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Mathematics
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.PREK: GRADE PreKindergarten
Know number names and the count sequence.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.K: GRADE K
Know number names and write and recite the count sequence.
Apply onetoone correspondence to count the number of objects.
Apply the concept of magnitude to compare numbers and quantities.
Use place value to compose and decompose numbers within 19.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.1: GRADE 1
Extend the counting sequence to read and write numerals to represent objects.
Use place value concepts to represent amounts of tens and ones and to compare two digit numbers.
Use place value concepts and properties of operations to add and subtract within 100.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.2: GRADE 2
Use place value concepts to represent amounts of tens and ones and to compare three digit numbers.
Use place value concepts to read, write, and skip count to 1000.
Use place value understanding and properties of operations to add and subtract within 1000.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.3: GRADE 3
Apply place value understanding and properties of operations to perform multidigit arithmetic.

Assessment Anchor  M03.AT.1 Use placevalue understanding and properties of operations to perform multidigit arithmetic.

Anchor Descriptor  M03.AT.1.1
Apply placevalue strategies to solve problems.

Eligible Content  M03.AT.1.1.1 Round two and threedigit whole numbers to the nearest ten or hundred, respectively.

Alternate Eligible Content  M03.AT.1.1.1a Round a twodigit number tothenearest ten.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M03.AT.1.1.2 Add two and threedigit whole numbers (limit sums from 100 through 1,000) and/or subtract two and threedigit numbers from threedigit whole numbers.

Alternate Eligible Content  M03.AT.1.1.2a Demonstrate understanding of addition with small sets.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards. 
Alternate Eligible Content  M03.AT.1.1.2b Demonstrate understanding subtraction with small sets.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M03.AT.1.1.3 Multiply onedigit whole numbers by twodigit multiples of 10 (from 10 through 90).

Eligible Content  M03.AT.1.1.4 Order a set of whole numbers from least to greatest or greatest to least (up through 9,999, and limit sets to no more than four numbers).

Alternate Eligible Content  M03.AT.1.1.4a Order 3 numbers under 10.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Explore and develop an understanding of fractions as numbers.

Assessment Anchor  M03.AF.1 Develop an understanding of fractions as numbers.

Anchor Descriptor  M03.AF.1.1 Develop and apply number theory concepts to compare quantities and magnitudes of fractions and whole numbers.

Eligible Content  M03.AF.1.1.1 Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).

Alternate Eligible Content  M03.AF.1.1.1a Identify the unit fraction or other proper fraction (denominators = 2, 3, 4, 6) that matches the representation.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M03.AF.1.1.2 Represent fractions on a number line (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).

Eligible Content  M03.AF.1.1.3 Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8 and limit numerators to whole numbers less than the denominator). Example 1: 1/2 = 2/4 Example 2: 4/6 = 2/3

Alternate Eligible Content  M03.AF.1.1.3b Identify equivalent fractions using representations.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M03.AF.1.1.4 Express whole numbers as fractions, and/or generate fractions that are equivalent to whole numbers (limit denominators to 1, 2, 3, 4, 6, and 8). Example 1: Express 3 in the form 3 = 3/1. Example 2: Recognize that 6/1 = 6.

Eligible Content  M03.AF.1.1.5 Compare two fractions with the same denominator (limit denominators to 1, 2, 3, 4, 6, and 8), using the symbols >, =, or <, and/or justify the conclusions.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.4: GRADE 4
Standard  CC.2.1.4.B.1Apply place value concepts to show an understanding of multidigit whole numbers.

Assessment Anchor  M04.AT.1 Generalize placevalue understanding for multidigit whole numbers.

Anchor Descriptor  M04.AT.1.1 Apply placevalue and numeration concepts to compare, find equivalencies, and round.

Eligible Content  M04.AT.1.1.1 Demonstrate an understanding that in a multidigit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the tens place.

Alternate Eligible Content  M04.AT.1.1.1a Model relationships between adjacent digits in a multidigit whole number.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AT.1.1.2 Read and write whole numbers in expanded, standard, and word form through 1,000,000.

Eligible Content  M04.AT.1.1.3 Compare two multidigit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols.

Alternate Eligible Content  M04.AT.1.1.3a Compare to determine if a value is greater than, less than, or equal to another value.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AT.1.1.4 Round multidigit whole numbers (through 1,000,000) to any place.


