Board Approved – April 24, 2003
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
NUMBER SENSE
Understand and use numbers (0–999) through
varied and multiple experiences, including:
NUMBER SENSE
Understand and use numbers (0–10,000) through
varied and multiple experiences, including:
NUMBER SENSE
Understand and use numbers (0.01 to 1,000,000)
through varied and multiple experiences, including:
number and numeration
number and numeration
number and numeration
use physical models, pictures, and symbols to
demonstrate the relationship between ones, tens
100s, and 1000s
recognize and represent whole numbers in
standard, expanded and word forms
use physical models and equations (symbols) to
demonstrate the commutative property related to
place value, for example, 100+4+60=100+60+4
use physical models, pictures and symbols to
order fractions with like denominators
explore decimals and fractional parts
represent parts of a whole and/or parts of a set
using symbols
compare amounts using the symbols for “greater
than,” “less than” and “equal to”
classify numbers as odd or even
identify, compare, and order numbers to
1,000,000 using standard form, expanded form
and word form
identify, compare and order fractions
use objects, pictures or symbols to illustrate the
meaning of commutative, associative and
identify properties of addition and multiplication
demonstrate understanding of fractions with
denominators of 2, 4, 8, 3, or 6
use objects, pictures or symbols to describe the
meaning of fractions, decimals, and percents
and the relationship between decimals and
fractional parts
identify, compare, and order non-negative whole
numbers
order fractions with fractions and decimals with
decimals, e.g. which is bigger 3/8 or 2/3?
identify equivalent fractions and simplify
fractions to lowest terms
use visual and physical models to describe
prime and composite numbers, factors and
multiples, and determine divisibility by 2, 5, and
10
use objects, pictures, and symbols to illustrate
equivalent ratios, e.g. 1:2 is equivalent to 4:8
make comparisons between two part:part
relationships, e.g. which makes a lighter paint –
2 white:3 blue or 4 white:5 blue?
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
NUMBER SENSE (continued)
NUMBER SENSE (continued)
NUMBER SENSE (continued)
computation
computation
computation
compute using addition and subtraction facts 1–
20
compute using multiplication facts using 1's, 2's,
5's, 10's and explore division
use mental math to multiply one-digit numbers
by 10s and 100s
use place value materials to solve addition and
subtraction problems containing multi-digit
whole numbers through hundreds
compute to solve problems in realistic
situations containing multi-digit numbers using
the addition or subtraction strategy most
appropriate to the situation (mental math
strategies, paper and pencil, calculator)
use models, diagrams, and symbols to
demonstrate the relationship between
multiplication and division
create and use strategies to solve multiplication
and division basic facts
compute using multiplication and division facts
to 10
estimate and solve realistic problems involving
multiplication and division using an appropriate
computation strategy
demonstrate meaning of multiplication and
division using physical models to solve
problems containing one- or two-digit factors
use physical models to solve problems involving
a combination of any two whole number
operations
write number sentences representing addition,
subtraction, multiplication, and division
situations
solve problems involving addition, subtraction,
multiplication, and division of multi-digit whole
numbers where the operations are not specified
divide by 10s and 100s
add, subtract, multiply and divide non-negative
whole numbers up to 12
add and subtract decimals, fractions, mixed
numbers, and whole numbers 0 to 999
use physical models to demonstrate and explain
the meaning of multiplication of a fraction by a
whole number and a fraction by a fraction
use mental math strategies, paper and pencil,
calculator, or computer as appropriate for a
given situation
estimation
estimation
estimation
describe and justify reasonableness of an
estimate in a multiplication context
use estimation strategies (i.e. multiples of 10
and 100, rounding, front-end estimation,
compatible numbers, clustering)
describe and justify reasonableness of an
estimate in computation
use mental math strategies to approximate
simple sums, differences, and products by using
rounded numbers
determine and justify the reasonableness of
answers by estimating prior to actual
computation with whole numbers
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
MEASUREMENT
MEASUREMENT
MEASUREMENT
attributes and dimensions
attributes and dimensions
use language and symbols to compare attributes
of perimeter and area
determine area and perimeter of irregular 2-D
figures
use physical models to determine volume or
rectangular solids
select an appropriate type of unit for measuring
area, perimeter and volume
use language and symbols to compare attributes
of perimeter, area, and volume
solve problems involving measurement of area,
perimeter, length, weight, time, and temperature
when given diagrams or objects
compare objects using attributes of perimeter,
area and volume
attributes and dimensions
compare and contrast perimeter, area and
volume for a variety of shapes
measure elapsed time and duration
explore and recognize the relationship between
area and perimeter
measure objects directly and apply procedures
for determining perimeter of polygons and area
