# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Applying the Quadratic Formula (Part 1): Algebra 1, Episode 24: Unit 7, Lesson 17 | Illustrative Math
Description:

In this video lesson, students return to some quadratic functions they have seen. They write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward (MP5).

The work in this lesson—writing equations, solving them, and interpreting the solutions in context—encourages students to reason quantitatively and abstractly (MP2).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: How Many Solutions?: Algebra 1, Episode 14: Unit 7, Lesson 5 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep14-75/how-many-solutions/
Description:

This video lesson builds on the idea that both graphing and rewriting quadratic equations in the form of expression = 0 are useful strategies for solving equations. It also reinforces the ties between the zeros of a function and the horizontal intercepts of its graph, which students began exploring in an earlier unit.

Here, students learn that they can solve equations by rearranging them into the form expression = 0, graphing the equation y = expression, and finding the horizontal intercepts. They also notice that dividing each side of a quadratic equation by a variable is not reliable because it eliminates one of the solutions. As students explain why certain maneuvers for solving quadratic equations are acceptable and others are not, students practice constructing logical arguments (MP3).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 3, Topic C: Transformations of Functions
URL: https://www.engageny.org/resource/algebra-i-module-3-topic-c-overview
Description:

In Module 3, Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex algebraic solutions to equations in one variable, seeing them as f(x) = g(x) and recognizing that the intersection of the graphs of f(x) and g(x) are solutions to the original equation (A-REI.D.11). Students use the absolute value function and other piecewise functions to investigate transformations of functions and draw formal conclusions about the effects of a transformation on the function’s graph (F-IF.C.7, F-BF.B.3).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 1, Topic C: Solving Equations and Inequalities
URL: https://www.engageny.org/resource/algebra-i-module-1-topic-c-overview
Description:

Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Module 1, Topic C, instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and non-linear equations (A-REI.1, A-REI.3, A-CED.4). Students take their experience solving systems of linear equations further as they prove the validity of the addition method, learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and graphically represent the solution to systems of linear inequalities (A-CED.3, A-REI.5, A-REI.6, A-REI.10, A-REI.12).

ALEX Classroom Resources: 4 