MAT09.NO.02

9^{th} Grade (MAT) Targeted Standard
(NO) Number and Operations
Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

MAT09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
Proficiency Scale
Progressions
Addition and Subtraction
 MAT01.NO.NBT.03 Add within 100 using a twodigit number and a onedigit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
 MAT02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
 MAT01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
 MAT01.NO.NBT.05 Mentally add or subtract 10 to or from a given twodigit number and explain the reasoning used.
 MAT02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
 MAT02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
 MAT03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
 MAT04.NO.NBT.04 Add and subtract multidigit whole numbers to the one million place using strategies flexibly, including the algorithm.
 MAT05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
 MAT07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multistep authentic and mathematical problems, including authentic problems.
 MAT07.NO.O.02 Add, subtract, multiply, and divide nonnegative fractions in multistep problems, including authentic problems.
 MAT07.NO.O.03 Add, subtract, multiply, and divide nonnegative decimals to the hundredth place in multistep problems using strategies or procedures, including authentic problems.
 MAT08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
 MAT09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
 MAT09.AR.11 Add, subtract, and multiply polynomials.
 MAT12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
 MAT12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
 MAT12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
 MAT12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
 MAT12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.
Multiplication and Division
 MAT03.NO.NBT.04 Multiply onedigit whole numbers by multiples of 10 within 100.
 MAT04.NO.NBT.05 Multiply a whole number up to four digits by a onedigit whole number and multiply two two digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.
 MAT05.NO.NBT.04 Multiply multidigit whole numbers using strategies flexibly, including the algorithm.
 MAT05.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 wholenumber exponents to denote powers of 10.
 MAT04.NO.NBT.06 Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors using place value strategies. Show and justify the calculation by using equations, rectangular arrays, and models.
 MAT05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
 MAT05.NO.NBT.06 Find wholenumber quotients and remainders with up to fourdigit dividends and twodigit divisors using place value strategies. Show and justify the calculation using equations, rectangular arrays, and/or area models.
 MAT06.NO.O.01 Divide multidigit whole numbers up to fourdigit dividends and twodigit divisors using strategies or procedures.
 MAT07.NO.O.01 Add, subtract, multiply, and divide integers and positive rational numbers using visual models and properties of operations in multistep problems, including authentic problems.
 MAT07.NO.O.02 Add, subtract, multiply, and divide nonnegative fractions in multistep problems, including authentic problems.
 MAT07.NO.O.03 Add, subtract, multiply, and divide nonnegative decimals to the hundredth place in multistep problems using strategies or procedures, including authentic problems.
 MAT08.NO.O.01 Evaluate mentally the square roots of perfect squares up to 225 and cube roots of perfect cubes up to 1000.
 MAT08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
 MAT09.NO.02 Perform basic operations on radicals and simplify radicals to write equivalent expressions.
 MAT09.AR.11 Add, subtract, and multiply polynomials.
 MAT12.NO.03 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
 MAT12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
 MAT12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
 MAT12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.
Multiplying and Dividing Fractions
 MAT04.NO.NF.07 Solve problems by multiplying fractions and whole numbers using visual fraction models (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
 MAT05.NO.NF.02 Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number and explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.
 MAT05.NO.NF.04 Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.
 MAT06.NO.O.03 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.
 MAT07.NO.O.02 Add, subtract, multiply, and divide nonnegative fractions in multistep problems, including authentic problems.
 MAT08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
 MAT09.NO.02 Perform basic operations of simple radical expressions to write a simplified equivalent expression.
 MAT12.NO.03 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
 MAT12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
 MAT12.AR.5 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
 MAT12.NO.06 Know there is a complex number i such that i² = 1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.
Exponents
 MAT05.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 wholenumber exponents to denote powers of 10.
 MAT06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
 MAT08.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.
 MAT09.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.
 MAT09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
 MAT09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
 MAT09.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.
 MAT09.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.
 MAT0.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.
 MAT12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
 MAT12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
 MAT12.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.
 MAT12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
 MAT12.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.
 MAT12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
 MAT12.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.
