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# McGuffey School District

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# Third Grade Math

### Third Grade Math Overview

The third grade year is a significant step forward in the mathematical journey, with students tackling multiplication and division for the first time and also diving headlong into the world of fractions. Third grade also marks the first year of formalized math assessment through the end of year PSSA exam. In addition to the Pennsylvania Core math standards that have been present since kindergarten, the 3rd grade year introduces big picture assessment anchors, along with anchor descriptors that add a level of specificity to the anchor. Each anchor descriptor also contains eligible content, which is the most specific level of skills and content available for reference.

In numbers and operations, the content is split out into sub categories of "Numbers and Operations in Base Ten" and "Numbers and Operations - Fractions." In base ten, students will be using place value understanding and properties of operations to perform multi-digit arithmetic (M-03.A-T.1; CC.2.1.3.B.1 ), while in fractions students will focus on developing an understanding of fractions as numbers (M03.A-F.1; CC.2.1.3.C.1 ).

In algebraic concepts, students will be representing and solving problems that involve multiplication and division (M03.B-O.1; CC.2.2.3.A.1 ). They will also begin developing an understanding of multiplication and the relationship between multiplication and division (M.03.B-O.2; CC.2.2.3.A.2 ). Additionally, students will be working on solving problems that involve the four operations of addition, subtraction, multiplication, and division while identifying and explaining patterns in arithmetic (M.03.B-O.3; CC.2.2.3.A.4 ).

In geometry, students will be focusing on their ability to reason with shapes and their attributes (M03.C-G.1; CC.2.3.3.A.1; CC.2.3.3.A.2 ).

In data analysis and probability, students will be focused on several key areas. They will be solving problems that involve measurement and estimation of intervals of time, money, liquid volumes, masses, and lengths of objects (M03.D-M.1;  CC.2.4.3.A.1; CC.2.4.3.A.2; CC.2.4.3.A.3). Students will also be representing and interpreting data (M03.D-M.2; CC.2.4.3.A.4). Additionally, students will be  learning about the concept of area and how it relates to multiplication and addition (M03.D-M.3; CC.2.4.3.A.5). Lastly, students will be learning to recognize perimeter as an attribute of plane figures and working to distinguish between linear and area measures (M03.D-M.4; CC.2.4.3.A.6).

### Third Grade Curriculum Alignment to Core Resource

 Beginning of Year Diagnostic Assessment

 Unit 1 - Math Is School Weeks Math Classifications: Numbers and Operations, Algebraic Concepts, Data Analysis and Probability CC.2.1.2.B.1 Use place value concepts to represent amounts of tens and ones and to compare three digit numbers. CC.2.1.2.B.2 Use place value concepts to read, write and skip count to 1000. CC.2.1.2.B.3 Use place value understanding and properties of operations to add and subtract within 1000. CC.2.2.2.A.3 Work with equal groups of objects to gain foundations for multiplication. CC.2.4.2.A.3 Solve problems using coins and paper currency with appropriate symbols.

 Unit 2 - Use Place Value to Fluently Add and Subtract Within 1,000 Math Classifications: Numbers and Operations (Base 10)Algebraic Concepts (Operations and Algebraic Thinking) Anchors:M03.A-T.1 Use place-value understanding and properties of operations to perform multi-digit arithmetic. Anchor Descriptors: M03.A-T.1.1 Apply place-value strategies to solve problems. Eligible Content Items:M03.A-T.1.1.1 Round two- and three-digit whole numbers to the nearest ten or hundred, respectively. M03.A-T.1.1.2 Add two- and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers. M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90). Reference Standard:CC.2.1.3.B.1 Apply place-value understanding and properties of operations to perform multi-digit arithmetic. Anchors:M03.B-O.1 Represent and solve problems involving multiplication and division.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Anchor Descriptors: M03.B-O.1.2 Solve mathematical and real world problems using multiplication and division, including determining the missing number in a multiplication and/or division equation. M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). Eligible Content Items:M03.B-O.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers. M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends. Reference Standard:CC.2.2.3.A.1 Represent and solve problems involving multiplication and division.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

 Unit 3 - Multiplication and Division Math Classifications: Algebraic Concepts Anchors:M03.B-O.1 Represent and solve problems involving multiplication and division.M03.B-O.2 Understand properties of multiplication and the relationship between multiplication and division. M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic Anchor Descriptors: M03.B-O.1.1 Understand various meanings of multiplication and division.M03.B-O.1.2 Solve mathematical and realworld problems using multiplication and division, including determining the missing number in a multiplication and/or division equation. M03.B-O.2.1 Use properties to simplify and solve multiplication problems.  M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). 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.M03.B-O.1.2.1 Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.M03.B-O.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.M03.B-O.2.1.1 Apply the commutative property of multiplication (not identification or definition of the property). M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers. Reference Standards:CC.2.2.3.A.1 Represent and solve problems involving multiplication and divisionCC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

