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Common Core Math Units
Grade 4
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 4 In the years prior to Grade 4, students gained an understanding of multiplication and division of whole numbers, generalized strategies for addition and
subtraction to multi-digit numbers, developed understanding of fractions as numbers, and reasoned with shapes and their attributes. They used arrays and
the concept of area to develop computational strategies for multiplication and division.
Throughout Grade 4, students continue to develop their understanding of number. They generalize their understanding of place value to
1,000,000. Students extend their understanding of the four operations to include multiplicative compare problems, operations with multi-digit numbers, and
multiplying fractions by whole numbers. Students further develop their understanding of fractions to include addition of fractions with like denominators and
comparison and ordering of fractions with either like numerators or like denominators. The geometry focus in Grade 4 is on reasoning about angle measurement
and lines.
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 14 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 4, 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.
Common Core Math Units
Grade 4
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 multiples and factors
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students develop understanding of multiples and factors, applying their understanding of multiplication from the previous year. This understanding lays a strong foundation
for generalizing strategies learned in previous grades to develop, discuss, and use efficient, accurate, and generalizable computational strategies involving multi-digit numbers. These
concepts and the terms "prime" and "composite" are new to Grade 4, so they are introduced early in the year to give students ample time to develop and apply this understanding.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 4.0A
B. Gain familiarity with factors and multiples. (S)
4. Find all factor pairs for a whole number in the
range 1-100. Recognize that a whole number
is a multiple of each of its factors. Determine
whether a given whole number in the range
1-100 is a multiple of a given one-digit
number. Determine whether a given whole
number in the range 1-100 is prime or
composite.
C. Generate and analyze patterns. (A)
5. Generate a number or shape pattern that
follows a given rule. Identify apparent
features of the pattern that were not explicit
in the rule itself. For example, given the rule
"Add 3” and the starting number 1, generate
terms in the resulting sequence and observe
that the terms appear to alternate between
odd and even numbers. Explain informally
why the numbers will continue to alternate in
this way.
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.
4.OA.4.1 Determine if a whole number
(1-100) is a multiple of a
given 1 digit number (ex. – Is
56 a multiple of 7? Is 45 a
multiple of 2) (MS)
4.OA.4.2 Find all factor pairs for a
whole number up to 100 (ex.
56 = __ x __) (MS)
4.OA.4.3 Determine if a whole number
(1-100) is prime or
composite.
4.OA.4.4 Recognize that a whole
number (1-100) is a multiple
of each of its factors. (MS)
4.OA.5.1 Use a rule to create a number or shape
pattern. (MS)
4.OA.5.2 Determine if there are other
relationships within a pattern (ex.4, 8, 16,
32… - all even. 5, 12, 19, 26… -
odd/even).
4.OA.5.3 Express a pattern using a formula.
While working on 4.0A.C.5,
students use manipulatives to
determine whether a number is
prime or composite. Although
there are shape patterns in arrays,
the focus of this unit is number
patterns. 4.0A.C.5 is repeated in
unit 13, where the focus will be on
identifying shape patterns.
The focus of this unit is not
necessarily to become fluent in
finding all factor pairs, but to use
student's understanding of the
concept and language to discuss the
structure of multiples and factors
(MP.3, MP.7).
Common Core Math Units
Grade 4
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
Unit 2: Using multiplication and division
strategies with larger numbers
Suggested number of days: 15
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students continue using computational and problem-solving strategies, with a focus on building conceptual understanding of multiplication of larger numbers and division
with remainders. Area and perimeter of rectangles provide one context for developing such understanding.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
3. Solve multistep word problems posed with
whole numbers and having whole-number
answers using the four operations, including
problems in which remainders must be
interpreted. 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.
Number and Operations in Base Ten2 - 4.NBT
B. Use place value understanding and properties
of operations to perform multi-digit arithmetic.
(M)
5. Multiply a whole number of up to four digits
4.OA.3.1 Solve multi-step word problems using
the four operations with whole
numbers (3 or 4 digits by a 1 digit
number or two two-digit numbers)
4.0A.3.2 Interpret remainders in various
situations.
4.OA.3.3 Find whole number quotients without
remainders (3 digit dividends and one
digit divisor). (MS)
4.OA.3.4 Find whole number quotients with
remainders (3 digit dividends and one
digit divisor). (MS)
4.OA.3.5 Find whole number quotients without
remainders (4 digit dividends and one
digit divisor). (MS)
4.OA.3.6 Find whole number quotients with
remainders (4 digit dividends and one
digit divisor). (MS)
4.OA.3.7 Justify an answer based upon the
interpretation of remainders.
4.OA.3.8
Justify an answer using mental math
and estimation.
4.NBT.5.1 Multiply a 4 digit number by a 1 digit
number.
4.NBT.5.2 Illustrate and explain multiplication using
rectangular arrays.
4.OA.A.3 is the first time students
are expected to interpret
remainders based upon the
context. All four operations will be
addressed in unit 8, and the
standard will be finalized in unit
14.
Common Core Math Units
Grade 4
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
by a one-digit whole number, and multiply
two two-digit numbers, using strategies
based on place value and the properties of
operations. Illustrate and
explain the calculation by using equations,
rectangular arrays, and/or area models.
6. Find whole-number quotients and
remainders with up to four-digit dividends
and one-digit divisors, using strategies based
on place value, the properties of operations,
and/or the relationship between
multiplication and division. Illustrate and
explain the calculation by using equations,
rectangular arrays, and/or area models.
NOTE: 2Grade 4 expectations in this domain are
limited to whole numbers less than or equal to
1,000,000.
