The Common Core in Pennsylvania

4.M04.A-T Numbers and Operations in Base Ten

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

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

    • 4.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.

      • Convert between standard and expanded form (4-A.2)
      • Convert between place values (4-A.5)

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

      • Convert between standard and expanded form (4-A.2)
      • Writing numbers up to one million in words: convert digits to words (4-A.13)

    • 4.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.

      • Compare numbers up to one billion (4-A.27)
      • Addition patterns over increasing place values (4-B.8)
      • Inequalities with multiplication (4-D.52)
      • Inequalities with division (4-E.30)
      • Inequalities involving addition, subtraction, multiplication, and division (4-F.19)

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

      • Rounding: up to millions place (4-A.21)
      • Estimate sums (4-B.10)
      • Estimate sums: word problems (4-B.11)
      • Estimate differences (4-C.8)
      • Estimate products: multiply by 1-digit numbers (4-D.32)
      • Estimate products: multiply by 2-digit numbers (4-D.33)
      • Divide by 1-digit numbers: pick the better estimate (4-E.25)
      • Estimate quotients (4-E.31)

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

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

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

      • Add two numbers up to seven digits (4-B.3)
      • Add two numbers up to seven digits: word problems (4-B.4)
      • Addition: fill in the missing digits (4-B.5)
      • Add 3 or more numbers up to millions (4-B.7)
      • Choose numbers with a particular sum (4-B.9)
      • Subtract numbers up to seven digits (4-C.3)
      • Subtract numbers up to seven digits: word problems (4-C.4)
      • Subtraction: fill in the missing digits (4-C.5)
      • Choose numbers with a particular difference (4-C.7)

    • 4.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.

      • Multiply 1-digit numbers by 2-digit numbers (4-D.15)
      • Multiply 1-digit numbers by 3-digit or 4-digit numbers (4-D.22)
      • Multiply 1-digit numbers by larger numbers (4-D.25)
      • Multiplication patterns over increasing place values (4-D.27)
      • Multiply a 2-digit number by a 2-digit number: complete the missing steps (4-D.41)
      • Multiply a 2-digit number by a 2-digit number (4-D.42)
      • Multiply numbers ending in zeroes (4-D.48)

    • 4.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.

      • Divide 2-digit numbers by 1-digit numbers (4-E.11)
      • Divide 2-digit numbers by 1-digit numbers: word problems (4-E.12)
      • Divide larger numbers by 1-digit numbers (4-E.17)
      • Divide larger numbers by 1-digit numbers: complete the table (4-E.19)
      • Divide larger numbers by 1-digit numbers: interpret remainders (4-E.20)
      • Division patterns over increasing place values (4-E.22)
      • Divide numbers ending in zeroes by 1-digit numbers (4-E.23)

    • 4.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).

      • Estimate sums (4-B.10)
      • Estimate sums: word problems (4-B.11)
      • Estimate differences (4-C.8)
      • Estimate differences: word problems (4-C.9)
      • Estimate products: multiply by 2-digit numbers (4-D.33)
      • Estimate products: word problems (4-D.34)

4.M04.A-F Numbers and Operations—Fractions

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

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

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

      • Identify equivalent fractions (4-O.8)
      • Patterns of equivalent fractions (4-O.12)
      • Write fractions in lowest terms (4-O.13)

    • 4.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.

      • Compare fractions using models (4-O.17)
      • Compare fractions (4-O.21)
      • Order fractions (4-O.26)

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

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

    • 4.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).

      • Add fractions with like denominators using number lines (4-P.7)
      • Subtract fractions with like denominators using number lines (4-P.11)
      • Add and subtract fractions with like denominators using number lines (4-P.13)
      • Add and subtract fractions with like denominators (4-P.14)
      • Add 3 or more fractions with like denominators (4-P.18)

    • 4.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).

      • Identify mixed numbers (4-O.4)
      • Decompose fractions into unit fractions (4-P.2)
      • Decompose fractions (4-P.3)
      • Decompose fractions multiple ways (4-P.4)
      • Add and subtract fractions with like denominators (4-P.14)
      • Add 3 or more fractions with like denominators (4-P.18)

    • 4.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).

