Download Domain: Cluster: Level: Mathematical Content Standard: Featured

Domain:
Reasoning with Equations and Inequalities A -RE I
Cluster:
Understand solving equations as a process of reasoning and explain
the reasoning
Mathematical Content Standard:
1. 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.
Featured Mathematical
Practice:
Standard Clarification/Example:
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High School: Algebra
Correlated WA Standard:
Pacing:
Assuming an equation has a solution, construct a convincing argument that justifies each step in the solution
process. Justifications may include the associative, commutative, and division properties, combining like terms,
multiplication by 1, etc.
Task Analysis:
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Level:
Understand properties such as associative, commutative, etc.
Solve a multi-step equation
Justify their reasoning for each step in the process of solving the equation
Vocabulary:
Prior
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Equation
Variable
Solve
Justify
Explicit
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Associative
Commutative
Introductory

Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -RE I
Understand solving equations as a process of reasoning and explain the
reasoning
High School: Algebra
Mathematical Content Standard:
2. Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Solve simple rational and radical equations in one variable and provide examples of how extraneous solutions
arise.
Task Analysis:
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Correlated WA Standard:
Know the difference between a rational and a radical equation is
Understand what an extraneous solution is
Solve simple rational and radical equations in one variable
Interpret the meaning of the derived solution and relate it to the context of the
problem in order to find possible extraneous solutions
Vocabulary:
Prior
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Radical
Rational
Explicit
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Extraneous
solutions
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve equations and inequalities in one variable
High School: Algebra
Mathematical Content Standard:
3. Solve linear equations and inequalities in one variable, including
equations with coefficients represented by letters.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Correlated WA Standard:
Pacing:
Solve linear equations in one variable, including coefficients represented by letters.
Solve linear inequalities in one variable, including coefficients represented by letters.
Task Analysis:
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Solve a one-step, two-step, and multi-step equations and inequalities
Solve a formula for the indicated variable
Understand that you can solve for a particular variable in terms of other
unknowns (coefficients as letters rather than numbers)
Understand the constraints letter coefficients have
Vocabulary:
Prior
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Coefficient
Variable
Explicit
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Introductory
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Constraints
Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve equations and inequalities in one variable
High School: Algebra
Mathematical Content Standard:
4. Solve quadratic equations 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. Derive the quadratic formula from this form.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Transform a quadratic equation written in standard form by completing the square. (x –
=q
Derive the quadratic formula by completing the square on the standard form of a quadratic equation.
Task Analysis:
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Recognize what a quadratic equation is
Organize the quadratic equation into standard form
Apply the rules of completing the square
Derive the quadratic formula by completing the square on the standard form
of a quadratic equation.
p)2
Vocabulary:
Prior
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Standard form
Quadratic formula
Explicit