Standard  CC.2.1.4.B.2Use place value understanding and properties of operations to perform multidigit arithmetic.

Assessment Anchor  M04.AT.2 Use placevalue understanding and properties of operations to perform multidigit arithmetic.

Anchor Descriptor  M04.AT.2.1 Use operations to solve problems.

Eligible Content  M04.AT.2.1.1 Add and subtract multidigit whole numbers (limit sums and subtrahends up to and including 1,000,000).

Alternate Eligible Content  M04.AT.2.1.1a Add or subtract whole numbers with sums and differences <1000.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AT.2.1.2 Multiply a whole number of up to four digits by a onedigit whole number and multiply 2 twodigit numbers.

Alternate Eligible Content  M04.AT.2.1.2a Demonstrate understanding of multiplication or division with small sets.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AT.2.1.3 Divide up to fourdigit dividends by onedigit divisors with answers written as wholenumber quotients and remainders.

Eligible Content  M04.AT.2.1.4 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10).

Alternate Eligible Content  M04.AT.2.1.4a Assess the plausibilityof results fromaddition or subtraction.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.4.C.1Extend the understanding of fractions to show equivalence and ordering.

Assessment Anchor  M04.AF.1 Extend understanding of fraction equivalence and ordering.

Anchor Descriptor  M04.AF.1.1 Find equivalencies and compare fractions.

Eligible Content  M04.AF.1.1.1 Recognize and generate equivalent fractions.

Alternate Eligible Content  M04.AF.1.1.1a Identify equivalent fractions.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AF.1.1.2 Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions.

Alternate Eligible Content  M04.AF.1.1.2a Compare two fractions with like denominators.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.4.C.2Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Assessment Anchor  M04.AF.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Anchor Descriptor  M04.AF.2.1 Solve problems involving fractions and whole numbers (straight computation or word problems).

Eligible Content  M04.AF.2.1.1 Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer).

Alternate Eligible Content  M04.AF.2.1.1a Add or subtract fractions with common denominators (denominators limited to 2, 3, 4, or 8).
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AF.2.1.2 Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = 1 + 1 + 1/12 = 12/12 + 12/12 + 1/12

Alternate Eligible Content  M04.AF.2.1.2a Decompose a proper fraction into multiple copies of a unit fraction (denominators limited to 3, 4, or 8).
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AF.2.1.3 Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers).

Eligible Content  M04.AF.2.1.4 Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).

Eligible Content  M04.AF.2.1.5 Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 × (1/4) = 5/4

Eligible Content  M04.AF.2.1.6 Multiply a whole number by a nonunit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 × (5/6) = 15/6

Eligible Content  M04.AF.2.1.7 Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).


Standard  CC.2.1.4.C.3Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g, 19/100).

Assessment Anchor  M04.AF.3 Understand decimal notation for fractions and compare decimal fractions.

Anchor Descriptor  M04.AF.3.1 Use operations to solve problems involving decimals, including converting between fractions and decimals (may include word problems).

Eligible Content  M04.AF.3.1.1 Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/100 + 4/100 = 34/100.

Eligible Content  M04.AF.3.1.2 Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa.

Alternate Eligible Content  M04.AF.3.1.2a Identify equivalent values in decimal or fraction form (limited to denominator of 10).
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M04.AF.3.1.3 Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.5: GRADE 5
Standard  CC.2.1.5.B.1Apply place value to show an understanding of operations and rounding as they pertain to whole numbers and decimals.

Assessment Anchor  M05.AT.1 Understand the placevalue system.

Anchor Descriptor  M05.AT.1.1 Demonstrate understanding of placevalue of whole numbers and decimals, and compare quantities or magnitudes of numbers.

Eligible Content  M05.AT.1.1.1 Demonstrate an understanding that in a multidigit number, a digit in one place represents 1/10 of what it represents in the place to its left. Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place.

Alternate Eligible Content  M05.AT.1.1.1a Identify place value in a 3digit number using models.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AT.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Example 1: 4 × 10^2 = 400 Example 2: 0.05 ÷ 10^3 = 0.00005

Alternate Eligible Content  M05.AT.1.1.2a Identify a pattern and change in place value when a number up to 99 is multiplied by powers of 10.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AT.1.1.3 Read and write decimals to thousandths using baseten numerals, word form, and expanded form. Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)

Eligible Content  M05.AT.1.1.4 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.

