GLE/Competency

First Trimester

Second Trimester

Third Trimester

1.1.1
Understand the concepts and symbolic representations of mixed numbers,
proper and improper fractions, and decimals. W

· Explain the value for a given digit and/or show how to read and write
decimals to at least the thousandths place.

· Represent parts of a Represent mixed numbers, proper and improper
fractions, and decimals using words, pictures, models, and/or numbers.
· Make a model when given a symbolic representation or write a fraction
or decimal when given a number line, picture, or model.
· Explain how the value of a fraction changes in relationship to the
size of the whole.
· Represent improper fractions as mixed numbers and mixed numbers as
improper fractions.


1.1.2
Understand the relative values of non‑negative fractions or
decimals. W


· Identify and/or explain the relationship among equivalent decimals
and fractions.
· Explain why one fraction is greater than, less than, or equal to
another fraction.
· Explain why one decimal is greater than, less than, or equal to
another decimal.
· Show how factors and multiples can be used to name equivalent
fractions.


1.1.3
Understand and apply the concept of divisibility including primes,
composites, factors, and multiples. W

· Illustrate prime or composite numbers by creating a physical
model.
· Identify prime or composite numbers between 1 and 100 and explain why
a whole number is prime or composite.
· Explain or demonstrate why a number is prime or composite.

· Use the concepts of odd and even numbers to check for
divisibility.
· Explain how to find the least common multiple (LCM) and greatest
common factor (GCF) of two numbers.
· Use factors, multiples, and prime and composite numbers in a variety
of situations.
· Factor a number into its prime factorization or into factor
pairs.
· Explain or show whether one number is a factor of another number.


1.1.5
Understand the meaning of addition and subtraction of
non‑negative decimals and fractions. W


· Represent or explain addition and subtraction of non‑negative
decimals through thousandths using words, pictures, models, or numbers.
· Select and/or use an appropriate operation(s) to show understanding
of addition and subtraction of non‑negative decimals and/or fractions.
· Explain the relationship between addition and subtraction of
non‑negative decimals and fractions.
· Translate a picture or illustration into an equivalent symbolic
representation of addition and subtraction of non‑negative fractions and
decimals.

· Represent addition and subtraction of fractions with denominators of
2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10.
· Explain a strategy for adding and subtracting fractions.

1.1.6
Apply strategies or uses computational procedures to add and subtract
non‑negative decimals and
like‑denominator fractions.


· Select and develop Add and subtract non‑negative decimals and
like‑denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12,
and/or 15.
· Find sums or differences of decimals or like‑denominator
fractions in given situations.
· Calculate sums of two numbers with decimals to the thousandths or
three numbers with decimals to hundredths.
· Calculate difference of numbers with decimals to thousandths.


1.1.7
Apply strategies and uses tools appropriate to tasks involving
addition and subtraction of non‑negative decimals or like‑denominator
fractions.

· Select and use appropriate tools from among mental computation,
estimation, calculators, manipulatives, and paper and pencil to compute in a
given situation.

· Explain why a selected strategy or tool is more efficient or more
appropriate than another strategy or tool for a situation.
· Describe strategies for mentally adding or subtracting
non‑negative decimals and/or like‑denominator fractions.


1.1.8
Apply estimation strategies involving addition and subtraction of
non‑negative decimals and like‑denominator fractions to predict
results or determine reasonableness of answers. W

· Compute to check the reasonableness of estimated answers for a given
situation.


· Explain when an estimation or exact answer is or is not
appropriate.
· Use a variety of estimation strategies to predict an answer prior to
computation
· Use estimation to verify the reasonableness of calculated
results.
· Explain an appropriate adjustment when an estimate and a computation
do not agree.
· Explain or describe a strategy used for estimation involving addition
and subtraction of non‑negative decimals and like‑denominator
fractions.

1.2.1
Understand the concept of angle measurement. W



· Explain and provide examples of how angles are formed.
· Identify or describe angles in pictures, diagrams, illustrations and
in the environment.
· Sort, classify, and label angles as equal to, less than, or greater
than 90°.
· Describe angles in shapes and figures as equal to, less than, or
greater than 90°.

1.2.2
Understand the concept of degree as a unit of measurement for angles.
W



· Sort, classify, and label angles as approximately 30°, 45°,
60°, 90°, or 180°.
· Explain how degrees are used as measures of angles.
· Describe an angle in relation to a 90° angle.
· Draw angles with approximate measures of 30°, 45°, 60°,
90°, and 180°.
· Identify or describe angles with approximate measures of 30°,
45°, 60°, 90°, or 180° with or without a protractor.

