Unit 1
Multiplication &
Division Patterns
& Relationships
Weeks 1 – 6
(6 weeks)
Standards codes:
4.OA.A.1
4.OA.A.2
4.OA.A.3
4.OA.B.4
4.OA.C.5
4.NBT.A.1
4.NBT.A.2
4.NBT.A.3
4.NBT.B.5
4.NBT.B.6
Key Concepts:
Multiplication and
Division of Whole
Numbers
Hopkins Public Schools Grade 4 Mathematics Overview and Pacing Guide
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Attributes &
Making Sense of
Using Big
Using Fractions
Using Perimeter
Angles of 2-D
Decimal Fractions Numbers:
and Area
Figures
Estimating and
Calculating
Weeks 7 – 12
Weeks 13 –16
Weeks 17 – 22
Weeks 23 – 29
Weeks 30 – 32
(6 weeks)
(4 weeks)
(6 weeks)
(7 weeks)
(3 weeks)
Standards codes:
Standards codes:
Standards codes:
Standards codes:
Standards codes:
4.MD.C.5
4.NF.A.1*
4.OA.A.2
4.NF.A.1
4.OA.A.1
4.MD.C.6
4.NF.A.2*
4.OA.A.3
4.NF.A.2
4.OA.A.2
4.MD.C.7
4.NF.B.3*
4.NBT.A.1
4.NF.B.3
4.OA.A.3
4.G.A.1
4.NF.C.5
4.NBT.A.2
4.NF.B.4
4.NBT.B.5
4.G.A.2
4.NF.C.6
4.NBT.A.3
4.MD.A.2
4.NBT.B.6
4.G.A.3
4.NF.C.7
4.NBT.A.4
4.MD.B.4
4.MD.A.2*
4.MD.A.2*
4.NBT.A.5
4.MD.A.3
4.NBT.A.6
Key Concepts:
Shapes and Angles
Measurement
Geometry
Key Concepts:
Fractions with
denominators of 10
and 100, Decimals
Key Concepts:
Multiplication and
Division of Large
Whole Numbers,
Estimation
Key Concepts:
Operations with
Fractions (all
types)
Problem Solving
with Fractions (all
types)
Unit 7
Units of Measure
and Equivalence
Weeks 33 – 36
(4 weeks)
Standards codes:
4.OA.A.1
4.OA.C.5
4.MD.A.1
4.MD.A.2
Key Concepts:
Measurement
Area
Perimeter
Shapes
Geometry
Key Concepts:
Measurement
Measurement
Systems (Metric
and U.S.
Customary)
Units of measure
Conversion
relationships
*These standards have been modified in this unit to account for their placement at the beginning of the year and/or for specific content related to the
unit in question. The full standard will always be met by end of year.
This Overview page is intended to give viewers a general sense of what content is taught in each unit throughout the year. Further details concerning
Common Core State Standards and Learning Targets can be found in the curriculum maps of each unit on the next pages. Viewers should keep in
mind that the Essential Questions are vital for focusing students on the main ideas of each unit. Learning Targets, while very important, help
students keep track only of the individual skills and understandings they must master, not the connections between them. Further information on the
Common Core State Standards for Mathematics can be found at: http://www.corestandards.org/Math.
Unit 1 – Multiplication and Division Patterns and Relationships
Pacing: 6 Weeks
Essential Question(s):
1. How do models help us better understand the relationship between multiplication and division? How can we represent remainders in
models?
2. How can we use the relationship between multiplication and division to help us solve multiplication and division problems?
3. How can we use our understanding of factors and multiples to help us solve multiplication and division problems?
4. How are additive and multiplicative comparisons alike and different?
5. How does the value of a digit in the hundreds place relate to the value of that digit in the tens place? (This question should be extended to
other place value relationships.)
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
CCSSM Standard
I Can…
Operations and Algebraic Thinking 4.OA
Use the four operations with whole numbers to solve
problems.
4.OA.A.1
Interpret a multiplication equation as a comparison, e.g.,
interpret 35 = 5 × 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.
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
4.OA.A.1
I can compare numbers using multiplication operations.
I can compare numbers using multiplicative reasoning and words such as “35 is 5 times
as many as 7.”
I can rewrite comparison statements using multiplication equations.
4.OA.A.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.
