• Grade 3 Overview

    1. Make sense of problems and persevere in

    solving them.

    2. Reason abstractly and quantitatively.

    3. Construct viable arguments and critique

    the reasoning of others.

    4. Model with mathematics.

    5. Use appropriate tools strategically.

    6. Attend to precision.

    7. Look for and make use of structure.

    8. Look for and express regularity in repeated



    Operations and Algebraic Thinking 3.OA

    Represent and solve problems involving multiplication and division.

    1. 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.

    2. 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.

    3. 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.1

    4. 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 = ?.

    Understand properties of multiplication and the relationship

    between multiplication and division.

    5. Apply properties of operations as strategies to multiply and

    divide.2 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


    6. Understand division as an unknown-factor problem. For example, find

    32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

    Multiply and divide within 100.

    7. 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.

    Solve problems involving the four operations, and identify and

    explain patterns in arithmetic.

    8. 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.3

    9. 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.

    1See Glossary, Table 2.

    2Students need not use formal terms for these properties.

    3This standard is limited to problems posed with whole numbers and having wholenumber

    answers; students should know how to perform operations in the conventional

    order when there are no parentheses to specify a particular order (Order of


    Common Core State Standards for MAT HEMAT ICS

    grade 3 | 24

    Number and Operations in Base Ten 3.NBT

    Use place value understanding and properties of operations to

    perform multi-digit arithmetic.4

    1. Use place value understanding to round whole numbers to the nearest

    10 or 100.

    2. 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.

    3. 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.

    Number and Operations—Fractions5 3.NF

    Develop understanding of fractions as numbers.

    1. 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.

    2. Understand a fraction as a number on the number line; represent

    fractions on a number line diagram.

    a. 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.

    b. 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


    3. Explain equivalence of fractions in special cases, and compare

    fractions by reasoning about their size.

    a. Understand two fractions as equivalent (equal) if they are the

    same size, or the same point on a number line.

    b. 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.

    c. 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.

    d. 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.

    Measurement and Data 3.MD

    Solve problems involving measurement and estimation of intervals

    of time, liquid volumes, and masses of objects.

    1. 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.

    4A range of algorithms may be used.

    5Grade 3 expectations in this domain are limited to fractions with denominators 2, 3,

    4, 6, and 8.

    Common Core State Standards for MAT HEMAT ICS

    grade 3 | 25

    2. Measure and estimate liquid volumes and masses of objects using

    standard units of grams (g), kilograms (kg), and liters (l).6 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.7

    Represent and interpret data.

    3. Draw a scaled picture graph and a scaled bar graph to represent a

    data set with several categories. Solve one- and two-step “how many

    more” and “how many less” problems 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.

    4. 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.

    Geometric measurement: understand concepts of area and relate

    area to multiplication and to addition.

    5. Recognize area as an attribute of plane figures and understand

    concepts of area measurement.

    a. A square with side length 1 unit, called “a unit square,” is said to

    have “one square unit” of 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.

    6. Measure areas by counting unit squares (square cm, square m, square

    in, square ft, and improvised units).

    7. 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 wholenumber

    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.

    Geometric measurement: recognize perimeter as an attribute of

    plane figures and distinguish between linear and area measures.

    8. 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


    6Excludes compound units such as cm3 and finding the geometric volume of a


    7Excludes multiplicative comparison problems (problems involving notions of

    “times as much”; see Glossary, Table 2).

    Common Core State Standards for MAT HEMAT ICS

    grade 3 | 26

    Geometry 3.G

    Reason with shapes and their attributes.

    1. 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.

    2. 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.