| Standard
4.1: All
Students Will Develop The Ability To Pose And Solve
Mathematical Problems In Mathematics, Other
Disciplines, And Everyday Experiences |
|
1. Use discovery-oriented,
inquiry-based, and problem-centered approaches to
investigate and understand mathematical content
appropriate to early elementary grades. |
|
2. Recognize, formulate,
and solve problems arising from mathematical
situations and everyday experiences. |
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3. Construct and use
concrete, pictorial, symbolic, and graphical models
to represent problem situations. |
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4. Pose, explore, and
solve a variety of problems, including non-routine
problems and open-ended problems with several
solutions and/or solution strategies. |
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5. Construct, explain,
justify, and apply a variety of problem-solving
strategies in both cooperative and independent
learning environments. |
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6. Verify the correctness
and reasonableness of results and interpret them in
the context of the problems being solved. |
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7. Know when to select and
how to use grade-appropriate mathematical tools and
methods (including manipulatives, calculators and
computers, as well as mental math and
paper-and-pencil techniques) as a natural and routine
part of the problem- solving process. |
|
8. Determine, collect,
organize, and analyze data needed to solve problems. |
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9. Recognize that there
may be multiple ways to solve a problem. |
| Standard
4.2: All
Students Will Communicate Mathematically Through
Written, Oral, Symbolic, And Visual Forms Of
Expression |
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1. Discuss, listen,
represent, read, and write as vital activities in
their learning and use of mathematics. |
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2. Identify and explain
key mathematical concepts, and model situations using
oral, written, concrete, pictorial, and graphical
methods. |
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3. Represent and
communicate mathematical ideas through the use of
learning tools such as calculators, computers, and
manipulatives. |
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4. Engage in mathematical
brainstorming and discussions by asking questions,
making conjectures, and suggesting strategies for
solving problems. |
|
5. Explain their own
mathematical work to others, and justify their
reasoning and conclusions. |
| Standard
4.3: All
Students Will Connect Mathematics To Other Learning
By Understanding The Interrelationships Of
Mathematical Ideas And The Roles That Mathematics And
Mathematical Modeling Play In Other Disciplines And
In Life |
|
1. View mathematics as an
integrated whole rather than as a series of
disconnected topics and rules. |
|
2. Relate mathematical
procedures to their underlying concepts. |
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3. Use models,
calculators, and other mathematical tools to
demonstrate the connections among various equivalent
graphical, concrete, and verbal representations of
mathematical concepts. |
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4. Explore problems and
describe and confirm results using various
representations. |
|
5. Recognize the
connections between mathematics and other
disciplines, and apply mathematical thinking and
problem solving in those areas. |
|
6. Recognize the role of
mathematics in their daily lives and in society. |
| Standard
4.4: All
Students Will Develop Reasoning Ability And Will
Become Self-Reliant, Independent Mathematical
Thinkers |
|
1. Make educated guesses
and test them for correctness. |
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2. Draw logical
conclusions and make generalizations. |
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3. Use models, known
facts, properties, and relationships to explain their
thinking. |
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4. Justify answers and
solution processes in a variety of problems. |
|
5. Analyze mathematical
situations by recognizing and using patterns and
relationships. |
| Standard
4.5: All
Students Will Regularly And Routinely Use
Calculators, Computers, Manipulatives, And Other
Mathematical Tools To Enhance Mathematical Thinking,
Understanding, And Power |
|
1. Select and use
calculators, software, manipulatives, and other tools
based on their utility and limitations and on the
problem situation. |
|
2. Use physical objects
and manipulatives to model problem situations, and to
develop and explain mathematical concepts involving
number, space, and data. |
|
3. Use a variety of
technologies to discover number patterns, demonstrate
number sense, and visualize geometric objects and
concepts. |
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4. Use a variety of tools
to measure mathematical and physical objects in the
world around them. |
|
5. Use technology to
gather, analyze, and display mathematical data and
information. |
| Standard
4.6: All
Students Will Develop Number Sense And An Ability To
Represent Numbers In A Variety Of Forms And Use
Numbers In Diverse Situations |
|
1. Use real-life
experiences, physical materials, and technology to
construct meanings for whole numbers, commonly used
fractions, and decimals. |
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2. Develop an
understanding of place value concepts and numeration
in relationship to counting and grouping. |
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3. See patterns in number
sequences, and use pattern-based thinking to
understand extensions of the number system. |
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4. Develop a sense of the
magnitudes of whole numbers, commonly used fractions,
and decimals. |
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5. Understand the various
uses of numbers including counting, measuring,
labeling, and indicating location. |
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6. Count and perform
simple computations with money. |
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7. Use models to relate
whole numbers, commonly used fractions, and decimals
to each other, and to represent equivalent forms of
the same number. |
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8. Compare and order whole
numbers, commonly used fractions, and decimals. |
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9. Explore real-life
settings which give rise to negative numbers. |
| Standard
4.7: All
Students Will Develop Spatial Sense And An Ability To
Use Geometric Properties And Relationships To Solve
Problems In Mathematics And In Everyday Life |
|
1. Explore spatial
relationships such as the direction, orientation, and
perspectives of objects in space, their relative
shapes and sizes, and the relations between objects
and their shadows or projections. |
|
2. Explore relationships
among shapes, such as congruence, symmetry,
similarity, and self-similarity. |
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3. Explore properties of
three- and two-dimensional shapes using concrete
objects, drawings, and computer graphics. |
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4. Use properties of
three- and two-dimensional shapes to identify,
classify, and describe shapes. |
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5. Investigate and predict
