\doc\web\98\03\washmath.txt
Washington State
Commission on Student Learning (CSL)
Essential Academic Learning Requirements
(EALR) - Benchmark 1
(March 3rd, 1997)
The benchmarks describe the necessary knowledge and essential skills
students would be expected to achieve at approximately grade 4.
[Image]
Introduction to Mathematics
Mathematics for Today and Tomorrow - Mathematics continues to
grow at a rapid rate, spreading into new fields and creating new
applications, in its open-ended search for patterns. Several factors
-- growth of technology, increased applications, impact of computers,
and expansion of mathematics itself -- have combined in the past
century to extend greatly both the scope and the application of the
mathematical sciences. The changes must be reflected in the schools if
our students are to be well prepared for tomorrow's world.
What is Mathematics? - Mathematics is a language and science of
patterns.
As a language of patterns, mathematics is a means for describing
the world in which we live. In its symbols and vocabulary, the
language of mathematics is a universal means of communication about
relationships and patterns.
As a science of patterns, mathematics is a mode of inquiry that
reveals fundamental understandings about order in our world. This mode
of inquiry relies on logic and employs observation, simulation, and
experimentation as means of challenging and extending our current
understanding.
Toward a deeper study of important mathematics - More than at any
other time in history, society is placing demands on citizens to
interpret and use mathematics to make sense of information and complex
situations. Computers and other technologies have increased our
capacities for dealing with numbers, for collecting, organizing,
representing, and analyzing data. Tables, lists of numbers, graphs of
data, and statistics summarizing information occur in every form of
the media.
To be well informed as adults and to have access to desirable
jobs, students today require an education in mathematics that goes far
beyond what was needed by students in the past. All students must
develop and sharpen their skills, deepen their understanding of
mathematical concepts and processes, and hone their problem-solving,
reasoning, and communication abilities while using mathematics to make
sense of, and to solve, compelling problems. All students need a deep
understanding of mathematics; for this to occur, rigorous mathematical
content must be reorganized, taught, and assessed in a problem-solving
environment. For students to develop this deeper level of
understanding, their knowledge must be connected to a variety of ideas
and skills across topic areas and grade levels in mathematics, to
other subjects taught in school, as well as to situations outside the
classroom.
The Essential Academic Learning Requirements in Mathematics:
1. The student understands and applies the concepts and procedures
of mathematics.
2. The student uses mathematics to define and solve problems.
3. The student uses mathematical reasoning.
4. The student communicates knowledge and understanding in both
everyday and mathematical language.
5. The student understands how mathematical ideas connect within
mathematics, to other subject areas, and to real-life situations.
----------------------------------------------------------------------
NOTE: [Image] The text repeats for each benchmark.
The arrow means that the skills or materials used becomes increasingly
complex.
[Image] ESSENTIAL LEARNING 1: The student understands and applies the
concepts and procedures of mathematics.
To meet this standard, the student will:
1.1 understand and apply concepts and procedures from number sense
number and numeration, computation, and estimation
1.2 understand and apply concepts and procedures from measurement
attributes and dimensions, approximation and precision, and
systems and tools
1.3 understand and apply concepts and procedures from geometric sense
shape and dimension, and relationships and transformations
1.4 understand and apply concepts and procedures from probability and
statistics
probability, statistics, and prediction and inference
1.5 understand and apply concepts and procedures from algebraic sense
relations and representations, and operations
COMPONENTS BENCHMARK 1 (GRADE 4)
1.1 understand number and numeration
and apply
concepts and use objects, pictures, or symbols to demonstrate
procedures from understanding of whole and fractional numbers, place
number sense value in whole numbers, and properties of the whole
number system
identify, compare, and order whole numbers and
simple fractions
computation
show understanding of whole number operations (+, -,
x, ÷) using blocks, sticks, beans, etc.