of rectangles
approximation and precision
approximation and precision
approximation and precision
understand the benefits of using standard units
of measurement
estimate and measure using standard units
describe and justify reasonableness of an
estimate involving length, weight, area, time,
and temperature
use physical models to estimate volume of
rectangular solids
determine and justify whether exact or
approximate measures are needed when given a
realistic situation
estimate to predict and determine when
measurements are reasonable
use estimation to obtain reasonable
approximations of linear measurements
systems and tools
systems and tools
systems and tools
measure to the nearest whole and common
fractional parts of standard units when given a
realistic situation
explore how to use measurement tools
select appropriate standard units of
measurement for given objects or situations
tell time using analog and digital clock displays
know approximate size of basic standard units
(U.S. and metric) and make reasonable
estimates based on approximations
identify application uses for various
measurements
use a ruler, tape measure, scale, and
thermometer to measure accurately
use a clock to tell standard and international
time to the minute
choose the appropriate standard unit and tool
and measure objects directly
choose standard units of measure yielding the
most appropriate measurement
explain the advantages of standard units of
measure
make conversions within the U.S. Customary
System and within the Metric System (length,
mass/weight, volume)
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
GEOMETRIC SENSE
GEOMETRIC SENSE
GEOMETRIC SENSE
properties and relationships
properties and relationships
properties and relationships
identify and describe irregular polygons
identify and describe attributes of 2-D and 3-D
identify and describe attributes of 2-D and 3-D
geometrical figures using appropriate
geometric figures using appropriate adjectives
vocabulary
identify and describe regular polygons
such as parallel, symmetric, congruent, similar,
and perpendicular
classify real world objects as containing squares,
draw or create 2-D geometric figures using
rectangles, triangles, circles, cubes, rectangular
appropriate tools, for example, toothpicks to
solids, spheres, cylinders, or pyramids
create 2-D shapes
construct models of 3-D shapes
identify geometric shapes in the surrounding
environment
identify and describe properties of geometric
figures (ray, angle, line segment, parallel,
symmetric, perpendicular, similar, and
congruent) and find examples in the physical
world
identify and draw multiple lines of symmetry
build and record similar and congruent figures
construct geometric figures using a variety of
tools
locations and transformations
locations and transformations
locations and transformations
identify, describe, and compare symmetrical
congruent and similar figures
explore relative size, direction, and position in
space
predict and verify transformations on a
geometric figure (translations, reflections, and
rotations)
describe the location of figures on a coordinate
plane using ordered pairs
describe the relative position of figures located
on a coordinate plane
identify, describe and compare symmetrical,
congruent, and similar figures
predict and verify transformations on a
geometric figure (translations, reflections, and
rotations)
describe the location of points on coordinate
grids in first quadrant
identify simple transformations using
combinations of translations, reflections, or
rotations
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
PROBABILITY AND STATISTICS
PROBABILITY AND STATISTICS
PROBABILITY AND STATISTICS
probability
probability
probability
places events in the order they would likely
occur
list possible outcomes of a simple probability
experiment
conduct experiments to determine the
probability of events
place events in the order they would likely occur prepare and organize displays of all possible
results for a given probability experiment
use organized counting to determine the number
use and describe strategies for determining the
of possible outcomes of an event
list all possible outcomes of a simple probability
probability of an event
experiment
explain why some outcomes are more or less
likely to happen than others
statistics
statistics
statistics
collect data in an organized way
formulate questions
describe measures of central tendency using
words like “middle” and “most often”
pose questions from data and choose and
explain one type of graph over another
describe pictographs, bar graphs and line graphs
and how they communicate solutions to
problems
identify or describe an appropriate method for
collecting data
describe measures of central tendency using
mean, median, and mode
pose simple questions and hypotheses, collect
data, and communicate results using graphs or
tables supported by written or oral explanations
identify a random sample taken from a
described population
differentiate between random and non-random
samples
organize and display data using frequency tables
identify outliers in a set of data
describe mean, median, mode, and range for
simple data
prediction and inference
prediction and inference
prediction and inference
use data to build an argument or point of view
predict and verify likelihood of occurrence
using physical objects such as number cubes or
coins
determine if games are fair or unfair
describe how data can be used to support an
argument
make inferences based on experimental results
using coins, spinners, number cubes, etc.
