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7-12.1
Students will expand number sense to understand, perform operations, and solve problems with real numbers.
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7-12.1.1
Represent real numbers as points on the number line and distinguish rational numbers from irrational numbers.
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7-12.1.1.a
Define a rational number as a point on the number line that can be expressed as the ratio of two integers, and points that cannot be so expressed as irrational.
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7-12.1.1.b
Classify numbers as rational or irrational, knowing that rational numbers can be expressed as terminating or repeating decimals and irrational numbers can be expressed as non-terminating, non-repeating decimals.
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7-12.1.1.c
Classify pi and square roots of non-perfect square numbers as irrational.
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7-12.1.1.d
Place rational and irrational numbers on a number line between two integers.
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7-12.1.2
Compute fluently and make reasonable estimates with rational and irrational numbers.
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7-12.1.2.a
Simplify, add, subtract, multiply, and divide expressions with square roots.
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7-12.1.2.b
Evaluate and simplify numerical expressions containing rational numbers and square roots using the order of operations.
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7-12.1.2.c
Compute solutions to problems, represent answers in exact form, and determine the reasonableness of answers.
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7-12.1.2.d
Calculate the measures of the sides of a right triangle using the Pythagorean Theorem.
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7-12.2
Students will extend concepts of proportion to represent and analyze linear relations.
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7-12.2.1
Represent and analyze the slope of a line.
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7-12.2.1.a
Identify the slope of a line when given points, a graph, or an equation.
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7-12.2.1.b
Identify horizontal and vertical lines given the equations or slopes.
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7-12.2.1.c
Determine the effect of changes in slope or y-intercept in y = mx + b.
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7-12.2.1.d
Determine and explain the meaning of slopes and intercepts using real-world examples.
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7-12.2.2
Model and interpret problems having a constant rate of change using linear functions.
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7-12.2.2.a
Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.
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7-12.2.2.b
Represent linear equations in slope-intercept form, y = mx + b, and standard form, Ax+ By =C.
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7-12.2.2.c
Distinguish between linear and non-linear functions by examining a table, equation, or graph.
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7-12.2.2.d
Interpret the slope of a linear function as a rate of change in real-world situations.
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7-12.2.3
Represent and analyze linear relationships using algebraic equations, expressions, and graphs.
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7-12.2.3.a
Write the equation of a line when given two points or the slope and a point on the line.
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7-12.2.3.b
Approximate the equation of a line given the graph of a line.
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7-12.2.3.c
Identify the x- and y-intercepts from an equation or graph of a line or a table of values.
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7-12.2.3.d
Graph linear relations and inequalities by plotting points, by finding x- and y-intercepts, or by using the slope and any point on the line.
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7-12.3
Students will develop fluency with the language and operations of algebra to analyze and represent relationships.
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7-12.3.1
Simplify polynomials and the quotient of monomials.
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7-12.3.1.a
Simplify and evaluate monomial expressions and formulas.
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7-12.3.1.b
Add and subtract polynomials.
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7-12.3.1.c
Multiply monomials by a polynomial.
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7-12.3.1.d
Multiply binomials.
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7-12.3.1.e
Simplify the quotient of monomials using positive exponents.
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7-12.3.2
Solve and interpret linear equations and inequalities in various situations including real-world problems.
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7-12.3.2.a
Solve single-variable linear equations and inequalities algebraically and graphically.
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7-12.3.2.b
Solve real-world problems involving constant rates of change.
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7-12.3.2.c
Solve equations for a specified variable.
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7-12.3.2.d
Solve proportions that include algebraic first-degree expressions.
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7-12.3.3
Solve and interpret pairs of linear equations and inequalities.
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7-12.3.3.a
Solve systems of two linear equations graphically and algebraically with and without technology.
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7-12.3.3.b
Determine the number of possible solutions for a system of two linear equations.
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7-12.3.3.c
Graph a system of linear inequalities and identify the solution.
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7-12.3.4
Factor polynomials with common monomial factors and factor simple quadratic expressions.
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7-12.3.4.a
Find the greatest common monomial factor of a polynomial.
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7-12.3.4.b
Factor trinomials with integer coefficients of the form x2 + bx + c.
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7-12.3.4.c
Factor the difference of two squares and perfect square trinomials.
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7-12.3.5
Solve quadratic equations using factoring or by taking square roots.
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7-12.3.5.a
Solve quadratic equations that can be simplified to the form x2 = a where a is greater than or equal to 0 by taking square roots.
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7-12.3.5.b
Solve quadratic equations using factoring.
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7-12.3.5.c
Write a quadratic equation when given the solutions.
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7-12.4
Students will understand concepts from statistics and apply statistical methods to solve problems.
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7-12.4.1
Summarize, display, and analyze bivariate data.
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7-12.4.1.a
Collect, record, organize, and display a set of data with at least two variables.
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7-12.4.1.b
Determine whether the relationship between two variables is approximately linear or non-linear by examination of a scatter plot.
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7-12.4.1.c
Characterize the relationship between two linear related variables as having positive, negative, or approximately zero correlation.
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7-12.4.2
Estimate, interpret, and use lines fit to bivariate data.
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7-12.4.2.a
Estimate the equation of a line of best fit to make and test conjectures.
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7-12.4.2.b
Interpret the slope and y-intercept of a line through data.
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7-12.4.2.c
Predict y-values for given x-values when appropriate using a line fitted to bivariate numerical data.
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IXL Learning. All rights reserved.