add, subtract, multiply, and divide whole numbers
use mental arithmetic, pencil and paper, or
calculator as appropriate to the task involving
whole numbers
estimation
identify situations involving whole numbers in which
estimation is useful
use estimation to predict computation results and to
determine the reasonableness of answers, for
example, estimating a grocery bill
1.2 understand attributes and dimensions
and apply
concepts and understand concepts of perimeter, area, and volume
procedures from
measurement use directly measurable attributes such as length,
perimeter, area, volume/capacity, angle,
weight/mass, money, and temperature to describe and
compare objects
approximation and precision
understand that measurement is approximate
estimate to predict and determine when measurements
are reasonable, for example, estimating the length
of the playground by pacing it off
systems and tools
understand the benefits of using standard units of
measurement for measuring length, area, and volume
understand appropriate units of measure for time,
money, length, area, volume, mass, and temperature
use appropriate tools for measuring time, money,
length, area, volume, mass, and temperature
1.3 understand shape and dimension
and apply
concepts and use shape and size to identify, name, and sort
procedures from geometric shapes
geometric sense
recognize geometric shapes in the surrounding
environment, for example, identify rectangles within
windows
relationships and transformations
describe the location of objects relative to each
other on grids or maps
understand concepts of parallel and perpendicular
understand concepts of symmetry, congruence, and
similarity
understand and construct simple geometric
transformations using slides, flips, or turns
construct simple shapes using appropriate tools such
as a straightedge or a ruler
1.4 understand probability
and apply
concepts and understand the difference between certain and
procedures from uncertain events
probability and
statistics know how to list all possible outcomes of simple
experiments
understand and use experiments to investigate
uncertain events
statistics
know that data can be represented in different forms
such as tabulations of events, objects, or
occurrences
collect data in an organized way
organize and display data in numerical and graphical
forms such as tables, charts, pictographs, and bar
graphs
use different measures of central tendency such as
"most often" and "middle" in describing a set of
data
prediction and inference
predict outcomes of simple activities and compare
predictions to experimental results
understand and make inferences based on experimental
results using coins, number cubes, spinners, etc.
1.5 understand relations and representations
and apply
concepts and recognize, create, and extend patterns of objects
procedures from and numbers using a variety of materials such as
algebraic sense beans, toothpicks, pattern blocks, calculator,
cubes, or colored tiles
understand and use guess and check in the search for
patterns
represent number patterns symbolically, for example,
using tiles, boxes, or numbers
use standard notation in reading and writing open
sentences, for example,
3 x __ = 18
operations
evaluate simple expressions using blocks, sticks,
beans, pictures, etc.
solve simple equations using blocks, sticks, beans,
pictures, etc.
[Image] ESSENTIAL LEARNING 2: The student uses mathematics to define and
solve problems.
To meet this standard, the student will:
2.1 investigate situations
by searching for patterns and exploring a variety of approaches
2.2 formulate questions and define the problem
2.3 construct solutions
by choosing the necessary information and using the appropriate
mathematical tools
COMPONENTS BENCHMARK 1 (GRADE 4)
2.1 investigate search for patterns in simple situations
situations
use a variety of strategies and approaches
recognize when information is missing or
extraneous
recognize when an approach is unproductive and
try a new approach
2.2 formulate questions identify questions to be answered in familiar
and define the problem situations
define problems in familiar situations
identify the unknowns in familiar situations
2.3 construct solutions organize relevant information
select and use appropriate mathematical tools
apply appropriate methods, operations, and
processes to construct a solution
[Image] ESSENTIAL LEARNING 3: The student uses mathematical reasoning.
To meet this standard, the student will:
3.1 analyze information
from a variety of sources; use models, known facts, patterns and
relationships to validate thinking
3.2 predict results and make inferences
and make conjectures based on analysis of problem situations
3.3 draw conclusions and verify results
support mathematical arguments, justify results, and check for
reasonableness of solutions
COMPONENTS BENCHMARK 1 (GRADE 4)
3.1 analyze interpret and compare information in familiar
information situations
validate thinking using models, known facts,
patterns, and relationships
3.2 predict results make conjectures and inferences based on
and make inferences analysis of familiar problem situations
3.3 draw conclusions test conjectures by finding examples to support
and verify results or contradict them
support arguments and justify results based on
own experiences
check for reasonableness of results
reflect on and evaluate procedures and results
in familiar situations
[Image] ESSENTIAL LEARNING 4: The student communicates knowledge and
understanding in both everyday and mathematical language.
