Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

MAT-12.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.

MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.

MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.

MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.

MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.

MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.

MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.

MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.

MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.

MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.

MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.

MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.

MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.

MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.

MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.

MAT-09.AR.11 Add, subtract, and multiply polynomials.

MAT-12.NO.03Demonstrate 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.

MAT-12.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.

MAT-12.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.

MAT-12.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.

MAT-12.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

MAT-04.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).

MAT-05.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.

MAT-05.NO.NF.04 Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.

MAT-06.NO.O.03 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.

MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.

MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.

MAT-09.NO.02 Perform basic operations of simple radical expressions to write a simplified equivalent expression.

MAT-12.NO.03Demonstrate 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.

MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.

MAT-12.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.

MAT-12.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.