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 A: Linear and Exponential Sequences
URL: https://www.engageny.org/resource/algebra-i-module-3-topic-overview
Description:

In Module 3, Topic A, students explore arithmetic and geometric sequences as an introduction to the formal notation of functions (F-IF.A.1, F-IF.A.2). They interpret arithmetic sequences as linear functions with integer domains and geometric sequences as exponential functions with integer domains (F-IF.A.3, F-BF.A.1a). Students compare and contrast the rates of change of linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change (F-IF.B.6, F-LE.A.1, F-LE.A.2, F-LE.A.3).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 3, Topic B: Functions and Their Graphs
URL: https://www.engageny.org/resource/algebra-i-module-3-topic-b-overview
Description:

In Module 3, Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and interpret functions in abstract and contextual situations (F-IF.A.1, F-IF.A.2). Students examine the graphs of a variety of functions and learn to interpret those graphs using precise terminology to describe such key features as domain and range, intercepts, intervals where the function is increasing or decreasing, and intervals where the function is positive or negative. (F-IF.A.1, F-IF.B.4, F-IF.B.5, F-IF.C.7a).

ALEX Classroom Resources: 4