To meet this standard, the student will:
4.1 gather information
read, listen, and observe to access and extract mathematical
information
4.2 organize and interpret information
4.3 represent and share information
share, explain, and defend mathematical ideas using terms,
language, charts, and graphs that can be clearly understood by a
variety of audiences
COMPONENTS BENCHMARK 1 (GRADE 4)
4.1 gather follow a plan for collecting information
information
use reading, listening, and observation skills to
access and extract mathematical information from a
variety of sources such as pictures, diagrams,
physical models, classmates, oral narratives, and
symbolic representations
use available technology to browse and retrieve
mathematical information from a variety of sources
4.2 organize and organize and clarify mathematical information in at
interpret least one way - reflecting, verbalizing, discussing,
information or writing
4.3 represent express ideas using mathematical language and notation
and share such as physical or pictorial models, tables, charts,
information graphs, or symbols
express mathematical ideas to familiar people using
everyday language
[Image] ESSENTIAL LEARNING 5: The student understands how mathematical
ideas connect within mathematics, to other subject areas, and to real-life
situations.
To meet this standard, the student will:
5.1 relate concepts and procedures within mathematics
recognize relationships among mathematical ideas and topics
5.2 relate mathematical concepts and procedures to other disciplines
identify and apply mathematical thinking and notation in other
subject areas
5.3 relate mathematical concepts and procedures to real-life
situations
understand the connections between mathematics and problem
solving skills used every day at work and at home
COMPONENTS BENCHMARK 1 (GRADE 4)
5.1 relate concepts connect conceptual and procedural understandings
and procedures among familiar mathematical content areas
within mathematics
recognize equivalent mathematical models and
representations in familiar situations
5.2 relate recognize mathematical patterns and ideas in
mathematical familiar situations in other disciplines
concepts and
procedures to other use mathematical thinking and modeling in familiar
disciplines situations in other disciplines
describe examples of contributions to the
development of mathematics such as the
contributions of women, men, and different cultures
5.3 relate give examples of how mathematics is used in
mathematical everyday life
concepts and
procedures to
real-life identify how mathematics is used in career settings
situations
[Image]
[Image] [Image] [Image] 7/7/97.gt [Image]
[Image] Commission on Student Learning (CSL)
Essential Academic Learning Requirements
(EALR) - Benchmark 2
(March 3rd, 1997)
The benchmarks describe the necessary knowledge and essential skills
students would be expected to achieve at approximately grade 7.
[Image]
Introduction to Mathematics
Mathematics for Today and Tomorrow - Mathematics continues to
grow at a rapid rate, spreading into new fields and creating new
applications, in its open-ended search for patterns. Several factors
-- growth of technology, increased applications, impact of computers,
and expansion of mathematics itself -- have combined in the past
century to extend greatly both the scope and the application of the
mathematical sciences. The changes must be reflected in the schools if
our students are to be well prepared for tomorrow's world.
What is Mathematics? - Mathematics is a language and science of
patterns.
As a language of patterns, mathematics is a means for describing
the world in which we live. In its symbols and vocabulary, the
language of mathematics is a universal means of communication about
relationships and patterns.
As a science of patterns, mathematics is a mode of inquiry that
reveals fundamental understandings about order in our world. This mode
of inquiry relies on logic and employs observation, simulation, and
experimentation as means of challenging and extending our current
understanding.
Toward a deeper study of important mathematics - More than at any
other time in history, society is placing demands on citizens to
interpret and use mathematics to make sense of information and complex
situations. Computers and other technologies have increased our
capacities for dealing with numbers, for collecting, organizing,
representing, and analyzing data. Tables, lists of numbers, graphs of
data, and statistics summarizing information occur in every form of
the media.