      • Add and subtract mixed numbers with like denominators (4-P.19)

    • 4.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).

      • Add and subtract fractions with like denominators: word problems (4-P.16)
      • Add and subtract fractions with like denominators in recipes (4-P.17)

    • 4.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).

      • Multiply unit fractions by whole numbers using number lines (4-R.1)
      • Multiply unit fractions by whole numbers: sorting (4-R.4)
      • Multiply unit fractions by whole numbers (4-R.5)
      • Fractions of a number (4-R.16)

    • 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).

      • Multiply fractions by whole numbers using number lines (4-R.7)
      • Multiply fractions by whole numbers: sorting (4-R.11)
      • Multiply fractions by whole numbers (4-R.12)

    • 4.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).

      • Multiply unit fractions by whole numbers: word problems (4-R.6)
      • Multiply fractions by whole numbers: word problems (4-R.13)
      • Multiply fractions and mixed numbers by whole numbers in recipes (4-R.15)
      • Fractions of a number: word problems (4-R.17)

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

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

    • 4.M04.A-F.3.1.1 Add two fractions with respective denominators 10 and 100.

      • Fractions with denominators of 10 and 100 (4-O.10)

    • 4.M04.A-F.3.1.2 Use decimal notation for fractions with denominators 10 or 100.

      • Graph decimals on number lines (4-S.8)
      • Graph fractions as decimals on number lines (4-S.10)
      • Convert fractions and mixed numbers to decimals (4-S.12)
      • Convert decimals to fractions and mixed numbers (4-S.13)
      • Convert decimals between standard and expanded form using fractions (4-S.14)

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

      • Compare money amounts (4-L.3)
      • Compare decimals on number lines (4-S.17)
      • Compare decimal numbers (4-S.18)
      • Put decimal numbers in order I (4-S.19)
      • Put decimal numbers in order II (4-S.20)
      • Compare decimals and fractions on number lines (4-S.21)

4.M04.B-O Operations and Algebraic Thinking

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

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

    • 4.M04.B-O.1.1.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.

      • Multiplication facts to 12: find the missing factor (4-D.5)
      • Properties of multiplication (4-D.28)

    • 4.M04.B-O.1.1.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.

      • Estimate products: word problems (4-D.34)
      • Multiply a 2-digit number by a 2-digit number: word problems (4-D.43)
      • Multiply a 2-digit number by a larger number: word problems (4-D.47)
      • Multiply numbers ending in zeroes: word problems (4-D.49)
      • Division word problems: factors up to 12 (4-E.4)
      • Divide larger numbers by 1-digit numbers: word problems (4-E.18)
      • Divide numbers ending in zeroes by multi-digit numbers: word problems (4-E.29)
      • Addition, subtraction, multiplication, and division word problems (4-F.5)
      • Estimate sums, differences, products, and quotients: word problems (4-F.6)
      • Compare customary units by multiplying (4-M.10)
      • Convert between metric and customary units (4-M.21)
      • Divide by 2-digit numbers: word problems (4)

    • 4.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.

      • Divide 2-digit numbers by 1-digit numbers: interpret remainders (4-E.14)
      • Divide larger numbers by 1-digit numbers: interpret remainders (4-E.20)
      • Word problems with extra or missing information (4-F.7)
      • Solve word problems using guess-and-check (4-F.8)
      • Multi-step word problems (4-F.12)
      • Choose numbers with a particular sum, difference, product, or quotient (4-F.15)
      • Write variable expressions: word problems (4-G.2)
      • Write variable equations to represent word problems (4-G.4)
      • Find two numbers based on sum and difference (4-J.2)
      • Find two numbers based on sum, difference, product, and quotient (4-J.3)

    • 4.M04.B-O.1.1.4 Identify the missing symbol (+, –, ×, ÷, =, <, and >) that makes a number sentence true (single-digit divisor only).

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

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

    • 4.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 one-digit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite.

