© Copyright 2014 J. Banfill. All Rights Reserved.Legal Notice
Note: The specification of each standard is followed by links to lessons on AAAMath.com/AAAKnow.com that may be relevant to that standard.
Grade 3 Common Core State Standards
Grade 3 » Operations & Algebraic Thinking
Represent and solve problems involving multiplication and division.
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.
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.
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
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.
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 property.)
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.
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.
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
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.
Grade 3 » Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Use place value understanding to round whole numbers to the nearest 10 or 100.
Fluently add and subtract within 1000 using strategies and algorithms based on
place value, properties of operations, and/or the relationship between addition
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
Grade 3 » Number & Operations—Fractions¹
Develop understanding of fractions as numbers.
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 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.
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
Grade 3 » Measurement & Data
Solve problems involving measurement and estimation.
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 and estimate liquid volumes and masses of objects using standard units
of grams (g), kilograms (kg), and liters (l).1 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.
Represent and interpret data.
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.
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.
Recognize area as an attribute of plane figures and understand concepts of area
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.
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.
Measure areas by counting unit squares (square cm, square m, square in, square
ft, and improvised units).
Relate area to the operations of multiplication and addition.
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.
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.
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.
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.
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.
Grade 3 » Geometry
Reason with shapes and their attributes.
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.
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.
Portions © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Portions © John Banfill 2014