Kindergarten through Fifth Grade
While connecting mathematical experiences to the world around them, young children are challenged to become increasingly sophisticated in dealing with mathematical concepts. The elementary mathematics curriculum builds on students' math understanding, skills, and proficiency at each grade level, as appropriate, by integrating concepts such as number and operations, algebra, geometry, measurement, and data analysis and probability. Students also engage in problem solving, reasoning, and communicating ideas while making connections to the world around them.
Scott Foresman/Addison Wesley Mathematics
Investigations in Number, Data, and Space - Dale Seymour Publishers
Topics (kindergarten)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Sense of numbers
* Basic counting techniques
* Size of numbers
* Number relationships
* Place value
* Addition and subtraction
* Computational fluency
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Classification, patterns and relations
* Operations with whole numbers
* Use of step-by-step processes
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Explore, investigate and discuss shapes and structures in the classroom
* Become proficient in describing and representing shapes in their environment
* Learn to represent two- and three-dimensional shapes
* Recognize and create shapes that have symmetry
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Attributes of length, volume, weight and time
* How to measure using standard and nonstandard units
* Select appropriate unit and tool for attribute being measured
* Use repetition of a single unit to measure something larger than the unit
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* Pose questions to investigate
* Organize responses
* Create representations of data
* Sort and classify objects according to their attributes
* Organize and display data through graphical displays using counts, tallies, pictures and graphs
* Analyze and describe data
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Develop and broaden range of problem-solving strategies
* Pose or formulate challenging problems
* Monitor and reflect on their own problem-solving ideas
* Solve problems from a variety of contexts, from daily routines to mathematical situations in stories
Topics (first grade)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Sense of numbers
* Basic counting techniques
* Size of numbers
* Number relationships
* Place value
* Addition and subtraction
* Computational fluency
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Classification, patterns and relations
* Operations with whole numbers
* Use of step-by-step processes
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Explore, investigate and discuss shapes and structures in the classroom
* Become proficient in describing and representing shapes in their environment
* Learn to represent two- and three-dimensional shapes
* Recognize and create shapes that have symmetry
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Attributes of length, volume, weight and time
* How to measure using standard and nonstandard units
* Select appropriate unit and tool for attribute being measured
* Use repetition of a single unit to measure something larger than the unit
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* Pose questions to investigate
* Organize responses
* Create representations of data
* Sort and classify objects according to their attributes
* Organize and display data through graphical displays using counts, tallies, pictures and graphs
* Analyze and describe data
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Develop and broaden range of problem-solving strategies
* Pose or formulate challenging problems
* Monitor and reflect on their own problem-solving ideas
* Solve problems from a variety of contexts, from daily routines to mathematical situations in stories
Topics (second grade)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Sense of numbers
* Basic counting techniques
* Size of numbers
* Number relationships
* Place value
* Addition and subtraction
* Computational fluency
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Classification, patterns and relations
* Operations with whole numbers
* Use of step-by-step processes
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Explore, investigate and discuss shapes and structures in the classroom
* Become proficient in describing and representing shapes in their environment
* Learn to represent two- and three-dimensional shapes
* Recognize and create shapes that have symmetry
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Attributes of length, volume, weight and time
* How to measure using standard and nonstandard units
* Select appropriate unit and tool for attribute being measured
* Use repetition of a single unit to measure something larger than the unit
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* Pose questions to investigate
* Organize responses
* Create representations of data
* Sort and classify objects according to their attributes
* Organize and display data through graphical displays using counts, tallies, pictures and graphs
* Analyze and describe data
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Develop and broaden range of problem-solving strategies
* Pose or formulate challenging problems
* Monitor and reflect on their own problem-solving ideas
* Solve problems from a variety of contexts, from daily routines to mathematical situations in stories
Topics (third grade)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Place value
* Multiplication and division
* Computational fluency
* Increased understanding of base-ten number system
* Fractions, decimals and percents
* Numbers less than zero
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Identify, build and represent numerical and geometric patterns with tables or symbols
* Make predictions based on relationships between varying quantities
* Use graphs to describe patterns and make predictions
