Mathematics – Grade 4
In fourth grade, students become proficient with multiplication and division of whole
numbers, while developing an understanding of fractions and decimals. In measurement,
they develop an understanding of area. The concept of probability as chance is developed
and fourth graders continue to expand their understanding of statistics using graphing
and measures of central tendency. Students refine their estimation skills for computation
and measurement and develop an understanding of the relations between and among
two-dimensional (plane) figures. They graph points in Quadrant 1 on a coordinate plane
and extend and duplicate patterns. Students recognize geometric reflections and
translations. They draw conclusions and support them in familiar situations.
EALR 1: The student understands and applies the concepts and
procedures of mathematics.
COMPONENT 1.1: Understand and apply concepts and procedures from number
sense.
1.1.1 Understand the concepts and symbolic representations of decimals in money
and fractions. W
EXAMPLES
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Represents part of a whole or parts of a set as fractions with common
denominators.
Represent decimals (money) in multiple ways including symbols, pictures, and
physical models.
Illustrate fractions as parts of a whole object, number, or set.
Explain or shows how a fraction can be decomposed as a sum of smaller
fractions.
1.1.2 Understand the relative values of decimals in money and fractions. W
EXAMPLES
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EX
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Describe or shows equivalent fractions using models including pictures, paper
folding, geoboards, and parallel number lines.
Approximate halves, thirds, and fourths in relationship to whole units on a
number line.
Order fractions with like-denominators using numbers, pictures, and objects.
Explain or shows equivalent relationships between decimals and fractions.
Explain how to order fractions and/or decimals related to money.
Explain why one fraction is greater than, less than, or equal to another fraction.
1.1.3 Understand and use the associative property of addition and multiplication
and the commutative, identity, and zero properties of multiplication on whole
numbers. W
EXAMPLES
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Explain the commutative property of multiplication and give examples.
Explain the identity property of addition and multiplication and give examples.
Explain why equations are true or false based on one of the properties of addition
or multiplication.
Illustrate and demonstrate the use of the commutative, associative, or identity
property of addition or multiplication using words, pictures, numbers, or objects.
Use addition or multiplication properties to replicate a computational strategy
when given an example.
Illustrate and demonstrate the use of the zero property of multiplication on whole
numbers.
1.1.5 Understand the meaning of addition and subtraction of like-denominator
fractions. W
EXAMPLES
EX
EX
EX
EX
Represent addition and subtraction of fractions with like-denominators using
numbers, pictures, and models including everyday objects, fraction circles,
number lines, and geoboards.
Use joining, separating, part-part-whole, and comparison situations to add and
subtract like-denominator fractions.
Translate a given picture or illustration into an equivalent symbolic representation
of addition and subtraction of like denominator fractions.
Select and/or use an appropriate operation to show understanding of addition and
subtraction of like-denominator fractions.
1.1.6 Use computational procedures for multiplication and division of whole
numbers. W
EXAMPLES
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EX
EX
EX
EX
Select and develop strategies that help with recall of multiplication and division
facts through 12s.
Select and test algorithms used in computational situations that involve
multiplication and division of whole numbers and explain strategies.
Compute with whole numbers using a combination of any two operations in a
given situation.
Explain and apply strategies or uses procedures to multiply 2-digits numbers by 3digits numbers and/or divide three or four digit numbers by two digit numbers
without remainders.
Appropriately apply and explain the concept of remainder in a given context.
1.1.7 Apply strategies and use tools appropriate to tasks involving multiplication
and division of whole numbers.
EXAMPLES
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EX
Select and use appropriate tools from among mental computation, estimation,
calculators, manipulatives, and paper and pencil to compute in a given situation.
Explains why a selected tool is most efficient for a situation.
1.1.8 Apply estimation strategies involving multiplication and division of whole
numbers to predict or determine the reasonableness of answers in situations.
W
EXAMPLES
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Explain when an estimation or exact answer is or is not appropriate.
