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Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 1
Sequenced Units for the Common Core State Standards in Mathematics Grade 3 In the years prior to Grade 3 students gained an understanding of number and used strategies based on place value, properties of operations, and the
relationship between addition and subtraction to add and subtract within 1000. They worked with standard units of measure for length and described attributes
of shapes.
Two major emphases of the Grade 3 year are the operations of multiplication and division and the concept of fractions. These concepts are introduced early in
the year in order to build a foundation for students to revisit and extend their conceptual understanding with respect to these concepts as the year progresses.
By the end of the year, students recall all products of two single-digit numbers. Third grade students develop understanding of fractions as numbers, and
compare and reason about fraction sizes. This work with fractions is a cornerstone for developing reasoning skills and conceptual understanding of fraction size
and fractions as part of the number system throughout this year and their future work with fractions and ratios. To continue the study of geometry, students
describe and analyze shapes by their sides, angles, and definitions. In the final unit in this sequence of units, students generalize and apply strategies for
computational fluency.
This document reflects our current thinking related to the intent of the Common Core State Standards for Mathematics (CCSSM) and assumes
160 days for instruction, divided among 15 units. The number of days suggested for each unit assumes 45-minute class periods and is included to convey how
instructional time should be balanced across the year. The units are sequenced in a way that we believe best develops and connects the mathematical content
described in the CCSSM; however, the order of the standards included in any unit does not imply a sequence of content within that unit. Some standards may be
revisited several times during the course; others may be only partially addressed in different units, depending on the focus of the unit. Strikethroughs in the text of
the standards are used in some cases in an attempt to convey that focus, and comments are included throughout the document to clarify and provide additional
background for each unit.
Throughout Grade 3, students should continue to develop proficiency with the Common Core's eight Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them. S. Use appropriate tools strategically.
2. Reason abstractly and quantitatively. 6. Attend to precision.
3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.
4. Model with mathematics. 8. Look for and express regularity in repeated reasoning.
These practices should become the natural way in which students come to understand and do mathematics. While, depending on the content to be understood or
on the problem to be solved, any practice might be brought to bear, some practices may prove more useful than others. Opportunities for highlighting certain
practices are indicated in different units in this document, but this highlighting should not be interpreted to mean that other practices should be neglected in
those units.
When using this document to help in planning your district's instructional program, you will also need to refer to the CCSSM document, relevant progressions
documents for the CCSSM, and the appropriate assessment consortium framework.
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ellan.com
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 2
Unit 1: Exploring equal groups as a foundation
for multiplication and division. Suggested
number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In Grade 2 students have added groups of objects by skip-counting and using repeated addition (2.0A.C.4). In this unit students connect these concepts to multiplication and division
by interpreting and representing products and quotients. Students begin developing these concepts by working with numbers with which they are more familiar, such as 2s, 5s,
and 10s, in addition to numbers that are easily skip counted, such as 3s and 4s. Since multiplication is a critical area for Grade 3, students will build on these concepts throughout
the year, working towards fluency by the end of the year.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 3.0A
A. Represent and solve problems involving
multiplication and division.
1. Interpret products of whole numbers, e.g.,
interpret 5 x 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 x 7.
2. Interpret whole-number quotients of whole
numbers, e.g., interpret 56 x 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.OA.1.1 Represent a situation in which a number of
groups can be expressed using multiplication. (MS)
3.OA.1.2 Identify a situation in which a number of
groups can be expressed using multiplication. (MS)
3.OA.1.3 Draw an array. (MS)
3.OA.1.4 Explain an array. (MS)
3.OA.1.5 Find the product using objects in groups.
3.OA.1.6 Find the product using objects in arrays.
3.OA.1.7 Find the product using objects in area
models.
3.OA.1.8 Find the product using measurement
quantities.
3.OA.1.9 Explain the objects in equal size groups.
(MS)
3.OA.2.1 Partition a whole number into equal shares
using arrays. (MS)
3.OA.2.2 Partition a whole number into equal parts
using area.
3.OA.2.3 Partition a whole number into equal parts
using measurement quantities.
3.OA.2.4 Identify each number in a division
expression as a quotient, divisor, and/or dividend.
(MS)
3.OA.2.5 Describe a situation in which a number of
groups can be expressed using division. (MS)
3.OA.2.6 Identify a situation in which a number of
groups can be expressed using division. (MS)
In 3.0A.A.1 situations with
discreet objects should be
explored first when developing a
conceptual understanding of
multiplication, followed by
measurement examples involving
area models.
3.0A.A.2 will be readdressed in unit
7 in order to provide students the
opportunity to develop
computational strategies as they
extend the range of numbers with
which they compute.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 3
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.
C. 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 x 5 =
40, one knows 40 x 5 = 8) or properties
3.OA.3.1 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using drawings. (MS)
3.OA.3.2 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.3 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using equations.
3.OA.3.4 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.5 Explain that an unknown number is
represented with a symbol/variable.
3.OA.3.6 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using drawings. (MS)
3.OA.3.7 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.8 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using equations. (MS)
3.OA.3.9 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.10 Divide an area by side length to find the
unknown side length
3.OA.7.1 Fluently (accurately and quickly) divide with
a dividend up to 100.
