Priority Academic Student Skills
Oklahoma State Department of Education 22 Grade 4
OVERVIEW
MATHEMATICS
Grades 1 - 5

Developmentally appropriate mathematics curriculum for Grades 1 - 5 must encourage
the exploration of a wide variety of mathematical ideas and promote in-depth levels of
understanding by focusing on the key concepts and processes. Programs should fit the needs of
the learner. Student success depends largely on the quality of the foundation that is established
during the first years of school. The mathematics curriculum for Grades 1 - 5 must:
Help children develop conceptual understanding of number, space, and situational
problems by designing explorations and investigations that make use of everyday objects and
specially designed materials (e.g., base-10 blocks).
Actively involve children in doing mathematics with extensive and thoughtful use of
manipulatives (concrete materials) in an environment that encourages children to develop,
discuss, test, and apply ideas.
Develop newly introduced mathematics concepts by beginning instruction with concrete
experiences, progressing to pictorial representations and culminating with abstract symbols.
Require appropriate reasoning and problem-solving experiences from the outset, instilling
in students a sense of confidence in their ability to think and communicate mathematically, to
detect patterns, and to analyze data.
Emphasize the power of mathematics in helping children understand and interpret their
world and solve problems that occur in it.
Include a broad range of content by incorporating an informal approach to measurement,
geometry, data analysis, and patterns (algebra). This helps students see the usefulness of
mathematics and establishes a foundation for further study.
Provide appropriate and ongoing use of technology by enabling children to explore
number ideas and patterns, to focus on problem-solving processes, and to investigate realistic
applications. Calculators do not replace the need for students to be fluent with basic facts, have
efficient computation strategies, be able to compute mentally, and do paper-and-pencil
computation.
NOTE:
Asterisks (*) have been used to identify standards and objectives that must be assessed by the
local school district. All other skills may be assessed by the Oklahoma School Testing Program
(OSTP).

Priority Academic Student Skills
Oklahoma State Department of Education 23 Grade 4

MATHEMATICS PROCESS STANDARDS
Grades 1-5

The National Council of Teachers of Mathematics (NCTM) has identified five process
standards: Problem Solving, Communication, Reasoning and Proof, Connections, and
Representation. Using these processes students are actively involved in deepening mathematical
understandings which lead to increasingly sophisticated abilities required to meet mathematical
challenges. Following is an outline of the five process standards and associated objectives.
NOTE: When examples are given there is a progression in levels of difficulty from basic to
more complex skills.
Process Standard 1: Problem Solving
1. Use problem-solving approaches (e.g., act out situations, represent problems with
drawings and lists, use concrete, pictorial, graphical, oral, written, and/or algebraic
models, understand a problem, devise a plan, carry out the plan, look back).
2. Formulate problems from everyday and mathematical situations (e.g., how many
forks are needed?, how many students are absent?, how can we share/divide these
cookies?, how many different ways can we find to compare these fractions?).
3. Develop, test, and apply strategies to solve a variety of routine and nonroutine
problems (e.g., look for patterns, make a table, make a problem simpler, process of
elimination, trial and error).
4. Verify and interpret results with respect to the original problem (e.g., students explain
verbally why an answer makes sense, explain in a written format why an answer
makes sense, verify the validity of each step taken to obtain a final result).
5. Distinguish between necessary and irrelevant information in solving problems (e.g.,
play games and discuss �best� clues, write riddles with sufficient information,
identify unnecessary information in written story problems).
Process Standard 2: Communication
1. Express mathematical ideas coherently and clearly to peers, teachers, and others
(e.g., with verbal ideas, models or manipulatives, pictures, or symbols).
2. Extend mathematical knowledge by considering the thinking and strategies of others
(e.g., agree or disagree, rephrase another student�s explanation, analyze another
student�s explanation).