1.2.3
Understand how measurement units of capacity, mass, and length are
organized in the metric system. W



· Explain and cite examples of the metric system units for capacity,
mass, and length.
· Explain or show the relationship between units in the metric system
for capacity, mass, or length.
· Convert between units in the metric system:
· Length  millimeter, centimeter, meter, kilometer
· Capacity  milliliter, liter
· Mass  gram, kilogram

1.2.4
Use a systematic procedure to measure and describe the area of
rectangles or triangles. W



· Suggested Procedure:
• Identify the attribute to measure.
• Select an appropriate unit to measure the attribute identified.
• Select a tool that matches the unit chosen.
• Use the selected tool to determine the number of units.
• Report or record the number of units and a label.
· Measure the area in figures composed of rectangles and triangles.
· Select and describe the appropriate units and/or tools for measuring
length, perimeter, and/or area.
· Demonstrate a procedure for measuring the area of a rectangle or
right triangle.
· Use procedures to measure length, perimeter, and/or area.
· Determine whether an area measurement has been done correctly.

1.2.5
Use formulas to determine perimeter and area of rectangles and right
triangles. W



· Explain how to find the perimeter or area of any rectangle using a
rule.
· Explain and use formulas to calculate the perimeter or area of a
rectangle and labels units.
· Determine and label right triangles and all rectangles with whole
number dimensions and a given perimeter or area.
· Explain why formulas are used to find area and/or perimeter.
· Explain and use a formula to determine or calculate the area of a
right triangle and labels units.

1.2.6
Understand and apply strategies to obtain reasonable estimates of
angle measurements and areas of rectangles and right triangles. W



· Describe situations in which estimated measurements are
appropriate.
· Explain an appropriate process for estimating perimeter or area of a
rectangle or right triangle or an angle measurement.
· Use estimation to determine reasonableness of an angle or area
measurement.
· Draw angles with measurements that are approximately 30^{o},
45^{o}, 60^{o}, 90^{o}, or 180^{o}.
· Estimate and label areas of rectangles and right triangles.
· Determine whether an angle is closest to 30°, 45°, 60°,
90°, or 180°.

1.3.1
Understand the attributes of angles and polygons. W



· Explain the difference between a regular and irregular polygon.
· Describe a 2‑dimensional shape and/or figure using properties
including number of sides, number of vertices, and types of angles.
· Use and/or explain mathematical conventions used to label vertices,
line segments, and angles.
· Draw a simple 2‑dimensional shape and/or figure having given
characteristics including number of sides, number of vertices, types of angle(s),
and/or congruence.

1.3.2
Use the properties of parallel and perpendicular lines and line of
symmetry. W



· Describe parallel and perpendicular lines and/or lines of
symmetry.
· Draw, describe, and/or label angles, quadrilaterals, parallel and/or
perpendicular lines, lines of symmetry, and congruent 2‑dimensional shapes
or figures.
· Sort, classify, and label shapes and figures using the properties of
parallel lines, perpendicular lines, and lines of symmetry.
· Complete pictures or designs from a variety of cultures that
incorporate parallel line(s), perpendicular line(s), and/or a line(s) of
symmetry.
· Draw, describe, and/or label a figure or design that includes a given
set of properties including parallel or perpendicular lines and/or line of
symmetry.
· Complete a picture or design using a line of symmetry.

1.3.3
Locate or plot points with whole number, fraction, and/or decimal
coordinates on a positive number line. W



· Plot points with positive coordinates on a number line.
· Describe the relative position of fractions and/or decimals on a
positive number line.
· Identify or move the coordinates of points on an incomplete number
line involving fractional or decimal increments.

1.3.4
Understand and apply translations or reflections to a
2‑dimensional shape or figure. W



· Describe whether a figure has been translated or reflected.
· Draw a translation or reflection of a given figure on a grid.
· Use translations or reflections to describe patterns in art,
architecture, or nature.
· Create designs using translations and/or reflections.
· Identify a picture or diagram of a particular translation or
reflection.

1.4.1
Understand the likelihood of simple events occurring. W



· Determine whether a real‑life event has zero probability, 50%
probability, or 100% probability of occurring.
· Predict and test how likely it is that a certain outcome will
occur.
· Given a fair game, create an advantage for one of the players.
· Explain whether a game for two people is fair.
· Create a spinner, game, or situation that would produce a fair
outcome or make it more or less likely for an event to happen.
· Explain why some outcomes are equally likely or more or less likely
to happen than others.

1.4.2
Use procedures to determine possible outcomes of situations or simple
experiments. W


· List and/or count possible outcomes of simple experiments.

· Use strategies, including pictures, lists, and tree diagrams, to show
the possible outcomes of a simple experiment.

1.4.3
Understand how different collection methods or different questions can
affect the data collected. W


· Write questions needed to obtain data about a specific topic.
· Explain how different data collection methods, including phone
survey, internet search, and person‑to‑person survey, affect the data
set for a given question.
· Describe an appropriate sample for a given question.
· Describe the appropriate sample for a given population.
· Explain how different samples, populations, or questions can affect
the data.


1.4.4
Understand and use the mean, median, and mode to describe a set of
data. W


· Explain how to determine the mean of a set of data and explain the
significance of the mean.
· Determine the mean of a given set of data using objects or
pictures.
· Determine and explain whether mean, median, or mode is the most
appropriate measure of central tendency in a given situation.
· Explain why the mean, median, or mode may be greater than or less
than the other measures for a given set of data.
· Determine the mean for two samples from the same population and
explain why they may not be the same.


1.4.5
Read data presented in text and circle graphs. W


· Read and interpret data from text and circle graphs in terms of
patterns.
· Explain the completeness and accuracy of data presented in circle
graphs.
· Explain whether line plots, pictographs, tables, charts, bar or
circle graphs are more appropriate for a given set of data, particular situation,
or purpose, or answers a question most effectively.
· Summarize data presented in a circle graph or text.
· Describe trends or patterns in data represented in a line plot or
pictograph.


1.5.1
Recognize, extend, and/or create patterns of objects or shapes or
patterns of numbers with a single arithmetic operation between terms.
W


· Extend, describe, or create patterns of shapes or objects.
· Extend and represent patterns using words, tables, numbers, models,
and pictures.
· Extend a pattern by supplying missing elements in the beginning,
middle, and/or end of the pattern.

· Recognize, extend, and/or create patterns of numbers using division
based on a single operation between terms.

1.5.2
Develop a rule for patterns, which may include combinations of two
arithmetic operations. W


· Generate a rule for a pattern to extend or fill in parts of the
pattern.
· Determine a rule for a pattern of alternating operations and explains
the rule.
· Identify a rule for a pattern with two operations between terms.
· Explain why a given rule with a single operation fits a given
pattern.
· Describe or write a rule for a pattern based on a single
operation.
· 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 equality and inequality and
uses the symbols for equal, not equal, less than and greater than.


· Express relationships between like denominator fractions and decimal
quantities using the symbols for equal, not equal, less than and greater
than.

· Describe a situation represented by an equation or inequality
involving like denominator fractions and/or decimals.
· Write a simple equation or inequality using non‑negative
decimals or like‑denominator fractions to represent a given situation.

1.5.4
Use variables to write expressions and equations that represent
situations involving addition and subtraction of non‑negative decimals and
like‑denominator fractions. W

· Write an expression or equation using a variable to represent a given
situation.
· Describe a situation that represents a given expression or equation
that includes a variable.
· Explain the meaning of a variable in a formula, expression, or
equation.
· Write or illustrate expressions or equations using manipulatives,
models, pictures, and symbols for given situations.

· Read expressions and equations involving variables.


1.5.5
Apply algebraic properties to evaluate expressions using
manipulatives, pictures, and/or symbols. W


· Show and/or explain how to substitute a numeric value for a symbol in
an expression.
· Determine the value of simple expressions or formulas involving
addition and subtraction of non‑negative decimals and like denominator
fractions and/or multiplication and division of whole numbers given the values of
the variables.
· Write an expression with a variable to represent a situation and
determine the value of the expression given a value for the variable.


1.5.6
Apply properties to solve equations involving multiplication and
division. W

· Write and solve an equation in a given situation.
· Explain or show the meaning of the solution to an equation.


· Solve a one‑step equation involving multiplication or division
using manipulatives, pictures, and/or symbols.

EALR 2: The student uses mathematics to define and solve
problems.
2.1 Define problems.
2.2 Construct solutions.

GLE/Competency

First Trimester

Second Trimester

Third Trimester

2.1.1
Formulate questions to be answered to solve a problem. W

· Define or clarify the question the problem presents.
· Generate questions that would need to be answered in order to solve
the problem.


· Investigate a situation and determines if there is a problem to
solve.

2.1.2
Determine what information is missing or extraneous. W

· Differentiate between information that is necessary or
extraneous.


· Determine what missing information is needed to solve the
problem.

2.1.3
Identify what is known and unknown in familiar situations.
W



· Determine what data, numbers, and information are known and
unknown.

2.2.2
Apply concepts and procedures from number sense, measurement,
geometric sense, and/or statistics to construct solutions. W

· Determine whether a given solution shows use of concepts and
procedures that are appropriate.


· Select and use appropriate concepts and procedures to construct a
solution.

2.2.3
Apply a variety of strategies and approaches, to construct solutions.
W

· Select and apply a variety of strategies and approaches to construct
a solution.
· Determine when an approach is unproductive and modify or try a new
approach.
· Determine whether a given solution shows the application of
strategies that are appropriate.


· Select and use tools such as rulers, manipulatives, calculators, and
technology to construct a solution.

2.2.4
Determine whether a solution is viable, is mathematically correct, and
answers the question(s). W

· Determine 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.


· Check work for mathematical accuracy.

EALR 3: The student uses mathematical reasoning.
3.1 Analyze information.
3.2 Conclude.
3.3 Verify results.

GLE/Competency

First Trimester

Second Trimester

Third Trimester

3.1.1
Analyze numerical, measurement, geometric, and/or statistical
information in familiar situations. W


· Analyze mathematical information or results represented in tables,
charts, graphs, text, diagrams, figures, or pictures.
· Compare mathematical information represented in tables, charts,
graphs, text, diagrams, figures, or pictures.
· Identify agreements and/or differences between mathematical
information, diagrams, and/or pictorial representations.
· Differentiate between valid and invalid analysis of mathematical
information or results.


3.2.1
Draw and support conclusions. W

· Use data or examples as evidence to support or contradict a given
conclusion.
· Identify a valid conclusion based on given information.


· Draw a conclusion from a given situation and support the conclusion
with appropriate numerical, measurement, geometric, and/or statistical data or
facts.

3.2.2
Evaluate selection and implementation of procedures and conclusions in
familiar situations. W

· Evaluate procedures and/or results based on a given situation.


· Check the viability and appropriate use of selected procedures in a
given situation.

3.3.1
Justify results using evidence.



· Justify results using evidence and information from the problem
situation as well as known facts, patterns, and relationships.

3.3.2
Evaluate reasonableness of results. W



· Check for reasonableness of results in a given situation.

3.3.3
Understand how to validate thinking about numerical, measurement,
geometric, and/or statistical ideas. W



· Explain and support thinking about mathematical ideas using models,
facts, patterns, or relationships.

EALR 4: The student communicates knowledge and understanding in both
everyday and mathematical language.
4.1 Gather information.
4.2 Organize, represent, and share information.

GLE/Competency

First Trimester

Second Trimester

Third Trimester

4.1.1
Understand how to develop and follow a plan for collecting numerical,
measurement, geometric, and/or statistical information. W


· Develop a plan, not a survey, for collecting mathematical
information, including what information is needed and where and how to find the
information.
· List or describe the general procedure or order of steps of a plan to
gather exactly the mathematical information sought with no irrelevant
information.
· Follow a plan, not a survey, to collect mathematical information for
a given audience and purpose.

· Determine appropriate mathematical information needed for a specific
purpose or audience.

4.1.2
Extract numerical, measurement, geometric, and/or statistical
information from multiple sources for a given purpose. W


· Extract and use mathematical information from various sources such as
pictures, symbols, text, tables, charts, bar graphs, line plots, pictographs,
circle graphs, and/or models for a purpose.
· Write questions to be answered using data sources such as magazines,
newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales
receipts.


4.2.1
Understand how to organize numerical, measurement, geometric, and/or
statistical information to communicate for a given purpose. W

· 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


· Represent mathematical information using tables, charts, pictographs,
bar graphs, line plots, circle graphs, pictures, models, drawings, or other forms
including titles, labels, appropriate and consistent scales, and accurate display
of data.


4.2.3
Use mathematical language to explain or describe numerical,
measurement, geometric, and/or statistical ideas and information in ways
appropriate for audience and purpose. W



· Use both everyday and mathematical language and notation to explain,
defend, or present mathematical ideas, facts, procedures or strategies
appropriate for a given audience or purpose.

EALR 5: The student understands how mathematical ideas connect within
mathematics, to other subject areas, and to real‑world
situations.
5.1 Relate concepts and procedures within mathematics.
5.2 Relate mathematical concepts and procedures to other disciplines.

GLE/Competency

First Trimester

Second Trimester

Third Trimester

5.1.1
Apply concepts and procedures from any two of the content strands,
including number sense, measurement, geometric sense, probability and statistics,
and/or algebraic sense, in a given problem or situation. W



· 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

· Explain how two or more different models represent the same
mathematical idea.
· Create a model or representation that is equivalent to a given
graphical, numerical, pictorial, geometric, and/or written model or
representation.


· Identify mathematical models or representations that are equivalent
to a given model or representation.

5.2.1
Use mathematical thinking, modeling, patterns, and ideas in other
disciplines.

· Use mathematical concepts and procedures in other disciplines.


· Give examples of mathematical patterns and ideas in other
disciplines.

5.2.2
Recognize the contributions of individuals and cultures to the
development of mathematics.



· Describe a contribution to the development of mathematics.

5.3.1
Understand that mathematics is used extensively in daily life outside
the classroom.

· Describe situations in which mathematics can be used to solve
problems with implications in a classroom or school.


· Generate examples and explain how mathematics is used in everyday
life.

5.3.2
Understand that mathematics is used in many occupations or
careers.

· Describe the mathematical requirements to enter a given career.
· Describe the mathematics used by workers in a specific job.


· Describe specific examples of mathematics associated with a given
career.