Measurement and Data - 4.MD
A. Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit. (S)
3. Apply the area and perimeter formulas for
4.NBT.5.3 Illustrate and explain multiplication using
area models.
4.NBT.5.4 Apply the properties of operations to
multiply numbers. (MS)
4.NBT.5.5 Multiply 2, two digit numbers (ex. 23 x
45). (MS)
4.NBT.5.6 Multiply numbers using written
equations. (MS)
4.NBT.6.1 Divide up to 4 digit number by a 1 digit
divisor. (MS)
4.NBT.6.2 Apply the properties of operations to
divide 4 digit numbers. (MS)
4.NBT.6.3 Apply strategies based on place value to
divide up to 4 digit number by a 1 digit
divisor. (MS)
4.NBT.6.4 Explore different strategies for the
division of 4 digit dividends and 1 digit
divisors. (MS)
4.NBT.6.5 Illustrate and explain division with a
rectangular array.
4.NBT.6.6 Illustrate and explain division with an
area model.
4.NBT.6.7 Illustrate and explain division with an
equation.
4.NBT.6.8 Explore the relationship between
multiplication and division. (MS)
4.MD.3.1
4.MD.3.2
Calculate the area of a rectangle using
the formula A=L x W or A= B x H when
side lengths are given.
Solve for the missing side length of a
rectangle using the formula A=L x W or
4.MD.A.3 provides the context of
area and perimeter of rectangles
to use for problem solving.
Students are first introduced to
formulas in this unit and make
Common Core Math Units
Grade 4
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
rectangles in real world and mathematical
problems. For example, find the width of a
rectangular room given the area of the
flooring and the length, by viewing the area
formula as a multiplication equation with
an unknown factor.
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
8. Look for and express regularity in repeated
reasoning.
A=B x H when the area is given along
with one other dimension.
4.MD.3.3
4.MD.3.4
Calculate the perimeter of a rectangle
using the formula P=S+S+S+S or P=2L +
2W when side lengths are given.
Solve for the missing side length of a
rectangle using the formula P=S+S+S+S
or P=2L + 2W when the perimeter is
given along with one other dimension.
4.MD.3.5 Apply the area and perimeter formula
to solve real-world problems.
sense of the formulas using their
prior work with area and
perimeter.
Students make sense of multi-step
problems (MP.1) and reason about
how the formulas connect to the
context (MP.2). The use of
generalized strategies and formulas
provides an opportunity to
investigate and use regularity in
repeated reasoning (MP.8).
Common Core Math Units
Grade 4
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
Unit 3: Decomposing and composing fractions
for addition and subtraction
Suggested number of days: 8
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students extend their prior knowledge of unit fractions with denominators of 2, 3, 4, 6, and 8 from Grade 3 to include denominators of 5, 10, 12, and 100. In Grade 4, they
use their understanding of partitioning to find unit fractions to compose and decompose fractions in order to add fractions with like denominators. This is foundational for further work
with fractions later in the year, such as comparing fractions and multiplying fractions by a whole number.
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions3 - 4.NF
B. Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers. (M)
3. Understand a fraction a/b with a > 1 as a sum
of fractions 1/b.
a. Understand addition and subtraction of
fractions as joining and separating parts
referring to the same whole.
b. Decompose a fraction into a sum of
fractions with the same denominator in
more than one way, recording each
decomposition by an equation. Justify
decompositions, e.g., by using a visual
fraction model. Examples: 3/8 = 1/8 + 1/8 +
1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =
8/8 + 8/8 + 1/8.
NOTE: 3Grade 4 expectations in this domain are
limited to fractions with denominators 2, 3, 4, 5,
6, 8, 10, 12, and 100.
Common Core State Standards for
Mathematical Practice
4. Model with mathematics.
4.NF.3a.1 Add or subtract fractions with like
denominators using manipulatives or
visual models. (MS)
4.NF.3a.2 Add and subtract improper fractions
with like denominators using
manipulatives or visual models.
4.NF.3b.1 Decompose a fraction into a sum of
fractions with the same denominator in
more than one way.
4.NF.3b.2 Create a visual model to justify
decompositions.
Students use visual and concrete
models to represent a fractional
situation in order to add and subtract
fractions (MP.4).
Common Core Math Units
Grade 4
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 4: Applying place value concepts in whole
number addition and subtraction
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
The focus of this unit is to provide students time to develop and practice efficient addition and subtraction of multi-digit whole numbers while developing place value concepts.
Common Core State Standards for
Mathematical Content
Number and Operations in Base Ten2 - 4.NBT
A. Generalize place value understanding for multi-
digit whole numbers. (M)
1. Recognize that in a multi-digit whole
number, a digit in one place represents ten
times what it represents in the place to its
right. For example, recognize that 700 ÷ 70 =
10 by applying concepts of place value and
division.
2. Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit
numbers based on meanings of the digits in
each place, using >, =, and < symbols to
record the results of comparisons.
3. Use place value understanding to round
multi-digit whole numbers to any place.
4.NBT.1.1
4.NBT.1.2
4.NBT.1.3
Recognize a digit in one place
represents 10 times as much as it
represents in the place to the right (3
digit numbers).
Recognize a digit in one place
represents 10 times as much as it
represents in the place to the right (4
digit numbers).
Recognize a digit in one place
represents 10 times as much as it
represents in the place to the right
(multi-digit numbers).
4.NBT.2.1
4.NBT.2.2
Read, write, and compare multi-digit
numbers in expanded form. (MS)
Read, write, and compare multi-digit
numbers using base ten numerals
(standard form). (MS)
4.NBT.2.3 Read, write, and compare multi-digit
numbers in word form. (MS)
4.NBT.2.4 Compare multi-digit numbers using <, >,
=. (MS)
4.NBT.3.1 Round multi-digit numbers up to the
millions place. (MS)
4.NBT.A.1 will be revisited in unit
6 connected to conversions
within the metric system of
measurement.