3.OA.7.2 Fluently (accurately and quickly) multiply
numbers 0-10.
3.OA.7.3 Memorize and recall my multiples from 0-9.
3.OA.7.4 Recognize the relationship between
3.0A.A.3 will be readdressed in unit
7 and finalized in unit 14 to include
measurement quantities in order to
provide students multiple
opportunities to develop and
practice these concepts.
3.0A.C.7 will be readdressed in unit 7
and unit 15 in order to provide
students the opportunity to develop
computational strategies as they
extend the range of numbers with
which they compute.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 4
of operations. By the end of Grade 3,
know from memory all products of two
one-digit numbers.
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
multiplication and division.
Students use concrete objects or
pictures to help conceptualize and
solve problems (MP.1). They use
arrays and other representations to
model multiplication and division
(MP.4) and contextualize given
expressions (MP.2).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 5
Unit 2: Developing conceptual understanding
of area. Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
This unit provides ample time, and should include multiple experiences, for students to explore the connections among counting tiles, skip counting the number of tiles in rows or
columns, and multiplying the side lengths of a rectangle to determine area. Students' understanding of these connections is critical content at this grade, and must occur early in the
school year, thereby allowing time for understanding and fluency to develop across future units.2
Common Core State Standards for Mathematical
Content 0perations and Algebraic Thinking - 3.0A
B. 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 x 4 = 24 is
known, then 4 x 6 = 24 is also known.
(Commutative property of multiplication.) 3 x
5 x 2 can be found by 3 x 5
= 15, then 15 x 2 = 30, or by 5 x 2 = 10, then
3 x 10 = 30. (Associative property of
multiplication.) Knowing that 8 x 5 = 40 and
8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) =
(8 x 5) + (8 x 2) = 40 + 16 =
56. (Distributive property.)
Note:2
Students need not use formal terms for
these properties. Measurement and Data - 3.MD
C. 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.
3.OA.5.1 Apply the properties to multiply 2 or more
factors using different strategies.
3.OA.5.2 Decompose an expression to represent the
distributive property.
3.OA.5.3 Justify the correctness of a problem based
on the use of the properties (commutative,
associative, distributive).
3.OA.5.4 Use properties of operations to construct
and communicate a written response based on
explanation/reasoning.
3.OA.5.5 Use properties of operations to clearly
construct and communicate a complete written
response.
3.MD.5a.1 Identify what a unit square is and know it
can be used to measure area of a figure.
3.0A.B.5 will be readdressed in unit
9 with a focus on the distributive
property and in unit 12 with a focus
on the associative property.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 6
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.
Common Core State Standards for Mathematical
Practice 2. Reason abstractly and quantitatively.
6. Attend to precision.
7. Look for and make use of structure.
3.MD.5b.1 Relate the area to real world objects.
3.MD.5b.2 Recognize area as an attribute of plane
figures with a visual model.
3.MD.5b.3 Explain area as an attribute of plane
figures.
3.MD.6.1 Determine the area of an object by
counting the unit squares in cm, m, in., ft., and
other units.
3.MD.6.2 Connect counting squares to multiplication
when finding area.
3.MD.7a.1 Use tiles to show the area of an rectangle.
3.MD.7a.2 Multiply (b x h) or (l x w) to determine the
area of a rectangle.
3.MD.7a.3 Justify that the area of a rectangle will be
the same using different methods. (Tiling and
formula)
Students analyze the structure of
multiplication and division (MP.7)
through their work with arrays
(MP.2) and work towards precisely
expressing their understanding of the
connection between area and
multiplication (MP.6).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 7
Unit 3: Developing strategies for addition and
subtraction. Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In Grade 2 students used addition and subtraction within 1000 using concrete objects and strategies. In this unit students increase the sophistication of computation strategies for
addition and subtraction that will be finalized by the end of the year. This unit introduces the concept of rounding, which provides students with another strategy to judge the
reasonableness of their answers in addition and subtraction situations. Perimeter provides a context in which students can practice both rounding and addition and subtraction (e.g.
estimating the perimeter of a polygon).
Common Core State Standards for
Mathematical Content Number and Operations in Base Ten - 3.NBT
A. 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.NBT.1.1 Explain the process for rounding numbers
using place value.
3.NBT.1.2 Identify the place value of the ones, tens,
and hundreds place in a whole number.
3.NBT.1.3 Round numbers to the nearest hundred.
3.NBT.1.4 Round numbers to the nearest ten.
3.NBT.2.1 Identify and apply the properties of
addition to solve problems.
3.NBT.2.2 Identify and apply the properties of
subtraction to solve problems.
3.NBT.2.3 Check a subtraction problem using
addition.
3.NBT.2.4 Check an addition problem using
subtraction.
3.NBT.2.5 Correctly align digits according to place
value, in order to add or subtract.
3.NBT.2.6 Explain and demonstrate the process of
regrouping.
3.NBT.2.7 Fluently add two 2-digit numbers.
(horizontal and vertical set up)
3.NBT.2.8 Fluently add two 3-digit numbers.