To be well informed as adults and to have access to desirable
jobs, students today require an education in mathematics that goes far
beyond what was needed by students in the past. All students must
develop and sharpen their skills, deepen their understanding of
mathematical concepts and processes, and hone their problem-solving,
reasoning, and communication abilities while using mathematics to make
sense of, and to solve, compelling problems. All students need a deep
understanding of mathematics; for this to occur, rigorous mathematical
content must be reorganized, taught, and assessed in a problem-solving
environment. For students to develop this deeper level of
understanding, their knowledge must be connected to a variety of ideas
and skills across topic areas and grade levels in mathematics, to
other subjects taught in school, as well as to situations outside the
classroom.
The Essential Academic Learning Requirements in Mathematics:
1. The student understands and applies the concepts and procedures
of mathematics.
2. The student uses mathematics to define and solve problems.
3. The student uses mathematical reasoning.
4. The student communicates knowledge and understanding in both
everyday and mathematical language.
5. The student understands how mathematical ideas connect within
mathematics, to other subject areas, and to real-life situations.
----------------------------------------------------------------------
NOTE: [Image] The text repeats for each benchmark.
The arrow means that the skills or materials used becomes increasingly
complex.
[Image] ESSENTIAL LEARNING 1: The student understands and applies the
concepts and procedures of mathematics.
To meet this standard, the student will:
1.1 understand and apply concepts and procedures from number sense
number and numeration, computation, and estimation
1.2 understand and apply concepts and procedures from measurement
attributes and dimensions, approximation and precision, and
systems and tools
1.3 understand and apply concepts and procedures from geometric sense
shape and dimension, and relationships and transformations
1.4 understand and apply concepts and procedures from probability and
statistics
probability, statistics, and prediction and inference
1.5 understand and apply concepts and procedures from algebraic sense
relations and representations, and operations
COMPONENTS BENCHMARK 2 (GRADE 7)
1.1 understand number and numeration
and apply
concepts and use pictures and symbols to demonstrate understanding
procedures from of fractions, decimals, percents, place value in
number sense non-negative decimals, and properties of the rational
number system
compare and order whole numbers, fractions, and
decimals
understand the concepts of prime and composite
numbers, factors and multiples, and divisibility
rules
understand the concepts of ratio and direct
proportion
computation
understand operations on rational numbers
add, subtract, multiply, and divide non-negative
fractions and decimals using rules for order of
operation
use mental arithmetic, pencil and paper, calculator,
or computer as appropriate to the task involving
rational numbers
estimation
identify situations involving rational numbers in
which estimation is sufficient and computation is not
required
use estimation to predict computation results and to
determine the reasonableness of answers involving
rational numbers, for example, estimating a tip
1.2 understand attributes and dimensions
and apply
concepts and understand the relationship among perimeter, area,
procedures from and volume
measurement
measure objects and events directly or using indirect
methods such as finding the area of a rectangle given
its length and width
understand the concept of rate and how to calculate
rates and determine units
approximation and precision
understand that precision is related to the unit of
measurement used and the calibration of the
measurement tool
use estimation to obtain reasonable approximations,
for example, estimating the length and width of the
playground to approximate its area
systems and tools
understand the benefits of standard units of
measurement for both direct and indirect measurement
understand the relationship among units within both
the U.S. and metric systems
select and use tools that will provide an appropriate
degree of precision, for example, using meters vs.
