ICCSD Student Goals/Standards
STANDARDS and BENCHMARKS
MATHEMATICS
What Students Are Expected To Know and Be Able to Do
Kindergarten through Twelfth Grade
Problem Solving - solve
mathematical problems
- use problem solving approaches to investigate and understand
mathematical content
- formulate problems from everyday and mathematical
situations
- develop and apply strategies to solve a wide variety of
problems including multistep and non-routine problems
- verify and interpret results with respect to the original
problem
- generalize solutions and strategies to new problem
situations
- acquire confidence in using mathematics meaningfully
- relate physical materials, pictures, and diagrams to
mathematical ideas
- reflect on and clarify thinking about mathematical ideas and
situations
- relate everyday language to mathematical language and
symbols
- realize that representing, discussing, reading, writing, and
listening to mathematics are a vital part of learning and using
mathematics
- discuss mathematical ideas and make conjectures and convincing
arguments
Communication - Use numerous
opportunities for mathematical communication
- relate physical materials, pictures, and diagrams to
mathematical ideas
- reflect on and clarify thinking about mathematical ideas and
situations
- relate everyday language to mathematical language and
symbols
- realize that representing, discussing, reading, writing, and
listening to mathematics are a vital part of learning and using
mathematics
- discuss mathematical ideas and make conjectures and convincing
arguments
Reasoning - Use mathematical
reasoning
- draw logical conclusions about mathematics
- use models, known facts, properties, proportions, graphs and
relationships to explain their thinking
- justify their answers and solution processes
- use patterns and relationships to analyze mathematical
situations
- believe that mathematics makes sense
Connections - Make mathematical
connections
- link conceptual and procedural knowledge
- relate various representations of concepts or procedures to
one another
- recognize relationships among different topics in
mathematics
- use mathematics in other curricular areas
- use mathematics in their daily lives
Estimation - Use estimation
- explore and develop estimation strategies
- recognize when an estimate is appropriate
- determine the reasonableness of results
- apply estimation when working with quantities, measurement,
computation and problem solving
- select and use an appropriate method for computing from among
mental arithmetic, paper-and-pencil, calculator and computer
methods.
Patterns and
Relationships - Use mathematical patterns and relationships
- recognize, describe, extend, analyze and create a wide variety
of patterns
- represent and describe mathematical relationships
- explore and use variables and open sentences to express
relationships
- use patterns to represent and solve problems
Algebra - Know how to explore algebraic
concepts and processes
- understand the concepts of variable, expression and
equation
- represent situations and number patterns with tables, graphs,
verbal rules, and equations and explore the interrelationships of
the representations
- analyze tables and graphs to identify properties and
relationships
- develop confidence in solving linear equations using concrete,
informal methods
- apply algebraic methods to solve simplistic, real-world
problems and mathematical problems
Whole Numbers:
Number Sense and Numeration - Demonstrate knowledge of whole
number mathematical concepts, skills and relationships
- construct number meanings through real-world experiences and
the use of physical materials
- understand our numeration system by relating counting,
grouping and place value concepts
- develop number sense
- interpret the multiple uses of numbers encountered in the real
world
Whole Numbers:
Concepts of Operations and Computation - Use addition,
subtraction, multiplication and division of whole numbers
- develop meaning for the operations by modeling and discussing
a rich variety of problem situations
- relate the mathematical language and symbolism of operations
to problem situation and informal language
- recognize that a wide variety of problem structure can be
represented by a single operation
- develop operation sense
- model, explain and develop reasonable proficiency with basic
facts and algorithms
- use a variety of mental computation and estimation
techniques
- use calculators in appropriate computational situations
- select and use computation techniques appropriate to specific
problems and determine whether the results are reasonable.
