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[7.EE.B.4.a] -
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Mathematics | Grade : 8
Domain - Expressions and Equations
Cluster - Analyze and solve linear equations and pairs of simultaneous linear equations.
[8.EE.C.8] - Analyze and solve pairs of simultaneous linear equations.
[8.EE.B.6] -
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
[AI.A-CED.A.2] -
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
[AI.A-CED.A.3] -
Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
[AI.A-CED.A.4] -
Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality).* For example, rearrange Ohm’s law R=V2/P to solve for voltage, V. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt.
[AI.A-REI.C.6] -
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
[AI.A-REI.C.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.
[MI.A-CED.A.2] -
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
[MI.A-CED.A.3] -
Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
[MI.A-CED.A.4] -
Rearrange formulas to highlight a quantity of interest, using the same reasoning (Properties of equality) as in solving equations.* For example, rearrange Ohm’s law, V = IR, to solve for resistance, R. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt .
[MI.A-REI.C.6] -
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
[MII.A-REI.C.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.