Alternate Eligible Content  M05.AT.1.1.4a Compare two numbers up to the hundredths place.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AT.1.1.5 Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place).

Alternate Eligible Content  M05.AT.1.1.5a Round a decimal from the tenths place to the nearest whole number.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.5.B.2Extend an understanding of operations with whole numbers to perform operations including decimals.

Assessment Anchor  M05.AT.2 Perform operations with multidigit whole numbers and with decimals to hundredths.

Anchor Descriptor  M05.AT.2.1 Use whole numbers and decimals to compute accurately (straight computation or word problems).

Eligible Content  M05.AT.2.1.1 Multiply multidigit whole numbers (not to exceed threedigit by threedigit).

Alternate Eligible Content  M05.AT.2.1.1a Multiply singledigit whole numbers.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AT.2.1.2 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors.

Alternate Eligible Content  M05.AT.2.1.2a Illustrate the concept of division using fair and equal shares.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AT.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

Alternate Eligible Content  M05.AT.2.1.3a Add or subtract decimals to the tenths place.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.5.C.1Use the understanding of equivalency to add and subtract fractions.

Assessment Anchor  M05.AF.1 Use equivalent fractions as a strategy to add and subtract fractions.

Anchor Descriptor  M05.AF.1.1 Solve addition and subtraction problems involving fractions (straight computation or word problems).

Eligible Content  M05.AF.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12

Alternate Eligible Content  M05.AF.1.1.1a Add or subtract proper fractions with common denominators to solve a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.5.C.2Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Assessment Anchor  M05.AF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Anchor Descriptor  M05.AF.2.1 Solve multiplication and division problems involving fractions and whole numbers (straight computation or word problems).

Eligible Content  M05.AF.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).

Eligible Content  M05.AF.2.1.2 Multiply a fraction (including mixed numbers) by a fraction.

Alternate Eligible Content  M05.AF.2.1.2a Multiply a fraction by a whole number less than 10.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M05.AF.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

Eligible Content  M05.AF.2.1.4 Divide unit fractions by whole numbers and whole numbers by unit fractions.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.6: GRADE 6
Standard  CC.2.1.6.D.1Understand ratio concepts and use ratio reasoning to solve problems.

Assessment Anchor  M06.AR.1 Understand ratio concepts and use ratio reasoning to solve problems.

Anchor Descriptor  M06.AR.1.1 Represent and/or solve realworld and mathematical problems using rates, ratios, and/or percents.

Eligible Content  M06.AR.1.1.1 Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities. Example 1: “The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys.” Example 2: “For every five votes candidate A received, candidate B received four votes.”

Eligible Content  M06.AR.1.1.2 Find the unit rate a/b associated with a ratio a:b (with b ≠ 0) and use rate language in the context of a ratio relationship. Example 1: “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” Example 2: “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

Alternate Eligible Content  M06.AR.1.1.2a Identify the ratio that matches a given statement and/or representation.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AR.1.1.3 Construct tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Eligible Content  M06.AR.1.1.4 Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Alternate Eligible Content  M06.AR.1.1.4a Solve a 1step realworld problem given the unit rate.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AR.1.1.5 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage.

Alternate Eligible Content  M06.AR.1.1.5a Calculate a percent of a quantity as a rate per 100.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.6.E.1Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Assessment Anchor  M06.AN.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Anchor Descriptor  M06.AN.1.1 Solve realworld and mathematical problems involving division of fractions.

Eligible Content  M06.AN.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4foot pieces can be cut from a 15 1/2foot board?


Standard  CC.2.1.6.E.2Identify and choose appropriate processes to compute fluently with multidigit numbers.

Assessment Anchor  M06.AN.2 Compute with multidigit numbers and find common factors and multiples.

Anchor Descriptor  M06.AN.2.1 Compute with multidigit numbers using the four arithmetic operations with or without a calculator.

Eligible Content  M06.AN.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.

Alternate Eligible Content  M06.AN.2.1.1a Solve a problemusing up to 3digit whole numbers and any of the four operations.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Anchor Descriptor  M06.AN.2.2 Apply number theory concepts (specifically, factors and multiples).