4.OA.A.2
I can use multiplication or division to solve word problems that involve thinking
multiplicatively.
I can use drawings or equations with symbols to represent word problems.
I can use drawings or equations to distinguish multiplicative comparison from additive
comparison.
4.OA.A.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
4.OA.A.3
I can perform each step of a multi-step problem using any of the four operations.
I can interpret remainders in word problems.
I can represent word problems using equations with a letter standing for the unknown
quantity.
with a letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and
estimation strategies including rounding.
Gain familiarity with factors and multiples.
4.OA.B.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.
Generate and analyze patterns.
4.OA.C.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.
Number and Operations in Base Ten² 4.NBT
Generalize place value understanding for multi-digit
whole numbers.
4.NBT.A.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.
4.NBT.A.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
I can use estimation strategies such as rounding to check my answer.
4.OA.B.4
I can write or say my multiplication facts 0-12.
I can describe a whole number as a multiple of both of its factors.
I can list all factor pairs for whole numbers in the range of 1-100.
I can determine multiples of a given whole number.
I can determine if a number is prime or composite.
4.OA.C.5
I can generate a number pattern that follows a given rule.
I can identify features of a pattern that are not given in the rule.
I can reason about the features of a pattern to explain why it will continue.
4.NBT.A.1
I can explain the value of each digit in a multi-digit number as ten times the digit to the
right.
I can use place value to justify answers to multiplication problems involving multiples
of 10.
I can use place value to justify answers to division problems involving multiples of 10.
4.NBT.A.2
I can read and write a multi-digit number in word form.
I can read and write a multi-digit number using base ten numerals.
I can write a multi-digit number in expanded form.
I can compare two multi-digit numbers using place value and record the comparison
of comparisons.
using symbols >, <, =.
4.NBT.A.3
Use place value understanding to round multi-digit whole
numbers to any place.
4.NBT.A.3
I can use the value of the digit to the right of the place to be rounded to determine
whether to round up or down.
I can write a multi-digit number rounded to any given place.
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
4.NBT.B.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.NBT.B.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.
Vocabulary:
area model
array model
compose/decompose
composite number
division
equation
factor pair
factor
inverse operation
multiple
multiplication
multiplicative comparison
prime number
properties of multiplication (commutative and associative)
remainder
4.NBT.B.5
I can multiply a multi-digit number of no more than 2 digits by a one digit number.
I can multiply a one-digit number by a three-digit number that is a multiple of 100 or a
four-digit number that is a multiple of 1000.
I can use an area model to explain the multiplication of multi-digit numbers.
I can use a rectangular array to explain the multiplication of multi-digit numbers.
4.NBT.B.6
I can divide a multi-digit number of no more than 2 digits by a one-digit number.
I can explain division calculations using the relationship between multiplication and
division.
I can explain division calculations using place value and the properties of operations.
I can illustrate and explain my calculations using equations.
I can illustrate and explain my calculations using an array/area model.
I can write an equation to represent a multi-digit division problem.
square number
unknown value
Unit 2 – Attributes and Angles of 2-D Figures
Pacing: 6 Weeks
Essential Question(s):
1. How do we use attributes to describe and define two dimensional figures?
2. How can we classify polygons using more than one attribute?
3. What measurements help to classify two dimensional shapes?
4. What does it mean for a figure to be line-symmetric? How do you identify its line of symmetry?
5. What strategies can we use to measure angles?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
CCSSM Standards
Measurement and Data 4.MD
Geometric measurement: understand concepts of angle and measure
angles.
4.MD.C.5
Recognize angles as geometric shapes that are formed wherever two rays
share a common endpoint, and understand concepts of angle
measurement:
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
4.MD.C.5
I can identify angles in diagrams, pictures, and shapes.
I can measure an angle using a protractor.
4.MD.C.5a
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.
4.MD.C.5a
I can explain how to measure an angle using a protractor.
I can explain where the markings on a protractor come from.
I can give the definition of a “one-degree angle.”
4.MD.C.5b
An angle that turns through n one-degree angles is said to have an angle
measure of n degrees.
4.MD.C.5b
I can explain how a “one-degree angle” is used to measure angles.
4.MD.C.6
Measure angles in whole-number degrees using a protractor. Sketch
angles of specified measure.
4.MD.C.6
I can use a protractor to measure angles in whole number degrees.
