South Dakota State Goals, Indicators, and Benchmarks

 

South Dakota has established six goals that are the same for K-12 instruction. Indicators and benchmarks are grouped by grade clusters. K-5 information is listed below. Goals are noted * and listed in bold, indicators are noted °and indented once, and benchmarks are indented twice.

•     K-2
•     3-5

 

ALGEBRA-Students will use the language of algebra to explore, describe, represent, and analyze number expressions and relations that represent variable quantities.

 

• Analyze procedures to transform algebraic expressions
• Identify equalities and inequalities
• Explore elements of sets
• Write mathematical statements to show relationships
• Explore properties of equality and inequality
• Explore various relationships among elements of a set
• Create equivalent algebraic statements using inverse operations and order of operations

• Use a variety of algebraic concepts and methods to solve problems
• Create algebraic expressions that represent problem situations
• Recognize various representations of a number sentence
• Use the number line to solve problems involving positive and negative quantities
• Use algebraic expressions to represent problems
• Create various representations for the same number sentence
• Use graphic representations to solve problems involving positive and negative quantities

• Analyze and describe the situations that involve one or more variables
• Identify the variables in open sentences
• Explore various representations of a given number
• Describe processes used to find answers to open sentences
• Determine solution sets for simple open sentences
• Model relationships between sets of numbers
• Explore how changing one variable can cause a change in another

 

GEOMETRY-Students will use the language of geometry to discover, analyze, and communicate geometric concepts, properties, and relationships.

 

• Apply deductive and inductive reasoning to analyze geometric properties to solve problems 0 Identify characteristics of two-and three-dimensional shapes
• Use geometric properties to identify shapes
• Investigate relationships between various geometric shapes
• Describe properties of geometric figures using geometric terms
• Classify objects using geometric properties
• Use geometric properties to solve problems

• Analyze geometric figures from a variety of perspectives
• Explore concepts of perspective using geometric shapes and figures 0 Describe spatial arrangements or positions of shapes and figures 0 Explore ways to arrange and/or transform geometric shapes
• Use perspective to create or identify geometric shapes and figures . Visualize and illustrate ways objects can be oriented in space
• Determine methods to transform objects

 

MEASUREMENT-Students will apply systems of measurement and use appropriate measurement tools to describe and analyze the world around them.

 

• Use various units of measure within a system of measurement
• Explore various types of measurement used
• Recognize specific standard measurement units
• Use non-standard units to explore measurement in unique situations
• Identify the referents used in different measurement scales
• Investigate appropriateness of scales selected for measurement situations
• Investigate scales that can be used in unique measurement situations

• Apply measurement concepts in practical applications
• Explore various tools that provide accurate measurements
• Apply physical senses in making measurements and estimations of measurements
• Explore the use of measurement in various situations
• Use various tools to make accurate measurements
• Apply measurement tools that assist the physical senses in making measurements
• Investigate the effectiveness of specific measurement systems

 

NUMBER SENSE-Students will develop and use number sense to investigate the characteristics of numbers in a variety of forms and modes of operation.

 

• Analyze the structural characteristics of the real number system and its various subsystems
• Explore the structure and applications of the rational number system
• Use physical materials to understand the rational number system
• Explore connections of the whole number system to the rational number system
• Examine the structure of the rational number system and investigate its appropriate applications and limitations
• Use physical materials and real-life experiences to understand the rational number system
• Model the connections of subsystems in the rational number system

• Apply number operations with real numbers and other number systems
• Model operations of addition and subtraction using rational numbers
• Construct meaning for whole numbers, common fractions, and decimals
• Apply the number operations of addition and subtraction in problem-solving situations
• Model the operations of addition, subtraction, multiplication, and division on rational numbers
• Represent numbers in a variety of equivalent ways
• Apply number operations to problem-solving situations

• Develop conjectures, predictions, or estimations to solve problems and verify or justify the results
• Explore properties of the whole number system
• Explore various problem-solving rules
• Estimate and/or predict results of various calculations
• Explore the properties of the rational number system
• Apply various problem solving rules
• Use estimation to test reasonableness of calculations

• Apply the concept of value, magnitude, and relative magnitude of real numbers
• Explore place value concepts using grouping and substitution
  
• Describe the impact of adding and subtracting on the magnitude of numbers
• Model order and value for commonly used fractions, decimals, and whole numben . Model the concept of magnitude using concrete materials
• Explore the effect of operations on magnitudes
• Describe, order, and value relationships of common decimals, fractions, and whole numbers

 

PATTERNS, RELATIONS, AND FUNCTIONS-Students will discover, analyze, extend, and creatf patterns, relations, or functions to model mathematical ideas in a variety of forms.

 

• Analyze and describe the properties and behaviors of relations, functions, and their invers( 0 Explore the relationship between two variables
• Recognize and explain the constants of a relationship
• Explore the properties of various relations
• Explore relationships between and among different variables
• Recognize the effects of change in coefficients on graphs of relations
• Identify the general properties and behaviors of a set of relations

• Apply relations and functions to complex problem solving situations
• Observe and describe patterns found in everyday events and experiences
• Use tables and graphs to explore solutions to problems
• Create rules to extend patterns and relationships
• Describe and reproduce patterns from real experiences
• Use tables, graphs, and open sentences to explain solutions to problems
• Apply pattern and relationship rules to solve problems

• Analyze the applications of the concept of mathematical limit
• Explore characteristics of bounded relationships
• Use concrete models to represent continuous or discrete patterns or functions
• Use concrete examples to demonstrate bounded relationships
• Explain characteristics of bounded relationships
• Create pictorial or numeric models to represent continuous or discrete patterns or functions
• Use pictorial examples to demonstrate bounded relationships

 

STATISTICS & PROBABILITY-Students will apply statistical methods to analyze data and exploJ probability for making decisions and predictions.

• Use various statistical models to gather data, study problems, and draw conclusions
• Use data gathered from the environment to create tallies, tables, and graphs of information
• Compare and discuss relationships of categories for classified collections of object
• Make convincing arguments to support simple conclusions drawn from collected data
• Investigate the different uses of various sampling techniques
• Determine mode, median, and mean for various sets of data
• Make and support inferences through data collection

• Apply the laws of probability to predict events/outcomes and solve problems
• Gather and compare sets of data based on chance events
• Explain consistency of results that occur in repeated experimental trials
• Predict outcomes, draw simple conclusions, and report results based on collected data
• Compare sample data sets to group data
• Explore the relationship between experimental and theoretical probabilities
• Predict and report possible combinations and arrangements of probability in chance situations

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