Eligible Content  M06.AN.2.2.1 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Alternate Eligible Content  M06.AN.2.2.1a Identify multiplesfor numbers 5, 10, 25, or 100.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AN.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express 36 + 8 as 4(9 + 2).


Standard  CC.2.1.6.E.3Develop and/or apply number theory concepts to find common factors and multiples.

Assessment Anchor  A1.1.1
Operations with Real Numbers and Expressions

Anchor Descriptor  A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Eligible Content  A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).

Eligible Content  A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).


Anchor Descriptor  A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.

Eligible Content  A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.


Anchor Descriptor  A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.

Eligible Content  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).


Anchor Descriptor  A1.1.1.4 Use estimation strategies in problemsolving situations.

Eligible Content  A1.1.1.4.1 Use estimation to solve problems.


Anchor Descriptor  A1.1.1.5 Simplify expressions involving polynomials.

Eligible Content  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).

Eligible Content  A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is equal to 1 after factoring out all monomial factors).

Eligible Content  A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



Assessment Anchor  M06.AN.2 Compute with multidigit numbers and find common factors and multiples.

Anchor Descriptor  M06.AN.2.1 Compute with multidigit numbers using the four arithmetic operations with or without a calculator.

Eligible Content  M06.AN.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.

Alternate Eligible Content  M06.AN.2.1.1a Solve a problemusing up to 3digit whole numbers and any of the four operations.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Anchor Descriptor  M06.AN.2.2 Apply number theory concepts (specifically, factors and multiples).

Eligible Content  M06.AN.2.2.1 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Alternate Eligible Content  M06.AN.2.2.1a Identify multiplesfor numbers 5, 10, 25, or 100.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AN.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express 36 + 8 as 4(9 + 2).


Standard  CC.2.1.6.E.4Apply and extend previous understandings of numbers to the system of rational numbers.

Assessment Anchor  M06.AN.3 Apply and extend previous understandings of numbers to the system of rational numbers.

Anchor Descriptor  M06.AN.3.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane.

Eligible Content  M06.AN.3.1.1 Represent quantities in realworld contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).

Alternate Eligible Content  M06.AN.3.1.1a Identify a specific integer in a realworld context.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AN.3.1.2 Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3; 0 is its own opposite).

Alternate Eligible Content  M06.AN.3.1.2a Identify the opposite of a number onthenumber line.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M06.AN.3.1.3 Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.

Alternate Eligible Content  M06.AN.3.1.3a Locate positive and negative numbers on the number line.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Anchor Descriptor  M06.AN.3.2 Understand ordering and absolute value of rational numbers.

Eligible Content  M06.AN.3.2.1 Write, interpret, and explain statements of order for rational numbers in realworld contexts. Example: Write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

Eligible Content  M06.AN.3.2.2 Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a realworld situation. Example: For an account balance of –30 dollars, write –30 = 30 to describe the size of the debt in dollars, and recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Eligible Content  M06.AN.3.2.3 Solve realworld and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Alternate Eligible Content  M06.AN.3.2.3a Identify points in all four quadrants of the coordinate plane.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.7: GRADE 7
Standard  CC.2.1.7.D.1Analyze proportional relationships and use them to model and solve realworld and mathematical problems.

Assessment Anchor  M07.AR.1 Demonstrate an understanding of proportional relationships.

Anchor Descriptor  M07.AR.1.1 Analyze, recognize, and represent proportional relationships and use them to solve realworld and mathematical problems.

Eligible Content  M07.AR.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour.

Alternate Eligible Content  M07.AR.1.1.1a Find the unit rate ina realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M07.AR.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

Eligible Content  M07.AR.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Alternate Eligible Content  M07.AR.1.1.3a Represent a proportional relationshipon a line graph.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M07.AR.1.1.4 Represent proportional relationships by equations. Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Eligible Content  M07.AR.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.

Alternate Eligible Content  M07.AR.1.1.5a Interpret an ordered pair in a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M07.AR.1.1.6 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease.

Alternate Eligible Content  M07.AR.1.1.6a Use percentages to solve a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.7.E.1Apply and extend previous understandings of operations with fractions to operations with rational numbers.

Assessment Anchor  M07.AN.1 Apply and extend previous understandings of operations to add, subtract, multiply, and divide rational numbers.