4.NBT.A.3 will be revisited
in unit 7 with multiplication
and division as a context.
Common Core Math Units
Grade 4
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
B. Use place value understanding and properties
of operations to perform multi-digit arithmetic.
(M)
4. Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
NOTE: 2Grade 4 expectations in this domain
are limited to whole numbers less than or
equal to 1,000,000.
Common Core State Standards for
Mathematical Practice
6. Attend to precision.
8. Look for and express regularity in repeated
reasoning.
4.NBT.4.1 Fluently add multi-digit numbers up to
millions place. (MS)
4.NBT.4.2 Fluently subtract multi-digit numbers
up to millions place. (MS)
4.NBT.B.4 will be revisited in
unit 8 and finalized in unit 14 for
fluency in addition and
subtraction of multi-digit whole
numbers.
Students use the structure of the
base-ten system to generalize their
strategies and to discuss
reasonableness of their
computations and work towards
fluency (MP.6, MP.8).
Common Core Math Units
Grade 4
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 5: Understanding fraction equivalence
and comparison
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students develop an understanding of fraction equivalence and various methods for comparing fractions. Students should understand that when comparing fractions, it is
not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to a benchmark, can be used to discuss relative sizes. The justification of
comparing or generating equivalent fractions using visual models is an emphasis of this unit.1
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions3 - 4.NF
A. Extend understanding of fraction equivalence
and ordering. (M)
1. Explain why a fraction a/b is equivalent to
a fraction (n x a)/(n x b) by using visual
fraction models, with attention to how
the number and size of the parts differ
even though the two fractions themselves
are the same size. Use this principle to
recognize and generate equivalent
fractions.
2. Compare two fractions with different
numerators and different denominators,
e.g., by creating common denominators or
numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize
that comparisons are valid only when the
two fractions refer to the same whole.
Record the results of comparisons with
symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction
model.
NOTE: 3
Grade 4 expectations in this domain
are limited to fractions with denominators 2, 3,
4, 5, 6, 8, 10, 12, and 100.
Common Core State Standards for
4.NF.1.1 Identify equivalent fractions.
4.NF.1.2 Create visual fraction models to
show why fractions are equal.
4.NF.1.3 Explain why two fractions are
equivalent, but have different
denominators.
4.NF.1.4 Create equivalent fractions in
number form (ie. ½ = 6/12) by
multiplying or dividing the
numerator and denominator by the
same number.
4.NF.2.1 Compare a fraction to a benchmark
fraction such as 1/2, using a visual
model.
4.NF.2.2 Compare fractions to a benchmark
fraction such as 1/2, using numerical
comparison. (ie. 3/6 ____ 7/12)
4.NF.2.3 Use multiples to find a LCD.
4.NF.2.4 Compare fractions using symbols (<,
>, =).
4.NF.2.5 Compare two fractions with different
numerators (like denominators).
4.NF.2.6 Compare two unlike fractions by
creating like denominators.
Students justify their methods for
generating equivalent fractions and
comparing fractions by using their
conceptual understanding and
models (MP.3, MP.5).
Common Core Math Units
Grade 4
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
Mathematical Practice
3. Construct viable arguments and critique the
reasoning of others.
5. Use appropriate tools strategically.
4.NF.2.7 Explain that the size of the whole
matters when comparing fractions
(ie. ½ of a medium pizza is not equal
to ½ of a large pizza).
4.NF.2.8 Justify comparisons by using a visual
fraction model.
4.NF.2.9 Create a visual model to explain the
comparison of fractions.
4.NF.2.10 Compare two unlike fractions using a
variety of methods.
Common Core Math Units
Grade 4
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 6: Introducing measurement conversions
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students build a conceptual understanding of the relative sizes of units of measure within a single system of measurement. Measurement conversions are used to
introduce multiplication as a comparison. The concepts in this unit are foundational for the concepts in unit 7 and unit 8.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
1. Interpret a multiplication equation as a
comparison, e.g., interpret 35 = 5 x 7 as a
statement that 35 is 5 times as many as 7 and 7
times as many as 5. Represent verbal statements
of multiplicative comparisons as multiplication
equations.
Number and Operations in Base Ten2 - 4.NBT
A. Generalize place value understanding for multi-
digit whole numbers. (M)
1. Recognize that in a multi-digit whole
number, a digit in one place represents ten
times what it represents in the place to its
right. For example, recognize that 700 ÷ 70 =
10 by applying concepts of place value and
division.
NOTE: 2Grade 4 expectations in this domain are
limited to whole numbers less than or equal to
1,000,000.
Measurement and Data - 4.MD
A. Solve problems involving measurement and
conversion of measurements from a larger unit
4.OA.1.1 Multiply two given numbers (one and
two digits).
4.OA.1.2 Write/compose a multiplication
equation.
4.OA.1.3 Interpret a verbal comparison into an
equation.
4.OA.1.4 Compare amounts using
multiplication. (for example – 5 times
as many…)
4.OA.1.5 Change a number sentence into a
word sentence.
4.OA.1.6 Translate (give an example of) verbal
statements as multiplication
statement.
4.NBT.1.1 Identify place values up to 1,000,000.
4.NBT.1.2 Use multiplication by a power of 10 to
determine the value of a digit in a
multi-digit whole number.
4.OA.A.l is repeated in unit 11,
in which the focus is on
multiplication of fractions.2
4.NBT.A.l was addressed in unit 4,
in which the focus was on addition
and subtraction. In this unit, metric
measurement provides an
opportunity to deepen the
students' understanding of place
value in relation to multiples of 10.
