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Are We Ready to Implement the Common Core
Standards in Mathematics
Katy White based on a presentation by
DR WESLEY BIRD WBIRDSOCKETNET
Criteria for Establishing Common Core Standards
Fewer clearer and higher Aligned with college and work expectations Include rigorous content and application of knowledge through high-order skills Build upon strengths and lessons of current state standards Internationally benchmarked so that all students are prepared to succeed in our global economy and society Based on evidence and research
CCSSO National Governors Conference March 2010
CCS ndash 3rd Determine the perimeter of polygons
Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area measures 8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters (Last part ndashformerly at grade 6) 19
Missouri Content Standards vs CCS Emphasis on Relationships
Missouri ndash 3rd
Determine the perimeter of polygons
Bird Educational Consulting
Current Math Curricula In many districts a fragmented mathematics program has been developed There is more emphasis on learning rules - not on conceptual understanding There is a greater focus on specific test items - not necessarily on good mathematics The curricula is not preparing all students for future employment or the global economy An environment has been created where it is impossible to teach to the depth needed for true understanding
Bird Educational Consulting
What does it take to make a mathematical mind Number sense ndash a sense of numerosity We recognize that collections may contain different number of objects and which may contain the most Numerical ability ndash able to continue number sequences indefinitely and to count large collections Algorithmic ability ndash can follow a specified sequence of steps that leads to a particular goal
The above attributes provide most of the ingredients to do arithmetic The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability
The Math Gene ndash Keith Devlin 26 Bird Educational Consulting
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Criteria for Establishing Common Core Standards
Fewer clearer and higher Aligned with college and work expectations Include rigorous content and application of knowledge through high-order skills Build upon strengths and lessons of current state standards Internationally benchmarked so that all students are prepared to succeed in our global economy and society Based on evidence and research
CCSSO National Governors Conference March 2010
CCS ndash 3rd Determine the perimeter of polygons
Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area measures 8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters (Last part ndashformerly at grade 6) 19
Missouri Content Standards vs CCS Emphasis on Relationships
Missouri ndash 3rd
Determine the perimeter of polygons
Bird Educational Consulting
Current Math Curricula In many districts a fragmented mathematics program has been developed There is more emphasis on learning rules - not on conceptual understanding There is a greater focus on specific test items - not necessarily on good mathematics The curricula is not preparing all students for future employment or the global economy An environment has been created where it is impossible to teach to the depth needed for true understanding
Bird Educational Consulting
What does it take to make a mathematical mind Number sense ndash a sense of numerosity We recognize that collections may contain different number of objects and which may contain the most Numerical ability ndash able to continue number sequences indefinitely and to count large collections Algorithmic ability ndash can follow a specified sequence of steps that leads to a particular goal
The above attributes provide most of the ingredients to do arithmetic The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability
The Math Gene ndash Keith Devlin 26 Bird Educational Consulting
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
CCS ndash 3rd Determine the perimeter of polygons
Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area measures 8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters (Last part ndashformerly at grade 6) 19
Missouri Content Standards vs CCS Emphasis on Relationships
Missouri ndash 3rd
Determine the perimeter of polygons
Bird Educational Consulting
Current Math Curricula In many districts a fragmented mathematics program has been developed There is more emphasis on learning rules - not on conceptual understanding There is a greater focus on specific test items - not necessarily on good mathematics The curricula is not preparing all students for future employment or the global economy An environment has been created where it is impossible to teach to the depth needed for true understanding
Bird Educational Consulting
What does it take to make a mathematical mind Number sense ndash a sense of numerosity We recognize that collections may contain different number of objects and which may contain the most Numerical ability ndash able to continue number sequences indefinitely and to count large collections Algorithmic ability ndash can follow a specified sequence of steps that leads to a particular goal
The above attributes provide most of the ingredients to do arithmetic The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability
The Math Gene ndash Keith Devlin 26 Bird Educational Consulting
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Current Math Curricula In many districts a fragmented mathematics program has been developed There is more emphasis on learning rules - not on conceptual understanding There is a greater focus on specific test items - not necessarily on good mathematics The curricula is not preparing all students for future employment or the global economy An environment has been created where it is impossible to teach to the depth needed for true understanding
Bird Educational Consulting
What does it take to make a mathematical mind Number sense ndash a sense of numerosity We recognize that collections may contain different number of objects and which may contain the most Numerical ability ndash able to continue number sequences indefinitely and to count large collections Algorithmic ability ndash can follow a specified sequence of steps that leads to a particular goal
The above attributes provide most of the ingredients to do arithmetic The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability
The Math Gene ndash Keith Devlin 26 Bird Educational Consulting
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
What does it take to make a mathematical mind Number sense ndash a sense of numerosity We recognize that collections may contain different number of objects and which may contain the most Numerical ability ndash able to continue number sequences indefinitely and to count large collections Algorithmic ability ndash can follow a specified sequence of steps that leads to a particular goal
The above attributes provide most of the ingredients to do arithmetic The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability
The Math Gene ndash Keith Devlin 26 Bird Educational Consulting
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
What does it take to make a mathematical mind The ability to handle abstractions ndash the limitation in coping with abstraction presents the greatest barrier to doing mathematics A sense of cause and effect ndash humans seem to acquire this sense at a very early age Logical reasoning ndash ability to construct and follow a step-by-step logical argument Relational reasoning ndash relationship between (abstract) objects Spatial reasoning ndash ability to reason about space and view problems in a spatial fashion
The Math Gene ndash Keith Devlin
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Domain Overarching ideas that connect topics across the grade levels
Clusters Demonstrate the grade by grade progression of task complexity
Standards Define what a student should be able to know and do at that grade level
Organization of Standards Document Bird Educational Consulting
The K-8 Math Standards are organized by Domain Clusters and Standards
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Operations and Algebraic Thinking (Domain) bull Represent and solve problems involving multiplication and division (Cluster) bull Understand properties of multiplication and the relationship between multiplication and division (Cluster)
bull Multiply and divide within 100 (Cluster)
bull Solve problems involving the four operations and identify and explain patterns in arithmetic (Cluster)
Bird Educational Consulting
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Represent and solve problems involving multiplication and division 1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
Bird Educational Consulting (Standards)
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Eight Standards of Mathematical Practice
1Make sense of problems and persevere in solving them 2Reason abstractly and quantitatively 3Construct viable arguments and critique the reasoning of others 4Model with mathematics 5Use appropriate tools strategically 6Attend to precision 7Look and make use of structure 8Look for and express regularity in repeated reasoning
Common Core Standards ndash State Standards Initiative Bird Educational Consulting
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Standards of Mathematical Content
High SchoolNumber and Quantity Algebra Functions Modeling Geometry Statistics and Probability
Elementary Counting Operations and Algebraic ThinkingNumber and Operations in Base TenMeasurement and DataGeometry Middle School
Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions
Bird Educational Consulting Common Core Standards ndash State Standards Initiative
Dr Wesley Bird wbirdsocketnet 573-864-4880
Dr Wesley Bird wbirdsocketnet 573-864-4880
