• Third Grade Common Core Learning Standards
MATH

Operations & Algebraic Thinking
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.
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 property.)
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.
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.

Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.

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 & Operations—Fractions
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 line.
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 & Data
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.
2. 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.
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 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.
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 perimeters.

Geometry
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.

Measurement & Data 2.MD
Measure and estimate lengths in standard units.

1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the
two measurements relate to the size of the unit chosen.
3. Estimate lengths using units of inches, feet, centimeters, and meters.
4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard
length unit.
Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by
using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the
numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
Work with time and money.
7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately.
Example: If you have 2 dimes and 3 pennies, how many cents do you have?
Represent and interpret data.
9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated
measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in
whole-number units.
10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve
simple put-together, take-apart, and compare problems1 using information presented in a bar graph.
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1 See Glossary, Table 1.
Geometry 2.G
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half
of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical
wholes need not have the same shape.
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1 Sizes are compared directly or visually, not compared by measuring.