4.MD.A.l introduces units of measure
new to
Grade 4.
In this unit students look for patterns
in different measurement systems
(MP.2, MP.7) and discuss precisely
how many times larger one unit is
than another (MP.6)
Common Core Math Units
Grade 4
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
to a smaller unit. (S)
1. Know relative sizes of measurement units
within one system of units including km,
m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.
Within a single system of measurement,
express measurements in a larger unit in
terms of a smaller unit. Record
measurement equivalents in a two-
column table. For example, know that 1 ft
is 12 times as long as 1 in. Express the
length of a 4 ft snake as 48 in. Generate a
conversion table for feet and inches listing
the number pairs (1, 12), (2, 24), (3, 36), ...
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
6. Attend to precision.
7. Look for and make use of structure.
4.MD.1.1 Identify and associate units of
measurements used to measure
length.
4.MD.1.2 Identify and associate units of
measurements used to measure
capacity.
4.MD.1.3 Identify and associate units of
measurements used to measure
weight.
4.MD.1.4 Identify and associate units of
measurements used to measure time.
4.MD.1.5 Compare units of measurement within
a given system (ie. 1 inch < 1 foot).
4.MD.1.6 Convert (change) from a larger unit to
a smaller unit.
4.MD.1.7 Create a table to record equivalent
measures listing number pairs.
Common Core Math Units
Grade 4
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 7: Solving problems using multiplicative
comparison
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students are introduced to multiplicative compare problems, extending their conceptual work with multiplicative comparison from unit 6. For students to develop this
concept, they must be provided rich problem situations that encourage them to make sense of the relationships among the quantities involved, model the situation, and check their
solution using a different method. CCSSM Table 2 is an important resource for understanding multiplicative comparison problems, which are new to Grade 4 students.3
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
2. Multiply or divide to solve word problems
involving multiplicative comparison, e.g., by
using drawings and equations with a symbol
for the unknown number to represent the
problem, distinguishing multiplicative
comparison from additive comparison.
Number and Operations in Base Ten2 - 4.NBT
A. Generalize place value understanding for multi-
digit whole numbers. (M)
3. Use place value understanding to round multi-
digit whole numbers to any place.
NOTE: 2Grade 4 expectations in this domain are
limited to whole numbers less than or equal to
1,000,000
4.OA.2.1 Identify variables, symbols, &
unknown numbers.
4.OA.2.2 Identify key words and relate words to
operations.
4.OA.2.3 Represent word problems and/or
equations with pictures and symbols.
4.OA.2.4 Compare amounts with multiplication.
(for example – 7 times as many as…)
*this is not repeated addition.
4.OA.2.5 Compare amounts with addition (7
more than).
4.OA.2.6 Solve word problems using
multiplication (4 digits by 1 digit or 2
digits by 2 digits).
4.OA.2.7 Solve word problems using division (4
digit dividends by 1 digit divisor).
4.OA.2.8 Identify multiplicative comparisons
from additive comparisons.
4.NBT.3.1 Round numbers up to the millions
place.
4.NBT.3.2 Explain why a number is rounded to a
given place.
4.NBT.3.3 Demonstrate understanding of place
value using a drawing, chart, table,
diagram, etc…
4.OA.A.2 is also addressed in unit
14 because of the time it takes to
master the concepts and its
importance to future
mathematics.4
4.NBT.A.3 was addressed in unit 4
with a focus on addition and
subtraction. In this unit, the focus
is on multiplication and division.
4.MD.A.2 is used as a context for
multiplicative compare problems
with whole numbers only. This
standard is revisited in unit 8 to
include the four operations, and
addressed in unit 12 with decimal
fractions.
Students use charts and diagrams to
explain their own methods as well
make sense of approaches taken by
others (MP.1).
Common Core Math Units
Grade 4
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 14
Measurement and Data - 4.MD
A. Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit. (S)
2. Use the four operations to solve word
problems involving distances, intervals of
time, liquid volumes, masses of objects, and
money, including problems involving simple
fractions or decimals, and problems that
require expressing measurements given in a
larger unit in terms of a smaller unit.
Represent measurement quantities using
diagrams such as number line diagrams that
feature a measurement scale.
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
4.MD.2.1 Represent measurement quantities
using diagrams with a measurement
scale.
4.MD.2.2 Apply the four operations to solve
word problems involving distance.
4.MD.2.3 Apply the four operations to solve
word problems involving elapsed time.
4.MD.2.4 Apply the four operations to solve
word problems involving liquid
volume.
4.MD.2.5 Apply the four operations to solve
word problems involving mass.
4.MD.2.6 Apply the four operations to solve
word problems involving money.
*Note:
− These problems are limited to converting
larger to smaller units.
− These problems include whole numbers,
fractions, and decimals.
Common Core Math Units
Grade 4
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 15
Unit 8: Solving measurement problems using
the four operations
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students combine competencies from different domains to solve measurement problems using the four operations.S
Measurement is included in this unit to provide a
context for problem solving. All of the problem types in Table 1 and Table 2 on pages 88 and 89 of the Common Core State Standards for Mathematics should be addressed in this unit.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
3. Solve multistep word problems posed with
whole numbers and having whole-number
answers using the four operations, including
problems in which remainders must be
interpreted. 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.
Number and Operations in Base Ten2 - 4.NBT
B. Use place value understanding and properties
of operations to perform multi-digit arithmetic.
(M)
4. Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
4.OA.3.1 Add, subtract, multiply and divide with
or without remainders.
4.OA.3.2 Identify key words to decide which
operation(s) to use to solve a word
problem.