3. Relate manipulatives, pictures, diagrams, and symbols to mathematical ideas.
4. Represent, discuss, write, and read mathematical ideas and concepts. Start by relating
everyday language to mathematical language and symbols and progress toward the
use of appropriate terminology (e.g., �add more� becomes �plus�, �repeated addition�
becomes �multiplication�, �fair share� becomes �divide�, �balance the equation�
becomes �solve the equation�).
Priority Academic Student Skills
Oklahoma State Department of Education 24 Grade 4
Process Standard 3: Reasoning
1. Explain mathematical situations using patterns and relationships (e.g., identify
patterns in situations, represent patterns in a variety of ways, extend patterns to
connect with more general cases).
2. Demonstrate thinking processes using a variety of age-appropriate materials and
reasoning processes (e.g., manipulatives, models, known facts, properties and
relationships, inductive [specific to general], deductive [general to specific], spatial,
proportional, logical reasoning [�and� �or� �not�] and recursive reasoning).
3. Make predictions and draw conclusions about mathematical ideas and concepts.
Predictions become conjectures and conclusions become more logical as students
mature mathematically.
Process Standard 4: Connections
1. Relate various concrete and pictorial models of concepts and procedures to one
another (e.g., use two colors of cubes to represent addition facts for the number 5,
relate patterns on a hundreds chart to multiples, use base-10 blocks to represent
decimals).
2. Link concepts to procedures and eventually to symbolic notation (e.g., represent
actions like snap, clap, clap with symbols A B B, demonstrate 3 � 4 with a geometric
array, divide a candy bar into 3 equal pieces that represent one piece as 13
).
3. Recognize relationships among different topics within mathematics (e.g., the length
of an object can be represented by a number, multiplication facts can be modeled with
geometric arrays, 12
can be written as .5 and 50%).
4. Use mathematical strategies to solve problems that relate to other curriculum areas
and the real world (e.g., use a timeline to sequence events, use symmetry in art work,
explore fractions in quilt designs and to describe pizza slices).
Process Standard 5: Representation
1. Create and use a variety of representations appropriately and with flexibility to
organize, record, and communicate mathematical ideas (e.g., dramatizations,
manipulatives, drawings, diagrams, tables, graphs, symbolic representations).
2. Use representations to model and interpret physical, social, and mathematical
situations (e.g., counters, pictures, tally marks, number sentences, geometric models;
translate between diagrams, tables, charts, graphs).

Priority Academic Student Skills
Oklahoma State Department of Education 25 Grade 4
MATHEMATICS CONTENT STANDARDS
Grade 4

The following concepts and skills are required by all students completing fourth grade. The
Major Concepts should be taught in depth using a variety of methods and applications so that
all students have accessibility to and an understanding of these concepts. Maintenance
Concepts have been taught previously and are a necessary foundation for success in
mathematics at this level.
MAJOR CONCEPTS MAINTENANCE CONCEPTS
Patterns and Algebraic Reasoning � Patterns and Algebraic Reasoning �
Extend Rules, Functions Rules
Number Sense - Number Sense-
Place Value through 6 Digits, Place Value through 4 Digits,
Decimals to the 100ths place, Fractions Fraction Concepts
Number Operations and Computation- Number Operations and Computation-
Estimation, Basic Division Facts, Addition & Subtraction with
Fraction Concepts Multidigits, Basic Multiplication Facts
Geometry and Measurement - Lines, Angles, Geometry and Measurement �
Customary & Metric Measurements 2- and 3-Dimensional Shapes,
Length, Weight, Estimation, Time
Data Analysis and Probability - Data Analysis and Probability �
Interpret Graphs, Probability Bar Graphs, Pictographs, Probability
Fourth Grade Suggested Materials Kit:
snap cubes, number cubes, pattern blocks, 1-inch color tiles, grid paper, hundreds charts, cereal
and shoe boxes, children�s books, journals, rods, counters, beans, base-10 blocks, calculators,
geoboards, dot paper, clay, toothpicks, mirrors, flexible straws, pipe cleaners, egg cartons,
containers, balance scales, rulers, tape measures, thermometers, cups, spoons, coins, clocks,
graph mats, spinners, painted beans or two-color counters
Standard 1: Patterns and Algebraic Reasoning - The student will use a variety of
problem-solving approaches to analyze, extend and create patterns.