* Explore number properties
* Use invented notation, standard symbols and variables to express a pattern, generalization or situation
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Properties and classification of geometric objects
* Relationships between geometric shapes
* Motion, location and orientation
* Increase capacity to visualize geometric relationships
* Make, test and justify conjectures about geometric relationships
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Use concepts and tools of measurement to collect data, and to describe and quantify the world
* Measure attributes such as area, perimeter and angle
* Increase focus on degree of accuracy and variety of measurement tools
* Begin to develop and use formulas for the measurement of certain attributes
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* See a set of data as a whole, describe its shape and compare data sets
* Describe similarities and differences between data sets
* Formulate conclusions and arguments based on data
* Consider data sets as samples from a larger population
* Use language and symbols to describe simple situations involving probability
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Solve problems that arise in mathematics and other contexts
* Apply and adapt a variety of appropriate strategies to solve problems
* Monitor and reflect on the process of mathematical problem solving
* Develop and carry out plans to solve mathematical problems
Topics (fourth grade)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Place value
* Multiplication and division
* Computational fluency
* Increased understanding of base-ten number system
* Fractions, decimals and percents
* Numbers less than zero
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Identify, build and represent numerical and geometric patterns with tables or symbols
* Make predictions based on relationships between varying quantities
* Use graphs to describe patterns and make predictions
* Explore number properties
* Use invented notation, standard symbols and variables to express a pattern, generalization or situation
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Properties and classification of geometric objects
* Relationships between geometric shapes
* Motion, location and orientation
* Increase capacity to visualize geometric relationships
* Make, test and justify conjectures about geometric relationships
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Use concepts and tools of measurement to collect data, and to describe and quantify the world
* Measure attributes such as area, perimeter and angle
* Increase focus on degree of accuracy and variety of measurement tools
* Begin to develop and use formulas for the measurement of certain attributes
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* See a set of data as a whole, describe its shape and compare data sets
* Describe similarities and differences between data sets
* Formulate conclusions and arguments based on data
* Consider data sets as samples from a larger population
* Use language and symbols to describe simple situations involving probability
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Solve problems that arise in mathematics and other contexts
* Apply and adapt a variety of appropriate strategies to solve problems
* Monitor and reflect on the process of mathematical problem solving
* Develop and carry out plans to solve mathematical problems
Topics (fifth grade)
NUMBERS AND OPERATIONS - Understanding of and proficiency with counting, numbers and arithmetic, as well as an understanding of number systems and their structures
* Place value
* Multiplication and division
* Computational fluency
* Increased understanding of base-ten number system
* Fractions, decimals and percents
* Numbers less than zero
ALGEBRA - Relationships among quantities, including ways of representing mathematical relationships and expression of relationships by using symbolic notation
* Identify, build and represent numerical and geometric patterns with tables or symbols
* Make predictions based on relationships between varying quantities
* Use graphs to describe patterns and make predictions
* Explore number properties
* Use invented notation, standard symbols and variables to express a pattern, generalization or situation
GEOMETRY - Geometric shapes and structures, and how to analyze their characteristics and relationships
* Properties and classification of geometric objects
* Relationships between geometric shapes
* Motion, location and orientation
* Increase capacity to visualize geometric relationships
* Make, test and justify conjectures about geometric relationships
MEASUREMENT - The assignment of a numerical value to an attribute of an object; understanding what a measurable attribute is, becoming familiar with the units and processes used in measuring attributes
* Use concepts and tools of measurement to collect data, and to describe and quantify the world
* Measure attributes such as area, perimeter and angle
* Increase focus on degree of accuracy and variety of measurement tools
* Begin to develop and use formulas for the measurement of certain attributes
DATA ANALYSIS AND PROBABILITY - How to collect, organize and display data in graphs and charts that will be useful in answering questions; methods of analyzing data, and of making inferences and conclusions from data
* See a set of data as a whole, describe its shape and compare data sets
* Describe similarities and differences between data sets
* Formulate conclusions and arguments based on data
* Consider data sets as samples from a larger population
* Use language and symbols to describe simple situations involving probability
PROBLEM SOLVING - Engaging in a task for which the solution method is not known in advance
* Solve problems that arise in mathematics and other contexts
* Apply and adapt a variety of appropriate strategies to solve problems
* Monitor and reflect on the process of mathematical problem solving
* Develop and carry out plans to solve mathematical problems