4.OA.3.3 Explain what a remainder is and how it
will affect a given problem.
4.OA.3.4 Determine if an answer makes sense,
based on the problem.
4.OA.3.5 Justify my answers using mental math
and estimation.
4.OA.3.6 Write an equation to solve the word
problem using a letter to represent the
missing number
4.OA.3.7 Solve multistep word problems with
whole numbers.
4.OA.3.8 Calculate long division with
remainders.
4.NBT.4.1 Add numbers up to millions place
value.
4.NBT.4.2 Subtract numbers up to millions place
value.
4.NBT.4.3 Justify an answer by using the
relationship between addition and
subtraction (inverse operations).
4.OA.A.3 and 4.NBT.B.4 are
repeated here to include all four
operations and will be finalized in
unit 14. Repeating these standards
throughout the year provides
students multiple opportunities to
develop these skills-which
are major areas of focus for this
grade level.
4.MD.A.2 is repeated from the
previous unit, but in this unit the
emphasis is on using the four
operations and all problem types.
This standard will be finalized in
unit 12 to include decimal
fractions.
Students use various diagrams and
precise language to solve
measurement problems and explain
their strategies (MP.1, MP.6). They
make connections between abstract
representations and the problem
situations (MP.2).
Common Core Math Units
Grade 4
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 16
Measurement and Data - 4.MD
A. Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit. (S)
2. Use the four operations to solve word
problems involving distances, intervals of
time, liquid volumes, masses of objects, and
money, including problems involving simple
fractions or decimals, and problems that
require expressing measurements given in a
larger unit in terms of a smaller unit.
Represent measurement quantities using
diagrams such as number line diagrams that
feature a measurement scale.
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
6. Attend to precision.
4.MD.2.1 Represent measurement quantities
using diagrams with a measurement
scale.
4.MD.2.2 Apply the four operations to solve
word problems involving distance.
4.MD.2.3 Apply the four operations to solve
word problems involving elapsed time.
4.MD.2.4 Apply the four operations to solve
word problems involving liquid
volume.
4.MD.2.5 Apply the four operations to solve
word problems involving mass.
4.MD.2.6 Apply the four operations to solve
word problems involving money.
*Note:
− These problems are limited to converting
larger to smaller units.
− These problems include whole numbers,
fractions, and decimals.
Common Core Math Units
Grade 4
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 17
Unit 9: Solving addition and subtraction word
problems involving fractions and mixed
numbers
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students will use their understanding of adding and subtracting fractions and generating equivalent fractions to solve problems involving fractions and mixed numbers.
Students rely on their previous work with whole numbers as fractions to compose and decompose whole numbers into fractional quantities.6
Data is used in this unit to support
students' understanding of fractional quantities both smaller and larger than 1.7
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions - 4.NF
B. Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers. (M)
3. Understand a fraction a/b with a > 1 as a sum
of fractions 1/b.
c. Add and subtract mixed numbers with like
denominators, e.g., by replacing each
mixed number with an equivalent fraction,
and/or by using properties of operations
and the relationship between addition and
subtraction.
d. Solve word problems involving addition
and subtraction of fractions referring to
the same whole and having like
denominators, e.g., by using visual
fraction models and equations to
represent the problem.
NOTE: Grade 4 expectations in this domain are
limited to fractions with denominators 2, 3, 4,
5, 6, 8, 10, 12, and 100.
4.NF.3c.1 Justify that a mixed number is a whole
number and a fraction by using a visual
model.
4.NF.3c.2 Change a mixed number into an
improper fraction.
4.NF.3c.3 Change an improper fraction into a
mixed number.
4.NF.3d.1 Solve word problems using addition
and subtraction of fractions with like
denominators using visual models and
equations.
4.MD.B.4 extends students' work
from Grade 3 with simple fractions
on a line plot (3.MD.B.4) to include
eighths and to now solve addition
and subtraction problems using the
data.
Students reason about fractions by
using abstract models to represent
both the data and the fractional
quantities (MP.2, MP.4).
Common Core Math Units
Grade 4
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 18
Measurement and Data - 4.MD
B. Represent and interpret data. (S)
4. Make a line plot to display a data set of
measurements in fractions of a unit (1/2,
1/4, 1/8). Solve problems involving addition
and subtraction of fractions by using
information presented in line plots. For
example, from a line plot find and interpret
the difference in length between the longest
and shortest specimens in an insect
collection.
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
4. Model with mathematics.
4.MD.4.1 Answer questions about data
measured on a line plot.
4.MD.4.2 Create a line plot to display (show) a
data set that includes fractions or
mixed numbers.
4.MD.4.3 Add and subtract fractions using
information from a line plot.
Common Core Math Units
Grade 4
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 19
Unit 10: Angle measurement
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
This unit is an introduction to angles and angle measurement. Students start this unit drawing points, lines, segments, rays and angles since it is foundational to the other standards in
this unit. Students use their understanding of equal partitioning and unit measurement to understand angle and turn measure.
Common Core State Standards for
Mathematical Content
Measurement and Data - 4.MD
C. Geometric measurement: understand concepts
of angle and measure angles. (A)
5. Recognize angles as geometric shapes that
are formed wherever two rays share a
common endpoint, and understand concepts
of angle measurement:
a. An angle is measured with reference to a
circle with its center at the common
endpoint of the rays, by considering the
fraction of the circular arc between the
points where the two rays intersect the
circle. An angle that turns through 1/360
of a circle is called a "one-degree angle,"
and can be used to measure angles.
b. An angle that turns through n one-
degree angles is said to have an angle
measure of n degrees.
6. Measure angles in whole-number degrees
using a protractor. Sketch angles of
specified measure.