I can use a protractor to sketch an angle of a given measure.
4.MD.C.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.MD.C.7
I can describe visually the process of adding angles.
I can write an equation with an unknown angle measurement.
I can use addition and subtraction to solve for the missing angle
measurements in problem situations.
Geometry 4.G
Draw and identify lines and angles, and classify shapes by properties
of their lines and angles.
4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.A.1
I can identify an example of a point, line, line segment, and ray.
I can draw an example of a point, line, line segment, and ray.
I can identify an example of a right angle, acute angle, and obtuse angle.
I can draw an example of a right angle, acute angle, and obtuse angle.
I can identify an example of perpendicular lines and parallel lines.
I can draw an example of perpendicular and parallel lines.
I can identify basic geometric objects in two-dimensional figures.
4.G.A.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.
4.G.A.2
I can classify two-dimensional shapes using parallel and perpendicular
lines.
I can classify two-dimensional shapes using acute, obtuse, and right
angles.
I can identify a right triangle.
4.G.A.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.
Vocabulary:
angle
angle addition
4.G.A.3
I can explain how to identify a line of symmetry in a two dimensional
figure.
I can identify a figure as having a line of symmetry or not.
I can draw a line of symmetry given a line-symmetric figure.
angle classification (obtuse, right, acute)
angle measurement
degree
lines
line segment
line symmetry
parallel lines
perpendicular lines
polygons
ray
two-dimensional
triangle classification
vertices
Unit 3 – Making Sense of Decimal Fractions
Pacing: 4 Weeks
Essential Question(s):
1. How can decimal fractions be represented visually and symbolically?
2. How might decimal fractions and place value help us make sense of fractions in decimal notation?
3. What strategies assist in comparing fractions in decimal notation?
4. How can we generate equivalent decimal fractions?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
Pre-requisite Knowledge:
CCSSM Standards
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
Number and Operations—Fractions³ 4.NF
Extend understanding of fraction equivalence and ordering.
4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.
4.NF.A.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.
Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.A.1
I can explain why fractions with denominators of 10 and 100 are
equivalent using visual models.
I can create equivalent fractions with denominators of 10 or 100 by
multiplying or dividing the numerator and the denominator by the same
number.
4.NF.A.2
I can compare two given fractions (with denominators of 10 or 100) by
creating equivalent fractions with common denominators (of 10 or 100).
I can compare two fractions (with denominators of 10 or 100) by creating
equivalent fractions with common numerators.
I can compare two fractions by reasoning about their size, the location on
a number line, or a benchmark fraction such as 1/2.
I can use <, >, and = symbols to record my comparisons of fractions.
I can justify my comparisons using visual fraction models.
4.NF.B.3
I can rewrite non-unit fractions as the sum of identical unit fractions.
4.NF.B.3a
Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
4.NF.B.3a
I can describe adding fractions as joining while referring to the same
whole for both fractions.
I can describe subtracting fractions as separating while referring to the
same whole for both fractions.
4.NF.B.3b
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/ ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 +
1/8.
4.NF.B.3b
I can rewrite fractions with denominators of 10 or 100 as sums in
multiple different ways using smaller fractions with the same
denominator.
I can justify my decompositions of fractions using visual fraction models.
4.NF.B.3c
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.
4.NF.B.3c
I can add mixed numbers with like denominators of 10 or 100 using
multiple strategies.
I can subtract mixed numbers with like denominators of 10 or 100 using
multiple strategies.
I can change mixed numbers with common denominators of 10 or 100
into equivalent fractions that I can add or subtract.
4.NF.B.3d
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.
4.NF.B.3d
I can solve word problems involving adding decimal fractions with like
denominators.
I can solve word problems involving subtracting decimal fractions with
like denominators.
I can use visual models or equations to represent word problems.
Understand decimal notation for fractions, and compare decimal
fractions.
4.NF.C.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.
4.NF.C.5
I can change a fraction with 10 as a denominator to an equivalent fraction
with 100 as a denominator.
I can add a fraction with a denominator of 10 and another fraction with a
denominator of 100.
4.NF.C.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.
4.NF.C.6
I can express a fraction with a denominator of 10 as a decimal.
I can express a fraction with a denominator of 100 as a decimal.
I can locate a decimal on a number line.
