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Common Core Mapping for Grade 4

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Common Core for Mathematics

In Grade 4, instructional time should focus on three critical areas:
(1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends
(2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers
(3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Operations and Algebraic Thinking





Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiplicative Comparison

Comparing with multiplication

Multiplication Statements


Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Multiply or Divide Word Problems

Multiplication and division word problems


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.

Multistep Problems

Check Multi-step Problems

Multi-step word problems with whole numbers


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 in the range 1- 100 is prime or composite.

Factors, Multiples Prime, Composite, Divisibility Rules

Prime numbers up to 20

Prime numbers up to 50

Composite numbers

Find Factors Using a Model

Factors & Multiples

Factor & Multiple Games


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. For example, given the rule ԁdd 3Ԡand the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Number & Shape Patterns

Math patterns

Function Machine

Number and 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Place Values

Multiplication Equation

10 times Value

Understanding place value

Place Values

Place Values

Place Value Games


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.

Whole Numbers

Understanding whole number representations

Compare Numbers

Place Value Games


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

Rounding Numbers

Rounding whole numbers

Rounding Games


Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Add & Subtract Numbers

4-digit addition

4-digit subtraction

Addition, Subtraction Games


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.

Multiply Numbers

Multiply 2-digit by 1-digit

Multiply 3-digit by 1-digit

Multiply 4-digit by 1-digit

Multiply 2-digit by 2-digit

Multiplication Games


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 Numbers

Divide 2-digit by 1-digit

Divide 3-digit by 1-digit

Divide 4-digit by 1-digit

Division without remainders

Division with remainders

Division Games

Number and Operations and Fractions





Explain why a fraction a/b is equivalent to a fraction (n-a)/(n-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.

Equivalent Fractions

Equivalent Fractions

Equivalent fractions

Visualizing equivalent fractions

Fractions cut & copy

Fraction Games


Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. 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, e.g., by using a visual fraction model.

Compare Fractions

Compare Fractions

Compare Fractions

Comparing fractions

Ordering fractions

Fraction Games

4.NF.B.3, 4.NF.B.3a, 4.NF.B.3b

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

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

B. 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, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Add, Subtract & Decompose Fractions

Decompose Fractions using Tape Diagrams

Fraction Worksheets

Adding fractions with like denominators

Subtracting fractions with like denominators

Decomposing fractions

Fraction word problems

Fraction Games


C. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Improper Fractions, Add & Subtract Mixed Numbers

Convert improper fractions to mixed numbers

Adding and subtracting mixed numbers

Fraction Games


D. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Fraction Word Problems

Adding and subtracting fractions with like denominators word problems

Fraction Word Problems

Fraction word problems

Fraction Games

4.NF.B.4, 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

A. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

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. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

C. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Multiply Fractions & Whole Numbers

Multiply Fractions & Whole Numbers

Multiplying fractions and whole numbers word problems


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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Add Fractions with denominators 10 & 100

Add fractions with denominators 10 and 100

Denominators 10 and 100


Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Decimals & Fractions

Converting decimals to fractions

Decimals on the number line (Tenths)

Decimals on the number line (Hundredths)

Fractions as division by a power of 10

Decimal Games


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, e.g., by using a visual model.

Compare Decimals

Comparing decimals

Comparing Decimals

Decimal Games

Measurement and 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...


Metric Length Conversion

Metric Weight Conversion

Unit sense

Measurement units

Measurement Games


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.

Measurement Word Problems

Customary unit word problems

Metric unit word problems

Time word problems

Money word problems

Measurement Worksheets


Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Area & Perimeter

Calculate Area & Perimeter

Area & Perimeter Word Problems

Word Problems

Area & Perimeter Games


Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Line Plots

Interpret line plots

Line Plots

4.MD.C.5, 4.MD.C.5a, 4.MD.C.5b

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

A. 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 1/360 of a circle is called a one-degree angle, and can be used to measure angles.

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

Circles & Angles

Understanding angles

Naming angles

Benchmark angles

Estimate Measures of Angles


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

Measure & Draw Angles

Drawing angles

Measuring angles

Angle Games


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, e.g., by using an equation with a symbol for the unknown angle measure.

Add Angles

Decomposing angles

Add Angles

Angle Games






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


Use Right Angles

Perpendicular Lines

Angle types

Drawing lines

Rays, lines and line segments

Parallel and perpendicular lines

Geometry Games


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.


Classify shapes

Triangle types

Quadrilateral types

Geometry Games


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.

Lines of Symmetry

Axis of symmetry

Symmetry Games

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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