4.MD.5.1 Identify an angle.
4.MD.5a.1 Recognize that a circle has 360
degrees.
4.MD.5a.2 Explain that an angle measurement is
a fraction of a circle.
4.MD.5b.1 Recognize that angles are measured
in degrees within a circle.
4.MD.6.1 Identify benchmark angles (90º, 180º,
270º, 360º).
4.MD.6.2 Measure angles using a protractor.
4.MD.6.3 Sketch angles of a given
measurement (degree) using a
protractor.
In this unit, 4.G.A.1 focuses on
drawing points, lines, line segments,
rays, and different types of angles.
The standard will be addressed in its
entirety in unit 13.
Students select and use a protractor
to measure angles and represent the
angles with drawings (MP.4, MP.S).
Common Core Math Units
Grade 4
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
Geometry - 4.G
A. Draw and identify lines and angles, and classify
shapes by properties of their lines and angles. (A)
1. Draw points, lines, line segments, rays,
angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify
these in two-dimensional figures.
Common Core State Standards for
Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
4.G.1.1 Identify points, lines, line segments,
rays, angles, perpendicular, and
parallel lines in two dimensional
figures.
4.G.1.2 Draw points, lines, line segments,
rays, angles, perpendicular, and
parallel lines in two dimensional
figures
4.G.1.3 Identify types of angles (right, acute,
obtuse) in two-dimensional figures.
Common Core Math Units
Grade 4
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 21
Unit 11: Multiplying fractions by whole
numbers
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students apply their understanding of composing and decomposing fractions to develop a conceptual understanding of multiplication of a fraction by a whole number.
Students also use and extend their previous understandings of operations with whole numbers and relate that understanding to fractions.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
1. Interpret a multiplication equation as a
comparison, e.g., interpret 35 = 5 x 7 as a
statement that 35 is 5 times as many as 7 and 7
times as many as 5. Represent verbal statements
of multiplicative comparisons as multiplication
equations.
Number and Operations-Fractions - 4.NF
B. Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers. (M)
4. Apply and extend previous understandings of
multiplication to multiply a fraction by a whole
number.
a. Understand a fraction a/b as a multiple of
1lb. For example, use a visual fraction
model to represent 5/4 as the product 5 x
(1/4), recording the conclusion by the
equation 5/4 = 5 x (1/4).
4.OA.1.1 Multiply two given numbers (one and
two digits).
4.OA.1.2 Write/compose a multiplication
equation.
4.OA.1.3 Interpret a verbal comparison into an
equation.
4.OA.1.4 Compare amounts using
multiplication. (for example – 5 times
as many…)
4.OA.1.5 Change a number sentence into a
word sentence.
4.OA.1.6 Translate (give an example of) verbal
statements as multiplication
statement.
4.NF.4a.1 Multiply a whole number by a fraction
by changing the whole number into a
fraction (ie. 5 x ¾ = 5/1 x ¾).
4.OA.A.1 is readdressed in this
unit to include multiplication of
fractions and apply the
understanding of "times as much"
(i.e. multiplication as comparison)
to multiplying a fraction by a
whole number.
Students use precise language to
communicate their comprehension
of the problem situations and defend
their various solution methods
(MP.1, MP.6)
Common Core Math Units
Grade 4
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 22
b. Understand a multiple of alb as a
multiple of 1lb, and use this
understanding to multiply a fraction by
a whole number. For example, use a
visual fraction model to express 3 x
(2/5) as 6 x (1/5), recognizing this
product as 6/5. (In general, n x (a/b) =
(n x a)/b.)
c. Solve word problems involving
multiplication of a fraction by a whole
number, e.g., by using visual fraction
models and equations to represent the
problem. For example, if each person at
a party will eat 3/8 of a pound of roast
beef, and there will be 5 people at the
party, how many pounds of roast beef
will be needed? Between what two
whole numbers does your answer lie?
NOTE: Grade 4 expectations in this domain
are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
Common Core State Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them.
6. Attend to precision.
4.NF.4b.1 Create a fraction from a whole number
by placing the whole number over 1
(ie. 5 = 5/1).
4.NF.4b.2 Use models to represent a fraction
times a whole number.
4.NF.4c.1 Solve multiplication problems by
multiplying the whole number by the
numerator.
4.NF.4c.2 Solve multiplication word problems
involving fractions and whole numbers
using visual models.
4.NF.4c.3 Solve multiplication word problems
involving fractions and whole numbers
using equations.
Common Core Math Units
Grade 4
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 23
Unit 12: Comparing decimal fractions and
understanding notation
Suggested number of days: 10
I Can Statements Notes/Comments Unit Materials and Resources
In this unit of study students use their previous work with fractions to represent special fractions in a new way. Students use their understanding of equivalent fractions to begin to use
decimal notation-however, it is not the intent at this grade level to connect this notation to the base-ten system. The focus is on solving word problems involving simple fractions or
decimals. Work with money can support this work with decimal fractions.
Common Core State Standards for
Mathematical Content
Number and Operations-Fractions - 4.NF
C. Understand decimal notation for fractions, and
compare decimal fractions. (M)
5. Express a fraction with denominator 10 as an
equivalent fraction with denominator 100,
and use this technique to add two fractions
with respective denominators 10 and 100. For
example, express 3/10 as 30/100, and add
3/10 + 4/100 = 34/100.
NOTE: Students who can generate
equivalent fractions can develop
strategies for adding fractions with
unlike denominators in general. But
addition and subtraction with unlike
denominators in general is not a
requirement at this grade.
6. Use decimal notation for fractions with
denominators 10 or 100. For example, rewrite
0.62 as 62/100; describe a length as 0.62
meters; locate 0.62 on a number line diagram.
