Mathematics
Grade 4
Level IV (Exceeds Standards)
Fourth-grade students performing at Level IV demonstrate a
thorough knowledge of
number sense by comparing and ordering decimals and writing money amounts in
words
and dollar-and-cent notation. These students rename improper fractions and mixed
numbers, add and subtract fractions, round whole numbers and decimals, and
recognize
equivalent forms of common fractions and decimals. These students consistently
solve
word problems that involve addition, subtraction, multiplication, and division
of whole
numbers. Students performing at Level IV write number sentences for word
problems
and complete addition and subtraction number sentences with a missing addend or
subtrahend. These students identify triangles, quadrilaterals, pentagons,
hexagons, or
octagons based on their characteristics and find locations on a map or grid
using ordered
pairs. They calculate elapsed time and measure length, width, weight, and
capacity using
both metric and customary units as well as temperature in degrees Fahrenheit and
Celsius. Fourth-grade students at Level IV represent categorical data using
tables, graphs,
and line plots ; de termine if outcomes of simple events are likely, unlikely,
certain,
equally likely, or impossible; and represent numerical data using tables and
graphs.
Level III (Meets Standards)
Fourth-grade students performing at Level III demonstrate
a fundamental knowledge of
number sense by comparing and ordering decimals and writing money amounts in
words
and dollar-and-cent notation. These students often rename improper fractions and
mixed
numbers, add and subtract fractions with common denominators , round whole
numbers
and decimals, and recognize equivalent forms of common fractions and decimals.
These
students frequently solve word problems that involve addition, subtraction,
multiplication, and division of whole numbers. Students performing at Level III
write
number sentences for word problems and complete addition and subtraction number
sentences with a missing addend or subtrahend. These students identify geometric
shapes
based on their characteristics and find locations on a map or grid using ordered
pairs.
They usually calculate elapsed time and measure length, width, weight, and
capacity
using both metric and customary units as well as temperature in degrees
Fahrenheit and
Celsius. Fourth-grade students at Level III represent categorical data using
tables and
graphs; determine if outcomes of simple events are likely, unlikely, certain,
equally
likely, or impossible; and represent numerical data using tables and graphs.
Level II (Partially Meets Standards)
Fourth-grade students performing at Level II demonstrate a
limited knowledge of number
sense by ordering whole numbers and writing money amounts. These students
sometimes
rename improper fractions, add and subtract fractions with common denominators,
round
whole numbers, and recognize equivalent forms of common fractions. These
students
sometimes solve word problems and occasionally complete addition and subtraction
number sentences with a missing addend or subtrahend. These students may
identify
basic geometric shapes based on their characteristics, sometimes calculate
elapsed time,
and measure using customary units. Fourth-grade students at Level II determine
if
outcomes of simple events are likely or unlikely, and inconsistently represent
numerical
data using tables and graphs.
Level I (Does not Meet Standards)
Fourth-grade students performing at Level I demonstrate
little or no ability to use the
mathematics skills and abilities required in Level II.
Mathematics
Grade 6
Level IV (Exceeds Standards)
Sixth-grade students performing at Level IV demonstrate
thorough computational
accuracy and fluency when adding, subtracting, multiplying, and dividing
fractions and
solving one or multi-step routine and/or non-routine problems with decimals,
percents,
fractions, and proportions. These students solve more complex problems using
numeric
and geometric patterns and identify and compare two-dimensional and
three-dimensional
figures based on attributes, properties, and component parts. They classify and
construct
acute, obtuse, and right angles and calculate perimeter and area of
parallelograms and
rectangles. Students at Level IV use proportional reasoning to determine
distances on a
scale drawing and can convert units of length, weight, or capacity within the
same system
or between customary or metric systems. Students performing at Level IV
interpret and
represent information using bar graphs, line graphs, and circle graphs as well
as
determine probability of events using fractions or percents.
