Note: Click any standard to move it to the center of the map.
[7.EE.A.1] -
Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.
For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
[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.7.b] - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
- Coefficient
Any of the factors of a product considered in relation to a specific factor. - Expression
A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a). - Linear equation
Any equation that can be written in the form Ax + By + C = 0 where A and B cannot both be 0. The graph of such an equation is a line. - Rational number
A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.
[8.SP.A.3] -
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
[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.A.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 or refute a solution method.
[AI.A-REI.B.3] -
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
[AI.A-REI.D.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 and make tables of values. Include cases where f(x) and/or g(x) are linear and exponential functions.*
[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.A.1] -
Explain each step in solving a simple linear 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 or refute a solution method.
[MI.A-REI.B.3] -
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
[MI.A-REI.D.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 and/or make tables of values. Include cases where f(x) and/or g(x) are linear and exponential functions.*