kilometers
1.3 understand shape and dimension
and apply
concepts and use multiple attributes to describe geometric shapes
procedures from
geometric sense identify and describe objects in the surrounding
environment in geometric terms, for example, describe
the triangles that make up a bridge structure
relationships and transformations
describe location of objects on coordinate grids
understand and identify properties and relationships
of plane geometry including ray; angle; isosceles;
equilateral; and degrees in a circle, triangle, or
quadrilateral
construct symmetric, congruent, and similar figures
understand and construct simple geometric
transformations using combinations of slides, flips,
or turns
use a compass and straightedge, and/or computer
software to perform geometric constructions
1.4 understand probability
and apply
concepts and know how to calculate numerical measures of
procedures from uncertainty for simple events
probability and
statistics understand procedures for counting outcomes to
determine probabilities
know how to conduct experiments and simulations and
to compare results with mathematical expectations
statistics
identify how statistics can be used to support
different points of view
collect a random sample of data that represents a
described population
organize and display data in appropriate forms such
as frequency tables, circle graphs, and stem-and-leaf
graphs
calculate and use mean, median, and mode as
appropriate in describing a set of data
prediction and inference
predict outcomes of experiments and simulations and
compare the predictions to experimental results
understand and make inferences based on experimental
results
1.5 understand relations and representations
and apply
concepts and recognize, create, and extend patterns and sequences
procedures from
algebraic sense represent number patterns with tables, graphs, and
rules
represent equalities and inequalities symbolically
using [Image]
understand and use variables in simple equations,
inequalities, and formulas, for example
3x > 18
operations
evaluate simple expressions
set up and solve single-variable equations
[Image] ESSENTIAL LEARNING 2: The student uses mathematics to define and
solve problems.
To meet this standard, the student will:
2.1 investigate situations
by searching for patterns and exploring a variety of approaches
2.2 formulate questions and define the problem
2.3 construct solutions
by choosing the necessary information and using the appropriate
mathematical tools
COMPONENTS BENCHMARK 2 (GRADE 7)
2.1 investigate search systematically for patterns in simple
situations situations
develop and use a variety of strategies and
approaches
identify missing or extraneous information
recognize the need to modify or abandon an
unproductive approach
2.2 formulate identify questions to be answered in new
questions and define situations
the problem
define problems in new situations
identify the unknowns in new situations
2.3 construct organize relevant information
solutions
[Image] select and use appropriate mathematical
tools
[Image] apply appropriate methods, operations,
and processes to construct a solution
[Image] ESSENTIAL LEARNING 3: The student uses mathematical reasoning.
To meet this standard, the student will:
3.1 analyze information
from a variety of sources; use models, known facts, patterns and
relationships to validate thinking
3.2 predict results and make inferences
and make conjectures based on analysis of problem situations
3.3 draw conclusions and verify results
support mathematical arguments, justify results, and check for
reasonableness of solutions
COMPONENTS BENCHMARK 2 (GRADE 7)
3.1 analyze interpret, compare, and contrast information from a
information variety of sources
validate thinking and mathematical ideas using
models, known facts, patterns, relationships, and
counter-examples
3.2 predict results make conjectures and inferences based on analysis
and make inferences of new problem situations
3.3 draw test conjectures and inferences and explain why
conclusions and they are true or false
verify results
support arguments and justify results using
inductive reasoning
[Image] check for reasonableness of results
reflect and evaluate on procedures and results in
new problem situations
[Image] ESSENTIAL LEARNING 4: The student communicates knowledge and
understanding in both everyday and mathematical language.
To meet this standard, the student will:
4.1 gather information
read, listen, and observe to access and extract mathematical
information
4.2 organize and interpret information
4.3 represent and share information
share, explain, and defend mathematical ideas using terms,
language, charts, and graphs that can be clearly understood by a
variety of audiences
COMPONENTS BENCHMARK 2 (GRADE 7)
4.1 gather develop a plan for collecting information
information
use reading, listening, and observation skills to
access and extract mathematical information from
multiple sources such as pictures, diagrams, physical
models, oral narratives, and symbolic representations
choose appropriate available technology to browse,
select, and retrieve relevant mathematical information
from a variety of sources
4.2 organize and
interpret organize and clarify mathematical information by
information reflecting, verbalizing, discussing, or writing
4.3 represent clearly and effectively express or present ideas and
and share situations using both everyday and mathematical such
information as models, tables, charts, graphs, written reflection,
or algebraic notation
express mathematical ideas with clarity using both
everyday and mathematical language appropriate to
audience
[Image] ESSENTIAL LEARNING 5: The student understands how mathematical
ideas connect within mathematics, to other subject areas, and to real-life
situations.