(horizontal and vertical set up)
3.NBT.2.9 Fluently subtract two 2-digit numbers with
and without regrouping. (horizontal and vertical set
up)
3.NBT.2.10 Fluently subtract two 3-digit numbers
with and without regrouping. (horizontal and
vertical set up)
3.NBT.A.1 introduces the concept of
rounding, which is new to students
and will be revisited in unit 8 in the
context of multiplication.
3.NBT.A.2 will be finalized in unit
15 in order to give students time to
reach fluency in addition and
subtraction within 1000 by the end
of the year.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 8
Measurement and Data - 3.MD
D. 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.
Common Core State Standards for
Mathematical Practice
6. Attend to precision.
8. Look for and express regularity in repeated
reasoning.
3.MD.8.1 Calculate the length of the sides when given
the perimeter of an object.
3.MD.8.2 Calculate the perimeter of a polygon when
given the side lengths.
3.MD.8.3 Solve mathematical problems involving
rectangles with equal area and different perimeter.
3.MD.8.4 Solve mathematical problems involving
rectangles with equal perimeter and different area.
3.MD.8.7 Distinguish between the area and the
perimeter.
3.MD.8.8 Relate perimeter and area to the real world.
3.MD.D.5 is the first time perimeter
appears in the CCSS-M. Students
are not expected to use formulas
until Grade 4 (4.MD.A.3). 3.MD.D.5
will be addressed in full in unit 13
after students have been
introduced to and worked with the
concept of area.
Students use precise language to
make sense of their solution in the
context of a problem and the
magnitude of the numbers (MP.6).
Students also generalize algorithms
and strategies and look for shortcuts
(MP.5).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 9
Unit 4: Understanding unit fractions
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In previous grades students have had experience partitioning shapes into fair shares (1.G.A.3 and 2.G.A.3), using words to describe the quantity. In this unit students extend this
understanding to partition shapes and number lines, representing these fair shares using fraction notation. Similar to how students view 1 as the building block of whole numbers,
students learn to view unit fractions as building blocks-understanding that every fraction is a combination of unit fractions.
Common Core State Standards for
Mathematical Content
Geometry - 3.G
A. Reason with shapes and their attributes.
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.
Number and Operations-Fractions5 - 3.NF
A. Develop understanding of fractions as numbers.
1. Understand a fraction 1Ib 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 1Ib 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 1Ib
3.G.2.1 Recognize that shapes can be divided into
equal parts.
3.G.2.2 Separate a given object into equal parts.
3.G.2.3 Describe the area of each part as a fractional
part of the whole.
3.G.2.4 Label each part as a fractional part of the
whole.
3.G.2.5 Partition shapes in multiple ways into parts
with equal areas and express the area as a unit
fraction of the whole.
3.NF.1.1 Explain that the fractional pieces get smaller
as the denominator gets larger.
3.NF.1.2 Explain that the denominator represents the
number of equal parts in the whole. (MS)
3.NF.1.3 Explain that the numerator is a count of the
number of equal parts (3/4 means there are three
¼’s; ¾ = ¼ + ¼ + ¼).
3.NF.1.4 Model fractions as parts of a whole or parts
of a group. (MS)
3.NF.2a.1 Partition (divide) a number line into equal
parts (intervals).
3.NF.2a.2 Identify a given fraction on a number line.
3.NF.2a.3 Represent and recognize a given fraction on
a number line.
The focus of 3.NF.A.1 and 3.NF.A.2a
in this unit is on fractions between
0 and 1. Fractions greater than 1
will be introduced in unit 5.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 10
and that the endpoint of the part based at 0
locates the number 1Ib on the number line.
NOTE: 5
Grade 3 expectations in this
domain are limited to fractions with
denominators 2, 3, 4, 6, and 8.
Common Core State Standards for
Mathematical Practice
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
6. Attend to precision.
Students use number lines to
represent fractions in a new way
(MP.4). It is key for students to have
meaningful conversations around
this concept to develop precise
language about the components of
fractions and location on the number
line (MP.3, MP.6).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 11
Unit 5: Using fractions in measurement and
data Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students extend their work with measurement and data involving whole numbers to include fractional quantities. Measurement and data are used as a context to support
students' understanding of fractions as numbers. In students' work with data, context is important, because data are not just numbers; they are numbers with meaning. Through
experience with measurement, students realize fractions allow us to represent data much more accurately than just representing data with whole numbers.4
Common Core State Standards for
Mathematical Content
Number and Operations-FractionsS - 3.NF
A. 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.
b. Represent a fraction a/b on a number line
diagram by marking off a lengths l/b from O.
Recognize that the resulting interval has size
a/b and that its endpoint locates the number
a/b on the number line.
NOTE: 5
Grade 3 expectations in this domain
are limited to fractions with denominators 2, 3,
4, 6, and 8.
Measurement and Data - 3.MD
B. Represent and interpret data.
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
3.NF.1.1 Explain that the fractional pieces get smaller
as the denominator gets larger.
3.NF.1.2 Explain that the denominator represents the
number of equal parts in the whole. (MS)
3.NF.1.3 Explain that the numerator is a count of the
number of equal parts (3/4 means there are three
¼’s; ¾ = ¼ + ¼ + ¼).