7. Compare two decimals to hundredths by
reasoning about their size. Recognize that
comparisons are valid only when the two
decimals refer to the same whole. Record the
4.NF.5.1 Use base ten models to represent
fractions.
4.NF.5.2 Convert unlike denominators to like
denominators (10,100) and add
fractions.
4.NF.5.3 Change a fraction with a denominator
of 10 into a fraction with a
denominator of 100 by multiplying the
numerator and denominator by 10.
4.NF.6.1 Write a fraction as a decimal to
represent its place value.
4.NF.6.2 Convert between decimals and
fractions (ie. 0.62 = 62/100).
4.NF.6.3 Locate fractions and decimals on a
number line (tenths and hundredths).
4.NF.7.1 Compare two decimals to the
hundredth place using a hundreds grid
and using symbols (<,>,=).
4.MD.A.2 was addressed in unit 7.
It is important to note that students
are not expected to do
computations with quantities in
decimal notation. Students can use
visual fraction models to solve
problems involving simple fractions
or decimals.
Students compare decimals fractions
and justify their comparisons using
either a fraction model or their
understanding of the notation (MP.3,
MP.7).
Common Core Math Units
Grade 4
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 24
results of comparisons with the symbols >, =,
or <, and justify the conclusions, e.g., by using
a visual model.
NOTE: Grade 4 expectations in this domain are
limited to fractions with denominators 2, 3, 4,
5, 6, 8, 10, 12, and 100.
Measurement and Data - 4.MD
A. Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit. (M)
2. Use the four operations to solve word
problems involving distances, intervals of
time, liquid volumes, masses of objects, and
money, including problems involving simple
fractions or decimals, and problems that
require expressing measurements given in a
larger unit in terms of a smaller unit.
Represent measurement quantities using
diagrams such as number line diagrams that
feature a measurement scale.
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.
4.NF.7.2 Recognize that in order to compare
decimals, they must have the same
place value.
4.NF.7.3 Create a model to justify an answer.
4.MD.2.1 Represent measurement quantities
using diagrams with a measurement
scale.
4.MD.2.2 Apply the four operations to solve
word problems involving distance.
4.MD.2.3 Apply the four operations to solve
word problems involving elapsed time.
4.MD.2.4 Apply the four operations to solve
word problems involving liquid
volume.
4.MD.2.5 Apply the four operations to solve
word problems involving mass.
4.MD.2.6 Apply the four operations to solve
word problems involving money.
*Note:
− These problems are limited to converting
larger to smaller units.
− These problems include whole numbers,
fractions, and decimals.
Common Core Math Units
Grade 4
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 25
Unit 13: Recognizing and analyzing attributes
of 2-dimensional shapes
Suggested number of days: 12
I Can Statements Notes/Comments Unit Materials and Resources
In this unit students develop their spatial reasoning skills by using a wide variety of attributes to talk about 2-dimensional shapes. Students analyze geometric figures based on angle
measurement, parallel and perpendicular lines, and symmetry.
Common Core State Standards for
Mathematical Content
0perations and Algebraic Thinking - 4.0A
C. Generate and analyze patterns. (A)
5. Generate a number or shape pattern that
follows a given rule. Identify apparent
features of the pattern that were not explicit
in the rule itself. For example, given the rule
"Add 3” and the starting number 1, generate
terms in the resulting sequence and observe
that the terms appear to alternate between
odd and even numbers. Explain informally
why the numbers will continue to alternate in
this way.
Measurement and Data - 4.MD
C. Geometric measurement: understand concepts
of angle and measure angles. (A)
7. Recognize angle measure as additive. When
an angle is decomposed into non-overlapping
parts, the angle measure of the whole is the
sum of the angle measures of the parts. Solve
addition and subtraction problems to find
unknown angles on a diagram in real world
and mathematical problems, e.g., by using an
equation with a symbol for the unknown
angle measure.
4.OA.5.1 Use rules to explain a pattern.
4.OA.5.2 Create a number or shape pattern.
4.OA.5.3 Create and explain a number or shape
pattern.
4.OA.5.4 Identify a pattern within a pattern.
(ex. 1,4,7,10)
4.MD.7.1 Decompose (separate) angles into
smaller angles.
4.MD.7.2 Add angle measures to make a larger
angle.
4.MD.7.3 Use addition and subtraction to find
unknown angles in real-world and
mathematical problems.
4.MD.7.4 Use an equation with a symbol for the
unknown angle measure.
In this unit, 4.0A.C.5 includes
repeated and growing shape
patterns.10
4.G.A.1 was first addressed in unit
10, and is addressed in its entirety
in this unit to include
perpendicular and parallel lines.
The concepts in this unit lend
themselves to using technology
applications (MP.S).
Students understand that geometric
figures can be classified by analyzing
various properties (MP.7) and justify
their conclusions by using viable
arguments (MP.3).
Common Core Math Units
Grade 4
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 26
Geometry - 4.G
A. Draw and identify lines and angles, and classify
shapes by properties of their lines and angles. (A)
1. Draw points, lines, line segments, rays,
angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify
these in two-dimensional figures.
2. Classify two-dimensional figures based on
the presence or absence of parallel or
perpendicular lines, or the presence or
absence of angles of a specified size.
Recognize right triangles as a category, and
identify right triangles.
3. Recognize a line of symmetry for a two-
dimensional figure as a line across the figure
such that the figure can be folded along the
line into matching parts. Identify line-
symmetric figures and draw lines of
symmetry.
Common Core State Standards for
Mathematical Practice
3. Construct viable arguments and critique the
reasoning of others.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
4.G.1.1 Identify points, lines, line segments,
rays, angles, perpendicular, and
parallel lines in two dimensional
figures.