To meet this standard, the student will:
5.1 relate concepts and procedures within mathematics
recognize relationships among mathematical ideas and topics
5.2 relate mathematical concepts and procedures to other disciplines
identify and apply mathematical thinking and notation in other
subject areas
5.3 relate mathematical concepts and procedures to real-life
situations
understand the connections between mathematics and problem
solving skills used every day at work and at home
COMPONENTS BENCHMARK 2 (GRADE 7)
5.1 relate connect conceptual and procedural understandings
concepts and among different mathematical content areas
procedures within
mathematics relate and use different mathematical models and
representations for the same situation
5.2 relate identify mathematical patterns and ideas in other
mathematical disciplines
concepts and
procedures to use mathematical thinking and modeling in other
other disciplines disciplines
[Image] describe examples of contributions to the
development of mathematics such as the contributions
of women, men, and different cultures
5.3 relate recognize the extensive use of mathematics outside
mathematical the classroom, for example, in banking or sports
concepts and statistics
procedures to
real-life investigate the use of mathematics within several
situations occupational/career areas of interest
[Image]
[Image] [Image] [Image] 7/7/97.gt [Image]
[Image] Commission on Student Learning (CSL)
Essential Academic Learning Requirements
(EALR) - Benchmark 3
(March 3rd, 1997)
The benchmarks describe the necessary knowledge and essential skills
students would be expected to achieve at approximately grade 10.
[Image]
Introduction to Mathematics
Mathematics for Today and Tomorrow - Mathematics continues to
grow at a rapid rate, spreading into new fields and creating new
applications, in its open-ended search for patterns. Several factors
-- growth of technology, increased applications, impact of computers,
and expansion of mathematics itself -- have combined in the past
century to extend greatly both the scope and the application of the
mathematical sciences. The changes must be reflected in the schools if
our students are to be well prepared for tomorrow's world.
What is Mathematics? - Mathematics is a language and science of
patterns.
As a language of patterns, mathematics is a means for describing
the world in which we live. In its symbols and vocabulary, the
language of mathematics is a universal means of communication about
relationships and patterns.
As a science of patterns, mathematics is a mode of inquiry that
reveals fundamental understandings about order in our world. This mode
of inquiry relies on logic and employs observation, simulation, and
experimentation as means of challenging and extending our current
understanding.
Toward a deeper study of important mathematics - More than at any
other time in history, society is placing demands on citizens to
interpret and use mathematics to make sense of information and complex
situations. Computers and other technologies have increased our
capacities for dealing with numbers, for collecting, organizing,
representing, and analyzing data. Tables, lists of numbers, graphs of
data, and statistics summarizing information occur in every form of
the media.
To be well informed as adults and to have access to desirable
jobs, students today require an education in mathematics that goes far
beyond what was needed by students in the past. All students must
develop and sharpen their skills, deepen their understanding of
mathematical concepts and processes, and hone their problem-solving,
reasoning, and communication abilities while using mathematics to make
sense of, and to solve, compelling problems. All students need a deep
understanding of mathematics; for this to occur, rigorous mathematical
content must be reorganized, taught, and assessed in a problem-solving
environment. For students to develop this deeper level of
understanding, their knowledge must be connected to a variety of ideas
and skills across topic areas and grade levels in mathematics, to
other subjects taught in school, as well as to situations outside the
classroom.
The Essential Academic Learning Requirements in Mathematics:
1. The student understands and applies the concepts and procedures
of mathematics.
2. The student uses mathematics to define and solve problems.
3. The student uses mathematical reasoning.
4. The student communicates knowledge and understanding in both
everyday and mathematical language.
5. The student understands how mathematical ideas connect within
mathematics, to other subject areas, and to real-life situations.
----------------------------------------------------------------------
NOTE: [Image] The text repeats for each benchmark.
The arrow means that the skills or materials used becomes increasingly
complex.