3.NF.1.4 Model fractions as parts of a whole or parts
of a group. (MS)
3.NF.2b.1 Recognize that a fraction a/b represents its
distance from 0 on a number line.
3.NF.2b.2 Recognize that a fraction a/b represents its
location on a number line.
3.MD.4.1 Use a ruler to measure an object to the
nearest whole, half, and quarter inch.
3.MD.4.2 Collect and organize data to create a line
plot (whole numbers, halves, and quarters).
3.MD.4.3 Create a line plot from given or collected
data, where the horizontal scale is marked off in
appropriate units (whole numbers, halves, and
3.NF.A.1 is repeated here to
include fractions greater than 1.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 12
numbers, halves, or quarters.
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
5. Use appropriate tools strategically.
quarters).
3.MD.4.4 Label a line plot to show whole numbers,
halves, and quarters.
3.MD.4.5 Use a line plot to answer questions or solve
problems.
Students use tools to generate
measurement data (MP.5) and make
connections among different
representations of the quantities and
their relation to the given data
context (MP.2).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 13
Unit 6: Solving addition and subtraction
problems involving measurement
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
The focus of this unit is to develop a conceptual understanding of measuring mass, liquid volume, intervals of time, and using measurement as a context for the development of
fluency in addition and subtraction.
Common Core State Standards for
Mathematical Content
Measurement and Data - 3.MD
A. 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). 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
NOTE: 6
Excludes
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
Mathematical Practice 1. Make sense of problems and persevere in solving
them.
5. Use appropriate tools strategically.
4. Model with mathematics.
3.MD.1.1 Explain time intervals.
3.MD.1.2 Identify minute marks on an analog clock.
3.MD.1.3 Identify minute position on a digital clock.
3.MD.1.4 Relate and explain a number line to the
minute marks on a clock.
3.MD.1.5 Use a “time” number line to measure and
solve addition or subtraction word problems to the
nearest minute.
3.MD.1.6 Use a “time” number line to measure and
solve two-step addition and subtraction word
problems to the nearest minute.
3.MD.1.7 Write time to the nearest minute.
3.MD.2.1 Measure liquid volume in metric units
(liters).
3.MD.2.2 Measure mass in metric units (kilograms,
grams).
3.MD.2.3 Estimate liquid volume using metric units
(liters).
3.MD.2.4 Estimate mass in metric units (kilograms,
grams).
3.MD.2.5 Use the appropriate unit to measure the
mass of objects.
3.MD.2.6 Use the appropriate unit to measure the
liquid volume of objects.
3.MD.2.7 Use the four basic operations to solve one
step word problems with mass.
3.MD.2.8 Use the four basic operations to solve one
step word problems with liquid volume.
3.MD.2.9 Use the four basic operations to solve two
step word problems with mass.
3.MD.2.10 Use the four basic operations to solve two
step word problems with liquid volume.
3.MD.A.1 is included here as an
opportunity to model addition and
subtraction situations with time as
the context.
3.MD.A.2 is addressed in full in
unit 14 to include multiplication
and division situations.
Students can apply the mathematics
they know to persevere in solving
problems arising in everyday life,
society, and the workplace
(MP.1l, MP.4). Selecting and using
appropriate
tools supports the development of
measurement concepts by asking
students to reason about which tools
are appropriate and how to use tools
efficiently (MP.5).
Common Core Math Units
Grade 3
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Page 14
Unit 7: Understanding the relationship
between multiplication and division
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
The emphasis of this unit is for students to develop a solid understanding of the connection between multiplication and division. Students recognize that multiplication strategies
can be used to make sense of and solve division problems. This unit provides students a solid foundation in solving problems with equal groups and arrays, which is necessary to
support future success with measurement problems.5
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 3.0A
A. Represent and solve problems involving
multiplication and division.
2. Interpret whole-number quotients of whole
numbers, e.g., interpret 56 x 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. 1NOTE:
1See Glossary, Table 2.
3.OA.2.1 Partition a whole number into equal shares
using arrays. (MS)
3.OA.2.2 Partition a whole number into equal parts
using area.
3.OA.2.3 Partition a whole number into equal parts
using measurement quantities.
3.OA.2.4 Identify each number in a division
expression as a quotient, divisor, and/or dividend.
(MS)
3.OA.2.5 Describe a situation in which a number of
groups can be expressed using division. (MS)
3.OA.2.6 Identify a situation in which a number of
groups can be expressed using division. (MS)
3.OA.3.1 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using drawings. (MS)
3.OA.3.2 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.3 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using equations.
3.OA.3.4 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.5 Explain that an unknown number is
represented with a symbol/variable.
3.0A.A.2 and 3.0A.C.7 are revisited
in this unit to extend the range of
numbers to include all numbers
within 100 when multiplying and
dividing.
3.0A.A.3 includes equal groups,
arrays, and area problem types.
Note that multiplicative compare
problems are introduced in Grade
4 (4.0A.A.2).
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Page 15
B. Understand properties of multiplication and the
relationship between multiplication and division.
6. Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by
finding the number that makes 32 when
multiplied by 8.
