MAT-12.AR.08

 12th Grade (MAT) Targeted Standard     (AR) Algebraic Reasoning  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.

Progressions

Exponents

• MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
• MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
• MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
• MAT-09.NO.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.
• MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
• MAT-10.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.
• MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
• MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
• 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.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
• MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
• MAT-12.AR.F.15 Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

Unit Size and Scale

• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line diagram and in authentic contexts.
• MAT-09.NO.03 Choose and interpret the scale and the origin in graphs and data displays.
• MAT-09.NO.04 Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
• MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-12.NO.04 Use units to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.