Math Scope and Sequence

Key Topics in Fourth Grade Math:

Operations and Algebraic Thinking

Numbers and Operations (Base 10)

  • Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • Multiply or divide to solve word problems involving multiplicative comparison
  • Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 - 100 is a whole number is prime or composite.
  • 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.
  • Use patterns and relationships to develop strategies to remember basic multiplication and division facts.
  • Use patterns to multiply by 10 and 100
  • Use organizational structures to analyze and describe patterns and relationships and describe the relationship between two sets of related data such as ordered pairs in a table.

  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • Use place value understanding to round multi-digit whole numbers to any place.
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • Divide to solve problems using no more than one-digit divisors and three-digit dividends.
  • Recall and apply basic multiplication and division facts through 12 x 12.

Number & Operations - Fractions

  • Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.
  • Understand a fraction a/b with a>1 as the sum of fractions 1/b.
  • Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
  • Use decimal notation for fractions with denominators 10 or 100.
  • Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, eq., by using a visual model.

Measurement and Data

Geometry

  • Know relative sizes of measurements units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
  • Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects and 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. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale
  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
  • Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurements:
  • Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  • Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.
  • Interpret bar graphs
  • Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
  • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence of absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles
  • 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 matching parts. Identify line-symmetric figures and draw lines of symmetry.
  • Use translations, reflections, and rotations to verify that two shapes are congruent.
  • Demonstrate transformation: translations, reflections, and rotations using concrete models
  • Describe two-dimensional and three-dimensional figures using attributes and formal geometric language (vocabulary)


Math Units

4th Grade

Topic

Category

Standard

Quarter

UNIT 1: Number & Operations in Base Ten, Part 1

Review of Third Grade Skills

1st

L1: Understand Place Value

Numbers & Operations in Base Ten

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

1st

L2: Compare Whole Numbers

Numbers & Operations in Base Ten

Read & Write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of the comparisons.

1st

L3: Add and Subtract Whole Numbers

Numbers & Operations in Base Ten

Fluently add and subtract multi-digit whole numbers to any place.

1st

L4: Round Whole Numbers

Numbers & Operations in Base Ten

Use place value understanding to round multi-digit whole numbers to any place.

1st

UNIT 1 Test : Number and Operations Base 10, Part 1

UNIT 2:  Operations and Algebraic Thinking

L5: Understand Multiplication

Operations & Algebraic Thinking

Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.

1st

L6: Multiplication & Division with Word Problems

Operations & Algebraic Thinking

Multiply or Divide to solve word problems involving multiplicative comparison.

1st

L7: Multiples and Factors

Operations & Algebraic Thinking

Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 - 100 is a multiple of a given one-digit number. Determine whether a given whole number is in the range 1 - 100 is prime or composite.

1st

L8: Number & Shape Patterns

Operations & Algebraic Thinking

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.

1st

L9: Model Multi-Step Problems

Operations & Algebraic Thinking

Solve multi-step word problems with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

1st

L10: Solve Multi-Step Problems

Operations & Algebraic Thinking

Solve multi-step word problems with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

1st

UNIT 2 Test : Operations & Algebraic Thinking

UNIT 3 : Numbers & Operations in Base Ten, Part 2

L11: Multiply Whole Numbers

Number & Operations in Base Ten

Multiply a whole number up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

2nd

L12: Division with Whole Numbers  

Number & Operations in Base Ten

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculations by using equations, rectangular arrays and/or area models.

2nd

UNIT 3 Test : Numbers & Operations in Base Ten, Part 2

UNIT 4 : Number & Operations - Fractions

L13: Understand Equivalent Fractions

Number & Operations - Fractions

Explain why a fraction a/b is equivalent to a fraction (n X a)/ (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

2nd

L14: Compare Fractions

Number & Operations - Fractions

Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.

2nd

L15: Understand Fraction Addition and Subtraction

Number & Operations - Fractions

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions.

2nd

L16: Add and Subtract Fractions

Number & Operations - Fractions

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

2nd

L17: Add and Subtract Mixed Numbers

Number & Operations - Fractions

Decompose a fraction into a sum of fractions with the same denominator in more that one way, recording each decomposition by an equation. Justify decompositions.

Add and Subtract mixed numbers with like denominators.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

2nd

L18: Understand Fraction Multiplication

Number & Operations - Fractions

Understand a fraction a/b as a multiple of 1/b.

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

3rd

L19: Multiply Fractions

Numbers & Operations - Fractions

Solve word problems involving multiplication of a fraction by a whole number.

3rd

L20: Fractions as Tenths and Hundredths

Numbers & Operations - Fractions

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

3rd

L21: Relate Decimals and Fractions

Numbers & Operations - Fractions

Use decimal notation for fractions with denominators 10 or 100.

3rd

L22: Compare Decimals

Numbers & Operations - Fractions

Compare two decimals to hundreths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole number. Record the results of comparisons with the symbols <. =, or >, and justify the conclusion.

3rd

Unit 4 Test : Number & Operations - Fractions

Unit 5 : Measurement & Data

L23: Convert Measurements

Measurement & Data

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l , ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

3rd

L24: Time and Money

Measurement & Data

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

3rd

L25: Length, Liquid Volume, and Mass

Measurement & Data

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

3rd

L26: Perimeter and Area

Measurement & Data

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

3rd

L27: Line Plots

Measurement & Data

Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

3rd

L28: Understand Angles

Measurement & Data

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle.

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4th

L29: Measure and Draw Angles

Measurement & Data

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4th

L30: Add and Subtract with Angles

Measurement & Data

Recognize angle measures as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

4th

Unit 5 Test : Measurement & Data

Unit 6 : Geometry

L31: Points, Lines, Rays and Angles

Geometry

Draw points, lines, and line segments, rays and angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4th

L32: Classify Two-Dimensional Figures

Geometry

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.

4th

L33: Symmetry

Geometry

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 matching parts. Identify line-symmetric figures and draw lines of symmetry.

4th

Unit 6 Test : Geometry