Apply a variety of estimation strategies, including multiples of 10 and 100,
rounding, and compatible numbers, to predict an answer prior to computation.
Use estimation to check the reasonableness of calculated results.
Explain an appropriate adjustment when an estimate and a calculation don’t agree.
COMPONENT 1.2: Understand and apply concepts and procedures from
measurement.
1.2.1 Understand the concept of area. W
EXAMPLES
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Demonstrate and explain how area covers a figure and perimeter encloses an area.
Illustrate the difference between perimeter and area with drawings.
Describe situations where area is the needed measurable attribute.
Describe objects using measurements of area.
Describe pictorial representations of objects or figures illustrating area
measurements.
1.2.2 Understand the differences between length (linear) units and area (square)
units in the U.S. or metric system. W
EXAMPLES
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Describe area measurements using different units.
Explain how the linear measurement units are related to area measurement units.
Determine the unit used to measure area.
Explain why area is measured in square units.
1.2.3 Understand how measurement units of time and weight are organized in the
U.S. system. W Understand how measurement units of length, mass, and
capacity are organized in the metric system.
EXAMPLES
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EX
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Explain and cite examples of the system of standard units for time.
Explain how standard units of weight are organized in the U.S. system.
Convert between units in the U.S. system:

Weight – ounce, pound

Time – second, minute, hour, day, week, month, year
Show how to convert units of length, mass, and capacity within the metric system
in order to answer a question.
1.2.4 Use a procedure to measure length, perimeter, and area. W
EXAMPLES
Suggested Procedure:
— Identifies the attribute to measure.
— Selects an appropriate unit to measure the attribute identified.
— Selects a tool that matches the unit chosen.
— Uses the selected tool to determine the number of units.
— Reports or records the number of units and a label.
EX
EX
EX
Measure length and perimeter using the suggested procedure.
Measure area using the suggested procedure with manipulatives or grid paper and
counting the square units.
Demonstrate why a given measurement is correct or incorrect.
1.2.6 Understand and apply strategies to obtain reasonable estimates of area
measurements for irregular figures. W
EXAMPLES
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Describe situations in which estimated measurements are appropriate.
Explain a process that can be used to find a reasonable estimate of the area
measurement of an irregular figure.
Determine and explains whether estimation or precision is needed in a given
situation.
Use estimation to determine the area of a rectangle and record the number of units
with a label.
COMPONENT 1.3: Understand and apply concepts and procedures from
geometric sense.
1.3.1 Understand the concepts of parallel and perpendicular lines and line
symmetry in 2-dimensional shapes and figures. W
EXAMPLES
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Explain parallel and perpendicular and give examples to demonstrate them.
Explain symmetry and use examples to demonstrate symmetry in 2-dimensional
shapes and figures.
Draw one or more lines of symmetry in a given 2-dimensional figure.
Describe properties of 2-dimensional figures including parallel and perpendicular
lines or lines of symmetry.
1.3.2 Use properties of 2-dimensional shapes and figures, including congruence.
W
EXAMPLES
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Draw and label 2-dimensional figures given particular attributes including
congruence.
Sort, classify, and label congruent 2-dimensional figures and shapes in multiple
orientations.
1.3.3 Locate or plot points in the first quadrant on a coordinate grid. W
EXAMPLES
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Locate points or objects in the first quadrant on a coordinate grid in terms of
horizontal and vertical position.
Plot a given set of ordered pairs in the first quadrant of a coordinate grid.
Use ordered pairs to name the location of points or objects in the first quadrant of
a coordinate grid.
1.3.4 Understand the change made to the position of a 2-dimensional shape or
figure by a single translation (slide) or reflection (flip) with or without a grid.
W
EXAMPLES
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Show and explain a translation or reflection using a 2-dimensional shape or
figure.
Record results of a translation or a reflection on a grid by listing the ordered pairs
of the new vertices.
Demonstrate or draw and describes a single translation or a single reflection.
