Beginning of Year Diagnostic Assessment - School Week 1

Unit 1 - Math Is

Math Classifications: 

• Numbers and Operations (Fractions)

• Algebraic Concepts (Operations and Algebraic Thinking) 

Anchors:

• M03.A-F.1 Develop an understanding of fractions as numbers.

Anchor Descriptors: 

• M03.A-F.1.1 Develop and apply number theory concepts to compare quantities and magnitudes of fractions and whole numbers. 

Eligible Content Items:

• M03.A-F.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). 

• M03.A-F.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). 

• M03.A-F.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 

• M03.A-F.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. 

• M03.A-F.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. 

Reference Standards:

• CC.2.1.3.C.1 Explore and develop an understanding of fractions as numbers. 

Anchors:

• M03.B-O.1 Represent and solve problems involving multiplication and division.

Anchor Descriptors: 

• M03.B-O.1.1 Understand various meanings of multiplication and division. 

Eligible Content Items:

• 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. 

• 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.

Reference Standards:

• CC.2.2.3.A.1 Represent and solve problems involving multiplication and division. 

Unit 2 - Generalize Place Value Structure 

Math Classifications: 

• Numbers and Operations (Base Ten)

Anchors:

• M04.A-T.1 Generalize place-value understanding for multi-digit whole numbers.

Anchor Descriptors: 

• M04.A-T.1.1 Apply place-value and numeration concepts to compare, find equivalencies, and round. 

Eligible Content Items:

• M04.A-T.1.1.1 Demonstrate an understanding that in a multi-digit 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. 

• M04.A-T.1.1.2 Read and write whole numbers in expanded, standard, and word form through 1,000,000. 

• M04.A-T.1.1.3 Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols. 

• M04.A-T.1.1.4 Round multi-digit whole numbers (through 1,000,000) to any place.

Reference Standards:

• CC.2.1.4.B.1 Apply place-value concepts to show an understanding of multi-digit whole numbers.

Unit 3 - Addition and Subtraction Strategies and Algorithms 

Math Classifications: 

• Numbers and Operations (Base Ten)

Anchors:

• M04.A-T.1 Generalize place-value understanding for multi-digit whole numbers.

• M04.A-T.2 Use place-value understanding and properties of operations to perform multi-digit arithmetic.

Anchor Descriptors: 

• M04.A-T.1.1 Apply place-value and numeration concepts to compare, find equivalencies, and round. 

• M04.A-T.2.1 Use operations to solve problems. 

Eligible Content Items:

• M04.A-T.1.1.2 Read and write whole numbers in expanded, standard, and word form through 1,000,000. 

• M04.A-T.2.1.1 Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000). 

• M04.A-T.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).

Reference Standards:

• CC.2.1.4.B.1 Apply place-value concepts to show an understanding of multi-digit whole numbers.

• CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic.

Unit 4 - Multiplication As A Comparison 

Math Classifications: 

• Algebraic Concepts (Operations and Algebraic Thinking) 

Anchors:

• M04.B-O.1 Use the four operations with whole numbers to solve problems.

Anchor Descriptors: 

• M04.B-O.1.1 Use numbers and symbols to model the concepts of expressions and equations. 

Eligible Content Items:

• M04.B-O.1.1.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3. 

• M04.B-O.1.1.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects. 

• M04.B-O.1.1.3 Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity.  

Reference Standards:

• CC.2.2.4.A.1 Represent and solve problems involving the four operations.

Benchmark 1 

Benchmark 1 is drawn from all of the skills and concepts covered in Units 2-4

Unit 5 - Numbers and Number Patterns 

Math Classifications: 

• Algebraic Concepts (Operations and Algebraic Thinking) 

Anchors:

• M04.B-O.2 Gain familiarity with factors and multiples.

• M04.B-O.3 Generate and analyze patterns.

Anchor Descriptors: 

• M04.B-O.2.1 Develop and apply number theory concepts to represent numbers in various ways. 

• M04.B-O.3.1 Recognize, describe, extend, create, and replicate a variety of patterns. 

