# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (9 - 12)
Title: Completing the Square (Part 1): Algebra 1, Episode 20: Unit 7, Lesson 12 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep20-712/completing-the-square-part-1/
Description:

Previously in this video series, students saw that a squared expression of the form (x + n)2 is equivalent to x2 + 2nx + n2. This means that, when written in standard form ax2 + bx + c (where a is 1), b is equal to 2n and c is equal to n2. Here, students begin to reason the other way around. They recognize that if ax2 + bx + c is a perfect square, then the value being squared to get c is half of b, or (b/2)2. Students use this insight to build perfect squares, which they then use to solve quadratic equations.

Students learn that if we rearrange and rewrite the expression on one side of a quadratic equation to be a perfect square, that is if we complete the square, we can find the solutions of the equation.

Subject: Mathematics (9 - 12)
Title: Algebra I Module 4, Topic A: Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles
URL: https://www.engageny.org/resource/algebra-i-module-4-topic-overview
Description:

Module 4, Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is extended and connected to factoring polynomial expressions and solving basic polynomial equations (A-APR.A.1, A-REI.D.11). They analyze, interpret, and use the structure of polynomial expressions to multiply and factor polynomial expressions (A-SSE.A.2). They understand factoring as the reverse process of multiplication. In this topic, students develop the factoring skills needed to solve quadratic equations and simple polynomial equations by using the zero-product property (A-SSE.B.3a). Students transform quadratic expressions from standard form, ax2 + bx + c, to factored form, f(x) = a(x - n)(x - m), and then solve equations involving those expressions. They identify the solutions of the equation as the zeros of the related function. Students apply symmetry to create and interpret graphs of quadratic functions (F-IF.B.4, F-IF.C.7a). They use the average rate of change on an interval to determine where the function is increasing or decreasing (F-IF.B.6). Using area models, students explore strategies for factoring more complicated quadratic expressions, including the product-sum method and rectangular arrays. They create one- and two-variable equations from tables, graphs, and contexts and use them to solve contextual problems represented by the quadratic function (A-CED.A.1, A-CED.A.2). Students then relate the domain and range for the function to its graph and the context (F-IF.B.5).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 4, Topic B: Using Different Forms for Quadratic Functions
URL: https://www.engageny.org/resource/algebra-i-module-4-topic-b-overview
Description:

Subject: Mathematics (9 - 12)
Title: Algebra I Module 1, Topic B: The Structure of Expressions
URL: https://www.engageny.org/resource/algebra-i-module-1-topic-b-overview
Description:

In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Module 1, Topic B, students use the structure of expressions to define what it means for two algebraic expressions to be equivalent. In doing so, they discern that the commutative, associative, and distributive properties help link each of the expressions in the collection together, even if the expressions look very different themselves (A-SSE.2). They learn the definition of a polynomial expression and build fluency in identifying and generating polynomial expressions as well as adding, subtracting, and multiplying polynomial expressions (A-APR.1). The Mid-Module Assessment follows Topic B.

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 1, Topic D: Creating Equations to Solve Problems
URL: https://www.engageny.org/resource/algebra-i-module-1-topic-d-overview
Description:

In Topic D, students are formally introduced to the modeling cycle through problems that can be solved by creating equations and inequalities in one variable, systems of equations, and graphing (N-Q.1, A-SSE.1, A-CED.1, A-CED.2, A-REI.3). The End-of-Module Assessment follows Topic D.

ALEX Classroom Resources: 5 