Geometry and Spatial
Sense - Use two and three dimensional geometry
- describe, model, draw, identify, compare and classify
shapes
- investigate and predict the results of combining, subdividing
and changing shapes
- develop spatial sense
- relate geometric ideas to number and measurement ideas
- explore transformations of geometric figures
- represent and solve problems using geometric models
- understand and apply geometric properties and
relationships
- recognize and appreciate geometry in the world
Measurement - Use measurement
- understand the attributes of length, capacity, weight, area,
volume, time, temperature and angle
- develop the process of measuring and concepts related to units
of measurement
- make and use estimates of measurement
- select appropriate units and tools to measure
- develop formulas and procedures for determining measures to
solve problems
- make and use measurements in problem and everyday
situations
- understand money values
- estimate and count amounts of money
- experience money transaction problems and everyday
situations
Statistics and
Probability - Use data analysis and probability
- collect, organize and describe data
- construct, read and interpret displays of data
- formulate and solve problems that involve collecting and
analyzing data
- make inferences and convincing arguments that are based on
data analysis
- represent numerical relationships in one and two dimensional
graphs
- explore concepts of chance
- model situations by devising and carrying out experiments or
simulations to determine probabilities
- appreciate the power of using a probability model by comparing
experimental results with mathematical expectations
- make predictions that are based on experimental or theoretical
probabilities
- develop an appreciation for the pervasive use of probability
in the real world
Fractions and Decimals
- Use fractions and decimals
- develop concepts of fractions, mixed numbers and decimals
- develop number sense for fractions and decimals
- use models to relate fractions to decimals and to find
equivalent fractions
- use models to explore operations on fractions and
decimals
- apply fractions and decimals to problem situations
- understand, represent and use numbers in a variety of
equivalent forms (fractions, decimals, percents) in a real-world
and mathematical problem situations
- select and use an appropriate method for computing from among
mental arithmetic, paper and pencil, calculator and computer
methods
- understand and apply ratios, proportions and percents in a
wide variety of situations
- investigate relationships among fractions, decimals and
percents
BENCHMARKS
Description of the Specific Level of Information and Skill by
Grade
Kindergarten
- Constructs, describes and extends patterns
- Recognizes basic shapes: square, circle, triangle,
rectangle
- Sequences events
- Puts objects into groups
- Groups and regroups same objects
- Orders a set of objects
- Inserts objects onto an ordered set
- Makes a one-to-one correspondence with objects
- Identifies more, same, less
- Constructs number sets and associates numerals for 1-10
- Raises questions which indicate a curiosity about the natural
world
- Applies problem solving strategies effectively
First and Second Grades
- Demonstrates problem-solving strategies
- Explains the thinking involved in his/her work
- Constructs, describes and extends patterns
- Demonstrates strategies for estimating
- Demonstrates an understanding of basic concepts of whole
number addition
- Demonstrates an understanding of basic concepts of whole
number subtraction
- Demonstrates an understanding of basic concepts of whole
number place value
- Demonstrates an understanding of addition and subtraction
basic facts
- Tells/writes number stories
- Demonstrates an understanding of 2-digit addition
- Demonstrates an understanding of 2-digit subtraction
- Demonstrates an understanding of concepts of fractions
- Demonstrates an understanding of basic concepts of
geometry
- Demonstrates an understanding of basic concepts of
measurement
- Demonstrates an understanding of basic concepts of time
- Demonstrates an understanding of basic concepts of money
- Collects, organizes, displays and interprets data in graph
form
Third and Fourth Grades
- Applies problem-solving strategies effectively
- Constructs, describes and extends patterns
- Applies estimation strategies effectively
- Explains process leading to appropriate results
- Understands concepts of whole numbers
- Understands concepts of decimals
- Understands concepts of fractions
- Computes accurately adding whole numbers
- Computes accurately subtracting whole numb.
- Computes accurately multiplying whole numb.