Describe translations and/or reflections in designs.
Draw the figure resulting from a particular translation or reflection on a grid.
COMPONENT 1.4: Understands and apply concepts and procedures from
probability and statistics.
1.4.1 Understand when events are certain, impossible, possible, more likely, less
likely, or equally likely. W
EXAMPLES
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Predict the likelihood of events and use the vocabulary of probability.
Explain why some outcomes are equally likely or more or less likely to happen
than others.
Explain why events are certain or uncertain.
Place events in order based on their likelihood of occurrence.
Identify and describe possible and impossible events.
Determine and explain which events are more likely, less likely, or equally likely
to happen, given an area model.
Construct a spinner game or situation to produce a given outcome.
1.4.3 Understand how to use appropriate questions and samples to collect
information about a specific topic. W
EX Develop appropriate questions and identify populations to obtain information
about a topic.
EX Determine which of several questions is most likely to give the needed
information.
EX Select data collection methods including conducting a survey, using observations,
or measuring.
EX
Make and explains a plan to collect, record, and organize data.
1.4.4 Understand, determine, and use median and mode to describe a set of data.
W
EXAMPLES
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Explain what the median represents and how to find it for a set of data.
Determine the median and mode for a set of data.
Explain whether the mode or median better describes a set of data.
Determine data points that would result in a given median.
Use pictures to illustrate median.
Complete a set of data based on a given median or mode and a partial set of data.
1.4.5 Read and understand data from line plots and pictographs. W
EXAMPLES
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Read and interpret data from line plots.
Describe a trend from a given line plot.
Summarize text and data in a given table, chart, line plot, pictograph, or bar
graph.
Describe the completeness and accuracy of data in a graph, given a set of data.
Explain whether the components of a graph are appropriate.
Explain whether a line plot, pictograph, table, chart, or bar graph is more
appropriate for a given situation or to answer a question most effectively.
Read and interpret a pictograph where the scale is more than one unit.
COMPONENT 1.5: Understand and apply concepts and procedures from algebraic
sense.
1.5.1 Recognize, understand, and extend a pattern of shapes and/or objects or a
pattern of numbers with a single addition, subtraction, or multiplication
between terms. W
EXAMPLES
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Extend, describe, or construct patterns of numbers, using addition, subtraction, or
multiplication, based on a single operation between terms.
Extend, describe, or construct patterns of shapes or objects.
Extend and represent patterns using words, tables, numbers, physical models,
and/or pictures.
Construct a number pattern and explain what makes it a pattern.
Determine missing elements in the beginning, middle, and/or end of a pattern.
1.5.2 Describe a rule for a pattern with a single arithmetic operation.
W
EXAMPLES
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Identify or generate a rule for a pattern with a single arithmetic operation in order
to extend or fill in parts of the pattern.
Show growing patterns using objects or pictures and explain the rule.
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Determine the operation that changes the elements of one set of numbers into the
elements of another set of numbers such as using a function machine.
Explain why a given rule fits a pattern based on a single arithmetic operation in
the rule.
1.5.3 Understand the concept of mathematical inequality and uses the symbols =,
<, and > in equations and inequalities W. Uses ≠ in inequalities.
EXAMPLES
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Explain inequality and the use of ≠, >, or < in inequalities.
Use the symbols >, <, and ≠ to show the relevant value of multiplication or
division expressions.
Identify or describes a situation that represents a given expression, equation, or
inequality using =, ≠, < or >.
Express relationships between quantities using =, ≠, <, or >.
1.5.4 Use a single variable to write expressions and equations that represent
situations involving multiplication and division of whole numbers. W
EXAMPLES
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Read formulas, expressions, and equations involving a single variable.
Use mathematical symbols including a single variable to write expressions and
equations to represent a given situation.
Describe a situation that represents a given expression or equation that includes a
single variable.
Explain the meaning of a single variable in a formula, expression, or equation.
