| Standard:
1 Uses a variety of strategies in the problem-solving process
Primary
(Grades K-2)
1-1
Draws pictures to represent problems
1-2
Uses discussions with teachers and other students to understand
problems
1-3 Explains to others how she or he
went about solving a numerical problem
1-4
Makes organized lists or tables of information necessary
for solving a problem
1-5
Uses whole number models (e.g., pattern blocks, tiles,
or other manipulative materials) to represent problems
Upper
Elementary (Grades 3-5)
1-1-(3,4,5)
Uses a variety of strategies to understand problem situations
(e.g., discussing with peers, stating problems in own
words, modeling problem with diagrams or physical objects,
identifying a pattern)
1-2-(3)
Represents problems situations in a variety of forms (e.g.,
translates from a diagram to a number or symbolic expression)
1-3-(4)
Understands that some ways of representing a problem are
more helpful than others
1-4-(5)
Uses trial and error and the process of elimination to
solve problems
1-5-(3,4,5)
Knows the difference between pertinent and irrelevant
information when solving problems
1-6-(3,4,5)
Understands the basic language mathematical situations
(e.g., "add," "subtract," "total",
“sum”, “divide”)
1-7-(5)
Uses explanations of the methods and reasoning behind
the problem solution to determine reasonableness of and
to verify results with respect to the original problem
Standard: 2 Understands and applies
basic and advanced properties of the concepts of numbers
Lower
Elementary (Grades K-2)
2-1
Understands that numbers are symbols used to represent
quantities or attributes of real-world objects
2-2
Counts whole numbers (i.e., both cardinal and ordinal
numbers)
2-3
Understands symbolic, concrete, and pictorial representations
of numbers (e.g., written numerals, objects in sets, number
lines)
2-4
Understands basic whole number relationships (e.g., 4
is less than 10, 30 is 3 tens)
2-5
Understands the concept of a unit and its subdivision
into equal parts (e.g., one object, such as a candy bar,
and its division into equal parts to be shared among four
people)
Upper
Elementary (Grades 3-5)
2-1-(5)
Understands the relationships among fractions, decimals,
mixed numbers, and whole numbers
2-2-(5)
Understands equivalent forms of basic fractions, and decimals
(e.g., ½ is equivalent to .5) and when one form
of a number might be more useful than another
2-3-(3)
Understands the basic difference between odd and even
numbers
2-4-(4)
Understands the basic meaning of place value
2-5-(5)
Uses models (e.g., number lines) to identify, order, and
compare numbers
Standard: 3 Uses basic and advanced
procedures while performing the processes of computation
Primary
(Grades K-2)
3-1
Adds and subtracts whole numbers
3-2
Solves real-world problems involving addition and subtraction
of whole numbers
3-3
Understands common terms used with estimation (e.g., "about,"
"near," "closer to," "between,"
"a little less than")
3-4
Understands the inverse relationship between addition
and subtraction
Upper
Elementary (Grades 3-5)
3-1-(3)
Adds, subtracts, multiplies, and divides whole numbers
3-2-(4)
Adds and subtracts simple fractions
3-3-(4)
Uses specific strategies (e.g., front-end estimation,
rounding) to estimate computations and to check the reasonableness
of computational results
3-4-(3,4,5)
Performs basic mental computations (e.g., addition and
subtraction of whole numbers)
3-5-(4)
Determines the effects of addition, subtraction, multiplication,
and division on size and order of numbers
3-6-(3)
Understands the properties of and the relationships among
addition, subtraction, multiplication, and division (e.g.,
reversing the order of two addends does not change the
sum; division is the inverse of multiplication)
3-7-(5)
Solves real-world problems involving number operations
(e.g., computations with dollars and cents)
Standard: 4 Understands and applies
basic and advanced properties of the concepts of measurement
Primary
(Grades K-2)
4-1
Understands the basic measures length, width, height,
weight, and temperature
4-2
Understands the concept of time and how it is measured
4-3
Knows processes for telling time, counting money, and
measuring length, weight, and temperature, using basic
standard and non-standard units
4-4
Makes quantitative estimates of familiar linear dimensions,
weights, and time intervals and checks them against measurements
Upper
Elementary (Grades 3-5)
4-1-(5)