C. 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 x 5 =
40, one knows 40 x 5 = 8) or properties
of operations. By the end of Grade 3,
know from memory all products of two
one-digit numbers.
3.OA.3.6 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using drawings. (MS)
3.OA.3.7 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.8 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using equations. (MS)
3.OA.3.9 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.10 Divide an area by side length to find the
unknown side length.
3.OA.6.1 Interpret division as an unknown factor
problem using the fact families.
3.OA.6.2 Interpret division as an unknown factor
problem using a bar model.
3.OA.6.3 Interpret division as an unknown factor
problem using a number line.
3.OA.6.4 Interpret division as an unknown factor
problem using arrays.
3.OA.6.5 Justify the correctness of a problem based
on the understanding of division as an unknown
factor problem.
3.OA.7.1 Fluently (accurately and quickly) divide with
a dividend up to 100.
3.OA.7.2 Fluently (accurately and quickly) multiply
numbers 0-10.
3.OA.7.3 Memorize and recall my multiples from 0-9.
3.OA.7.4 Recognize the relationship between
multiplication and division.
3.0A.C.7 is finalized in unit 15.
This gives students the
opportunity to develop and
practice strategies in order to
achieve fluency by the end of the
year.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 16
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
7. Look for and make use of structure.
Students make sense of and solve
various types of multiplication and
division problems (MP.1) by using
the relationship between the two
operations (MP.7).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 17
Unit 8: Investigating patterns in number and
operations. Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
The focus of this unit is for students to identify arithmetic patterns in order to develop a deeper understanding of number and number relationships. In subsequent units, students will
use the understanding of pattern developed in this unit to strengthen their computational strategies and skills.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 3.OA
D. 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
NOTE: 3This standard is limited to problems
posed with whole numbers and having whole-
number 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).
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.
3.OA.8.1 Construct an equation with a letter
(variable) to represent the unknown quantity.
3.OA.8.2 Explain or demonstrate how to solve two-
step word problems using addition and subtraction
3.OA.8.3 Explain or demonstrate how to solve two-
step word problems using multiplication and
division (Of single digit factors and products less
than 100).
3.OA.8.4 Represent a word problem with an equation
using a letter to represent the unknown quantity.
3.OA.8.5 Solve two-step word problems which
include multiple operations.
3.OA.8.6 Use mental math to estimate the answer of
a single step word problem. (MS)
3.OA.8.7 Use mental math to estimate the answer of
a two-step word problem.
3.OA.8.8 Justify my answers using mental math and
estimation. (MS)
3.OA.9.1 Explain and model the relationship of odd
and even number patterns with addition facts.
Examples:
• Recognize that the sum of two even numbers is
even.
• Recognize that the sum of two odd numbers is
even.
• Recognize that the sum of an even and an odd
number is odd.
3.OA.9.2 Explain and model the relationship of odd
and even number patterns with multiplication facts.
• Recognize that if at least 1 factor is even, the
3.OA.D.8 will be revisited in unit
15 to address the use of equations
and letters for unknown
quantities.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 18
Number and Operations in Base Ten - 3.NBT
A. 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.
3. Multiply one-digit whole numbers by
multiples of 10 in the range 10-90 (e.g., 9
x 80, 5 x 60) using strategies based on
place value and properties of operations.
NOTE: 4A range of algorithms may be used.
Measurement and Data - 3.MD
B. 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.
product will be even.
• Use divisibility rules identify arithmetic patterns.
3.OA.9.3 Use a multiplication table to locate
examples of the commutative, identity, and zero
properties of multiplication.
3.OA.9.4 Use an addition table to locate examples of
the commutative and identity properties of
addition.
3.NBT.1.1 Explain the process for rounding numbers
using place value.
3.NBT.1.2 Identify the place value of the ones, tens,
and hundreds place in a whole number.
3.NBT.1.3 Round numbers to the nearest hundred.
3.NBT.1.4 Round numbers to the nearest ten.
3.NBT.3.1 Correctly align digits according to place
value, in order to multiply.
3.NBT.3.2 Explain and demonstrate the process of
multiplying a two digit number by a one digit
number using various algorithms.
3.NBT.3.3 Multiply 1-digit whole numbers by
multiples of 10 in the range of 1-90 using different
strategies.
3.MD.3.1 Complete a scaled bar graph to represent
data.
3.MD.3.2 Complete a scaled picture graph to
represent data.
3.MD.3.3 Read and analyze data on horizontal and
vertical scaled bar graphs.
3.MD.3.4 Read and analyze data on scaled picture
graphs.
3.MD.3.5 Use information from a bar graph to solve
1-step “how many more” and “how many less”
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 19
Common Core State Standards for
Mathematical Practice
3. Construct viable arguments and critique the
reasoning of others.
7. Look for and make use of structure.
problems.
3.MD.3.6 Use information from a bar graph to solve
2-step “how many more” and “how many less”
problems.
3.MD.3.7 Create problems/scenarios from
information presented on a graph.
