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.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-03.NO.NBT.04 Multiply one-digit whole numbers by multiples of 10 within 100.

MAT-04.NO.NBT.05 Multiply a whole number up to four digits by a one-digit whole number and multiply two two digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.

MAT-05.NO.NBT.04 Multiply multi-digit whole numbers using strategies flexibly, including the algorithm.

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-04.NO.NBT.06 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using place value strategies. Show and justify the calculation by using equations, rectangular arrays, and models.

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-05.NO.NBT.06 Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using place value strategies. Show and justify the calculation using equations, rectangular arrays, and/or area models.

MAT-06.NO.O.01 Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.

MAT-07.NO.O.01 Add, subtract, multiply, and divide integers and positive rational numbers using visual models and properties of operations in multi-step 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.01 Evaluate mentally the square roots of perfect squares up to 225 and cube roots of perfect cubes up to 1000.

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

MAT-09.NO.02 Perform basic operations on radicals and simplify radicals to write equivalent expressions.

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

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-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.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.

Adding and Subtracting Fractions

MAT-04.NO.NF.06 Solve authentic word problems by adding and subtracting fractions and mixed numbers with like denominators (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).

MAT-05.NO.NF.03 Solve authentic word problems by adding and subtracting fractions and mixed numbers with unlike denominators using a visual fraction model and/or equation.

MAT-06.NO.O.02 Add and subtract fractions and decimals up to the hundredth place, including in 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-12.NO.04Demonstrate 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.05 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.