4.NF.C.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 results of comparisons with the symbols >,
=, or <, and justify the conclusions, e.g., by using a visual model.
4.NF.C.7
I can reason about the size of decimals by comparing them to the same
whole.
I can compare decimals by using symbols, <,>, or = and use a visual
model to demonstrate the comparison.
Measurement and Data 4.MD
Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.
4.MD.A.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
4.MD.A.2
I can use the four operations to solve word problems involving only one
type of unit and/or quantity.
I can represent measurement using diagrams.
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.
Vocabulary:
compare
decimal fraction
decimal notation
denominator
equivalent
fraction
hundredths
numerator
partitioning
place value
tenths
unit fraction
I can solve word problems involving various measurements with like
units expressed by whole numbers, simple fractions, and decimals.
Unit 4 – Using Big Numbers: Estimating and Calculating
Pacing: 6 Weeks
Essential Question(s):
1. How does place value and properties of operations help in developing and understanding strategies for multiplication and division?
2. How does composing and decomposing multi-digit numbers assist in problem solving?
3. How is using estimation helpful in seeing the reasonableness of an answer when solving problems?
4. How does a story context affect interpreting and using a remainder?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
CCSSM Standards
Operations and Algebraic Thinking 4.OA
Use the four operations with whole numbers to solve problems.
4.OA.A.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.
4.OA.A.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.
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
4.OA.A.2
I can use multiplication or division to solve word problems that involve
thinking multiplicatively.
I can use drawings or equations with symbols to represent word
problems.
I can use drawings or equations to distinguish multiplicative comparison
from additive comparison.
4.OA.A.3
I can perform each step of a multi-step problem using any of the four
operations.
I can interpret remainders in word problems.
I can represent word problems using equations with a letter standing for
the unknown quantity.
I can use estimation strategies such as rounding to check my answer.
Number and Operations in Base Ten² 4.NBT
Generalize place value understanding for multi-digit whole numbers.
4.NBT.A.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.
4.NBT.A.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.
4.NBT.A.1
I can explain the value of each digit in a multi-digit number as ten times
the digit to the right.
I can use place value to justify answers to multiplication problems
involving multiples of 10.
I can use place value to justify answers to division problems involving
multiples of 10.
4.NBT.A.2
I can read and write a multi-digit number in word form.
I can read and write a multi-digit number using base ten numerals.
I can write a multi-digit number in expanded form.
I can compare two multi-digit numbers using place value and record the
comparison using symbols >, <, =.
4.NBT.A.3
4.NBT.A.3
Use place value understanding to round multi-digit whole numbers to any I can use the value of the digit to the right of the place to be rounded to
place.
determine whether to round up or down.
I can write a multi-digit number rounded to any given place.
Use place value understanding and properties of operations to
perform multi-digit arithmetic.
4.NBT.B.4
4.NBT.B.4
Fluently add and subtract multi-digit whole numbers using the standard
I can add whole numbers using a standard algorithm.
algorithm.
I can subtract whole numbers using a standard algorithm.
I can add and subtract whole numbers without getting “stuck” in the
problems.
4.NBT.B.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.NBT.B.5
I can multiply a multi-digit number of no more than 4 digits by a one
digit number.
I can multiply a two digit number by a two digit number.
I can use an area model to explain the multiplication of multi-digit
numbers.
I can use a rectangular array to explain the multiplication of multi-digit
numbers.
4.NBT.B.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.
Vocabulary:
algorithm
base ten system
properties (distributive, associative, and commutative)
estimation
fact families
multiplication strategy
patterns
place value
problem solving
product
rounding
partial products
area model
composing
decomposing
multiplicative comparisons
expanded notation
standard form
4.NBT.B.6
I can divide a multi-digit number of no more than 4 digits by a one-digit
number.
I can explain division calculations using the relationship between
multiplication and division.
I can explain division calculations using place value and the properties of
operations.
I can illustrate and explain my calculations using equations.
I can illustrate and explain my calculations using an array/area model.
I can write an equation to represent a multi-digit division problem.
Unit 5 – Using Fractions
Pacing: 7 Weeks
Essential Question(s):
1. How are fractions used in everyday life?
2. How can understanding unit fractions help us make sense of, build, and use other fractions?
3. How and when are equivalent fractions helpful in solving problems? What models or strategies are useful for generating equivalent
fractions?