[Image] ESSENTIAL LEARNING 1: The student understands and applies the
concepts and procedures of mathematics.
To meet this standard, the student will:
1.1 understand and apply concepts and procedures from number sense
number and numeration, computation, and estimation
1.2 understand and apply concepts and procedures from measurement
attributes and dimensions, approximation and precision, and
systems and tools
1.3 understand and apply concepts and procedures from geometric sense
shape and dimension, and relationships and transformations
1.4 understand and apply concepts and procedures from probability and
statistics
probability, statistics, and prediction and inference
1.5 understand and apply concepts and procedures from algebraic sense
relations and representations, and operations
COMPONENTS BENCHMARK 3 (GRADE 10)
1.1 understand number and numeration
and apply
concepts and understand and use properties and symbolic
procedures from representations of real numbers
number sense
explain the magnitude of numbers by comparing and
ordering real numbers
understand concepts of and use processes involving
prime and composite numbers, factors and multiples,
and divisibility
understand and apply the concepts of ratio and both
direct and indirect proportion
computation
understand operations on real numbers
compute with real numbers, powers, and roots
use mental arithmetic, pencil and paper, calculator,
or computer as appropriate to the task involving real
numbers
estimation
identify situations involving real numbers in which
estimation is sufficient and computation is not
required
use estimation to predict computation results and to
determine the reasonableness of answers involving
real numbers, for example, estimating the interest on
a loan
1.2 understand attributes and dimensions
and apply
concepts and understand how changes in dimension affect perimeter,
procedures from area, and volume
measurement
measure objects and events directly or use indirect
methods such as finding the volume of a cone given
its height and diameter
calculate rate and other derived and indirect
measurements
approximation and precision
understand that the precision and accuracy of
measurement is affected by the measurement tools and
calculating procedures
use estimation to obtain reasonable approximations,
for example, estimating how much paint is needed to
paint the walls of a classroom
systems and tools
understand the benefits of standard units of
measurement and the advantages of the metric system
compare, contrast, and use both the U.S. and metric
systems
select and use tools that will provide an appropriate
degree of precision, for example, using kilometers
vs. light years
1.3 understand shape and dimension
and apply
concepts and compare, describe, and classify 2- and 3-dimensional
procedures from geometric figures
geometric sense
construct geometric models and scale drawings using
tools as appropriate, for example, designing a house
plan or building a model of a bridge
relationships and transformations
understand and use coordinate grids
identify simple differences between geometric
properties of a plane and a sphere
understand and use properties of symmetry,
similarity, and congruence
understand and construct multiple geometric
transformations using combinations of translation,
reflection, or rotation
use a variety of tools and technologies to perform
geometric constructions
1.4 understand probability
and apply
concepts and understand the properties of dependent and
procedures from independent events
probability and
statistics understand and use appropriate counting procedures to
determine probabilities
use both experimental and theoretical methods to
determine probabilities
statistics
use statistics to support different points of view,
for example, in a debate or a position paper
collect data using appropriate methods and technology
organize and display data in appropriate forms such
as tables, graphs, scatter plots, and box plots
calculate and use the different measures of central
tendency, variability, and range as appropriate in
describing sets of data
prediction and inference
design and conduct experiments to verify or disprove
predictions
understand and make inferences based on the analysis
of experimental results
1.5 understand relations and representations
and apply
concepts and recognize, create, extend, and generalize patterns,
procedures from sequences, and series
algebraic sense
understand, develop, and express rules describing
patterns
translate among tabular, symbolic, and graphical
representations of relations, for example, displaying
information from a table as a graph
represent situations that involve variable quantities
with expressions, formulas and equations, and
inequalities
operations
evaluate and simplify expressions
create and solve equations and inequalities
[Image] ESSENTIAL LEARNING 2: The student uses mathematics to define and
solve problems.