Students examine patterns in
arithmetic (MP.7)
and discuss what they discover
(MP.3).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 20
Unit 9: Developing strategies for
multiplication and division Suggested number
of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
The focus for this unit is developing a conceptual understanding of decomposing multiplication problems through the use of the distributive property and the concept of area. Students
are not required to use the properties explicitly, but are encouraged to discuss this concept and use area diagrams to support their reasoning.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 3.0A
B. 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 x 4 = 24 is
known, then 4 x 6 = 24 is also known.
(Commutative property of multiplication.) 3 x
5 x 2 can be found by 3 x 5= 15, then 15 x 2 =
30, or by 5 x 2 = 10, then 3 x 10 = 30.
(Associative property of multiplication.)
Knowing that 8 x 5 = 40 and 8 x 2 = 16, one
can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) =
40 + 16 = 56. (Distributive property.)
Note: 2Students need not use formal terms for
these properties.
Measurement and Data - 3.MD
C. Geometric measurement: understand concepts
of area and relate area to multiplication and to
addition.
7. Relate area to the operations of multiplication
and addition.
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 x b
and a x c. Use area models to represent
the distributive property in mathematical
reasoning.
3.OA.5.1 Apply the properties to multiply 2 or more
factors using different strategies.
3.OA.5.2 Decompose an expression to represent the
distributive property.
3.OA.5.3 Justify the correctness of a problem based
on the use of the properties (commutative,
associative, distributive).
3.OA.5.4 Use properties of operations to construct
and communicate a written response based on
explanation/reasoning.
3.OA.5.5 Use properties of operations to clearly
construct and communicate a complete written
response.
3.MD.7c.1 Use tiling to explain the understanding
of the distributive property in area problems.
3.0A.B.5 will be revisited in unit 12
to address the associative property
of multiplication.
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© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 21
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.
Common Core State Standards for
Mathematical Practice
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
3.MD.7d.1 Explain that a rectilinear figure is
composed of smaller rectangles.
3.MD.7d.2 Model and separate a rectilinear figure
into 2 different rectangles.
3.MD.7d.3 Determine the area of a figure by
separating the figure into smaller rectangles and
adding the area of each rectangle together.
3.MD.7d.4 Solve real world problems involving area
of irregular shapes.
Students use area diagrams and tiling
(MP.5) to model the distributive
property and generalize this
experience to calculations (MP.7,
MP.8).
Common Core Math Units
Grade 3
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Page 22
Unit 10: Understanding equivalent fractions
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students develop a conceptual understanding of equivalence. Multiple types of models and representations should be used to help students develop this understanding.
Students will apply their understanding of equivalence in the next unit as they learn to compare fractions. Through repeated experience locating fractions on the number line,
students will recognize that many fractions label the same point and use this to support their understanding of equivalency.
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions5 - 3.NF
A. Develop understanding of fractions as numbers.
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.
NOTE: SGrade 3 expectations in this domain
are limited to fractions with denominators
2, 3, 4, 6, and 8.
Common Core State Standards for
Mathematical Practice
4. Model with mathematics.
6. Attend to precision.
3.NF.3a/b.1 Recognize and generate equivalent
fractions. (Denominators are 2, 3, 4, 6, and 8)
3.NF.3c.1 Explain that a fraction with the same
numerator and denominator will always equal 1.
3.NF.3c.2 Write a whole number as a fraction.
3.NF.3c.3 Recognize that some fractions are
equivalent to whole numbers.
[3.NF.A.3] The focus of this unit is
around equivalence. Although the
cluster heading includes
comparison of fraction, fraction
comparisons (3.NF.A.3d) will be
addressed in unit 11.
Students develop understanding of
equivalence by modeling fractions
(MP.4) and communicating their
understanding of what it means for
fractions to be equivalent (MP.6).
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Grade 3
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Page 23
Unit 11: Comparing fractions Suggested
number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students build on their prior work with fractions to reason about fraction size and structure to compare quantities. This unit focuses on a single standard to provide time for
students to develop conceptual understanding of fraction comparisons and practice reasoning about size. Students defend their reasoning and critique the reasoning of others using
both visual models and their understanding of the structure of fractions. This reasoning is important to develop a solid understanding of fraction magnitudes.
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions5 - 3.NF
A. Develop understanding of fractions as numbers.
3. Explain equivalence of fractions in special
cases, and compare fractions by reasoning
about their size.
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.
NOTE: 5
Grade 3 expectations in this domain
are limited to fractions with denominators 2, 3,
4, 6, and 8.
Common Core State Standards for
Mathematical Practice
3. Construct viable arguments and critique the
reasoning of others. S. Use appropriate tools
strategically.
7. Look for and make use of structure.
3.NF.3d.1 Compare fractions based on the size of the
numerator and denominator.
3.NF.3d.2 Compare and explain two fractions with
the same denominator by drawing a visual model
(using <,>,=).
3.NF.3d.3 Compare and explain two fractions with
the same numerator by drawing a visual model
(using <,>,=).
Students will use their
understanding of structure (i.e.,
the role of the numerator and
denominator) (MP.7) to reason
about relative sizes of fractions
(MP.3). Students use various tools
to justify their comparisons,
paying particular attention to the
same-sized wholes (MP.5).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 24
Unit 12: Solving problems involving area
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
The focus of this unit is to use area as a context to further develop multiplicative thinking. In this work, students bridge between concrete and abstract thinking, and use strategies to solve
problems. This includes solving problems involving rectangular areas by multiplying side lengths and solving for an unknown number in related multiplication and division equations.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 3.0A
A. Represent and solve problems involving
multiplication and division.