4. How is estimating useful when performing operations with fractions?
5. What models help visualize, reason about, and generalize operations with fractions?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
Pre-requisite Knowledge:
CCSSM Standards
Number and Operations—Fractions³ 4.NF
Extend understanding of fraction equivalence and ordering.
4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.
4.NF.A.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.
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
4.NF.A.1
I can explain why fractions are equivalent using visual models.
I can create equivalent fractions by multiplying or dividing the numerator
and the denominator by the same number.
4.NF.A.2
I can compare two given fractions by creating equivalent fractions with
common denominators.
I can compare two fractions by creating equivalent fractions with
common numerators.
I can compare two fractions by reasoning about their size, the location on
a number line, or a benchmark fraction.
I can use <, >, and = symbols to record my comparisons of fractions.
I can justify my comparisons using visual fraction models.
Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3
I can rewrite non-unit fractions as the sum of identical unit fractions.
4.NF.B.3a
Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
4.NF.B.3a
I can describe adding fractions as joining while referring to the same
whole for both fractions.
I can describe subtracting fractions as separating while referring to the
same whole for both fractions.
4.NF.B.3b
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.
4.NF.B.3b
I can rewrite fractions as sums in multiple different ways using smaller
fractions with the same denominator.
I can justify my decompositions of fractions using visual fraction models.
4.NF.B.3c
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.
4.NF.B.3c
I can add mixed numbers using multiple strategies.
I can subtract mixed numbers using multiple strategies.
I can change mixed numbers with common denominators into equivalent
fractions that I can add or subtract.
4.NF.B.3d
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.
4.NF.B.3d
I can solve word problems involving adding fractions with like
denominators.
I can solve word problems involving subtracting fractions with like
denominators.
I can use visual models or equations to represent word problems.
4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a
fraction by a whole number.
4.NF.B.4
I can multiply a fraction by a whole number.
I can use what I know about multiplication to explain how to multiply a
fraction by a whole number.
I can use a visual model to show the product of a whole number and a
fraction.
4.NF.B.4a
Understand a fraction a/b as a multiple of 1/b. For example, use a visual
fraction model to represent 5/4 as the product 5 × (1/4), recording the
conclusion by the equation 5/4 = 5 × (1/4).
4.NF.B.4b
Understand a multiple of a/b as a multiple of 1/b, and use this
understanding to multiply a fraction by a whole number. For example,
use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing
this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
4.NF.B.4c
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?
Measurement and Data 4.MD
Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.
4.MD.A.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.
4.MD.B.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.
Vocabulary:
addition of fractions (joining)
4.NF.B.4a
I can describe a fraction a/b as a whole number multiplied by a unit
fraction.
I can change a multiplication fraction model to an equivalent
multiplication fraction model.
4.NF.B.4b
I can multiply a fraction by a whole number using my understanding of
fractions as multiples of unit fractions.
I can use reasoning about fractions as multiples to generalize about
multiplying fractions by whole numbers.
4.NF.B.4c
I can solve word problems involving multiplying a fraction by a whole
number.
I can use visual fraction models to represent word problems.
I can use equations to represent word problems.
4.MD.A.2
I can use the four operations to solve word problems involving units and
quantities.
I can represent measurement using diagrams.
I can solve word problems involving various measurements expressed by
whole numbers, fractions, and decimals.
4.MD.B.4
I can create a line plot to represent data.
I can create a line plot with a given data set of measurements using
fractions as a unit.
I can use information presented in a line plot to solve problems involving
addition and subtraction.
benchmark fractions
compare
compose/decompose
denominator
equipartitioning
equivalency
estimation
improper fraction
like/common denominator
mixed numbers
multiplication of fractions
numerator
proper fraction
subtraction of fractions (separating)
unit fractions
Unit 6 – Using Perimeter and Area
Pacing: 3 Weeks
Essential Question(s):
1. How might paying attention to units of measurement assist in solving problems?
2. What structures in polygons help in solving measurement problems?
3. How can we use equations and symbols to represent the relationship between linear measurement in a polygon and its perimeter?
4. How can we use equations and symbols to represent the relationship between measurements in a rectangle and its area?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
CCSSM Standards
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
Operations and Algebraic Thinking 4.OA
Use the four operations with whole numbers to solve problems.