Understands the basic measures perimeter, area, volume,
and capacity
4-2-(3)
Selects and uses appropriate tools for given measurement
situations (e.g., rulers for length, measuring cups for
capacity)
4-3-(5)
Knows approximate size of basic standard units (e.g.,
centimeters, feet, grams) and relationships between them
(e.g., between inches and feet)
4-4-(4)
Understands relationships between measures (e.g., between
length, perimeter, and area)
4-5-(4)
Uses specific strategies to estimate quantities and measurements
4-6-(3)
Selects and uses appropriate units of measurement,
according to type and size of unit
Standard: 5 Understands and applies
basic and advanced properties of the concepts of geometry
Primary
(Grades K-2)
5-1
Understands basic properties of (e.g., number of sides,
corners, square corners) and similarities and differences
between simple geometric shapes
5-2
Understands the common language of spatial sense (e.g.,
"inside," "between," "above,"
"below," "behind")
5-3
Understands that geometric shapes are useful for representing
and describing real world situations
5-4
Understands that patterns can be made by putting different
shapes together or taking them apart
Upper
Elementary (Grades 3-5)
5-1-(4)
Knows basic geometric language for describing and naming
shapes (e.g., trapezoid, cylinder, cube, sphere)
5-2-(4)
Understands basic properties of figures (e.g., two- or
three-dimensionality, symmetry, number of faces, type
of angle)
5-3-(3)
Understands that shapes can be congruent or similar
5-4-(4)
Understands characteristics of lines (e.g., parallel,
intersecting) and angles (e.g., right)
5-5-(5)
Understands how scale in maps and drawings shows relative
size and distance
Standard: 6 Understands and applies
basic and advanced concepts of statistics and data analysis
Primary
(Grades K-2)
6-1
Understands that observations about objects or events
can be organized and displayed in simple graphs
6-2
Understands that one can find out about a group of things
by studying just a few of them
Upper
Elementary (Grades 3-5)
6-1-(3)
Understands that data represent specific pieces of information
about real-world objects or activities
6-2-(5)
Organizes and displays data in simple bar graphs, pie
charts, and line graphs
6-3-(3)
Reads and interprets simple bar graphs, pie charts, and
line graphs
6-4-(4)
Understands that data come in many different forms and
that collecting, organizing, and displaying data can be
done in many ways
Standard: 7 Understands and applies basic and advanced
concepts of probability
Primary
(Grades K-2)
7-1
Understands that some events are more likely to happen
than others
7-2
Understands that some events can be predicted fairly well
but others cannot because we do not always know everything
that may affect an event
Upper
Elementary (Grades 3-5)
7-1-(3)
Understands that the word "chance" refers to
the likelihood of an event
7-2-(4)
Recognizes events that are sure to happen, events
that are sure not to happen, and events that may or may
not happen (e.g., in terms of "certain," "uncertain,"
"likely," "unlikely")
7-3-(5)
Understands that when predictions are based on what is
known about the past, one must assume that conditions
stay the same from the past event to the predicted future
event
Standard: 8 Understands and applies basic
and advanced properties of functions and algebra
Primary
(Grades K-2)
8-1
Recognizes regularities in a variety of contexts (e.g.,
events, designs, shapes, sets of numbers)
8-2
Extends simple patterns (e.g., of numbers, physical objects,
geometric shapes)
Upper
Elementary (Grades 3-5)
8-1-(3)
Recognizes a wide variety of patterns (e.g.,
basic linear patterns such as [2, 4, 6, 8 .]; simple repeating
and growing patterns) and the rules that explain them
8-2-(5)
Knows that a variable is a letter or symbol that
stands for one or more numbers
8-3-(4)
Understands the basic concept of an equality relationship
(i.e., an equation is a number sentence that shows two
quantities that are equal)
8-4-(5)
Knows basic characteristics and features of the rectangular
coordinate system (e.g., the horizontal axis is the X
axis and the vertical axis is the Y axis)
Standard: 9 Understands the general nature
and uses of mathematics
Primary
(Grades K-2)
Not
appropriate for this level
Upper
Elementary (Grades 3-5)
9-1-(3,4,5)
Understands a numerical equation in the real world
9-2-(5)
Understands that mathematical ideas and concepts can be
represented concretely, graphically, and symbolically
|
