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Common Core Mapping for Grade 3


In Grade 3, instructional time should focus on four critical areas:
(1) developing understanding of multiplication and division and strategies for multiplication and division within 100
(2) developing understanding of fractions, especially unit fractions (fractions with numerator 1)
(3) developing understanding of the structure of rectangular arrays and of area
(4) describing and analyzing two-dimensional shapes.

Related Topics:
Common Core for Mathematics

Lesson Plans and Worksheets for Common Core Grade 3

Operations and Algebraic Thinking







Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.



Meaning of multiplication


Array Maker


Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of  shares or a number of groups can be expressed as 56 ÷ 8.


Meaning of Division

Meaning of Division



Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Word Problems

Word Problems

Multiplication and division word problems

Word Problems


Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?

Multiplication Division Equations

Multiplying 1-digit numbers

1-digit Division

Basic division

Multiplication Equations

Division Equations


Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Properties of Operations

Distributive & Commutative Properties

Distributive Property

Associative Property

Properties of multiplication 1

Commutative Property

Associative Property


Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.


Missing Factor

Missing Factor

Relate division to multiplication

Missing Factor Game


Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Multiply & Divide

Multiplication Facts

Division Facts

Number Line

Multiplication Games

Division Games


Solve two-step word problems using the four operations. 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.

Word Problems

Multi-step word problems with whole numbers

Word Problem Games


Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Arithmetic Patterns

Patterns in Multiplication and Division

Math Patterns

Arithmetic Patterns

Number and Operations in Base Ten







Use place value understanding to round whole numbers to the nearest 10 or 100.


Round to nearest Ten

Round to nearest Hundred

Rounding (10)

Rounding (100)


Rounding Games


Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add & Subtract

Add Measurements

Addition with regrouping

Subtraction with regrouping

Addition, Subtraction Games


Multiply one-digit whole numbers by multiples of 10 in the range 10 -90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Multiply by Multiples of 10

Multiply by multiples of 10

Word Problems

Multiplication Games


Number and Operations and Fractions







Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Understand Fractions

Partition into equal parts

Unit Fractions

Build Non-Unit Fractions

Fractions greater than one

Recognize fractions

Numerators and denominators

Build fractions

Identify Fractions

Fraction Games




Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Fractions on the Number Line

Unit Fractions - Number Line

Fractions - Number Line

Equivalent Fractions - Number Line

Place Fractions on the Number Line

Compare Fractions on the Number Line

Fractions on the number line 1

Fractions on the number line 2

Find 1 on the number line

Fraction Games






Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Equivalent Fractions

Compare Unit Fractions - Fraction Strips

Compare Unit Fractions - different sized models

Fractions - Specify the Whole

Fractions - Change the Whole

Equivalent Fractions - Same size

Equivalent Fractions- Number Line

Equivalent Fractions - Visual Model

Whole Number Fractions

Fractions with Same Numerator

Equivalent Fractions

Comparing fractions (same denominator)

Equivalent fraction models

Compare fractions (same numerator)

Fraction Games

Measurement and Data







Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Measure Time

Time Interval Word Problems

Time Interval - Number Line

Elapsed Time

Telling Time

Time Difference

Time Games


Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Measure Liquid Volume & Mass

Word Problems - Metric Weight

Decompose a Liter

Mass word problems

Volume word problems

Milliliters & Liters


Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step Ԩow many moreԠand Ԩow many lessԠproblems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Picture & Bar Graphs

Generate and Organize Data

Create Bar Graphs

Problems involving Graphs

Create bar charts

Create picture and bar charts

Picture graph word problems



Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units, whole numbers, halves, or quarters.

Measure Lengths

Interpret Data using Line Plots

Draw Line Plots

Create line plots

Measure It

Measurement Games




Recognize area as an attribute of plane figures and understand concepts of area measurement.

A. A square with side length 1 unit, called ԡ unit square,Ԡis said to have ԯne square unitԠof area, and can be used to measure area.

B. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Understand Area

Area of Plane Figures

Decompose and Recompose Shapes

Area of Rectangle

Area (Unit squares)

Find Area

Area Explorer


Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Measure Area

Area Word Problems

Find Area

Measure Area

Area Explorer






Relate area to the operations of multiplication and addition.

A. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

B. 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.

C. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a ×b and a ×c. Use area models to represent the distributive property in mathematical reasoning.

D. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Area of Rectangles

Find Area - Decompose and Composite Figures

Area of Rectangles


Find area by multiplying

Compare areas by multiplying

Decompose shapes to find area

Area and the distributive property

Area Games


Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Perimeter of Polygons

Perimeter of Rectangles

Compare area and perimeter

Finding perimeter


Perimeter Games









Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.


Compare and Classify Quadrilaterals

Categorize quadrilaterals


Shape Games


Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Partition Shapes

Fraction Strips

Fraction - Area Model

Fractional Parts

Cutting shapes into equal parts

Equal Parts

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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