Anchor Descriptor  M07.AN.1.1 Solve realworld and mathematical problems involving the four operations with rational numbers.

Eligible Content  M07.AN.1.1.1 Apply properties of operations to add and subtract rational numbers, including realworld contexts.

Alternate Eligible Content  M07.AN.1.1.1a Solve a 1step addition orsubtraction problem with fractions, decimals, or positive/negative integers.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M07.AN.1.1.2 Represent addition and subtraction on a horizontal or vertical number line.

Alternate Eligible Content  M07.AN.1.1.2a Identify the difference between two numbers on the number line.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M07.AN.1.1.3 Apply properties of operations to multiply and divide rational numbers, including realworld contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

Alternate Eligible Content  M07.AN.1.1.3a Solve a multiplication ordivision problem with positive/negative rational numbers.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.8: GRADE 8
Standard  CC.2.1.8.E.1Distinguish between rational and irrational numbers using their properties.

Assessment Anchor  A1.1.1
Operations with Real Numbers and Expressions

Anchor Descriptor  A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Eligible Content  A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).

Eligible Content  A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).


Anchor Descriptor  A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.

Eligible Content  A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.


Anchor Descriptor  A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.

Eligible Content  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).


Anchor Descriptor  A1.1.1.4 Use estimation strategies in problemsolving situations.

Eligible Content  A1.1.1.4.1 Use estimation to solve problems.


Anchor Descriptor  A1.1.1.5 Simplify expressions involving polynomials.

Eligible Content  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).

Eligible Content  A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is equal to 1 after factoring out all monomial factors).

Eligible Content  A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



Assessment Anchor  M08.AN.1 Demonstrate an understanding of rational and irrational numbers.

Anchor Descriptor  M08.AN.1.1 Apply concepts of rational and irrational numbers.

Eligible Content  M08.AN.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

Eligible Content  M08.AN.1.1.2 Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).

Alternate Eligible Content  M08.AN.1.1.2a Convert a fraction to a decimalup to the hundredths place.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M08.AN.1.1.3 Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2.

Eligible Content  M08.AN.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers.

Eligible Content  M08.AN.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line.

Alternate Eligible Content  M08.AN.1.1.5a Locate a nonterminating decimal at its approximate location on thenumber line.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.



Standard  CC.2.1.8.E.4Estimate irrational numbers by comparing them to rational numbers.

Assessment Anchor  A1.1.1
Operations with Real Numbers and Expressions

Anchor Descriptor  A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Eligible Content  A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).

Eligible Content  A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).


Anchor Descriptor  A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.

Eligible Content  A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.


Anchor Descriptor  A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.

Eligible Content  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).


Anchor Descriptor  A1.1.1.4 Use estimation strategies in problemsolving situations.

Eligible Content  A1.1.1.4.1 Use estimation to solve problems.


Anchor Descriptor  A1.1.1.5 Simplify expressions involving polynomials.

Eligible Content  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).

Eligible Content  A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is equal to 1 after factoring out all monomial factors).

Eligible Content  A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



Assessment Anchor  M08.AN.1 Demonstrate an understanding of rational and irrational numbers.

Anchor Descriptor  M08.AN.1.1 Apply concepts of rational and irrational numbers.

Eligible Content  M08.AN.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

Eligible Content  M08.AN.1.1.2 Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).

Alternate Eligible Content  M08.AN.1.1.2a Convert a fraction to a decimalup to the hundredths place.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.


Eligible Content  M08.AN.1.1.3 Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2.

Eligible Content  M08.AN.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers.

Eligible Content  M08.AN.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line.

Alternate Eligible Content  M08.AN.1.1.5a Locate a nonterminating decimal at its approximate location on thenumber line.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
 Standard Area  CC.2.1: Numbers and Operations
 Grade Level  CC.2.1.HS: GRADE High School
Standard  CC.2.1.HS.F.1Apply and extend the properties of exponents to solve problems with rational exponents

Assessment Anchor  A1.1.1
Operations with Real Numbers and Expressions

Anchor Descriptor  A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Eligible Content  A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).

Eligible Content  A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).


Anchor Descriptor  A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.

Eligible Content  A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.


Anchor Descriptor  A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.

Eligible Content  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).


Anchor Descriptor  A1.1.1.4 Use estimation strategies in problemsolving situations.

