CC.2.2.K.A.1 
Extend concepts of putting together and taking apart to add and subtract within 10.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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CC.2.2.1.A.1
Represent and solve problems involving addition and subtraction within 20.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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CC.2.2.1.A.2
Understand and apply properties of operations and the relationship between addition and subtraction.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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CC.2.2.2.A.1
Represent and solve problems involving addition and subtraction within 100.
When grade appropriate instruction pertaining to an eligible content should begin
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CC.2.2.2.A.1
Represent and solve problems involving addition and subtraction within 100.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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CC.2.2.2.A.2
Use mental strategies to add and subtract within 20.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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CC.2.2.2.A.3
Work with equal groups of objects to gain foundations for multiplication.
When grade appropriate instruction pertaining to an eligible content should begin
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CC.2.2.2.A.3
Work with equal groups of objects to gain foundations for multiplication.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M03.B-O.1.1.1
Interpret and/or describe products of whole numbers (up to and including 10 × 10). Example 1: Interpret 35 as the total number of objects in 5 groups, each containing 7 objects. Example 2: Describe a context in which a total number of objects can be expressed as 5 × 7.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M03.B-O.1.1.2
Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10). Example 1: Interpret 48 ÷ 8 as the number of objects in each share when 48 objects are partitioned equally into 8 shares, or as a number of shares when 48 objects are partitioned into equal shares of 8 objects each. Example 2: Describe a context in which a number of shares or a number of groups can be expressed as 48 ÷ 8.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M03.B-O.2.1.1
Apply the commutative property of multiplication (not identification or definition of the property).
When grade appropriate instruction pertaining to an eligible content should begin
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M03.B-O.2.1.1
Apply the commutative property of multiplication (not identification or definition of the property).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M03.B-O.2.1.2
Apply the associative property of multiplication (not identification or definition of the property).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M04.B-O.2.1.1
Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the interval 1 through 100 is a multiple of a given onedigit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite.
When grade appropriate instruction pertaining to an eligible content should begin
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M04.B-O.2.1.1
Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the interval 1 through 100 is a multiple of a given onedigit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M05.B-O.1.1.2
Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.
When grade appropriate instruction pertaining to an eligible content should begin
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M05.B-O.1.1.2
Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M05.B-O.1.1.1
Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.1.1.1
Write and evaluate numerical expressions involving whole-number exponents.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.1.1.2
Write algebraic expressions from verbal descriptions. Example: Express the description “five less than twice a number” as 2y – 5.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.1.1.3
Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors.
When grade appropriate instruction pertaining to an eligible content should begin
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M06.B-E.1.1.3
Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.1.1.4
Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems. Example: Evaluate the expression b^2 – 5 when b = 4.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.2.1.2
Write algebraic expressions to represent real-world or mathematical problems.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.1.1.5
Apply the properties of operations to generate equivalent expressions. Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M07.B-E.1.1.1
Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. Example 1: The expression 1/2 • (x + 6) is equivalent to 1/2 • x + 3. Example 2: The expression 5.3 – y + 4.2 is equivalent to 9.5 – y (or –y + 9.5). Example 3: The expression 4w – 10 is equivalent to 2(2w – 5).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M07.B-E.2.1.1
Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50 an hour (or 1.1 × $25 = $27.50).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.1.1.1
Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: 3^12 x 3^-15 = 3^-3 = 1/(3^3)
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.2.1.1
Use exponential expressions to represent rational numbers.
When grade appropriate instruction pertaining to an eligible content should begin
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A2.1.2.1.1
Use exponential expressions to represent rational numbers.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.1.1.2
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator. Example: If x^2 = 25 then x = ±√25.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.1.1.3
Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9 and determine that the world population is more than 20 times larger than the United States’ population.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-E.1.1.3
Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9 and determine that the world population is more than 20 times larger than the United States’ population.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-E.1.1.3
Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9 and determine that the world population is more than 20 times larger than the United States’ population.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.1.1.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 10^9).
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-E.1.1.4
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 10^9).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.1.1.3.1
Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.2.1.2
Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
When grade appropriate instruction pertaining to an eligible content should begin
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A2.1.2.1.2
Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A1.1.1.5.1
Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
When grade appropriate instruction pertaining to an eligible content should begin |
A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A1.1.1.5.3
Simplify/reduce a rational algebraic expression.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.2.2.2
Simplify rational algebraic expressions.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.1.2.1.2
Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.1.2.1
Add and subtract complex numbers(e.g., (7 – 3i) – (2 + i) = 5 – 4i).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.1.2.2
Multiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
When grade appropriate instruction pertaining to an eligible content should begin |
A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