Eligible Content Items:

• 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.  

• M04.B-O.3.1.1 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule “add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.

• M04.B-O.3.1.2 Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money). 

Reference Standards:

• CC.2.2.4.A.2 Develop and/or apply number theory concepts to find factors and multiples.

• CC.2.2.4.A.4 Generate and analyze patterns using one rule.

Unit 6 - Multiplication Strategies With Multi-Digit Numbers 

Math Classifications: 

• Numbers and Operations (Base Ten)

• Algebraic Concepts (Operations and Algebraic Thinking) 

Anchors:

• M04.A-T.2 Use place-value understanding and properties of operations to perform multi-digit arithmetic

Anchor Descriptors: 

• M04.A-T.2.1 Use operations to solve problems. 

Eligible Content Items:

• M04.A-T.2.1.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers.  

• M04.A-T.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).

Reference Standards:

• CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic

Anchors:

• M04.B-O.1 Use the four operations with whole numbers to solve problems.

Anchor Descriptors: 

• M04.B-O.1.1 Use numbers and symbols to model the concepts of expressions and equations. 

Eligible Content Items:

• M04.B-O.1.1.3 Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity. 

Reference Standards:

• CC.2.2.4.A.1 Represent and solve problems involving the four operations.

Unit 7 - Division Strategies With Multi-Digit Dividends and One-Digit Divisors 

Math Classifications: 

• Numbers and Operations (Base Ten)

• Algebraic Concepts (Operations and Algebraic Thinking) 

Anchors:

• M04.A-T.2 Use place-value understanding and properties of operations to perform multi-digit arithmetic

Anchor Descriptors: 

• M04.A-T.2.1 Use operations to solve problems. 

Eligible Content Items:

• M04.A-T.2.1.3 Divide up to four-digit dividends by one-digit divisors with answers written as whole-number quotients and remainders. 

• M04.A-T.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).

Reference Standards:

• CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic

Anchors:

• M04.B-O.1 Use the four operations with whole numbers to solve problems.

Anchor Descriptors: 

• M04.B-O.1.1 Use numbers and symbols to model the concepts of expressions and equations. 

Eligible Content Items:

• M04.B-O.1.1.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects. 

• M04.B-O.1.1.3 Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity. 

Reference Standards:

• CC.2.2.4.A.1 Represent and solve problems involving the four operations.

Benchmark 2 

Benchmark 1 is drawn from all of the skills and concepts covered in Units 2-7

Unit 8 - Fraction Equivalence 

Math Classifications: 

• Numbers and Operations (Fractions)

Anchors:

• M04.A-F.1 Extend understanding of fraction equivalence and ordering.

Anchor Descriptors: 

• M04.A-F.1.1 Find equivalencies and compare fractions. 

Eligible Content Items:

• M04.A-F.1.1.1 Recognize and generate equivalent fractions. 

• M04.A-F.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.  

Reference Standards:

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

Unit 9 - Addition And Subtraction Meanings And Strategies With Fractions

Math Classifications: 

• Numbers and Operations (Fractions)

Anchors:

• M04.A-F.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Anchor Descriptors: 

• M04.A-F.2.1 Solve problems involving fractions and whole numbers (straight computation or word problems). 

Eligible Content Items:

• M04.A-F.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). 

• M04.A-F.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 

• M04.A-F.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). 

• M04.A-F.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). 

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Reference Standards:

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

Unit 10 - Addition And Subtraction Strategies With Mixed Numbers 

Math Classifications: 

• Numbers and Operations (Fractions)

Anchors:

• M04.A-F.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Anchor Descriptors: 

• M04.A-F.2.1 Solve problems involving fractions and whole numbers (straight computation or word problems). 

Eligible Content Items:

• M04.A-F.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). 

• M04.A-F.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 

• M04.A-F.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). 

• M04.A-F.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). 

Reference Standards:

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

Benchmark 3 

Benchmark 1 is drawn from all of the skills and concepts covered in Units 2-10

Unit 11 - Multiply Fractions By Whole Numbers 

Math Classifications: 

• Numbers and Operations (Fractions)

Anchors:

• M04.A-F.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Anchor Descriptors: 

• M04.A-F.2.1 Solve problems involving fractions and whole numbers (straight computation or word problems). 