Level III (Meets Standards)
Sixth-grade students performing at Level III demonstrate
fundamental computational
fluency by adding, subtracting, multiplying, and dividing fractions and by
solving onestep
routine problems involving decimals, percents, fractions, and proportions. They
solve problems using simple numeric and geometric patterns and can often
identify twodimensional
and three-dimensional figures based on attributes, properties, and component
parts as well as plot coordinates on grids , graphs, and maps. They classify
angles as
acute, obtuse, right, or straight; calculate perimeter and area of
parallelograms and
rectangles; and determine the distance between two points on a scale drawing.
These
students convert customary or metric units of length, weight, or capacity that
require one
step. They interpret information from graphs and determine the probability of a
simple
event when expressed as a fraction.
Level II (Partially Meets Standards)
Sixth-grade readers performing at Level II demonstrate
limited computational fluency
when adding, subtracting, multiplying, and dividing decimals. They solve simple
problems using numeric and geometric patterns and sometimes identify
two-dimensional
figures and determine locations on a map or grid. Students at this level
classify angles as
acute, obtuse, right, or straight and calculate the perimeter of rectangles.
These students
determine the distance between two points to the nearest inch and can compare
units of
customary length, weight, and capacity. They read information from bar graphs
and
determine if the probability of an event is likely or unlikely.
Level I (Does not Meet Standards)
Sixth-grade students performing at Level I demonstrate
little or no ability to use the
mathematics skills and abilities required in Level II.
Mathematics
Grade 8
Level IV (Exceeds Standards)
Eighth-grade students performing at Level IV demonstrate a
thorough ability to apply
various strategies and operations to solve problems with real numbers, simplify
expressions containing natural number exponents, and use order of ope rations to
evaluate
and simplify algebraic expressions . These students are consistently able to
graph linear
relations by plotting points or using the slope and y - intercept ; solve problems
involving
linear functions ; and solve multi-step linear equations , including the use of
the
distributive property . They consistently solve problems using the Pythagorean
Theorem
and can compare quadrilaterals, triangles, and solids using their properties and
characteristics. Students at Level IV determine the measures of special angle
pairs,
including adjacent, vertical, supplementary, and complementary angles; find the
perimeter and area of regular and irregular plane figures; calculate the surface
area and
volume of rectangular prisms, cylinders, and pyramids; and determine the lengths
of
missing sides and measures of angles in similar and congruent figures. Students
performing at Level IV interpret data from populations and determine the
theoretical
probability of an event.
Level III (Meets Standards)
Eighth-grade students performing at Level III demonstrate
a fundamental ability to apply
various strategies and operations to solve problems with real numbers, simplify
expressions containing natural number exponents, and use order of operations to
evaluate
and simplify algebraic expressions. These students are able to graph linear
relations by
plotting points; solve problems involving linear functions, and solve multi-step
linear
equations. They solve problems using the Pythagorean Theorem and can compare
some
quadrilaterals, triangles, and solids using their properties and
characteristics. Students at
Level III determine the measures of special angle pairs; find the perimeter and
area of
regular and irregular plan figures; calculate the surface area and volume of
rectangular
prisms, cylinders, and pyramids; and determine the lengths of missing sides and
measures
of angles in similar figures. Students performing at Level III interpret data
from
populations and determine the theoretical probability of an event.
Level II (Partially Meets Standards)
Eighth-grade students performing at Level II demonstrate a
limited ability to apply
various strategies and operations to solve problems with real numbers, simplify
expressions, and use order of operations to simplify algebraic expressions.
These students
are sometimes able to graph linear relations by plotting points and solve
problems
involving linear functions. They may solve problems using the Pythagorean
Theorem and
occasionally determine the measures of special angle pairs. Students performing
at Level
II may interpret data from populations
Level I (Does not Meet Standards)
Eighth-grade students performing at Level I demonstrate
little or no ability to use the
mathematics skills and abilities required in Level II.