4.G.1.2 Draw points, lines, line segments, rays,
angles, perpendicular, and parallel
lines in two dimensional figures
4.G.1.3 Identify types of angles (right, acute,
obtuse) in two-dimensional figures.
4.G.2.1 Identify two dimensional shapes that
have parallel or perpendicular lines.
4.G.2.2 Identify two dimensional shapes that
have angles of a specific size.
4.G.2.3 Recognize and label a right triangle.
4.G.2.4 Classify two dimensional shapes on the
presence or absence of designated
lines and angles.
4.G.3.1 Recognize a line of symmetry.
4.G.3.2 Draw a line of symmetry.
4.G.3.3 Recognize figures that have lines of
symmetry.
4.G.3.4 Draw figures that have lines of
symmetry.
Common Core Math Units
Grade 4
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: Problem solving with whole numbers
Suggested number of days: 15
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 the standard algorithms in addition and subtraction. They demonstrate
computational fluency with all problem types.
All standards in this unit have been addressed in prior units. These concepts require greater emphasis due to the depth of the ideas, the time they take to master, and/or their
importance to future mathematics.
Common Core State Standards for
Mathematical Content
Operations and Algebraic Thinking - 4.OA
A. Use the four operations with whole numbers to
solve problems. (M)
2. Multiply or divide to solve word problems
involving multiplicative comparison, e.g., by
using drawings and equations with a symbol
for the unknown number to represent the
problem, distinguishing multiplicative
comparison from additive comparison. 1
NOTE: 1See Glossary, Table 2.
3. Solve multistep word problems posed with
whole numbers and having whole-number
answers using the four operations,
including problems in which remainders
must be interpreted. Represent these
problems using equations with a letter
standing for the unknown quantity. Assess
the reasonableness of answers using
mental computation and estimation
4.OA.2.1 Identify variables, symbols, & unknown
numbers.
4.OA.2.2 Identify key words and relate words to
operations.
4.OA.2.3 Represent word problems and/or
equations with pictures and symbols.
4.OA.2.4 Compare amounts with multiplication.
(for example – 7 times as many as…)
*this is not repeated addition.
4.OA.2.5 Compare amounts with addition (7
more than).
4.OA.2.6 Solve word problems using
multiplication (4 digits by 1 digit or 2
digits by 2 digits).
4.OA.2.7 Solve word problems using division (4
digit dividends by 1 digit divisor).
4.OA.2.8 Identify multiplicative comparisons
from additive comparisons.
4.OA.3.1 Add, subtract, multiply and divide with
or without remainders.
4.OA.3.2 Identify key words to decide which
operation(s) to use to solve a word
problem.
4.OA.3.3 Explain what a remainder is and how it
will affect a given problem.
In demonstrating fluency, students
explain and flexibly use properties of
operations and place value to solve
problems, looking for shortcuts and
applying generalized strategies
(MP.2, MP.8).
Common Core Math Units
Grade 4
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
strategies including rounding.
Number and Operations in Base Ten - 4.NBT
B. Use place value understanding and properties
of operations to perform multi-digit arithmetic.
(M)
4. Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
5. Multiply a whole number of up to four digits
by a one-digit whole number, and multiply
two two-digit numbers, using strategies
based on place value and the properties of
operations. Illustrate and explain the
calculation by using equations, rectangular
arrays, and/or area models.
4.OA.3.4 Determine if an answer makes sense,
based on the problem.
4.OA.3.5 Justify my answers using mental math
and estimation.
4.OA.3.6 Write an equation to solve the word
problem using a letter to represent the
missing number
4.OA.3.7 Solve multistep word problems with
whole numbers.
4.OA.3.8 Calculate long division with
remainders.
4.NBT.4.1 Add numbers up to millions place
value.
4.NBT.4.2 Subtract numbers up to millions place
value.
4.NBT.4.3 Justify an answer by using the
relationship between addition and
subtraction (inverse operations).
4.NBT.5.1 Multiply a 4 digit number by a 1 digit
number.
4.NBT.5.2 Illustrate and explain multiplication
using rectangular arrays.
4.NBT.5.3 Illustrate and explain multiplication
using area models.
4.NBT.5.4 Apply the properties of operations to
multiply numbers.
4.NBT.5.5 Multiply 2, two digit numbers (ex. 23
x 45).
4.NBT.5.6 Multiply numbers using written
equations.
Common Core Math Units
Grade 4
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
6. Find whole-number quotients and remainders
with up to four-digit dividends and one-digit
divisors, using strategies based on place value,
the properties of operations, and/or the
relationship between multiplication and
division. Illustrate and explain the calculation
by using equations, rectangular arrays, and/or
area models.
NOTE: Grade 4 expectations in this domain are
limited to whole numbers less than or equal to
1,000,000.
Common Core State Standards for
Mathematical Practice
2. Reason abstractly and quantitatively.
8. Look for and express regularity in repeated
reasoning.
4.NBT.6.1 Divide up to 4 digit number by a 1
digit divisor.
4.NBT.6.2 Apply the properties of operations to
divide 4 digit numbers.
4.NBT.6.3 Apply strategies based on place value
to divide up to 4 digit number by a 1
digit divisor.
4.NBT.6.4 Explore different strategies for the
division of 4 digit dividends and 1
digit divisors.
4.NBT.6.5 Illustrate and explain division with a
rectangular array.
4.NBT.6.6 Illustrate and explain division with an
area model.
4.NBT.6.7 Illustrate and explain division with an
equation.
4.NBT.6.8 Explore the relationship between
multiplication and division.