Learners will look for, generate, and make sense of patterns, relationships, and algebraic symbols to represent mathematical models while adopting approaches and solutions in novel situations.

MAT-12.AR.09 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non- viable options in a modeling context.

MAT-00.NO.NBT.02 Compare two numbers between 1 and 20 using words greater than, less than, or equal to.

MAT-01.NO.NBT.02 Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the number of tens and ones.

MAT-02.NO.NBT.02 Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.

MAT-03.NO.NBT.01 Compare two four-digit numbers using symbols, >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.

MAT-04.NO.NBT.02 Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.

MAT-05.NO.NBT.02 Compare two decimals to thousandths using symbols >, <, and =. Justify comparisons based on the value of the digits.

MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.

MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.

MAT-07.NO.NS.01 Describe the absolute value of a number as its distance from zero on a number line.

MAT-08.NO.NS.01 Compare and classify real numbers within the real number system.

MAT-08.NO.NS.02 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.

MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.

MAT-09.AR.08 Graph the solution set to a two-variable system of linear equations. Create and graph the solution set to a two-variable system of linear inequalities in context.

MAT-09.AR.09 Solve absolute value equations and inequalities in one or two variables.

MAT-12.AR.09Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

Inequalities

MAT-06.AR.EE.04 Describe the concept of a solution to an equation or an inequality. Determine whether a given number is a solution to an equation or an inequality.

MAT-06.AR.EE.06 Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

MAT-07.AR.EE.03 Write and solve one- and two-step inequalities where coefficients and solutions are integers and/or non-negative fractions and decimals, including authentic problems. Graph the solution set of the inequality and interpret it in the context of the problem.

MAT-08.AR.EE.07 Solve and graph inequalities in one variable with rational number coefficients and variables on both sides, including equations that require using the distributive property and/or combining like terms.

MAT-08.AR.EE.08 Graph linear inequalities in two variables on a coordinate plane. Interpret the possible solutions in the context of authentic problems.

MAT-09.AR.03 Create equations and inequalities in two variables and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.

MAT-09.AR.07 Solve a system of linear equations graphically and algebraically. Create and solve a system of linear equations in context and interpret the results.

MAT-09.AR.08 Graph the solution set to a two-variable system of linear inequalities. Create and graph the solution set to a two-variable system of linear inequalities in context.

MAT-09.AR.09 Solve absolute value equations and inequalities in one or two variables.

MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.

MAT-12.AR.09Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.