the results of combining, subdividing, and changing
shapes. |
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6. Use tessellations to
explore properties of geometric shapes and their
relationships to the concepts of area and perimeter. |
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7. Explore geometric
transformations such as rotations (turns),
reflections (flips), and translations (slides). |
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8. Develop the concepts of
coordinates and paths, using maps, tables, and grids. |
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9. Understand the variety
of ways in which geometric shapes and objects can be
measured. |
|
10. Investigate the
occurrence of geometry in nature, art, and other
areas. |
| Standard
4.8: All
Students Will Understand, Select, And Apply Various
Methods Of Performing Numerical Operations |
|
1. Develop meaning for the
four basic arithmetic operations by modeling and
discussing a variety of problems. |
|
2. Develop proficiency
with and memorize basic number facts using a variety
of fact strategies (such as "counting on"
and "doubles"). |
|
3. Construct, use, and
explain procedures for performing whole number
calculations in the various methods of computation. |
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4. Use models to explore
operations with fractions and decimals. |
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5. Use a variety of mental
computation and estimation techniques. |
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6. Select and use
appropriate computational methods from mental math,
estimation, paper- and-pencil, and calculator
methods, and check the reasonableness of results. |
|
7. Understand and use
relationships among operations and properties of
operations. |
| Standard
4.9: All
Students Will Develop An Understanding Of And Will
Use Measurement To Describe And Analyze Phenomena |
|
1. Use and describe
measures of length, distance, capacity, weight, area,
volume, time, and temperature. |
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2. Compare and order
objects according to some measurable attribute. |
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3. Recognize the need for
a uniform unit of measure. |
|
4. Develop and use
personal referents for standard units of measure
(such as the width of a finger to approximate a
centimeter). |
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5. Select and use
appropriate standard and non-standard units of
measurement to solve real-life problems. |
|
6. Understand and
incorporate estimation and repeated measures in
measurement activities. |
| Standard
4.10: All
Students Will Use A Variety Of Estimation Strategies
And Recognize Situations In Which Estimation Is
Appropriate |
|
1. Judge without counting
whether a set of objects has less than, more than, or
the same number of objects as a reference set. |
|
2. Use personal referents,
such as the width of a finger as one centimeter, for
estimations with measurement. |
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3. Visually estimate
length, area, volume, or angle measure. |
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4. Explore, construct, and
use a variety of estimation strategies. |
|
5. Recognize when
estimation is appropriate, and understand the
usefulness of an estimate as distinct from an exact
answer. |
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6. Determine the
reasonableness of an answer by estimating the result
of operations. |
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7. Apply estimation in
working with quantities, measurement, time,
computation, and problem solving. |
| Standard
4.11: All
Students Will Develop An Understanding Of Patterns,
Relationships, And Functions And Will Use Them To
Represent And Explain Real-World Phenomena. |
|
1. Reproduce, extend,
create, and describe patterns and sequences using a
variety of materials. |
|
2. Use tables, rules,
variables, open sentences, and graphs to describe
patterns and other relationships. |
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3. Use concrete and
pictorial models to explore the basic concept of a
function. |
|
4. Observe and explain how
a change in one physical quantity can produce a
corresponding change in another. |
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5. Observe and recognize
examples of patterns, relationships, and functions in
other disciplines and contexts. |
|
6. Form and verify
generalizations based on observations of patterns and
relationships. |
| Standard
4.12: All
Students Will Develop An Understanding Of Statistics
And Probability And Will Use Them To Describe Sets Of
Data, Model Situations, And Support Appropriate
Inferences And Arguments |
|
1. Formulate and solve
problems that involve collecting, organizing, and
analyzing data. |
|
2. Generate and analyze
data obtained using chance devices such as spinners
and dice. |
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3. Make inferences and
formulate hypotheses based on data. |
|
4. Understand and
informally use the concepts of range, mean, mode, and
median. |
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5. Construct, read, and
interpret displays of data such as pictographs, bar
graphs, circle graphs, tables, and lists. |
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6. Determine the
probability of a simple event, assuming equally
likely outcomes. |
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7. Make predictions that
are based on intuitive, experimental, and theoretical
probabilities. |
|
8. Use concepts of
certainty, fairness, and chance to discuss the
probability of actual events. |
| Standard
4.13: All
Students Will Develop An Understanding Of Algebraic
Concepts And Processes And Will Use Them To Represent
And Analyze Relationships Among Variable Quantities
And To Solve Problems |
|
1. Understand and
represent numerical situations using variables,
expressions, and number sentences. |
|
2. Represent situations
and number patterns with concrete materials, tables,
graphs, verbal rules, and number sentences, and
translate from one to another. |
|
3. Understand and use
properties of operations and numbers. |
|
4. Construct and solve
open sentences (example: 3 + ___ = 7) that describe
real-life situations. |
| Standard
4.14: All
Students Will Apply The Concepts And Methods Of
Discrete Mathematics To Model And Explore A Variety
Of Practical Situations. |
|
1. Explore a variety of
puzzles, games, and counting problems |
|
2. Use networks and tree
diagrams to represent everyday situations. |
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3. Identify and
investigate sequences and patterns found in nature,
art, and music. |
|
4. Investigate ways to
represent and classify data according to attributes,
such as shape or color, and relationships, and
discuss the purpose and usefulness of such
classification. |
|
5. Follow, devise, and
describe practical lists of instructions. |
| Standard
4.15: All
Students Will Develop An Understanding Of The
Conceptual Building Blocks Of Calculus And Will Use
Them To Model And Analyze Natural Phenomena |
|
1. Investigate and
describe patterns that continue indefinitely. |
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2. Investigate and
describe how certain quantities change over time. |
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3. Experiment with
approximating length, area, and volume, using
informal measurement instruments. |