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Standards

• CCSS.MATH.CONTENT.HSG.GPE.B.7 — Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
• CCSS.MATH.CONTENT.HSA.REI.C.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).
• CCSS.MATH.CONTENT.HSG.GPE.B.6 — Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
• CCSS.MATH.CONTENT.HSA.REI.B.4.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.
• CCSS.MATH.CONTENT.HSA.CED.A.2 — Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• CCSS.MATH.CONTENT.4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
• CCSS.MATH.CONTENT.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.
• CCSS.MATH.CONTENT.8.EE.C.7.A — Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
• CCSS.MATH.CONTENT.HSA.REI.C.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.
• CCSS.MATH.CONTENT.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.
• CCSS.MATH.CONTENT.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.
• CCSS.MATH.CONTENT.HSA.REI.B.4 — Solve quadratic equations in one variable.
• CCSS.MATH.CONTENT.7.RP.A.2.C — Represent proportional relationships by equations.
• CCSS.MATH.CONTENT.6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
• CCSS.MATH.CONTENT.6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
• CCSS.MATH.CONTENT.HSG.GPE.B.4 — Use the properties of exponents to interpret expressions for exponential functions.
• CCSS.MATH.CONTENT.8.EE.C.8.A — Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
• CCSS.MATH.CONTENT.8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
• CCSS.MATH.CONTENT.HSA.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
• CCSS.MATH.CONTENT.HSG.GPE.A.3 — (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
• CCSS.MATH.CONTENT.6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
• CCSS.MATH.CONTENT.8.F.A.3 — Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
• CCSS.MATH.CONTENT.HSA.REI.C.8 — (+) Represent a system of linear equations as a single matrix equation in a vector variable.
• CCSS.MATH.CONTENT.1.OA.D.7 — Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
• CCSS.MATH.CONTENT.HSA.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
• CCSS.MATH.CONTENT.8.EE.C.7 — Solve linear equations in one variable.
• CCSS.MATH.CONTENT.HSG.GPE.B.5 — Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
• CCSS.MATH.CONTENT.HSA.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 a solution method.
• CCSS.MATH.CONTENT.8.EE.C.8.B — Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
• CCSS.MATH.CONTENT.HSA.CED.A.1 — 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.
• CCSS.MATH.CONTENT.HSG.GPE.A.2 — Derive the equation of a parabola given a focus and directrix.
• CCSS.MATH.CONTENT.1.OA.D.8 — Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.
• CCSS.MATH.CONTENT.HSA.REI.D.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).
• CCSS.MATH.CONTENT.8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
• CCSS.MATH.CONTENT.7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
• CCSS.MATH.CONTENT.4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• CCSS.MATH.CONTENT.HSA.REI.C.7 — Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
• CCSS.MATH.CONTENT.HSA.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
• CCSS.MATH.CONTENT.8.EE.A.2 — Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ?2 is irrational.
• CCSS.MATH.CONTENT.7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• CCSS.MATH.CONTENT.HSA.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, 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.
• CCSS.MATH.CONTENT.HSA.REI.B.4.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.
• CCSS.MATH.CONTENT.8.EE.C.8.C — Solve real-world and mathematical problems leading to two linear equations in two variables.
• CCSS.MATH.CONTENT.HSA.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.