 Unit 4 - Use Patterns to Multiply By 0, 1, 2, 5, and 10 Math Classifications: Algebraic Concepts (Operations and Algebraic Thinking)Numbers and Operations (Base Ten) Anchors:M03.A-T.1 Use place-value understanding and properties of operations to perform multi-digit arithmetic. Anchor Descriptors: M03.A-T.1.1 Apply place-value strategies to solve problems. Eligible Content Items:M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90). Reference Standards:CC.2.1.3.B.1 Apply place-value understanding and properties of operations to perform multi-digit arithmetic. Anchors:M03.B-O.1 Represent and solve problems involving multiplication and division.M03.B-O.2 Understand properties of multiplication and the relationship between multiplication and division.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Anchor Descriptors: M03.B-O.1.2 Solve mathematical and realworld problems using multiplication and division, including determining the missing number in a multiplication and/or division equation. M03.B-O.2.2 Relate division to a missingnumber multiplication equation. M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). Eligible Content Items:M03.B-O.1.2.1 Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities. M03.B-O.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.M03.B-O.2.2.1 Interpret and/or model division as a multiplication equation with an unknown factor. Example: Find 32 ÷ 8 by solving 8 × ? = 32.M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends.M03.B-O.3.1.7 Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true. Reference Standards:CC.2.2.3.A.1 Represent and solve problems involving multiplication and division.CC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

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

 Unit 5 - Use Properties to Multiply by 3, 4, 6, 7, 8, and 9 Math Classifications: Algebraic Concepts (Operations and Algebraic Thinking) Anchors:M03.B-O.1 Represent and solve problems involving multiplication and division.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Anchor Descriptors: M03.B-O.1.1 Understand various meanings of multiplication and division. M03.B-O.1.2 Solve mathematical and realworld problems using multiplication and division, including determining the missing number in a multiplication and/or division equation. M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). 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.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. Example: Determine the unknown number that makes an equation true.M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends. Reference Standards:CC.2.2.3.A.1 Represent and solve problems involving multiplication and divisionCC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

 Unit 6 - Connect Area to Multiplication Math Classifications: GeometryData Analysis and Probability (Measurements and Data) Anchors:M03.C-G.1 Reason with shapes and their attributes. Anchor Descriptors: M03.C-G.1.1 Analyze characteristics of polygons. Eligible Content Items:M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example 1: Partition a shape into 4 parts with equal areas. Example 2: Describe the area of each of 8 equal parts as 1/8 of the area of the shape. Reference Standards:CC.2.3.3.A.1 Identify, compare, and classify shapes and their attributes. CC.2.3.3.A.2 Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole. Anchors:M03.D-M.1 Solve problems involving measurement and estimation of intervals of time, money, liquid volumes, masses, and lengths of objects. Anchor Descriptors: M03.D-M.1.1 Determine or calculate time and elapsed time. Eligible Content Items:M03.D-M.1.1.1 Tell, show, and/or write time (analog) to the nearest minute. M03.D-M.1.1.2 Calculate elapsed time to the minute in a given situation (total elapsed time limited to 60 minutes or less). Reference Standards:CC.2.4.3.A.2 Tell and write time to the nearest minute and solve problems by calculating time intervals.

 Unit 7 - Fractions Math Classifications: Numbers and Operations (Fractions) 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.1.1.4 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 Reference Standards:CC.2.1.3.C.1 Explore and develop an understanding of fractions as numbers.

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

 Unit 8 - Fraction Equivalence and Comparison Math Classifications: Numbers and Operations (Fractions) 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.1.1.3 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 = ?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.