4.OA.A.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5
× 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.
4.OA.A.1
I can compare numbers using multiplication operations.
I can compare numbers using multiplicative reasoning and words such as
“35 is 5 times as many as 7.”
I can rewrite comparison statements using multiplication equations.
4.OA.A.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.
4.OA.A.2
I can use multiplication or division to solve word problems that involve
thinking multiplicatively.
I can use drawings or equations with symbols to represent word
problems.
I can use drawings or equations to distinguish multiplicative comparison
from additive comparison.
4.OA.A.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.
4.OA.A.3
I can perform each step of a multi-step problem using any of the four
operations.
I can interpret remainders in word problems.
I can represent word problems using equations with a letter standing for
the unknown quantity.
I can use estimation strategies such as rounding to check my answer.
Number and Operations in Base Ten² 4.NBT
Use place value understanding and properties of operations to
perform multi-digit arithmetic.
4.NBT.B.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.NBT.B.5
I can multiply a multi-digit number of no more than 4 digits by a one
digit number.
I can multiply a two digit number by a two digit number.
I can use an area model to explain the multiplication of multi-digit
numbers.
I can use a rectangular array to explain the multiplication of multi-digit
numbers.
4.NBT.B.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.
Measurement and Data 4.MD
Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.
4.MD.A.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.
4.MD.A.3
Apply the area and perimeter formulas for 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.
Vocabulary:
area
area measurement
equation
formula
linear measurement
perimeter
unknown
4.NBT.B.6
I can divide a multi-digit number of no more than 4 digits by a one-digit
number.
I can explain division calculations using the relationship between
multiplication and division.
I can explain division calculations using place value and the properties of
operations.
I can illustrate and explain my calculations using equations.
I can illustrate and explain my calculations using an array/area model.
I can write an equation to represent a multi-digit division problem.
4.MD.A.2
I can use the four operations to solve word problems involving units and
quantities.
I can represent measurement using diagrams.
I can solve word problems involving various measurements expressed by
whole numbers, fractions, and decimals.
4.MD.A.3
I can explain and apply the formula for area of a rectangle.
I can explain and apply the formula for perimeter of a rectangle.
I can view the formula for area of a rectangle in multiple different ways.
I can view the formula for the perimeter of a rectangle in multiple
different ways.
Unit 7 – Units of Measure and Equivalence
Pacing: 4 Weeks
Essential Question(s):
1. Why is knowing relative sizes within a system important?
2. Why is it helpful to convert from a larger unit of measurement to a smaller unit of measurement within a system?
3. What can you learn by creating and analyzing conversion tables?
4. How is developing models for representing and solving measurement problems helpful?
Mathematical Practices:
**Make sense of problems and persevere in solving them.
**Reason abstractly and quantitatively.
**Construct viable arguments and critique the reasoning of others.
**Model with Mathematics.
CCSSM Standards
**Use appropriate tools strategically.
Attend to precision.
**Look for and make use of structure.
Look for and express regularity in repeated reasoning.
I Can…
Operations and Algebraic Thinking 4.OA
Use the four operations with whole numbers to solve problems.
4.OA.A.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5
× 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.
4.OA.A.1
I can compare numbers using multiplication operations.
I can compare numbers using multiplicative reasoning and words such as
“35 is 5 times as many as 7.”
I can rewrite comparison statements using multiplication equations.
Generate and analyze patterns.
4.OA.C.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
Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.
4.MD.A.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.
4.OA.C.5
I can generate a number pattern that follows a given rule.
I can generate a shape pattern that follows a given rule.
I can identify features of a pattern that are not given in the rule.
I can reason about the features of a pattern to explain why it will
continue.
4.MD.A.1
I can describe the relative size of measurement units.
I can represent a larger unit as a multiple of smaller units within the same
system of measurement.
I can generate conversion tables to help me reason about units and
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), ...
quantities.
I can convert units within the same system of measurement.
4.MD.A.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.
4.MD.A.2
I can use the four operations to solve word problems involving units and
quantities.
I can represent measurement using diagrams.
I can solve word problems involving various measurements expressed by
whole numbers, fractions, and decimals.
Vocabulary:
conversion
conversion table
customary
decompose
distance
equivalent
liquid volume
mass
metric
patterns
regrouping
relative sizes of measurement
units of length, volume, mass, and time