Eligible Content Items:

• M04.A-F.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 

• M04.A-F.2.1.6 Multiply a whole number by a non-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: 3 × (5/6) = 15/6 

• M04.A-F.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). 

Reference Standards:

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

Unit 12 - Decimal Fractions 

Math Classifications: 

• Numbers and Operations (Fractions)

Anchors:

• M04.A-F.1 Extend understanding of fraction equivalence and ordering.

• M04.A-F.3 Understand decimal notation for fractions and compare decimal fractions.

Anchor Descriptors: 

• M04.A-F.1.1 Find equivalencies and compare fractions. 

• M04.A-F.3.1 Use operations to solve problems involving decimals, including converting between fractions and decimals (may include word problems). 

Eligible Content Items:

• M04.A-F.1.1.1 Recognize and generate equivalent fractions. 

• M04.A-F.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. 

• M04.A-F.3.1.2 Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa. 

• M04.A-F.3.1.3 Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions. 

Reference Standards:

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

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

Unit 13 - Units of Measurement and Data

Math Classifications: 

• Data Analysis and Probability (Measurement and Data)

Anchors:

• M04.D-M.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

• M04.D-M.2 Represent and interpret data.

Anchor Descriptors: 

• M04.D-M.1.1 Solve problems involving length, weight (mass), liquid volume, time, area, and perimeter. 

• M04.D-M.2.1 Organize, display, and answer questions based on data. 

Eligible Content Items:

• M04.D-M.1.1.1 Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and mL, L), and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. A table of equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48 in.

• M04.D-M.1.1.2 Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

• M04.D-M.1.1.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems (may include finding a missing side length). Whole numbers only. The formulas will be provided.

• M04.D-M.2.1.1 Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8). 

• M04.D-M.2.1.2 Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4). 

• M04.D-M.2.1.3 Translate information from one type of display to another (table, chart, bar graph, or pictograph). 

Reference Standards:

• CC.2.4.4.A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit.

• CC.2.4.4.A.2 Translate information from one type of data display to another.

• CC.2.4.4.A.4 Represent and interpret data involving fractions using information provided in a line plot.

Unit 14 - Geometric Figures 

Math Classifications: 

• Data Analysis and Probability (Measurement and Data)

• Geometry

Anchors:

• M04.D-M.3 Geometric measurement: understand concepts of angle; measure and create angles.

Anchor Descriptors: 

• M04.D-M.3.1 Use appropriate tools and units to sketch an angle and determine angle measurements. 

Eligible Content Items:

• M04.D-M.3.1.1 Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure. 

• M04.D-M.3.1.2 Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.) 

Reference Standards:

• CC.2.4.4.A.6 Measure angles and use properties of adjacent angles to solve problems. 

Anchors:

• M04.C-G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Anchor Descriptors: 

• M04.C-G.1.1 List properties, classify, draw, and identify geometric figures in two dimensions. 

Eligible Content Items:

• M04.C-G.1.1.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

• M04.C-G.1.1.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

• M04.C-G.1.1.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry). 

Reference Standards:

• CC.2.3.4.A.1 Draw lines and angles and identify these in two-dimensional figures.

• CC.2.3.4.A.2 Classify two-dimensional figures by properties of their lines and angles.

• CC.2.3.4.A.3 Recognize symmetric shapes and draw lines of symmetry.

PSSA MATH EXAM

The PSSA Math Exam includes all eligible content covered during the course of the fourth grade year. Content covered during the third grade year may also appear on the 4th grade PSSA exam. This exam typically occurs during the end of April and beginning of May. 

For the 2021-2022 school year, the PSSA Math exam window will take place between May 2 and May 27, 2022

For the 2022-2023 school year, the PSSA Math exam window will take place between May 1 and 12, 2023

End of Year Benchmark

The end of year benchmark is drawn from all of the skills and concepts covered during the course of the fourth grade year