Eligible Content  A1.1.1.4.1 Use estimation to solve problems.


Anchor Descriptor  A1.1.1.5 Simplify expressions involving polynomials.

Eligible Content  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).

Eligible Content  A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is equal to 1 after factoring out all monomial factors).

Eligible Content  A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



Assessment Anchor  A2.1.2
NonLinear Expressions

Anchor Descriptor  A2.1.2.1 Use exponents, roots and/or absolute values to represent equivalent forms or to solve problems.

Eligible Content  A2.1.2.1.1 Use exponential expressions to represent rational numbers.

Eligible Content  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).

Eligible Content  A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x^{6} * x^{7} = x^{13}), powers of powers (e.g., (x^{6})^{7}=x^{42}) and powers of products (2x^{2})^{3}=8x^{6 }(limit to rational exponents).

Eligible Content  A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log_{2}8 = 3 or log_{4}2 = ½).


Anchor Descriptor  A2.1.2.2 Simplify expressions involving polynomials.

Eligible Content  A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is not equal to 0).

Eligible Content  A2.1.2.2.2 Simplify rational algebraic expressions.


Standard  CC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.

Assessment Anchor  A1.1.1
Operations with Real Numbers and Expressions

Anchor Descriptor  A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Eligible Content  A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).

Eligible Content  A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).


Anchor Descriptor  A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.

Eligible Content  A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.


Anchor Descriptor  A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.

Eligible Content  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).


Anchor Descriptor  A1.1.1.4 Use estimation strategies in problemsolving situations.

Eligible Content  A1.1.1.4.1 Use estimation to solve problems.


Anchor Descriptor  A1.1.1.5 Simplify expressions involving polynomials.

Eligible Content  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).

Eligible Content  A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax^{2}+bx+c where a is equal to 1 after factoring out all monomial factors).

Eligible Content  A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



Alternate Eligible Content  CC.2.1.HS.F.2.a Convert between fractions and decimals in a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
Standard  CC.2.1.HS.F.3Apply quantitative reasoning to choose and Interpret units and scales in formulas, graphs and data displays.

Assessment Anchor  A1.1.2
Linear Equations

Anchor Descriptor  A1.1.2.1 Write, solve and/or graph linear equations and inequalities using various methods.

Eligible Content  A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).

Eligible Content  A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).

Eligible Content  A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).


Anchor Descriptor  A1.1.2.2 Write, solve and/or graph systems of linear equations using various methods.

Eligible Content  A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).

Eligible Content  A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).



Assessment Anchor  A1.2.1
Functions

Anchor Descriptor  A1.2.1.1 Analyze and/or use patterns or relations.

Eligible Content  A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

Eligible Content  A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.

Eligible Content  A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).


Anchor Descriptor  A1.2.1.2 Interpret and/or use linear functions and their equations, graphs or tables.

Eligible Content  A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.

Eligible Content  A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).



Assessment Anchor  A2.2.2
Applications of Functions

Anchor Descriptor  A2.2.2.1 Create, interpret and/or use polynomial, exponential and/or logarithmic functions and their equations, graphs or tables.

Eligible Content  A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).

Eligible Content  A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).

Eligible Content  A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.

Eligible Content  A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).


Anchor Descriptor  A2.2.2.2 Describe and/or determine families of functions.

Eligible Content  A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x^{2} and y = x^{2} + 3, or y = x^{2 }and y = 3x^{2}).



Assessment Anchor  A2.2.3
Data Analysis

Anchor Descriptor  A2.2.3.1 Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.

Eligible Content  A2.2.3.1.1 Draw, identify, find and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.

Eligible Content  A2.2.3.1.2 Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.


Anchor Descriptor  A2.2.3.2 Apply probability to practical situations.

Eligible Content  A2.2.3.2.1 Use combinations, permutations, and the fundamental counting principle to solve problems.

Eligible Content  A2.2.3.2.2 Use odds to find probability and/or use probability to find odds.

Eligible Content  A2.2.3.2.3 Use probability for independent, dependent or compound events to predict outcomes.



Alternate Eligible Content  CC.2.1.HS.F.3.a Identify and interpret scale in a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
Standard  CC.2.1.HS.F.4Use units as a way to understand problems and to guide the solution of multistep problems.