- Computes accurately dividing whole numbers
- Demonstrates skill in addition/subtraction of Decimals
- Chooses addition and/or subtraction
- Recalls basic facts for addition
- Recalls basic facts for subtraction
- Recalls basic facts for multiplication
- Recalls basic facts for division
- Understands and applies basic concepts of measurement
- Understands and applies basic concepts of time
- Understands and applies basic concepts of money
- Demonstrates skill in choosing multiplication and/or division
to solve problems
- Understands and applies basic concepts of probability
- Understands and applies basic concepts of geometry
- Collects, organizes, displays and interprets data
Fifth Grade
- Applies problem solving strategies effectively
- Applies estimation strategies effectively
- Understands concepts of whole numbers
- Understands concepts of fractions
- Accurately subtracts whole numbers
- Accurately adds decimals
- Chooses addition, subtraction, multiplication and/or division
appropriately to solve problems
- Knows basic facts for addition
- Recalls basic facts for multiplication
- Understands and applies basic concepts of measurement
- Understands and applies basic concepts of probability
- Collects, organizes, displays and interprets data
- Constructs, describes and extends patterns
- Explains processes leading to appropriate results
- Understands concepts of decimals
- Accurately adds whole numbers
- Accurately multiplies whole numbers
- Accurately subtracts decimals
- Applies mental math strategies
- Knows basic facts for subtraction
- Recalls basic facts for division
- Understands and applies basic concepts of time
- Understands and applies basic concepts of geometry
Sixth Grade
- Applies varied strategies in problem solving
- Explains processes that lead to appropriate results
- Understands the concepts of whole numbers
- Understands the concepts of fractions
- Computes whole numbers accurately
- Computes fractions accurately
- Knows basic facts
- Understands and applies concepts of measurement
- Constructs, describes and extends patterns
- Selects and uses the appropriate mode of computation
- Understands the concepts of decimals
- Understands the concepts of ratio, proportion, and
percent
- Computes decimals accurately
- Chooses addition, subtraction, multiplication and/or division
appropriately to solve problems
- Understands and applies concepts of geometry
- Understands and applies concepts of probability
Eighth Grade
- Uses number and operation sense for whole numbers
- Uses number and operation sense for decimals
- Is confident in using math. meaningfully
- Uses problem-solving approaches to investigate and understand
math. content
- Reflects on, clarifies, justifies, and communicates one's own
thinking about mathematical ideas and situations
- Understands the role of mathematics in our culture and
society
- Selects and uses an appropriate method for computing from
among mental arithmetic, paper/pencil, calculator, and computer
methods
- Understands and applies the concepts of variable, expression,
and equation
- Uses number and operation sense for fractions
- Uses number and operation sense for integers
- Develops and applies a variety of strategies to solve
non-routine problems
- Models situations using oral, written, concrete, pictorial,
and graphical methods
- Applies mathematical thinking and modeling to solve problems
that arise in other disciplines
- Understands, represents, and uses numbers in a variety of
equivalent forms in real-world and mathematical problem
situations
- Describes and represents relationships with tables, graphs,
and verbal rules and equations
- Demonstrates an understanding of plane and solid geometric
figures and the various ways to describe and measure their
characteristics
- Applies probability concepts
Eleventh Grade
- Uses appropriate mathematical approaches and tools
(estimation, mental computation, trial and error, paper/pencil,
calculator, and/or computer) to formulate and solve problems
- Comprehends, develops, and uses mathematical concepts and
generalizations
- Recognizes fallacies of reasoning
- Identifies and formulates mathematical problems in real world
situations, as well as
- proposes and evaluates ways to solve problems.
- Estimates, approximates, and judges reasonableness of
answers
- Constructs, reads, and interprets graphs with accuracy
- Makes connections among various concepts within and outside
mathematics
- Makes accurate inferences or predictions based on data or
information
- Uses basic concepts of probability and statistics to interpret
data, draw conclusions, and make inferences
- Performs, with accuracy, the operations (addition,
subtraction, multiplication, division) using whole numbers,
integers, fractions, decimals, and rational numbers
- Uses metric and customary units to measure lengths, areas,
volumes, weights, time, and other quantities
- Understands spatial relationships
- Uses inductive and deductive thinking
- Organizes and processes information by comparing, classifying,
and ordering
- Identifies examples and counterexamples of mathematical
concepts
- Applies quantitative procedures to relatively novel
situations
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Standards
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Benchmarks