      1. Discover, describe, extend, and create a wide variety of patterns using tables, graphs,
rules, and models (e.g., use 1-inch tiles to demonstrate that doubling the length of the
side of a square more than doubles the area, explore the characteristics of odd and
even numbers, extend patterns of geometric shapes).
     2. Elementary Function Concepts
          a. Use a variety of techniques to generalize number patterns (e.g., use function
machines and �t-tables� to demonstrate "What is the rule?").
          b. Solve simple open sentences involving operations on whole numbers (with a
variable, e.g., a + 17 = 23).
        Note: Asterisks (*) have been used to identify standards and objectives that must be assessed by the local school district. All other skills may be assessed by the Oklahoma School Testing Program (OSTP).
Priority Academic Student Skills
Oklahoma State Department of Education 26 Grade 4
Standard 2: Number Sense - The student will use numbers and number relationships to
acquire basic number facts.
     1. Place Value
          a. Apply the concept of place value through 6 digits (e.g., write numbers in
expanded form, play a trading game involving place value).
          b. Read, write and rename whole numbers through 6 digits and decimal numbers
to the hundredths (e.g., money, numerals to words).
     2. Compare and order whole numbers and decimals to the hundredths place (e.g.,
pictures of shaded regions of two-dimensional figures, use >, < , = symbols).
     3. Fractions
          a. Use 0, 12, and 1 or 0, 0.5, and 1, as benchmarks and place additional fractions
and decimals on a number line (e.g., 13, 34, 0.7, 0.4).
          b. Create physical and pictorial models of equivalent and nonequivalent fractional
parts to be compared, added or subtracted (e.g., egg cartons, fraction strips, circles, and squares).
Standard 3: Number Operations and Computation - The student will estimate and
compute with whole numbers.
      1. Estimate and find the product of 2- and 3-digit numbers to solve application
problems.
      2. Division Concepts
           a. Demonstrate fluency with basic division facts and fact families.
          *b. Develop division algorithms (e.g., use physical materials to show 12 objects
arranged in 3 groups, show division as repeated subtraction and as the inverse of
multiplication).
          c. Estimate and find the quotient (with and without remainders) with a 1-digit
divisor and a 2- or 3-digit dividend to solve application problems.
     3. Apply a variety of estimation and mental math techniques to simplify computations
(e.g., use rounding to estimate 82 - 58 is about 80 - 60 or 20, use 30 � 5 to find the
product of 300 � 5).
     *4. Develop operation sense by applying the associative property of multiplication (e.g.,
6 � (2 � 3) = (6 � 2) � 3).
Priority Academic Student Skills
Oklahoma State Department of Education 27 Grade 4
Standard 4: Geometry and Measurement - The student will use geometric properties and
relationships to analyze shapes and use standard units of customary and
metric measurements to solve problems.
     1. Basic Characteristics of Lines and Angles
          a. Identify, draw, and construct models of intersecting, parallel, and perpendicular
lines (e.g., use spaghetti, straws, toothpicks).
          b. Identify and compare angles equal to, less than, or greater than 90 degrees (e.g.,
use right angles to determine the approximate size of other angles; make a
variety of angles using flexible straws and compare).
     *2. Identify basic characteristics of the rectangular coordinate system and find the
distance between horizontal and vertical lines of a rectangular coordinate system
(e.g., the x-axis is the horizontal axis).
     3. Spatial Reasoning
          a. Describe the effects on two- and three-dimensional objects when they slide
(translate), flip (reflect), and turn (rotate) (e.g., tessellations).
          b. Predict and verify the effects of combining, subdividing, and changing two- and
three-dimensional figures (e.g., folding paper, tiling, and rearranging pieces of solids).