1.5.5 Apply algebraic properties to evaluate expressions and formulas with
addition, subtraction, or multiplication involving whole numbers. W
EXAMPLES
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Illustrate expressions using manipulatives, physical models, pictures, and/or
symbols.
Substitute a numeric value for a symbol in an expression or formula and compute
as indicated.
1.5.6 Apply algebraic properties to solve equations involving multiplication and
division. W
EXAMPLES
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Solve a simple equation using addition, subtraction, multiplication, or division. .
Write and solve a one-step equation for a given situation.
Explain the meaning of the solution for an equation.
EALR 2: The student uses mathematics to define and solve problems.
COMPONENT 2.1: Define problems.
2.1.1 Identify questions to be answered to solve a problem in familiar situations. W
EXAMPLES
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Investigate the situation and determine if there is a problem to solve.
Define or clarify the question the problem presents.
Generate questions that would need to be answered in order to solve the problem.
2.1.2 Determine what information is missing or extraneous in familiar situations.
W
EXAMPLES
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Identify missing information that is needed to solve the problem.
Differentiate between information that is needed or not needed to solve the
problem.
2.1.3 Identify what is known and unknown in familiar situations. W
EXAMPLES
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Examine information to identify what is known and unknown.
COMPONENT 2.2: Construct solutions.
2.2.1 Select and use relevant information to construct solutions. W
EXAMPLES
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Select and use relevant data and information in a problem situation.
2.2.2 Selects and use appropriate concepts and procedures from number sense,
measurement, geometric sense, and/or statistics to construct solutions. W
EXAMPLES
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Use addition, subtraction, multiplication, and/or division of whole numbers to
construct a solution.
Use measurements related to length, perimeter, time, money value, weight/mass,
capacity, temperature, or area to construct a solution.
Use properties of 2-dimensional figures, congruence, location, translation, or
reflection in the first quadrant of a grid to construct a solution.
Use median and/or mode to construct a solution.
2.2.3 Apply a variety of strategies to construct solutions. W
EXAMPLES
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Use tools such as manipulatives, pictures, charts, calculators, or measurement
tools to construct a solution.
Select and apply appropriate strategies to construct a solution.
Determine when an approach is unproductive and tries a new approach.
Explain whether a given solution applies strategies appropriately.
2.2.4 Determine whether a solution is viable, is mathematically correct, and
answers the question(s). W
EXAMPLES
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Check work for mathematical accuracy.
Check whether the solution is reasonable for the situation.
Check the solution with an estimate or results from an alternate approach.
Check to be certain the solution answers the question.
EALR 3: The student uses mathematical reasoning.
COMPONENT 3.1: Analyze information.
3.1.1 Analyze and compare numerical, measurement, geometric, and/or statistical
information in familiar situations. W
EXAMPLES
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Compare mathematical information and results represented in tables, charts,
pictographs, bar graphs, line plots, text, diagrams, figures, or pictures.
Examine mathematical information diagrams and/or pictorial representations and
describe agreements or differences.
Differentiate between a valid and invalid comparison of mathematical information
or results.
COMPONENT 3.2: Conclude.
3.2.1 Draw and support conclusions. W
EXAMPLES
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Draw a conclusion from a given situation and support the conclusion with
appropriate numerical, measurement, geometric, and/or statistical data or facts.
Use evidence, data, or facts to support or challenge a conclusion.
3.2.2 Evaluate procedures and conclusions in familiar situations. W
EXAMPLES
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Evaluate selection and implementation of procedures in given situations.
Check the viability and appropriate use of a selected procedure in a given
situation.
COMPONENT 3.3: Verify results.
3.3.1 Justify results using evidence. W
EXAMPLES
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3.3.2
Justifies results using evidence and information from the problem situation as
well as known facts, patterns, and relationships.
Evaluate reasonableness of results. W
EXAMPLES
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Check for reasonableness of results in a given situation.
Verify that the solution to a problem makes sense in relation to the situation.
