Caudle, Kenneth L
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 Vienna Elementary School
 What Your Child Will Learn in Math

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
reasoning.
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 wholenumber 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
property.)
6. Understand division as an unknownfactor 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 onedigit numbers.
Solve problems involving the four operations, and identify and
explain patterns in arithmetic.
8. Solve twostep 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
Operations).
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 multidigit 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 onedigit 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
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 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 onestep 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 twostep “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 wholenumber 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 wholenumber products as
rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle
with wholenumber 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 nonoverlapping rectangles and adding
the areas of the nonoverlapping 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.
6Excludes compound units such as cm3 and finding the geometric volume of a
container.
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.