Completing the
square
Introductory

Correlated WA Standard:
Pacing:
Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve equations and inequalities in one variable
High School: Algebra
Mathematical Content Standard:
4. Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking
square roots, completing the square, the quadratic formula and factoring,
as appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write them as a ± bi for
real numbers a and b.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Solve quadratic equations in one variable by simple inspection, taking the square root, factoring, and
completing the square.
Understand why taking the square root of both sides of an equation yields two solutions.
Use the quadratic formula to solve any quadratic equation, recognizing the formula produces all complex
solutions. Write the solutions in the form a ± bi, where a and b are real numbers.
Explain how complex solutions affect the graph of a quadratic equation.
Task Analysis:
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Correlated WA Standard:
Recognize a quadratic equation
Determine the appropriate solving method
Recognize the effect square root has on the number of possible real solutions
Understand the consequence of taking the square root of a negative number
Solve quadratic equations involving imaginary numbers
Explain how complex solutions affect the graph of a quadratic equation
Vocabulary:
Prior
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Square root
Completing the
square
Quadratic formula
Factoring
Solving
Explicit
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Complex numbers
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve systems of equations
High School: Algebra
Mathematical Content Standard:
5. Prove that, given a system of two equations in two variables, replacing
one equation by the sum of that equation and a multiple of the other
produces a system with the same solutions.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Solve systems of equations using the elimination method (sometimes called linear combinations).
Solve a system of equations by substitution (solving for one variable in the first equation and substitution it into
the second equation).
Task Analysis:
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Correlated WA Standard:
Recognize a system of equations
Solve the system of equations by elimination
Solve the system of equations by substitution
Prove that given a system of equations in two variables has the same solution
using the elimination method and the substitution method
Vocabulary:
Prior
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System
Explicit
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Elimination
Substitution
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve systems of equations
High School: Algebra
Mathematical Content Standard:
6. Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Solve systems of equations using graphs.
Task Analysis:
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Correlated WA Standard:
Create a graph with appropriate labels and scale
Graph a linear equation
Graph two linear equations on the same graph
Determine the point of intersection
Describe what the point of intersection represents within the context of the
problem
Vocabulary:
Prior
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Graph
Labels
Scale
Explicit
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Point of intersection
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve systems of equations
High School: Algebra
Mathematical Content Standard:
7. Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. For example, find
the points of intersection between the line y = –3x and the circle x2+ y2=3.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Solve a system containing a linear equation and a quadratic equation in two variables (conic sections possible)
graphically and symbolically.
Task Analysis:
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Correlated WA Standard:
Create a graph with appropriate labels and scale
Graph a linear equation
Graph a quadratic equation in two variables (including circles)
Find the points of intersection
Describe what the point of intersection represents within the context of the
problem
Solve a linear equation for one variable
Apply the substitution method of solving a system by substituting the linear
expression into the quadratic equation
Simplify the new quadratic equation
Solve the quadratic equation in one variable
Apply the solution(s) back into an original equation and solve for the other
variable
Describe the solution within the context of the problem
Vocabulary:
Prior
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Explicit
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Conic sections
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve systems of equations
High School: Algebra
Mathematical Content Standard:
8. (+) Represent a system of linear equations as a single matrix equation
in a vector variable.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Write a system of linear equations as a single matrix equation.
Task Analysis:
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Correlated WA Standard:
Vocabulary:
Construct a matrix from a given system of equations
Prior
Understand the idea of the number of equations to be as least as many as the
number of unknown
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Use row operations to solve the matrix
Explicit
Understand when a matrix is in reduced row echelon form
Determine the values of the unknowns from the reduced row echelon form
 Matrix
 Reduced row
echelon form
Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Solve systems of equations
High School: Algebra
Mathematical Content Standard:
9. (+) Find the inverse of a matrix if it exists and use it to solve systems of
linear equations (using technology for matrices of dimension 3 × 3 or
greater).
Featured Mathematical
Practice:
Standard Clarification/Example:
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
Pacing:
Find the inverse of the coefficient matrix in the equation, if it exits. Use the inverse of the
coefficient matrix to solve the system. Use technology for matrices with dimensions 3 by 3 or
greater.
Task Analysis:
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Correlated WA Standard:
Find the dimension of matrices.
Understand when matrices can be multiplied.
Understand that matrix multiplication is not commutative.
Understand the concept of an identity matrix.
Understand why multiplication by the inverse of the coefficient matrix
yields a solution to the system (if it exists).
Use the inverse of the coefficient matrix to solve the system.
Vocabulary:
Prior
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Inverse
Matrix
System
Commutative
Explicit
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Determinant
Identity matrix
Introductory

Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Represent and solve equations and inequalities graphically
High School: Algebra
Mathematical Content Standard:
10. Understand that the graph of an equation in two variables is the set of
all its solutions plotted in the coordinate plane, often forming a curve
(which could be a line).
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Understand that all solutions to an equation in two variables are contained on the graph of that equation.
Task Analysis:
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Correlated WA Standard:
Understand that the graph represents the infinite number of solutions to the
equation
Explain what the solutions are within the context of the problem
Vocabulary:
Prior
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Infinite
Explicit
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Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Represent and solve equations and inequalities graphically
High School: Algebra
Mathematical Content Standard:
11. 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.*
Featured Mathematical
Practice:
Standard Clarification/Example:
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Pacing:
Explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear,
polynomial, rational, absolute value, exponential, and logarithmic functions.
Task Analysis:

Correlated WA Standard:
Use technology to graph the equations and determine their point of
intersection,
Use tables of values, or
Use successive approximations that become closer and closer to the actual
value.
Understand how a particular input of x gives you the same output of y within
the system of equations
Vocabulary:
Prior
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Function
System of
equations
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Explicit
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Introductory
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Sample Assessment Item:
Domain:
Cluster:
Level:
Reasoning with Equations and Inequalities A -REI
Represent and solve equations and inequalities graphically
High School: Algebra
Mathematical Content Standard:
12. 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.
Featured Mathematical
Practice:
Standard Clarification/Example:
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Correlated WA Standard:
Pacing:
Graph the solutions to a linear inequality in two variables as a half-plane, excluding the boundary for noninclusive inequalities.
Graph the solution set to a system of linear inequalities in two variables as the intersection of their
corresponding half-planes.
Task Analysis:
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Graph a linear inequality
Understand that the plane is the solution set (shaded region)
Understand if the boundary is open or closed (solid or dotted line)
Graph a system of linear inequalities
Identify the solution to the system as the overlapping half-planes
Vocabulary:
Prior
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Linear inequality
System
Explicit
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Planes
Open/closed
boundary
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Introductory
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Sample Assessment Item: