Math GPS Standards
Grade 4
By the end of grade four, students will add and subtract decimal fractions and common
fractions with common denominators. They will also understand how and when it is
appropriate to use rounding. Students will use common measurement units to determine
weight. Students will develop their understanding of measuring angles with appropriate
units and tools. Students will understand the characteristics of geometric plane and solid
figures. They will also use tables, graphs, and charts to record and analyze data.
Instruction and assessment should include the use of manipulatives and appropriate
technology. Topics should be represented in multiple ways including concrete/pictorial,
verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be
introduced and used in the context of real world phenomena.
Concepts / Skills to Maintain
Multiplication and Division of whole numbers
Area
Perimeter
Place Value
Length
Elapsed Time
NUMBER AND OPERATIONS
Students will further develop their understanding of whole numbers and master the four
basic operations with whole numbers by solving problems. They will also understand
rounding and when to use it appropriately. Students will further develop their
understanding of addition and subtraction of decimal fractions and common fractions
with like denominators.
M4N1. Students will further develop their understanding of how whole numbers
and decimals are represented in the base-ten numeration system.
a. Identify place value names and places from hundredths through one million.
b. Equate a number’s word name, its standard form, and its expanded form.
M4N2. Students will understand and apply the concept of rounding numbers.
a. Round numbers to the nearest ten, hundred, or thousand.
b. Describe situations in which rounding numbers would be appropriate and
determine whether to round to the nearest ten, hundred, or thousand.
c. Determine to which whole number or tenth a given decimal is closest using
tools such as a number line, and/or charts.
d. Round a decimal to the nearest whole number or tenth.
e. Represent the results of computation as a rounded number when appropriate
and estimate a sum or difference by rounding numbers.
3-5 Mathematics Georgia Performance Standards
Grade 4
M4N3. Students will solve problems involving multiplication of 2-3 digit numbers by
1 or 2 digit numbers.
M4N4. Students will further develop their understanding of division of whole
numbers and divide in problem solving situations without calculators.
a. Know the division facts with understanding and fluency.
b. Solve problems involving division by 1 or 2-digit numbers (including those
that generate a remainder).
c. Understand the relationship between dividend, divisor, quotient, and
remainder.
d. Understand and explain the effect on the quotient of multiplying or dividing
both the divisor and dividend by the same number. (2050 ÷ 50 yields the
same answer as 205 ÷ 5).
M4N5. Students will further develop their understanding of the meaning of decimals
and use them in computations.
a. Understand decimals are a part of the base-ten system.
b. Understand the relative size of numbers and order two digit decimals.
c. Add and subtract both one and two digit decimals.
d. Model multiplication and division of decimals by whole numbers.
e. Multiply and divide both one and two digit decimals by whole numbers.
M4N6. Students will further develop their understanding of the meaning of decimal
fractions and common fractions and use them in computations.
a. Understand representations of equivalent common fractions and/or decimal
fractions.
b. Add and subtract fractions and mixed numbers with like denominators.
(Denominators should not exceed twelve.)
c. Use mixed numbers and improper fractions interchangeably.
M4N7. Students will explain and use properties of the four arithmetic operations to
solve and check problems.
a. Describe situations in which the four operations may be used and the
relationships among them.
b. Compute using the order of operations, including parentheses.
c. Compute using the commutative, associative, and distributive properties.
d. Use mental math and estimation strategies to compute.
MEASUREMENT
Students will measure weight in appropriate metric and standard units. They will also
measure angles.
M4M1. Students will understand the concept of weight and how to measure weight.
a. Use standard and metric units to measure the weight of objects.
b. Know units used to measure weight (gram, kilogram, ounces, pounds, and
tons).
c. Compare one unit to another within a single system of measurement.
M4M2. Students will understand the concept of angles and how to measure them.
a. Use tools, such as a protractor or angle ruler, and other methods such as
paper folding, drawing a diagonal in a square, to measure angles.
b. Understand the meaning and measure of a half rotation (180°) and a full
rotation (360°).
c. Determine that the sum of the three angles of a triangle is always 180°.
GEOMETRY
Students will understand and build plane and solid geometric figures. They will also
graph points on the coordinate plane.
M4G1. Students will define and identify the characteristics of geometric figures
through examination and construction.
a. Examine and compare angles in order to classify and identify triangles by
their angles.
b. Describe parallel and perpendicular lines in plane geometric figures.
c. Examine and classify quadrilaterals (including parallelograms, squares,
rectangles, trapezoids, and rhombi) by their properties.
d. Compare and contrast the relationships among quadrilaterals.
M4G2. Students will understand fundamental solid figures.
a. Compare and contrast a cube and a rectangular prism in terms of the number
and shape of their faces, edges, and vertices.
b. Describe parallel and perpendicular lines and planes in connection with the
rectangular prism.
c. Build/collect models for solid geometric figures (cubes, prisms, cylinders,
pyramids, spheres, and cones) using nets and other representations.
M4G3. Students will use the coordinate system.
a. Understand and apply ordered pairs in the first quadrant of the coordinate
system.
b. Locate a point in the first quadrant in the coordinate plane and name the
ordered pair.
c. Graph ordered pairs in the first quadrant.
ALGEBRA
Students will investigate and represent mathematical relationships between
quantities using mathematical expressions in problem-solving situations.
M4A1. Students will represent and interpret mathematical relationships in
quantitative expressions.
a. Understand and apply patterns and rules to describe relationships and solve
problems.
b. Represent unknowns using symbols, such as □ and Δ.
c. Write and evaluate mathematical expressions using symbols and different
values.
DATA ANALYSIS AND PROBABILITY
Students will gather, organize, and display data. They will also compare features of
graphs.
M4D1. Students will gather, organize, and display data according to the situation
and compare related features.
a. Construct and interpret line graphs, line plot graphs, pictographs, Venn
diagrams, and bar graphs.
b. Investigate the features and tendencies of graphs.
c. Compare different graphical representations for a given set of data.
d. Identify missing information and duplications in data.
e. Determine and justify the range, mode, and median of a set of data.
PROCESS STANDARDS
Each topic studied in this course should be developed with careful thought toward
helping every student achieve the following process standards.
M4P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M4P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M4P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M4P4. Students will make connections among mathematical ideas and to other
disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to
produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M4P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate
mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve
problems.
c. Use representations to model and interpret physical, social, and mathematical
phenomena.
The following terms and symbols are often misunderstood. These concepts are not an
inclusive list and should not be taught in isolation. However, due to evidence of frequent
difficulty and misunderstanding associated with these concepts, instructors should pay
particular attention to them and how their students are able to explain and apply them.
The definitions are for teacher reference only and are not to be memorized by students.
Teachers should present these concepts to students with models and real life examples.
Students should understand the concepts involved and be able to recognize and/or
demonstrate them with words, models, pictures, or numbers.
Terms / Symbols:
mixed fraction, proper fraction, improper fraction, point, ray, line, line segment, parallel,
perpendicular, diagonal line, plane, weight, ounce, pound, ton, gram, kilogram,
protractor, degree, rotation, parallelogram, trapezoid, rhombus, rectangular prism,
pyramid, coordinate system, ordered pair, line graph, right triangle, acute triangle, obtuse
triangle, net, median, mode, range, straight angle
By the end of grade four, students will add and subtract decimal fractions and common
fractions with common denominators. They will also understand how and when it is
appropriate to use rounding. Students will use common measurement units to determine
weight. Students will develop their understanding of measuring angles with appropriate
units and tools. Students will understand the characteristics of geometric plane and solid
figures. They will also use tables, graphs, and charts to record and analyze data.
Instruction and assessment should include the use of manipulatives and appropriate
technology. Topics should be represented in multiple ways including concrete/pictorial,
verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be
introduced and used in the context of real world phenomena.
Concepts / Skills to Maintain
Multiplication and Division of whole numbers
Area
Perimeter
Place Value
Length
Elapsed Time
NUMBER AND OPERATIONS
Students will further develop their understanding of whole numbers and master the four
basic operations with whole numbers by solving problems. They will also understand
rounding and when to use it appropriately. Students will further develop their
understanding of addition and subtraction of decimal fractions and common fractions
with like denominators.
M4N1. Students will further develop their understanding of how whole numbers
and decimals are represented in the base-ten numeration system.
a. Identify place value names and places from hundredths through one million.
b. Equate a number’s word name, its standard form, and its expanded form.
M4N2. Students will understand and apply the concept of rounding numbers.
a. Round numbers to the nearest ten, hundred, or thousand.
b. Describe situations in which rounding numbers would be appropriate and
determine whether to round to the nearest ten, hundred, or thousand.
c. Determine to which whole number or tenth a given decimal is closest using
tools such as a number line, and/or charts.
d. Round a decimal to the nearest whole number or tenth.
e. Represent the results of computation as a rounded number when appropriate
and estimate a sum or difference by rounding numbers.
3-5 Mathematics Georgia Performance Standards
Grade 4
M4N3. Students will solve problems involving multiplication of 2-3 digit numbers by
1 or 2 digit numbers.
M4N4. Students will further develop their understanding of division of whole
numbers and divide in problem solving situations without calculators.
a. Know the division facts with understanding and fluency.
b. Solve problems involving division by 1 or 2-digit numbers (including those
that generate a remainder).
c. Understand the relationship between dividend, divisor, quotient, and
remainder.
d. Understand and explain the effect on the quotient of multiplying or dividing
both the divisor and dividend by the same number. (2050 ÷ 50 yields the
same answer as 205 ÷ 5).
M4N5. Students will further develop their understanding of the meaning of decimals
and use them in computations.
a. Understand decimals are a part of the base-ten system.
b. Understand the relative size of numbers and order two digit decimals.
c. Add and subtract both one and two digit decimals.
d. Model multiplication and division of decimals by whole numbers.
e. Multiply and divide both one and two digit decimals by whole numbers.
M4N6. Students will further develop their understanding of the meaning of decimal
fractions and common fractions and use them in computations.
a. Understand representations of equivalent common fractions and/or decimal
fractions.
b. Add and subtract fractions and mixed numbers with like denominators.
(Denominators should not exceed twelve.)
c. Use mixed numbers and improper fractions interchangeably.
M4N7. Students will explain and use properties of the four arithmetic operations to
solve and check problems.
a. Describe situations in which the four operations may be used and the
relationships among them.
b. Compute using the order of operations, including parentheses.
c. Compute using the commutative, associative, and distributive properties.
d. Use mental math and estimation strategies to compute.
MEASUREMENT
Students will measure weight in appropriate metric and standard units. They will also
measure angles.
M4M1. Students will understand the concept of weight and how to measure weight.
a. Use standard and metric units to measure the weight of objects.
b. Know units used to measure weight (gram, kilogram, ounces, pounds, and
tons).
c. Compare one unit to another within a single system of measurement.
M4M2. Students will understand the concept of angles and how to measure them.
a. Use tools, such as a protractor or angle ruler, and other methods such as
paper folding, drawing a diagonal in a square, to measure angles.
b. Understand the meaning and measure of a half rotation (180°) and a full
rotation (360°).
c. Determine that the sum of the three angles of a triangle is always 180°.
GEOMETRY
Students will understand and build plane and solid geometric figures. They will also
graph points on the coordinate plane.
M4G1. Students will define and identify the characteristics of geometric figures
through examination and construction.
a. Examine and compare angles in order to classify and identify triangles by
their angles.
b. Describe parallel and perpendicular lines in plane geometric figures.
c. Examine and classify quadrilaterals (including parallelograms, squares,
rectangles, trapezoids, and rhombi) by their properties.
d. Compare and contrast the relationships among quadrilaterals.
M4G2. Students will understand fundamental solid figures.
a. Compare and contrast a cube and a rectangular prism in terms of the number
and shape of their faces, edges, and vertices.
b. Describe parallel and perpendicular lines and planes in connection with the
rectangular prism.
c. Build/collect models for solid geometric figures (cubes, prisms, cylinders,
pyramids, spheres, and cones) using nets and other representations.
M4G3. Students will use the coordinate system.
a. Understand and apply ordered pairs in the first quadrant of the coordinate
system.
b. Locate a point in the first quadrant in the coordinate plane and name the
ordered pair.
c. Graph ordered pairs in the first quadrant.
ALGEBRA
Students will investigate and represent mathematical relationships between
quantities using mathematical expressions in problem-solving situations.
M4A1. Students will represent and interpret mathematical relationships in
quantitative expressions.
a. Understand and apply patterns and rules to describe relationships and solve
problems.
b. Represent unknowns using symbols, such as □ and Δ.
c. Write and evaluate mathematical expressions using symbols and different
values.
DATA ANALYSIS AND PROBABILITY
Students will gather, organize, and display data. They will also compare features of
graphs.
M4D1. Students will gather, organize, and display data according to the situation
and compare related features.
a. Construct and interpret line graphs, line plot graphs, pictographs, Venn
diagrams, and bar graphs.
b. Investigate the features and tendencies of graphs.
c. Compare different graphical representations for a given set of data.
d. Identify missing information and duplications in data.
e. Determine and justify the range, mode, and median of a set of data.
PROCESS STANDARDS
Each topic studied in this course should be developed with careful thought toward
helping every student achieve the following process standards.
M4P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M4P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M4P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M4P4. Students will make connections among mathematical ideas and to other
disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to
produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M4P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate
mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve
problems.
c. Use representations to model and interpret physical, social, and mathematical
phenomena.
The following terms and symbols are often misunderstood. These concepts are not an
inclusive list and should not be taught in isolation. However, due to evidence of frequent
difficulty and misunderstanding associated with these concepts, instructors should pay
particular attention to them and how their students are able to explain and apply them.
The definitions are for teacher reference only and are not to be memorized by students.
Teachers should present these concepts to students with models and real life examples.
Students should understand the concepts involved and be able to recognize and/or
demonstrate them with words, models, pictures, or numbers.
Terms / Symbols:
mixed fraction, proper fraction, improper fraction, point, ray, line, line segment, parallel,
perpendicular, diagonal line, plane, weight, ounce, pound, ton, gram, kilogram,
protractor, degree, rotation, parallelogram, trapezoid, rhombus, rectangular prism,
pyramid, coordinate system, ordered pair, line graph, right triangle, acute triangle, obtuse
triangle, net, median, mode, range, straight angle