 Unit 9 - Use Multiplication to Divide Math Classifications: Algebraic Concepts (Operations and Algebraic Thinking) Anchors:M03.B-O.1 Represent and solve problems involving multiplication and division.M03.B-O.2 Understand properties of multiplication and the relationship between multiplication and division.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Anchor Descriptors: M03.B-O.1.1 Understand various meanings of multiplication and division. M03.B-O.2.2 Relate division to a missing number multiplication equation. M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). 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.M03.B-O.2.2.1 Interpret and/or model division as a multiplication equation with an unknown factor. Example: Find 32 ÷ 8 by solving 8 × ? = 32.M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers. M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends. Reference Standards:CC.2.2.3.A.1 Represent and solve problems involving multiplication and division.CC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

 Unit 10 - Use Properties and Strategies to Multiply and Divide Math Classifications: Algebraic Concepts (Operations and Algebraic Thinking) Anchors:M03.B-O.2 Understand properties of multiplication and the relationship between multiplication and division.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Anchor Descriptors: M03.B-O.2.1 Use properties to simplify and solve multiplication problems.M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems). Eligible Content Items:M03.B-O.2.1.2 Apply the associative property of multiplication (not identification or definition of the property). M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers. M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers. M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers. M03.B-O.3.1.4 Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols). M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends Reference Standards:CC.2.2.3.A.2 Understand properties of multiplication and the relationship between multiplication and division.

 Benchmark 3 Benchmark 3 is drawn from all of the skills and concepts covered in Units 2-10

 Unit 11 - Perimeter Math Classifications: Data Analysis and Probability (Measurements and Data) Anchors:M03.D-M.4 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Anchor Descriptors: M03.D-M.4.1 Find and use the perimeters of plane figures. Eligible Content Items:M03.D-M.4.1.1 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, exhibiting rectangles with the same perimeter and different areas, and exhibiting rectangles with the same area and different perimeters. Use the same units throughout the problem. Reference Standards:CC.2.4.3.A.6 Solve problems involving perimeters of polygons and distinguish between linear and area measures.

 Unit 12 - Measurement and Data Math Classifications: M03.D-M.1 Solve problems involving measurement and estimation of intervals of time, money, liquid volumes, masses, and lengths of objects. Anchors:M03.D-M.1 Solve problems involving measurement and estimation of intervals of time, money, liquid volumes, masses, and lengths of objects.M03.D-M.2 Represent and interpret data. Anchor Descriptors: M03.D-M.1.1 Determine or calculate time and elapsed time. M03.D-M.1.2 Use the attributes of liquid volume, mass, and length of objects.  M03.D-M.2.1 Organize, display, and answer questions based on data. Eligible Content Items:M03.D-M.1.1.1 Tell, show, and/or write time (analog) to the nearest minute. M03.D-M.1.1.2 Calculate elapsed time to the minute in a given situation (total elapsed time limited to 60 minutes or less). M03.D-M.1.2.1 Measure and estimate liquid volumes and masses of objects using standard units (cups [c], pints [pt], quarts [qt], gallons [gal], ounces [oz.], and pounds [lb]) and metric units (liters [l], grams [g], and kilograms [kg]). M03.D-M.1.2.2 Add, subtract, multiply, and divide to solve onestep word problems involving masses or liquid volumes that are given in the same units. M03.D-M.1.2.3 Use a ruler to measure lengths to the nearest quarter inch or centimeter. M03.D-M.2.1.2 Solve one- and two-step problems using information to interpret data presented in scaled pictographs and scaled bar graphs (scales limited to 1, 2, 5, and 10). Example 1: (One-step) “Which category is the largest?” Example 2: (Two-step) “How many more are in category A than in category B?”M03.D-M.2.1.4 Translate information from one type of display to another. Limit to pictographs, tally charts, bar graphs, and tables. Example: Convert a tally chart to a bar graph. Reference Standards:CC.2.4.3.A.2 Tell and write time to the nearest minute and solve problems by calculating time intervals.CC.2.4.3.A.1 Solve problems involving measurement and estimation of temperature, liquid volume, mass or length.CC.2.4.3.A.4 Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.

 Unit 13 - Describe and Analyze Two-Dimensional Shapes Math Classifications: Geometry Anchors:M03.C-G.1 Reason with shapes and their attributes. Anchor Descriptors: M03.C-G.1.1 Analyze characteristics of polygons. Eligible Content Items:M03.C-G.1.1.1 Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category. Example 1: A rhombus and a rectangle are both quadrilaterals since they both have exactly four sides. Example 2: A triangle and a pentagon are both polygons since they are both multi-sided plane figures. M03.C-G.1.1.2 Recognize rhombi, rectangles, and squares as examples of quadrilaterals and/or draw examples of quadrilaterals that do not belong to any of these subcategories. Reference Standards:CC.2.3.3.A.1 Identify, compare, and classify shapes and their attributes. CC.2.3.3.A.2 Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.

 PSSA MATH EXAM The PSSA Math Exam includes all eligible content covered during the course of the third grade year. 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, 2022For 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 third grade year