3.3.3 Understand how to validate thinking about numerical, measurement,
geometric, and/or statistical ideas. W
EXAMPLES
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Explain and support thinking about numerical, measurement, geometric, and/or
statistical ideas, using patterns and relationships.
Explain and support thinking about numerical, measurement, geometric, and/or
statistical ideas using models and known facts.
EALR 4: The student communicates knowledge and understanding in
both everyday and mathematical language.
COMPONENT 4.1: Gather information.
4.1.1 Understand how to develop and follow a plan for collecting numerical,
measurement, geometric, and/or statistical information. W
EXAMPLES
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Determine and explain what mathematical information is needed for a specific
purpose.
Develop and explain a plan, not a survey, to collect mathematical information
including what information is needed and where and how to find the information.
Develop and follow a plan, not a survey, to collect mathematical information for a
specific purpose by reading, listening, or observing.
4.1.2 Extract numerical, measurement, geometric, and/or statistical information
from one or two different sources for a given purpose. W
EXAMPLES
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Extract and use mathematical information from various sources such as pictures,
symbols, text, tables, charts, models, pictographs, bar graphs, or line plots for a
specific purpose.
Write questions that could be answered using data sources such as magazines,
newspapers, menus, sales or travel brochures, TV or bus schedules, or sales
receipts.
EX
Use reading, listening, and observation skills and strategies to extract
mathematical information for a given purpose.
COMPONENT 4.2: Organize, represent, and share information.
4.2.1 Understand how to organize numerical, measurement, geometric, and/or
statistical information to communicate for a given purpose. W
EXAMPLES
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Select a useful format and organize mathematical information for a given purpose
4.2.2 Understand how to represent numerical, measurement, geometric, and/or
statistical information in graphs or other appropriate forms. W
EXAMPLES
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Represent mathematical information in pictures, tables, charts, pictographs, bar
graphs, line plots, drawings, or other appropriate forms and include title, labels,
appropriate and consistent scales, and accurate data display.
4.2.3 Use mathematical language to explain or describe numerical, measurement,
geometric, and/or statistical ideas and information in ways appropriate for
audience or purpose. W
EXAMPLES
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Use both everyday and mathematical language and notation to explain, describe,
or defend mathematical ideas, facts, properties, procedures, or strategies
appropriate for a given purpose or audience.
EALR 5: The student understands how mathematical ideas connect
within mathematics, to other subject areas, and to real-world situations.
COMPONENT 5.1: Relate concepts and procedures within mathematics.
5.1.1 Apply concepts and procedures from any two of the content strands,
including number sense, measurement, geometric sense, statistics, and/or
algebraic sense, in a given problem or situation. W
EXAMPLES
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Use concepts and procedures from two or more content strands in a given
problem or situation.
5.1.2 Use equivalent mathematical models to represent a mathematical idea. W
EXAMPLES
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Identify mathematical models equivalent to a given mathematical model or
representation.
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Explain how two different models represent the same mathematical idea.
Create a mathematical model or representation that is equivalent to a given
graphical, numerical, pictorial, geometric, and/or written model or representation.
COMPONENT 5.2: Relate mathematical concepts and procedures to other
disciplines.
5.2.1 Use mathematical thinking, modeling, patterns, and ideas in other
disciplines.
EXAMPLES
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Identify how mathematics is used in other disciplines.
Use mathematics in other disciplines.
5.2.2 Recognize contributions of individuals and cultures to the development of
mathematics.
EXAMPLES
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Identify or describe contributions of various cultures to mathematics.
COMPONENT 5.3: Relate mathematical concepts and procedures to real-world
situations.
5.3.1 Understand that mathematics is used extensively in daily life outside the
classroom.
EXAMPLES
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Generate examples and explain how mathematics is used in everyday life.
Describe real-world situations in which mathematics can be used to solve
problems with implications for home and the classroom.
5.3.2 Identify how mathematics is used in career settings.
EXAMPLES
EX
Describe examples of mathematics associated with a given career.