The Common Core in Pennsylvania

3.M03.A-T Numbers and Operations in Base Ten

• 3.M03.A-T.1 Use place-value understanding and properties of operations to perform multi-digit arithmetic.

  • 3.M03.A-T.1.1 Apply place-value strategies to solve problems.

    • 3.M03.A-T.1.1.1 Round two- and three-digit whole numbers to the nearest ten or hundred, respectively.

      • Round to the greatest place value (3-P.4)

    • 3.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.

      • Add two numbers up to three digits (3-C.1)
      • Add two numbers up to three digits: word problems (3-C.3)
      • Complete the addition sentence: up to three digits (3-C.4)
      • Balance addition equations: up to three digits (3-C.5)
      • Addition patterns over increasing place values (3-C.16)
      • Subtract numbers up to three digits (3-D.1)
      • Subtract numbers up to three digits: word problems (3-D.3)
      • Complete the subtraction sentence: up to three digits (3-D.5)
      • Balance subtraction equations: up to three digits (3-D.6)
      • Subtraction patterns over increasing place values (3-D.8)

    • 3.M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90).

      • Multiply by 10 (3-F.11)
      • Multiply by a multiple of ten (3-H.2)

    • 3.M03.A-T.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).

      • Compare numbers (3-A.9)
      • Which number is greatest/least? (3-A.10)
      • Order numbers (3-A.11)

3.M03.A-F Numbers and Operations—Fractions

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

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

    • 3.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).

      • Understand fractions: fraction bars (3-V.5)
      • Understand fractions: area models (3-V.6)
      • Show fractions: fraction bars (3-V.7)
      • Show fractions: area models (3-V.8)
      • Match fractions to models: halves, thirds, and fourths (3-V.9)
      • Match unit fractions to models (3-V.10)
      • Match fractions to models (3-V.11)
      • Fractions of a group: word problems (3-V.28)

    • 3.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).

      • Fractions of number lines: unit fractions (3-V.13)
      • Identify unit fractions on number lines (3-V.16)
      • Identify fractions on number lines (3-V.17)

    • 3.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).

      • Identify equivalent fractions (3-W.6)
      • Find equivalent fractions (3-W.7)
      • Write fractions in lowest terms (3-W.13)

    • 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).

      • Select fractions equivalent to whole numbers using models (3-W.9)
      • Find fractions equivalent to whole numbers (3-W.11)

    • 3.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.

      • Graph and compare fractions with like denominators on number lines (3-X.5)
      • Compare fractions (3-X.10)
      • Compare fractions in recipes (3-X.11)
      • Order fractions with like denominators (3-X.15)

3.M03.B-O Operations and Algebraic Thinking

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

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

    • 3.M03.B-O.1.1.1 Interpret and/or describe products of whole numbers (up to and including 10 × 10).

      • Write multiplication sentences for equal groups (3-E.3)
      • Relate addition and multiplication (3-N.10)

    • 3.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).

      • Division word problems (3-L.5)

  • 3.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.

    • 3.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.

      • Multiplication input/output tables: find the rule (3-H.6)
      • Multiplication word problems (3-H.7)
      • Multiplication word problems: find the missing factor (3-H.8)
      • Multiply three or more numbers: word problems (3-H.21)
      • Division input/output tables: find the rule (3-L.4)
      • Division word problems (3-L.5)

    • 3.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.

      • Multiplication facts up to 12: find the missing factor (3-G.17)
      • Division facts up to 10: find the missing number (3-K.10)

• 3.M03.B-O.2 Understand properties of multiplication and the relationship between multiplication and division.

  • 3.M03.B-O.2.1 Use properties to simplify and solve multiplication problems.

    • 3.M03.B-O.2.1.1 Apply the commutative property of multiplication (not identification or definition of the property).

    • 3.M03.B-O.2.1.2 Apply the associative property of multiplication (not identification or definition of the property).

      • Solve using properties of multiplication (3-N.9)

  • 3.M03.B-O.2.2 Relate division to a missing-number multiplication equation.

    • 3.M03.B-O.2.2.1 Interpret and/or model division as a multiplication equation with an unknown factor.

      • Multiplication facts up to 12: find the missing factor (3-G.17)
      • Multiplication word problems: find the missing factor (3-H.8)
      • Relate multiplication and division (3-N.11)
      • Solve for the variable (3-O.4)

• 3.M03.B-O.3 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

  • 3.M03.B-O.3.1 Use operations, patterns, and estimation strategies to solve problems (may include word problems).

    • 3.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.

      • Addition, subtraction, multiplication, and division facts (3-M.1)
      • Complete the addition, subtraction, multiplication, or division sentence (3-M.2)
      • Add, subtract, multiply, and divide (3-M.8)
      • Addition, subtraction, multiplication, and division word problems (3-M.13)
      • Two-step mixed operation word problems (3-M.17)

    • 3.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.

      • Solve for the variable: addition and subtraction only (3-O.2)
      • Solve for the variable (3-O.4)
      • Write variable equations to represent word problems (3-O.6)

    • 3.M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.