     4. Measurement
          a. Establish benchmarks for customary and metric units and estimate the measures
of a variety of objects and compare units (e.g., mass: the mass of a raisin is
about 1 gram, length: the width of a finger is about 1 centimeter).
          b. Select appropriate customary and metric units of measure to solve application
problems involving length, weight, mass, and volume.
          c. Solve application problems involving money, time and temperature (e.g.,
elapsed time).
Standard 5: Data Analysis and Probability - The student will demonstrate an
understanding of data collection, display and interpretation.
     1. Data Analysis
          a. Examine data displays such as tallies, tables, charts and graphs and use the
observations to pose and answer questions (e.g., choose a table in social studies
of population data and write problems).
          b. Collect, organize and record data in tables and graphs (e.g., bar, pictograph, line
plots).
     *2. Investigate and record probabilities by experimenting with devices that generate
random outcomes (e.g., coins, number cubes, spinners).
Priority Academic Student Skills
Oklahoma State Department of Education 28 Grade 4
GLOSSARY
addend - in the addition problem 3 + 2 + 6 = 11, the addends are 3, 2, and 6.
algorithm - step-by-step procedure for solving a problem.
analog time - time displayed on a timepiece having hour and minute hands.
array - (rectangular) an orderly arrangement of objects into a rectangular configuration (e.g.,
take six tiles and arrange two long and three wide to form a rectangle).
attribute - characteristics (e.g., size, shape, color, weight).
combinations - a selection of objects without regard to order.
complementary angles - two angles whose measure have a sum of 90 degrees.
complex numbers - numbers of the form a + bi, where a and b are real numbers and i equals the
square root of -1.
composite numbers - any positive integer exactly divisible by one or more positive integers
other than itself and 1.
congruent - geometric figures having exactly the same size and shape.
conic sections - circles, parabolas, ellipses, and hyperbolas which can all be represented by
passing a plane through a hollow double cone.
conjecture - a statement believed to be true but not proved.
cosine - in a right triangle, the cosine of an acute angle is the ratio of the length of the leg
adjacent to the angle to the length of the hypotenuse.
dependent events - events that influence each other. If one of the events occurs, it changes the
probability of the other event.
domain of a relation - the set of all the first elements or x-coordinates of a relation.
exponential function - an exponential function with base b is defined by y = bx, where b > 0
and b is not equal to 1.
expression - a mathematical phrase that can include operations, numerals and variables. In
algebraic terms: 2m + 3x; in numeric terms: 2.4 - 1.37.
Fibonacci sequence - the sequence of numbers, 1, 1, 2, 3, 5, 8, 13, 21, . . . where each number,
except the first two, is the sum of the two preceding numbers.
function - a relation in which each element of the domain is paired with exactly one element of
the range.
function machine - an input/output box (often made with milk cartons, boxes, or drawn on the
board) to show one number entering and a different number exiting. Students guess the rule that
produced the second number (e.g., enter 3, exit 5, rule: add 2).
Priority Academic Student Skills
Oklahoma State Department of Education 29 Grade 4
histogram - a bar graph of a frequency distribution.
imaginary number - any complex number, a + bi, for which a = 0 and b does not = 0.
independent events - events that do not influence one another. Each event occurs without
changing the probability of the other event.
integers - . . . -2, -1, 0, 1, 2, . . .
intercepts (x & y) - the x (y)-coordinate of the point where a graph intercepts the x (y)- axis.
inverse operations - operations that undo each other (e.g., addition and subtraction are inverse
operations; multiplication and division are inverse operations).
irrational numbers - nonterminating, nonrepeating decimals (e.g., square root of 2, pi).
logarithmic functions - logarithmic function with base b is the inverse of the exponential
function, and is defined by x = logb y (y > 0, b > 0, b not equal to 1).
manipulatives - concrete materials (e.g., buttons, beans, egg and milk cartons, counters, attribute
and pattern blocks, interlocking cubes, base-10 blocks, geometric models, geoboards, fractions
pieces, rulers, balances, spinners, dot paper) to use in mathematical calculations.