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 x ? = 48, 5 = D ÷ 3, 6 x 6 = ?.
B. 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 x 4 = 24 is
known, then 4 x 6 = 24 is also known.
(Commutative property of multiplication.) 3 x 5 x
2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or
by 5 x 2 = 10, then 3 x 10 = 30. (Associative
property of multiplication.) Knowing that 8 x 5 =
40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2)
= (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive
property.)
NOTE: 2Students need not use formal terms for
these properties.
3.OA.4.1 Determine the unknown number to make a
division equation true with both factors that are ≤
5. (MS)
3.OA.4.2 Determine the unknown number to make a
division equation true with one of the factors is ≤ 5.
(MS)
3.OA.4.3 Determine the unknown number to make a
division equation true. (MS)
3.OA.4.4 Determine the unknown number to make a
multiplication equation true with both factors that
are ≤ 5. (MS)
3.OA.4.5 Determine the unknown number to make a
multiplication equation true with one of the factors
is ≤ 5. (MS)
3.OA.4.6 Determine the unknown number to make a
multiplication equation true. (MS)
3.OA.5.1 Apply the properties to multiply 2 or more
factors using different strategies.
3.OA.5.2 Decompose an expression to represent the
distributive property.
3.OA.5.3 Justify the correctness of a problem based
on the use of the properties (commutative,
associative, distributive).
3.OA.5.4 Use properties of operations to construct
and communicate a written response based on
explanation/reasoning.
3.OA.5.5 Use properties of operations to clearly
construct and communicate a complete written
response.
3.0A.B.5 introduces the
associative property explicitly for
the first time. This property is
fundamental for developing
higher-level computation
strategies.
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Page 25
Measurement and Data - 3.MD
C. Geometric measurement: understand concepts
of area and relate area to multiplication and to
addition.
7. Relate area to the operations of multiplication
and addition.
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.
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
6. Attend to precision.
8. Look for and express regularity in repeated
reasoning.
3.MD.7b.1 Solve word problems using the formula (b
x h) or (l x w). (real world objects)
3.MD.7b.2 Relate product and factors with area and
sides of a rectangle.
In unit 9, students used various
strategies to solve area problems.
In 3.MD.C.7b students recognize
that they can find area in real-
world situations by multiplying side
lengths-without necessarily using
a rectangular array.
Students move in and out of context
to solve these types of problems
(MP.2) and use their repeated
experience with area models to
recognize that area problems can be
solved using multiplication (MP.8).
Students also explain precisely how
an array corresponds to an
expression (MP.6).
Common Core Math Units
Grade 3
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© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
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Page 26
Unit 13: Solving problems involving shapes
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
The focus of this unit is reasoning with shapes and their attributes, including area and perimeter. The standards in this unit strongly support one another because perimeter, like
area, is an attribute of shape. Prior work with area and perimeter allows students differentiate between the two measures in this unit.12
Common Core State Standards for
Mathematical Content
Measurement and Data - 3.MD
D. 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 - 3.G
A. 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.
Common Core State Standards for
Mathematical Practice 1. Make sense of problems and persevere in solving
them.
3. Construct viable arguments and critique the
reasoning of others.
7. Look for and make use of structure.
3.MD.8.1 Calculate the length of the sides when given
the perimeter of an object.
3.MD.8.2 Calculate the perimeter of a polygon when
given the side lengths.
3.MD.8.3 Solve mathematical problems involving
rectangles with equal area and different perimeter.
3.MD.8.4 Solve mathematical problems involving
rectangles with equal perimeter and different area.
3.MD.8.7 Distinguish between the area and the
perimeter.
3.MD.8.8 Relate perimeter and area to the real world.
3.G.1.1 Define shapes according to their attributes.
3.G.1.2 Compare and contrast quadrilaterals based
on their attributes.
3 G.1.3 Sort geometric figures to identify rhombuses,
rectangles, trapezoids, and squares as
quadrilaterals.
3.G.1.4 Draw examples of quadrilaterals that are NOT
squares, rhombuses, or rectangles.
3.MD.D.8 is addressed in full in
this unit and focuses on
distinguishing between linear
and area measures and
examining their relationship.
Students look for and make use of
structure (MP.7) as they determine
categories and subcategories of
shapes by identifying and reasoning
about their attributes. Students make
conjectures involving the attributes
and measures of shapes and analyze
various ways of approaching
problems (MP.1, MP.3)
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 27
Unit 14: Using multiplication and division to
solve measurement problems Suggested
number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
This unit extends students' work in unit 6 to include multiplication and division to solve problems involving measurement quantities.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 3.0A
A. Represent and solve problems involving
multiplication and division.
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.
3.OA.3.1 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using drawings. (MS)
3.OA.3.2 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.3 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve equal groups and
arrays using equations.