      • Round to the nearest ten or hundred (3-P.2)
      • Round to the greatest place value (3-P.4)
      • Estimate sums by rounding: up to 1,000 (3-P.7)
      • Estimate sums by rounding: up to 1,000,000 (3-P.8)
      • Estimate to compare sums and differences (3-P.15)
      • Estimate products (3-P.17)
      • Estimate quotients (3-P.18)

    • 3.M03.B-O.3.1.4 Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols).

    • 3.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.

      • Addition input/output tables: up to three digits (3-C.2)
      • Subtraction input/output tables: up to three digits (3-D.2)
      • Multiplication input/output tables (3-H.5)
      • Multiplication input/output tables: find the rule (3-H.6)
      • Division input/output tables (3-L.3)
      • Division input/output tables: find the rule (3-L.4)

    • 3.M03.B-O.3.1.6 Create or match a story to a given combination of symbols (+, –, ×, ÷, <, >, and =) and numbers.

      • Write variable equations to represent word problems (3-O.6)

    • 3.M03.B-O.3.1.7 Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true.

3.M03.C-G Geometry

• 3.M03.C-G.1 Reason with shapes and their attributes.

  • 3.M03.C-G.1.1 Analyze characteristics of polygons.

    • 3.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.

      • Identify two-dimensional shapes (3-AA.1)
      • Count and compare sides and vertices (3-AA.2)
      • Parallel sides in quadrilaterals (3-BB.3)

    • 3.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.

      • Classify quadrilaterals (3-BB.8)

    • 3.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.

      • Match unit fractions to models (3-V.10)

3.M03.D-M Measurement and Data

• 3.M03.D-M.1 Solve problems involving measurement and estimation of intervals of time, money, liquid volumes, masses, and lengths of objects.

  • 3.M03.D-M.1.1 Determine or calculate time and elapsed time.

    • 3.M03.D-M.1.1.1 Tell, show, and/or write time (analog) to the nearest minute.

      • Read clocks and write times (3-T.3)

    • 3.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).

      • Elapsed time: find the end time (3-T.6)
      • Elapsed time word problems: find the elapsed time (3-T.9)

  • 3.M03.D-M.1.2 Use the attributes of liquid volume, mass, and length of objects.

    • 3.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]).

      • Which customary unit is appropriate? (3-Z.8)
      • Which metric unit is appropriate? (3-Z.17)

    • 3.M03.D-M.1.2.2 Add, subtract, multiply, and divide to solve one-step word problems involving masses or liquid volumes that are given in the same units.

    • 3.M03.D-M.1.2.3 Use a ruler to measure lengths to the nearest quarter inch or centimeter.

      • Measure using an inch ruler (3-Z.3)

  • 3.M03.D-M.1.3 Count, compare, and make change using a collection of coins and one-dollar bills.

    • 3.M03.D-M.1.3.1 Compare total values of combinations of coins (penny, nickel, dime, and quarter) and/or dollar bills less than $5.00.

      • Count coins and bills - up to $5 bill (3-S.1)
      • Which picture shows more? (3-S.4)
      • Inequalities with money (3-S.7)

    • 3.M03.D-M.1.3.2 Make change for an amount up to $5.00 with no more than $2.00 change given (penny, nickel, dime, quarter, and dollar).

      • Correct amount of change (3-S.5)
      • Making change (3-S.6)

    • 3.M03.D-M.1.3.3 Round amounts of money to the nearest dollar.

      • Round money amounts to the nearest dollar (3-P.5)

• 3.M03.D-M.2 Represent and interpret data.

  • 3.M03.D-M.2.1 Organize, display, and answer questions based on data.

    • 3.M03.D-M.2.1.1 Complete a scaled pictograph and a scaled bar graph to represent a data set with several categories (scales limited to 1, 2, 5, and 10).

      • Create bar graphs (3-U.8)
      • Create pictographs (3-U.13)

    • 3.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).

      • Interpret bar graphs (3-U.6)
      • Interpret pictographs (3-U.12)

    • 3.M03.D-M.2.1.3 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Display the data by making a line plot, where the horizontal scale is marked in appropriate units—whole numbers, halves, or quarters.

    • 3.M03.D-M.2.1.4 Translate information from one type of display to another. Limit to pictographs, tally charts, bar graphs, and tables.

      • Create bar graphs (3-U.8)
      • Create pictographs (3-U.13)

• 3.M03.D-M.3 Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

  • 3.M03.D-M.3.1 Find the areas of plane figures.

    • 3.M03.D-M.3.1.1 Measure areas by counting unit squares (square cm, square m, square in., square ft, and non-standard square units).

      • Find the area of figures made of unit squares (3-DD.7)

    • 3.M03.D-M.3.1.2 Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

      • Find the area of rectangles and squares (3-DD.14)
      • Find the area of rectangles: word problems (3-DD.17)
      • Use area and perimeter to determine cost (3-DD.22)

• 3.M03.D-M.4 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

  • 3.M03.D-M.4.1 Find and use the perimeters of plane figures.

    • 3.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.

      • Perimeter of rectangles (3-DD.1)
      • Perimeter: find the missing side length (3-DD.5)
      • Compare area and perimeter of two figures (3-DD.21)
      • Use area and perimeter to determine cost (3-DD.22)
      • Relationship between area and perimeter: find the perimeter (3-DD.23)