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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) 21 :
21 ) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]

[MA2015] AL2 (9-12) 27 :
27 ) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]

[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) 21 :
21 ) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]

[MA2015] ALT (9-12) 27 :
27 ) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]

[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) 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) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
[MA2019] AL1-19 (9-12) 12 :
12. Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2019] AL1-19 (9-12) 14 :
14. Given a relation defined by an equation in two variables, identify the graph of the relation as the set of all its solutions plotted in the coordinate plane.
Note: The graph of a relation often forms a curve (which could be a line).
[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.
[MA2019] AL1-19 (9-12) 19 :
19. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

a. Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate.
Note: Include cases where f(x) is a linear, quadratic, exponential, or absolute value function and g(x) is constant or linear.
[MA2019] AL1-19 (9-12) 20 :
20. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes, using technology where appropriate.
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).

 



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Solutions to Systems of Linear Equations
URL: https://teacher.desmos.com/activitybuilder/custom/564a325345d9115d06270607
Description:

Students will use a Desmos activity to find solutions to systems of linear equations. This activity will help students understand what it means for a point to be a solution to a system of equations–both graphically and algebraically. This Desmo activity offers sample student responses and a teacher guide.



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Systems of Two Linear Equations
URL: https://teacher.desmos.com/activitybuilder/custom/5807d7306ef115e7053a142a
Description:

Students will use a Desmos activity to solve systems of linear equations. In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they have learned to similar situations. This Desmos activity offers sample student responses and a teacher guide.



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Card Sort: Linear Systems
URL: https://teacher.desmos.com/activitybuilder/custom/5798d64583de446662ea8ddd
Description:

In this Desmos activity, students practice what they have learned about solving systems of linear equations. The activity begins with a review of the graphical meaning of a solution to a system. Later, students consider which algebraic method is most efficient for solving a given system. Finally, students practice solving equations using substitution and elimination. Prior to beginning this activity, students should have experience solving systems of linear equations graphically and algebraically. This Desmos activity offers sample student responses and a teacher guide.



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Line Zapper
URL: https://teacher.desmos.com/activitybuilder/custom/5df166d1fa83ee79c328d37d
Description:

In this Desmos activity, students "zap" lines by identifying their solutions to systems of equations. Students begin by zapping individual lines and then turn their attention to systems of linear equations where a single "zap" aimed at a point of intersection will capture multiple lines at once. Prior to beginning this activity, students should have experience solving systems of linear equations graphically and algebraically. This Desmos activity offers sample student responses and a teacher guide.



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Playing Catch-Up
URL: https://teacher.desmos.com/activitybuilder/custom/5818fb314e762b653c3bf0f3
Description:

In this Desmos activity, students will develop their understanding of systems of equations, particularly as they're represented as tables, equations, and graphs. The students apply that understanding to the question, "Will one racer catch another?" This Desmos activity offers sample student responses and a teacher guide.



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Solving Systems of Equations by Elimination
URL: https://www.youtube.com/watch?v=vA-55wZtLeE
Description:

In this video from Khan Academy, students learn about solving systems of equations by elimination. This video can be used during a lesson on solving systems of equations. The video is 12 minutes and 43 seconds in length and can be assigned through Google Classroom



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Solving Linear Systems by Graphing
URL: https://www.youtube.com/watch?v=5a6zpfl50go
Description:

In this YouTube video from Khan Academy, students learn about solving linear systems by graphing. This video can be used during a lesson on solving systems of equations. The video is 8 minutes and 29 seconds in length and can be assigned through Google Classroom



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 10 :
10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.
Subject: Mathematics (9 - 12)
Title: Systems of Equations
URL: https://www.youtube.com/watch?v=nok99JOhcjo
Description:

In this video from Khan Academy, students learn about solving linear systems of equations. This video can be used during a lesson on solving systems of equations. The video is 9 minutes and 57 seconds in length and can be assigned through Google Classroom



ALEX Classroom Resources: 9

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