carry out experiments to determine probabilities
and compare predictions to experimental results
ask questions and collect data from specific
samples and infer data to the population
make inferences and note trends on data
collected from bar graphs and line graphs
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
ALGEBRAIC SENSE
ALGEBRAIC SENSE
ALGEBRAIC SENSE
patterns
patterns
patterns
analyze, extend, and find a rule for numeric and
geometric patterns when given manipulatives or
pictorial displays
recognize patterns involved in a variety of
estimation and computation strategies
create, analyze and extend number patterns
using words, tables and graphs
investigate patterns using 100's chart to extend
understanding of numbers
recognize and create sequential number patterns
and generate rules for them
create and extend number patterns that may
involve a combination of addition, subtraction,
and multiplication using words, tables and
graphs
describe patterns using rules, tables, graphs and
charts
recognize number patterns and sequences
use variables to describe patterns and sequences
representations
representations
use symbols to describe equality and inequality
use standard notation in reading and writing
open sentences, for example, 3 x  = 18
translate problem-solving situations into
expressions and equations that use geometric
symbols for the unknown
represent and describe patterns using tables and
graphs with terms such as interval, pattern, rule
and sequence
use symbols to represent the process of
maintaining equality and inequality in number
sentences (e.g., 8 + 4  7 + 3)
represent numbers as letters in formulas and
equations
substitute values in formulas (e.g., / [length] x
w [width] = a [area])
operations
operations
operations
use blocks, sticks, beans, pictures, etc. to
evaluate simple expressions
solve equations involving multiplication and
division using manipulatives
use manipulatives and pictorial representations
to illustrate processes for maintaining equality
in an equation
use standard notation in reading and writing
open number sentences (e.g., 7 + ? = 20)
use manipulatives to solve open-ended
equations involving addition, subtraction,
multiplication or division
use physical or visual materials to model
operations performed on both sides of an
equation
evaluate simple expressions using manipulatives
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
PROBLEM SOLVING
PROBLEM SOLVING
PROBLEM SOLVING
investigate situations
investigate situations
investigate situations
develop and apply a variety of strategies, such
as make a table, find a pattern, or solve a
simpler problem, to solve problems
recognize when an approach is unproductive
and try a new approach (in computation as well
as problem solving)
use a variety of strategies and approaches to
solve problems, for example, work backwards,
make an organized list, make a table or graph,
write number sentences
recognize when an approach is unproductive
and tries a new approach (in computation as
well as in problem solving)
develop and use a variety of strategies, such as
act it out, make a physical model, and look for a
pattern
formulate questions and define the problem
formulate questions and define the problem
formulate questions and define the problem
identify the unknown in everyday situations, for
example, tell that the number of kids going on a
field trip and the number of seats on each bus
must be known to calculate how many buses are
needed
identify the unknown in familiar situations, for
example, tell what information is needed in
order to solve any problem
identify missing or extraneous information
define questions to be answered in new
situations, e.g., after being presented with new
information or witnessing an unfamiliar event
construct solutions
construct solutions
construct solutions
apply viable strategies, concepts, and procedures apply viable strategies, concepts, and procedures organize relevant information from multiple
to construct a solution
to construct a solution
sources such as firsthand experimental data, data
reported by others, books, or internet
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
REASONING
REASONING
REASONING
analyze information
analyze information
analyze information
validate thinking using models, known facts,
patterns and relationships, for example, use a
fraction kit to illustrate the relative sizes of three
fractions
validate thinking using models, known facts,
patterns and relationships, for example, use
fraction bars to illustrate the meaning of
addition with unlike denominators
validate thinking and mathematical ideas using
models, known facts and patterns, e.g., use
manipulatives to demonstrate addition of
fractions with unlike denominators
predict results
predict results
predict results