      • Prime and composite: up to 20 (4-A.18)
      • Choose the multiples of a given number up to 12 (4-D.6)
      • Identify factors (4-D.7)
      • Choose numbers with a particular product (4-D.8)
      • Divisibility rules (4-E.26)

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

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

    • 4.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.

      • Multiplication input/output tables (4-D.53)
      • Input/output tables with addition, subtraction, multiplication, and division (4-F.4)
      • Use a rule to complete a number pattern (4-K.5)
      • Complete an increasing number pattern (4-K.9)
      • Complete a geometric number pattern (4-K.10)
      • Number patterns: word problems (4-K.11)
      • Number patterns: mixed review (4-K.12)
      • Time patterns (4-N.10)
      • Complete a table for a two-variable relationship (4)

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

      • Input/output tables with addition, subtraction, multiplication, and division (4-F.4)
      • Complete a table for a two-variable relationship (4)

    • 4.M04.B-O.3.1.3 Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).

      • Write a two-variable equation (4)

4.M04.C-G Geometry

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

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

    • 4.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 two-dimensional figures.

      • Points, lines, line segments, rays, and angles (4-V.3)
      • Parallel, perpendicular, and intersecting lines (4-V.4)
      • Acute, right, obtuse, and straight angles (4-Y.1)

    • 4.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.

      • Acute, obtuse, and right triangles (4-W.1)
      • Classify triangles (4-W.3)
      • Parallel sides in quadrilaterals (4-W.4)
      • Classify quadrilaterals (4-W.10)
      • Identify three-dimensional figures (4-Z.1)

    • 4.M04.C-G.1.1.3 Recognize a line of symmetry for a two-dimensional 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).

      • Identify lines of symmetry (4-X.1)

4.M04.D-M Measurement and Data

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

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

    • 4.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 ofa smaller unit. A table of equivalencies will be provided.

      • Which customary unit is appropriate? (4-M.4)
      • Compare and convert customary units of length (4-M.5)
      • Compare and convert customary units of weight (4-M.6)
      • Compare and convert customary units of volume (4-M.7)
      • Compare and convert customary units (4-M.8)
      • Conversion tables - customary units (4-M.9)
      • Convert mixed customary units (4-M.11)
      • Which metric unit is appropriate? (4-M.13)
      • Compare and convert metric units of length (4-M.14)
      • Compare and convert metric units of weight (4-M.15)
      • Compare and convert metric units of volume (4-M.16)
      • Compare and convert metric units (4-M.17)
      • Conversion tables - metric units (4-M.18)
      • Convert time units (4-N.1)
      • Fractions of time units (4-N.4)

    • 4.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.

      • Find the change, price, or amount paid (4-L.7)
      • Price lists with addition and subtraction (4-L.8)
      • Add and subtract mixed customary units (4-M.12)
      • Add and subtract mixed time units (4-N.3)
      • Elapsed time (4-N.6)
      • Elapsed time: word problems (4-N.7)
      • Find start and end times: multi-step word problems (4-N.8)
      • Solve decimal problems using diagrams (4-T.12)
      • Add and subtract fractions with unlike denominators in recipes (4)

    • 4.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.

      • Perimeter of polygons (4-AA.2)
      • Find the area or missing side length of a rectangle (4-AA.7)
      • Compare area and perimeter of two figures (4-AA.11)
      • Relationship between area and perimeter (4-AA.12)
      • Use area and perimeter to determine cost (4-AA.16)

    • 4.M04.D-M.1.1.4 Identify time (analog or digital) as the amount of minutes before or after the hour.

      • Time words: o'clock, half, quarter (2-Q.6)

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

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

    • 4.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).

      • Create line plots (4-I.7)

    • 4.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).

      • Interpret line plots (4-I.6)

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

      • Create line graphs (4-I.3)
      • Create bar graphs (4-I.5)
      • Create line plots (4-I.7)

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

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

    • 4.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.

      • Measure angles with a protractor (4-Y.6)
      • Estimate angle measurements (4-Y.8)

    • 4.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.)

      • Adjacent angles (4-Y.9)