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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] AL1 (9-12) 16 :
16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]

[MA2015] AL1 (9-12) 17 :
17 ) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3]

[MA2015] AL2 (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] AL2 (9-12) 13 :
13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]

Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

[MA2015] AL2 (9-12) 20 :
20 ) Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]

[MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

[MA2015] AL2 (9-12) 29 :
29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

[MA2015] ALT (9-12) 4 :
4 ) Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2015] ALT (9-12) 13 :
13 ) Use the structure of an expression to identify ways to rewrite it. [A-SSE2]

Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

[MA2015] ALT (9-12) 20 :
20 ) Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1]

[MA2015] ALT (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

[MA2015] ALT (9-12) 29 :
29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

[MA2019] AL1-19 (9-12) 5 :
5. Use the structure of an expression to identify ways to rewrite it.

Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
[MA2019] AL1-19 (9-12) 6 :
6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

c. Use the properties of exponents to transform expressions for exponential functions.

Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

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. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
[MA2019] AL1-19 (9-12) 11 :
11. Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.
[MA2019] AL1-19 (9-12) 15 :
15. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Applying the Quadratic Formula (Part 1): Algebra 1, Episode 24: Unit 7, Lesson 17 | Illustrative Math
URL: https://aptv.pbslearningmedia.org/resource/im20-math-ep24-717/applying-the-quadratic-formula-part-1/
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).



   View Standards     Standard(s): [MA2015] AL2 (9-12) 19 :
19 ) Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system. [A-APR6]

[MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

[MA2019] AL1-19 (9-12) 9 :
9. Select an appropriate method to solve a quadratic equation in one variable.

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. Explain how the quadratic formula is derived from this form.

b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 1, Topic C: Solving and Applying Equations--Polynomial, Rational, and Radical
URL: https://www.engageny.org/resource/algebra-ii-module-1-topic-c-overview
Description:

Students solve polynomial, rational, and radical equations, and apply these types of equations to real-world situations. They examine the conditions under which an extraneous solution is introduced. They rewrite rational expressions in different forms and work with radical expressions as part of this process. Students work with systems of equations that include quadratic and linear equations and apply their work to understanding the definition of a parabola.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Radical Equations Easy Part 1
URL: https://www.youtube.com/watch?v=TJct6AGxVTI&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=32
Description:

This YouTube video will help explain how to teach radical equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos available to fully teach this concept. The videos are labeled Radical Equations Easy Part 1, Radical Equations Easy Part 2, and Radical Equations Easy Part 3. This video can be played to introduce a lesson on radical equations. This video is 8 minutes and 38 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Radical Equations Easy Part 2
URL: https://www.youtube.com/watch?v=E-XG7aJEgHs&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=33
Description:

This YouTube video will help explain how to teach radical equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos available to fully teach this concept. The videos are labeled Radical Equations Easy Part 1, Radical Equations Easy Part 2, and Radical Equations Easy Part 3. This video can be played as a continuation of a lesson on radical equations. This video is 7 minutes and 52 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Radical Equations Easy Part 3
URL: https://www.youtube.com/watch?v=59fO2FnRWHk&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=34
Description:

This YouTube video will help explain how to teach radical equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of three videos available to fully teach this concept. The videos are labeled Radical Equations Easy Part 1, Radical Equations Easy Part 2, and Radical Equations Easy Part 3. This video can be played as a continuation of a lesson on radical equations. This video is 7 minutes and 25 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Rational Equations Easy Part 1
URL: https://www.youtube.com/watch?v=i-jvxc1qlN8&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=35
Description:

This YouTube video will help explain how to teach rational equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of four videos available to fully teach this concept. The videos are labeled Rational Equations Easy Part 1, Rational Equations Easy Part 2, Rational Equations Easy Part 3, and Rational Equations Part 4. This video can be played to introduce a lesson on rational equations. This video is 10 minutes and 55 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Rational Equations Easy Part 2
URL: https://www.youtube.com/watch?v=TzWjyEHWWTQ&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=36
Description:

This YouTube video will help explain how to teach rational equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of four videos available to fully teach this concept. The videos are labeled Rational Equations Easy Part 1, Rational Equations Easy Part 2, Rational Equations Easy Part 3, and Rational Equations Part 4. This video can be played to introduce a lesson on rational equations. This video can be played as a continuation of a lesson on rational equations. This video is 10 minutes and 41 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Rational Equations Easy Part 3
URL: https://www.youtube.com/watch?v=jtToRmuq_wQ&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=37
Description:

This YouTube video will help explain how to teach rational equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of four videos available to fully teach this concept. The videos are labeled Rational Equations Easy Part 1, Rational Equations Easy Part 2, Rational Equations Easy Part 3, and Rational Equations Easy Part 4. This video can be played to introduce a lesson on rational equations. This video can be played as a continuation of a lesson on rational equations. This video is 12 minutes and 37 seconds in length.



   View Standards     Standard(s): [MA2015] AL2 (9-12) 24 :
24 ) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]

Subject: Mathematics (9 - 12)
Title: KutaSoftware: Algebra 1 - Rational Equations Easy Part 4
URL: https://www.youtube.com/watch?v=ojSRUwytO_8&list=PLD7NSlqW6HTGDhLkT5T71rw1e5m9xgFxq&index=38
Description:

This YouTube video will help explain how to teach rational equations using a worksheet from Kuta Software. Kuta Software is free software for math teachers that creates worksheets in a matter of minutes. There are a series of four videos available to fully teach this concept. The videos are labeled Rational Equations Easy Part 1, Rational Equations Easy Part 2, Rational Equations Easy Part 3, and Rational Equations Easy Part 4. This video can be played to introduce a lesson on rational equations. This video can be played as a continuation of a lesson on rational equations. This video is 9 minutes and 28 seconds in length and can be assigned through Google Classroom.



ALEX Classroom Resources: 9

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