Assessment Anchor  A1.1.2
Linear Equations

Anchor Descriptor  A1.1.2.1 Write, solve and/or graph linear equations and inequalities using various methods.

Eligible Content  A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).

Eligible Content  A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).

Eligible Content  A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).


Anchor Descriptor  A1.1.2.2 Write, solve and/or graph systems of linear equations using various methods.

Eligible Content  A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).

Eligible Content  A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).



Assessment Anchor  A1.2.1
Functions

Anchor Descriptor  A1.2.1.1 Analyze and/or use patterns or relations.

Eligible Content  A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

Eligible Content  A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.

Eligible Content  A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).


Anchor Descriptor  A1.2.1.2 Interpret and/or use linear functions and their equations, graphs or tables.

Eligible Content  A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.

Eligible Content  A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).



Assessment Anchor  A2.2.2
Applications of Functions

Anchor Descriptor  A2.2.2.1 Create, interpret and/or use polynomial, exponential and/or logarithmic functions and their equations, graphs or tables.

Eligible Content  A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).

Eligible Content  A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).

Eligible Content  A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.

Eligible Content  A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).


Anchor Descriptor  A2.2.2.2 Describe and/or determine families of functions.

Eligible Content  A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x^{2} and y = x^{2} + 3, or y = x^{2 }and y = 3x^{2}).



Alternate Eligible Content  CC.2.1.HS.F.4.a Determine the necessary units and solve a realworld problem.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
Standard  CC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Assessment Anchor  A1.1.2
Linear Equations

Anchor Descriptor  A1.1.2.1 Write, solve and/or graph linear equations and inequalities using various methods.

Eligible Content  A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).

Eligible Content  A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).

Eligible Content  A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).


Anchor Descriptor  A1.1.2.2 Write, solve and/or graph systems of linear equations using various methods.

Eligible Content  A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).

Eligible Content  A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).



Assessment Anchor  A1.1.3
Linear Inequalities

Anchor Descriptor  A1.1.3.1 Write, solve and/or graph linear inequalities using various methods.

Eligible Content  A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

Eligible Content  A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.

Eligible Content  A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).


Anchor Descriptor  A1.1.3.2 Write, solve and/or graph systems of linear inequalities using various methods.

Eligible Content  A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).

Eligible Content  A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).



Assessment Anchor  A2.2.3
Data Analysis

Anchor Descriptor  A2.2.3.1 Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.

Eligible Content  A2.2.3.1.1 Draw, identify, find and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.

Eligible Content  A2.2.3.1.2 Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.


Anchor Descriptor  A2.2.3.2 Apply probability to practical situations.

Eligible Content  A2.2.3.2.1 Use combinations, permutations, and the fundamental counting principle to solve problems.

Eligible Content  A2.2.3.2.2 Use odds to find probability and/or use probability to find odds.

Eligible Content  A2.2.3.2.3 Use probability for independent, dependent or compound events to predict outcomes.


Standard  CC.2.1.HS.F.6Extend the knowledge of arithmetic operations and apply to complex numbers.

Assessment Anchor  A2.1.1
Operations with Complex Numbers

Anchor Descriptor  A2.1.1.1 Represent and/or use imaginary numbers in equivalent forms (e.g., square roots and exponents).

Eligible Content  A2.1.1.1.1
Simplify square roots in terms of i. (e.g., √–24 = 2i√6).

Eligible Content  A2.1.1.1.2
Simplify/evaluate expressions involving imaginary numbers powers of i (e.g., i^{6} + i^{3} = –1 + i).


Anchor Descriptor  A2.1.1.2 Apply the order of operations in computation and in problemsolving situations.

Eligible Content  A2.1.1.2.1 Add and subtract complex numbers(e.g., (7 – 3i) – (2 + i) = 5 – 4i).

Eligible Content  A2.1.1.2.2 Multiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i).


Standard  CC.2.1.HS.F.7Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.

Assessment Anchor  A2.2.1
Patterns, Relations, and Functions

Anchor Descriptor  A2.2.1.1 Analyze and/or use patterns or relations.

Eligible Content  A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.

Eligible Content  A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20^{th} term).

Eligible Content  A2.2.1.1.3 Determine the domain, range or inverse of a relation.

Eligible Content  A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
















