify Radical Expressions

(A) Simplify numerical radical expressions involving square roots

A2.7.G(G) Rewrite radical expressions that contain variables to equivalent forms

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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## Verify if an Ordered Pair is a Solution to a Linear Equation

This Algebra 1 lesson teaches students how to verify that an ordered pair is the solution to a linear equation. The lesson includes research-based strategies and strategic questions that prepare students for assessments. Students will identify the linear equation, and verify if the ordered pair is a solution by substituting values into the linear equation and evaluating. Finally, they will plot the point on the coordinate plane and interpret the result both algebraically and graphically. In addition to the lesson, there is one page of Independent Practice and three pages of periodic review.

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## Solve a System of Two Linear Equations in Two Variables Algebraically

HSA.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

HSA.REI.6HSA.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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## Add Rational Expressions

This Algebra 1 lesson teaches students how to add rational expressions. The lesson includes research-based strategies and strategic questions that prepare students for assessments. Students will factor the polynomials in the denominator completely, if possible, and then create equivalent fractions by finding the common denominator by multiplying the numerator and denominator of each fraction by the same rational expression. Finally, they will add the rational expressions by combining like terms in the numerator, and simplifying if needed. In addition to the lesson, there is one page of Independent Practice and three pages of periodic review.

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## Solve Quadratic Equations by Factoring

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 ± bi for real numbers a and b.

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## Solve Quadratic Equations Using the Quadratic Formula

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

HSA.REI.4.AHSA.REI.4.A 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.

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 ± bi for real numbers a and b.

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

(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

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

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 ± bi for real numbers a and b.

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## Identify Types of Systems of Linear Equations

8.EE.8.B Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

HSA.REI.6HSA.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA.REI.10HSA.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).