make conjectures, collect data, support
arguments, and justify results, for example,
when asked “Do larger pumpkins have more
seeds?” make conjectures and devise and carry
out a plan to test the conjecture
make conjectures, collect data, support
arguments, and justify results, for example,
devise and carry out a plan to test the conjecture
that smaller rubber balls will bounce more times
than larger ones when dropped from the same
height
make conjectures and inferences based on
analysis of new problem situations, e.g., make a
hypothesis when asked if there is a relationship
between the area and perimeter of quadrilaterals
draw conclusions and verify results
draw conclusions and verify results
draw conclusions and verify results
reflect on and evaluate procedures, for example,
after completing the pumpkin experiment,
decide if the method used was the best for
answering the question
reflect on and evaluate procedures, for example,
after completing the rubber ball experiment,
decide if the method used was the best for
answering the question
test conjectures and inferences and explain why
they are true or false, e.g., devise, carry out, and
evaluate a plan to test the hypothesis that an
increase in area results in an increase in
perimeter
check for reasonableness of results
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
COMMUNICATION
COMMUNICATION
COMMUNICATION
gather information
gather information
gather information
use available technology to browse and retrieve
mathematical information, for example, use email to collect, share, and analyze experimental
data with other third graders throughout the
country
use available technology to browse and retrieve
mathematical information, for example, use the
Internet and/or CD ROMs to find information
on the use of symmetry in architecture
develop a plan for collecting mathematical
information (from both print and nonprint
sources)
organize and interpret information
organize and interpret information
organize and interpret information
organize and clarify mathematical information
through narrative expression, such as writing in
a math journal
organize and clarify mathematical information
through reflection and discussion, for example,
writing in a math journal following class
discussion about strategies used to solve a
problem
organize and clarify mathematical information
by reflecting and verbalizing, e.g., after a class
discussion on measurement, explain precision in
own words
represent and share information
represent and share information
represent and share information
express mathematical ideas with appropriate
vocabulary using everyday language, models,
charts, tables, graphs, and symbols, for example,
when describing/justifying results of a
measurement experiment
express mathematical ideas using everyday
language, models, charts, tables, graphs, and
symbols, for example, when
describing/justifying results of a probability
experiment
clearly and effectively express ideas using both
everyday and mathematical language (models,
tables, charts) appropriate to the audience
MATHEMATICS K-10 – Grade Level Expectations
Grade 3
Grade 4
Grade 5
CONNECTIONS
CONNECTIONS
CONNECTIONS
to other disciplines
within mathematics
within mathematics
use mathematical thinking in familiar situations
in other disciplines, for example, devise and
conduct an experiment to determine if plants
grow better in natural or artificial light
recognize relationships within mathematics
relate and use different models and
representations for the same situation e.g.,
explain the meaning of multiplication of
fractions using physical and visual models
to real-life situations
to other disciplines
to other disciplines
recognize mathematics in familiar settings, for
example, recognize geometry as the basis for
buildings, bridges, etc.
identify how mathematics is used in career
settings
use mathematical thinking in familiar situations
in other disciplines, for example, determine how
to construct a garden that provides the most
space for the lowest cost of fencing material
identify mathematical patterns and relationships
in other disciplines e.g., understand patterns,
shapes, time, distances, and relative distances to
other objects within our solar system
use mathematical thinking and modeling in
other disciplines
describe examples of contributions to the
development of mathematics (such as the
contributions of women)
to real-life situations
to real-life situations
recognize mathematics in familiar settings, for
example, recognize the use of statistics in sports
identify how mathematics is used in career
settings
recognize the extensive use of mathematics
outside the classroom
investigate the use of mathematics within
several occupational/career areas e.g.,
aerospace, medicine, carpentry, banking, sales