*CCSS Math Grade 4 Year at a Glance*|

*Grade 4 Scope and Sequence Common Core Math Standards*

*Grade 4 Scope and Sequence Common Core Math Standards*

*Summary of Year*

*Fourth grade CCSS mathematics is about (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3)*

*understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions—concepts, skills, and problem solving*

**CCSS Math Year at a Glance**

- 1st Grade Scope and Sequence Year at A Glance
- 2nd Grade Scope and Sequence Year at A Glance
- 3rd Grade Scope and Sequence Year at A Glance
- 4th Grade Scope and Sequence Year at A Glance
- 5th Grade Scope and Sequence Year at A Glance
- 6th Grade Scope and Sequence Year at A Glance
- 7th Grade Scope and Sequence Year at A Glance
- 8th Grade Scope and Sequence Year at A Glance

**CCSS Math Content Emphasis by Cluster (PARCC/SBAC)**

**Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction**

**Module 2: Unit Conversions and Problem Solving with Metric Measurement**

**Module 3: Multi-Digit Multiplication and Division**

**Module 4: Angle Measure and Plane Figures**

**Module 5: Fraction Equivalence, Ordering, and Operations**

**Module 6: Decimal Fractions**

**Module 7: Exploring Multiplication**

**Grade 4 CCLS Major Emphasis Clusters**

**Operations and Algebraic Thinking**

• Use the four operations with whole
numbers to solve problems.

**Number and Operations in Base Ten**

• Generalize place value
understanding for multi-digit whole numbers.

• Use place value understanding and
properties of operations to perform multi-digit arithmetic.

**Number and Operations – Fractions**

• Extend understanding of fraction
equivalence and ordering.

• Build fractions from unit fractions
by applying and extending previous understandings of operations on
whole numbers.

• Understand decimal notation for
fractions, and compare decimal fractions.

**Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction (25 days)**

**4.OA.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.NBT.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.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.3**Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding and
properties of operations to perform multi-digit arithmetic.

**4.NBT.4**Fluently add and subtract multi-digit whole numbers using the standard algorithm.

**Module 2: Unit Conversions and Problem Solving with Metric Measurement (7 days)**

*Solve problems involving measurement and conversion of measurements from a larger unit to a smaller*

*unit.*

**4.MD.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), …

**4.MD.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.

**Module 3: Multi-Digit Multiplication and Division (43 days)**

**4.OA.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.

**4.OA.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. (See Glossary, Table 2.)

**4.OA.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. Gain familiarity
with factors and multiplies.

**4.OA.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. Use place
value understanding and properties of operations to perform
multi-digit arithmetic. (Grade 4 expectations in this domain are
limited to whole numbers less than or equal to 1,000,000.)

**4.NBT.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.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. Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit.

**4.MD.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.

**Module 4: Angle Measure and Plane Figures (20 days)**

*Geometric measurement: understand concepts of angle and measure angles.*

**4.MD.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.

**4.MD.6**Measure angles in whole-number degrees using a protractor. Sketch angles of specified

measure.

**4.MD.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.

Draw and identify lines and angles, and
classify shapes by properties of their lines and angles.

Draw points, lines, line segments,
rays, angles (right, acute, obtuse), and perpendicular and

parallel lines. Identify these in
two-dimensional figures.

**Module 5: Fraction Equivalence, Ordering, and Operations (45 days)**

*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. 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. Generate and analyze patterns.*

**4.OA.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. Extend
understanding of fraction equivalence and ordering. (Grade 4
expectations in this domain are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

**4.NF.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.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
understanding of operations on whole numbers.

**4.NF.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.

**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.**4.NF.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 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). b. 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.)

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? Solve problems involving
measurement and conversion of measurements from a larger unit to a
smaller unit.

**4.MD.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.
Represent and interpret data.

**4.MD.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.

**Module 6: Decimal Fractions (20 days)**

*Understand decimal notations for fractions, and compare decimal fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)*

**4.NF.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. (Students who can

generate equivalent fractions can
develop strategies for adding fractions wit unlike denominators in
general. But addition and subtraction with unlike denominators in
general is not a requirement at this grade.) For example, express
3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

4.NF.6

**4.NF.7**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. Compare two decimals to
hundredths by reasoning about their size. Recognize that comparison
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. Solve
problems involving measurement and conversion of measurements from a
larger unit to a smaller unit.

**4.MD.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.

**Module 7: Exploring Multiplication (20 days)**

*Use the four operations with whole numbers to solve problems.*

**4.OA.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.

**4.OA.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.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 place
value understanding and properties of operations to perform
multi-digit arithmetic.

**4.NBT.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.

Solve problems involving measurement
and conversion of measurements from a larger unit to a smaller

unit.

**4.MD.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), …

**4.MD.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.

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