To meet this standard, the student will:
2.1 investigate situations
by searching for patterns and exploring a variety of approaches
2.2 formulate questions and define the problem
2.3 construct solutions
by choosing the necessary information and using the appropriate
mathematical tools
COMPONENTS BENCHMARK 3 (GRADE 10)
2.1 investigate search systematically for patterns in complex
situations situations
analyze and use multiple strategies
identify what information is missing or
extraneous and compensate for it
analyze an unproductive approach and attempt to
modify it or try a new approach
2.2 formulate identify questions to be answered in complex
questions and define situations
the problem
define problems in complex situations
identify the unknowns in complex situations
2.3 construct organize and synthesize information from
solutions multiple sources
[Image] select and use appropriate mathematical
tools
[Image] apply appropriate methods, operations,
and processes to construct a solution
[Image] ESSENTIAL LEARNING 3: The student uses mathematical reasoning.
To meet this standard, the student will:
3.1 analyze information
from a variety of sources; use models, known facts, patterns and
relationships to validate thinking
3.2 predict results and make inferences
and make conjectures based on analysis of problem situations
3.3 draw conclusions and verify results
support mathematical arguments, justify results, and check for
reasonableness of solutions
COMPONENTS BENCHMARK 3 (GRADE 10)
3.1 analyze interpret and integrate information from multiple
information sources
validate thinking and mathematical ideas using
models, known facts, patterns, relationships,
counter-examples, and proportional reasoning
3.2 predict
results and make make and explain conjectures and inferences based on
inferences analysis of problem situations
3.3 draw test conjectures and inferences by formulating a
conclusions and proof or by constructing a counterexample
verify results
support arguments and justify results using
inductive and deductive reasoning
[Image] check for reasonableness of results
reflect on and evaluate procedures and results and
make necessary revisions
[Image] ESSENTIAL LEARNING 4: The student communicates knowledge and
understanding in both everyday and mathematical language.
To meet this standard, the student will:
4.1 gather information
read, listen, and observe to access and extract mathematical
information
4.2 organize and interpret information
4.3 represent and share information
share, explain, and defend mathematical ideas using terms,
language, charts, and graphs that can be clearly understood by a
variety of audiences
COMPONENTS BENCHMARK 3 (GRADE 10)
4.1 gather develop or select an efficient system for collecting
information information
use reading, listening, and observation skills to
access and extract mathematical information from
multiple, self-selected sources such as pictures,
diagrams, physical models, oral narratives, and
symbolic representations
integrate the use of a variety of available
technologies to browse, select, and retrieve
mathematical information from multiple sources
4.2 organize and organize, clarify, and refine mathematical information
interpret in multiple ways - reflecting, verbalizing,
information discussing, or writing
4.3 represent express complex ideas and situations using
and share mathematical language and notation in appropriate and
information efficient forms
express or present mathematical ideas clearly and
effectively using both everyday and mathematical
language appropriate to audience
[Image] ESSENTIAL LEARNING 5: The student understands how mathematical
ideas connect within mathematics, to other subject areas, and to real-life
situations.
To meet this standard, the student will:
5.1 relate concepts and procedures within mathematics
recognize relationships among mathematical ideas and topics
5.2 relate mathematical concepts and procedures to other disciplines
identify and apply mathematical thinking and notation in other
subject areas
5.3 relate mathematical concepts and procedures to real-life
situations
understand the connections between mathematics and problem
solving skills used every day at work and at home
COMPONENTS BENCHMARK 3 (GRADE 10)
5.1 relate relate and use conceptual and procedural
concepts and understandings among multiple mathematical content
procedures within areas
mathematics
relate and use multiple equivalent mathematical
models and representations
5.2 relate extend mathematical patterns and ideas to other
mathematical disciplines
concepts and
procedures to apply mathematical thinking and modeling in other
other disciplines disciplines
[Image] describe examples of contributions to the
development of mathematics such as the contributions
of women, men, and different cultures
5.3 relate identify situations in which mathematics can be used
mathematical to solve problems with local, national, or
concepts and international implications such as calculating
procedures to resources necessary for interstate highway
real-life maintenance
situations
investigate the mathematical knowledge and training
requirements for occupational/career areas of
interest
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