mean - in a set of n numbers, the sum of the numbers divided by n.
median - the middle number in the set, or the mean of the two middle numbers, when the
numbers are arranged in order from least to greatest.
mode - a number in a set of data that occurs most often.
multiple - a number that is the product of a given integer and another integer (e.g., 6 and 9 are
multiples of 3).
natural numbers - (counting numbers) 1, 2, 3, 4, . . .
nonstandard measurement - a measurement determined by the use of nonstandard units like
hands, paper clips, beans, cotton balls, etc.
number sense - involves the understanding of number size (relative magnitude), number
representations, number operations, referents for quantities and measurements used in everyday
situations, etc.
operation - addition, subtraction, multiplication, division, etc.
order of operations - rules for evaluating an expression: work first within parentheses; then
calculate all powers, from left to right; then do multiplications or divisions, from left to right;
then do additions and subtractions, from left to right.
ordinal - a number that is used to tell order (e.g., first, fifth).
permutation - an arrangement of a set of objects in a particular order (the letters a, b, c have the
following permutations: abc, acb, bac, bca, cab, cba).
Priority Academic Student Skills
Oklahoma State Department of Education 30 Grade 4
prime number - an integer greater than one whose only positive factors are 1 and itself (e.g., 2,
3, 5, 7, 11, 13 . . .).
probability - the study and measure of the likelihood of an event happening.
properties of arithmetic - for all real numbers a, b and c:
commutative property: a + b = b + a and a � b = b � a
associative property: (a+ b) + c = a + (b + c) and (a � b) � c = a � (b � c)
distributive property: a (b + c) = (a � b) + (a � c)
identity property: a + 0 = a and a � 1 = a
inverse property: a + (-a) = 0 and a � 1a
= 1
proportion - a statement that ratios are equal.
quadrants - the four regions formed by the axes in a coordinate plane.
quadratic equation - an equation of the form ax2 + bx + c = 0, where a, b and c are real numbers
and a is not equal to 0.
quadratic formula - if ax2 + bx + c = 0, where a, b and c are real numbers and a is not equal to
0, then x = .
range of a relation - the set of all the second elements or y-coordinates of a relation is called the
range.
ratio - the comparison of two quantities by division.
rational numbers - quotients of integers (commonly called fractions - includes both positive and
negative).
real numbers - the set of all rational and irrational numbers.
recursive patterns - patterns in which each number is found from the previous number by
repeating a process (e.g., Fibonacci numbers).
relation - a set of one or more pairs of numbers.
relative magnitude - the size of an object or number compared to other objects and numbers.
scatter plot - a dot or point graph of data.
sequence - a set of numbers arranged in a pattern.
sine - in a right triangle, the sine of an acute angle is the ratio of the length of the leg opposite the
angle to the length of the hypotenuse.
slope of a line - the ratio of the change in y to the corresponding change in x. For any
two points (x1, y1) and (x2, y2), m = .
(y2 - y1)
(x2 - x1)
-b � b2 - 4ac
2a
Priority Academic Student Skills
Oklahoma State Department of Education 31 Grade 4
spatial sense - involves building and manipulating mental representations of 2- and
3-dimensional objects and ideas.
standard deviation - measures how much each value in the data differs from the mean of the
data.
statistics - the study of data.
stem-and-leaf plot - a frequency distribution made by arranging data in the following way (e.g.,
student scores on a test were 96, 87, 77, 93, 85, 85, and 75 would be displayed as
9 | 6, 3
8 | 7, 5, 5
7 | 7, 5
supplementary angles - two angles whose measures have a sum of 180 degrees.
supposition - (act of supposing) making a statement or assumption without proof.
tangent - in a right triangle, the tangent is the ratio of the length of the leg opposite the angle to
the length of the leg adjacent to the angle.
transformation - motion of a geometric figure (rotation [turn], translation [slide], and reflection
[flip]).
whole numbers - 0, 1, 2, 3, 4, . . .