3.OA.3.4 Use multiplication (factors ≥ 5 and ≤ 10) to
solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.5 Explain that an unknown number is
represented with a symbol/variable.
3.OA.3.6 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using drawings. (MS)
3.OA.3.7 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
drawings.
3.OA.3.8 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve equal groups
and arrays using equations. (MS)
3.OA.3.9 Use division (quotient/divisor ≥ 5 and ≤ 10)
to solve word problems that involve area and other
measurement quantities other than area using
equations.
3.OA.3.10 Divide an area by side length to find the
unknown side length.
3.0A.A.3 includes the use of all of
the problem types Table 2 in ((SSM
except for multiplicative compare
problems-which will be
introduced in Grade 4.13
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 28
Measurement and Data - 3.MD
A. Solve problems involving measurement and
estimation of intervals of time, liquid volumes,
and masses of objects.
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
NOTE: 6
Excludes 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
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
5. Use appropriate tools strategically.
3.MD.2.1 Measure liquid volume in metric units
(liters).
3.MD.2.2 Measure mass in metric units (kilograms,
grams).
3.MD.2.3 Estimate liquid volume using metric units
(liters).
3.MD.2.4 Estimate mass in metric units (kilograms,
grams).
3.MD.2.5 Use the appropriate unit to measure the
mass of objects.
3.MD.2.6 Use the appropriate unit to measure the
liquid volume of objects.
3.MD.2.7 Use the four basic operations to solve one
step word problems with mass.
3.MD.2.8 Use the four basic operations to solve one
step word problems with liquid volume.
3.MD.2.9 Use the four basic operations to solve two
step word problems with mass.
3.MD.2.10 Use the four basic operations to solve two
step word problems with liquid volume.
Students use strategies for
multiplication and division to
conceptualize and solve
measurement problems (MP.1,
MP.2). Students select appropriate
tools and justify their selection for
measuring different quantities
(MP.5).
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 29
Unit 15: Demonstrating computational fluency
in problem solving. Suggested number of
days: 10
I Can Statements Notes/Comments Unit Materials and Resources
This is a culminating unit in which students focus on problem solving in order to demonstrate fluency with addition and subtraction to 1000 and demonstrate fluency for multiplication
and division within 100.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 3.OA
C. 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 x 5 =
40, one knows 40 x 5 = 8) or properties
of operations. By the end of Grade 3,
know from memory all products of two
one-digit numbers.
D. 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
NOTE: 3This standard is limited to problems
posed with whole numbers and having
whole- number 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).
3.OA.7.1 Fluently (accurately and quickly) divide with
a dividend up to 100.
3.OA.7.2 Fluently (accurately and quickly) multiply
numbers 0-10.
3.OA.7.3 Memorize and recall my multiples from 0-9.
3.OA.7.4 Recognize the relationship between
multiplication and division.
3.OA.8.1 Construct an equation with a letter
(variable) to represent the unknown quantity.
3.OA.8.2 Explain or demonstrate how to solve two-
step word problems using addition and
subtraction
3.OA.8.3 Explain or demonstrate how to solve two-
step word problems using multiplication and
division (Of single digit factors and products less
than 100).
3.OA.8.4 Represent a word problem with an equation
using a letter to represent the unknown quantity.
3.OA.8.5 Solve two-step word problems which
include multiple operations.
3.OA.8.6 Use mental math to estimate the answer of
a single step word problem. (MS)
3.OA.8.7 Use mental math to estimate the answer of
a two-step word problem.
3.OA.8.8 Justify my answers using mental math and
3.OA.D.8 was introduced in unit 8
and is finalized in this unit to include
the use of letters to represent
unknown quantities in equations.
Common Core Math Units
Grade 3
Adapted from NGA Center CCSS are the sole owners and developers of the Common Core State Standards.
© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The Charles A. Dana Center at The University of Texas at Austin January 13, 2013
Page 30
Number and Operations in Base Ten - 3.NBT
A. Use place value understanding and properties
of operations to perform multi-digit arithmetic. 4
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.
NOTE: 4A range of algorithms may be used.
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
8. Look for and express regularity in repeated
reasoning.
estimation. (MS)
3.NBT.2.1 Identify and apply the properties of
addition to solve problems.
3.NBT.2.2 Identify and apply the properties of
subtraction to solve problems.
3.NBT.2.3 Check a subtraction problem using
addition.
3.NBT.2.4 Check an addition problem using
subtraction.
3.NBT.2.5 Correctly align digits according to place
value, in order to add or subtract.
3.NBT.2.6 Explain and demonstrate the process of
regrouping.
3.NBT.2.7 Fluently add two 2-digit numbers.
(horizontal and vertical set up)
3.NBT.2.8 Fluently add two 3-digit numbers.
(horizontal and vertical set up)
3.NBT.2.9 Fluently subtract two 2-digit numbers with
and without regrouping. (horizontal and vertical
set up)
3.NBT.2.10 Fluently subtract two 3-digit numbers
with and without regrouping. (horizontal and
vertical set up)
Students demonstrate fluency in
multiplication and division within 100
using various strategies and the
properties of these operations
(MP.5). They also represent these
calculations and problem situations
abstractly using letters (MP.2).