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Note: The specification of each standard is followed by links to lessons on AAAMath.com/AAAKnow.com that may be relevant to that standard.
Grade 4 Common Core State Standards
Grade 4 » Operations & Algebraic Thinking
Use the four operations with whole numbers to solve problems.
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.
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
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.
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.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
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.
Grade 4 » Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
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.
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
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.
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
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.
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.
Grade 4 » Number & Operations—Fractions
Extend understanding of fraction equivalence and ordering.
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.
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.
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
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.
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.
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.
Apply and extend previous understandings of multiplication to multiply a fraction
by a whole number.
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).
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.)
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?
Understand decimal notation for fractions, and compare decimal fractions.
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.
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
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.
Grade 4 » Measurement & Data
Solve problems involving measurement and conversion of measurements.
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), ...
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.
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.
Represent and interpret data.
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.
Geometric measurement: understand concepts of angle and measure angles.
Recognize angles as geometric shapes that are formed wherever two rays share a
common endpoint, and understand concepts of angle measurement:
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.
An angle that turns through n one-degree angles is said to have an angle measure
of n degrees.
Measure angles in whole-number degrees using a protractor. Sketch angles of
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.
Grade 4 » Geometry
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.
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.
Portions © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Portions © John Banfill 2014