mathematics scope & sequence for the common core state standards
TRANSCRIPT
MathematicsScope & Sequence
for the Common Core State Standards
Presented By: Dorea Hardy, Shani Moore, & Torrey Williams
Handouts
ObjectivesTo define curriculum
To discuss the historical perspective on mathematics curriculum
To understand the implementation of scope and sequence in K-12 mathematics curriculum.
To understand how to read grade level standards
What is Curriculum?
“Field of Utter Confusion” (Oliva, 2000, p. 3)
Various interpretations
“A unit, a course, a sequence of courses, the school's entire program of studies…”(Oliva, 2000, p. 8)
HistoryA decade’s worth of research
International Competition
Country Wide Improvement
(Georgia Department of Education, 2013)
What is…Scope in education?
The extent of a curriculum (aim & purpose)A K-12 scope = curriculum mastery Horizontal Axis (y)
Sequence in education?Arranged organized elements or centersRecurrence, Repetition and DepthVertical Axis (x)
Types of Sequences
Psychological ApproachesFamiliar-to-Unfamiliar SequenceConcrete-Pictorial-Abstract Sequence
(Sowell, 2004, pp. 53-54)
Logical ApproachPart-to-Whole SequenceWhole-to-Part Sequence
Scope & Sequence
Questions to askWhat have the students learned prior to the current grade level? What skills have already been mastered?
What new skills and knowledge should students be mastering in this scope and sequence?
How long should this scope & sequence last, and how will it be broken down and fit in over the year?
Which of the Common Core Standards should be the focus of mastery for the students during this time?
Sequencing Chart using
Mathematics StandardsGrade
LevelStrand: Operations and Algebraic Thinking
Kindergarten • Understand addition as putting together and adding to, & understand subtraction as taking apart & taking from.
First Grade • Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.• Work with addition and subtraction equations.
Second Grade
• Represent and solve problems involving addition and subtraction.
• Add and subtract within 20.• Work with equal groups of objects to gain
foundations for multiplication.
Sequencing Options for
Mathematics StandardsFlowchart for Students Entering Ninth Grade in School
Year 2012-2013Grad
eOption 1 Option 2 Option 3 Option 4 Option 5
Advanced Accelerated
Accelerated
6 Grade 6 GPS
Grade 6 GPS Grade 6 Advanced
GPS Grade 6-8Advanced
GPS
Grade 6-8Advanced
GPS7 Grade 7 GPS
Grade 7 GPS Grade 7 Advanced
GPS
82011-2012
Grade 8 GPS
Grade 8 GPS Grade 8 Advanced
GPS
GPS Mathematics I
orGPS Algebra
Accelerated GPS
Mathematics I or Accelerated
GPS Algebra/Geome
try
92012-2013
CCGPS Coordin
ate Algebra
Accelerated CCGPS
Coordinate Algebra/Anal
ytic Geometry A
Accelerated CCGPS
Coordinate Algebra/Ana
lytic Geometry A
GPS Mathemati
cs II orGPS
Geometry
Accelerated GPS
Mathematics II or Accelerated
GPS Geometry/Advanced Algebra
StandardsFewer versus Focused
StandardsFewer versus FocusedDesign towards:
Key ideasOrganizing principles
StandardsFewer versus FocusedDesign towards:
Key ideasOrganizing principles
Sequence must respect the students
Understanding Mathematics
Ability to justify / Explaining the “rules”
Understanding &Procedural Skills
Standards are not…
Intervention Methods
Materials
Complete Support
Standards allow for…
Widest range of studentsAppropriate accommodations
Clear Signposts
How to read theGrade Level Standards
Term: Standards
Define what students should understand and
be able to do.
(Georgia Department of Education, 2013, p. 5)
Term: ClustersGroups of related standards.
Note that standards from different clusters may sometimes
be closely related, because mathematics is a connected
subject.
(Georgia Department of Education, 2013, p. 5)
Term: DomainsLarger groups of
related standards.
Standards from different domains may sometimes
be closely related. (Georgia Department of Education, 2013, p. 5)
Example
(Georgia Department of Education, 2013, p. 5)
The End Questions?
Comments?
ReferencesGeorgia Department of Education. (2013) Common core state
standards for mathematics. Online. Available: https://eboard.eboardsolutions.com/meetings/TempFolder/Meetings/Common%20Core%20State%20Standards%20for%20Math_245076rodujz55jwtn4ujqra3cnnml.pdf
Georgia Department of Education. (2011) Mathematics Course Sequence Information for Students Entering Ninth Grade in 2012-2013. Online. Available: http://www.doe.k12.ga.us/Curriculum-Instruction-and-Assessment/Curriculum-and-Instruction/Documents/Mathematics/7.11.122012-2013MathematicsGraduationRequirementGuidance.pdf.
ReferencesOliva, P. (2000). Developing the curriculum.
Boston: Allyn & Bacon.
Sowell, E. (2004). Curriculum: An integrative introduction. New Jersey: Prentice Hall.
AppendixGrade Level
Strand: Operations and Algebraic Thinking
Kindergarten • Understand addition as putting together and adding to, & understand subtraction as taking apart & taking from.
First Grade • Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.• Work with addition and subtraction equations.
Second Grade
• Represent and solve problems involving addition and subtraction.
• Add and subtract within 20.• Work with equal groups of objects to gain
foundations for multiplication.
AppendixGrade Level
Strand: Operations and Algebraic Thinking
Third Grade • Represent and solve problems involving multiplication and division.
• Understand properties of multiplication and the relationship between multiplication and division.
• Multiply and divide within 100.• Solve problems involving the four operations,
and identify and explain patterns in arithmetic. Fourth Grade • Use the four operations with whole numbers to
solve problems.• Gain familiarity with factors and multiples.• Generate and analyze patterns.
Fifth Grade • Write and interpret numerical expressions.• Analyze patterns and relationships.
AppendixGrade Level
Strand: Operations and Algebraic Thinking
Sixth Grade • Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities.
• Represent and analyze quantitative relationships between dependent and independent variables.
Seventh Grade
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Eighth Grade • Work with radicals and integer exponents.• Understand the connections between
proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
AppendixGrade Level
Strand: Operations and Algebraic Thinking
High School – Number and Quantity
The Complex Number System• Perform arithmetic operations with complex
numbers• Represent complex numbers and their
operations on the complex plane• Use complex numbers in polynomial identities
equations Algebra Reasoning with Equations and Inequalities
• Understand solving equations as a process of reasoning and explain the reasoning
• Solve equations and inequalities in one variable
• Solve systems of equations• Represent & solve equations & inequalities
graphically
AppendixGrade Level
Strand: Operations and Algebraic Thinking
Functions Interpreting Functions• Understand the concept of a function and use
function notation• Interpret functions that arise in applications in
terms of the context• Analyze functions using different
representations Geometry Expressing Geometric Properties with
Equations• Translate between the geometric description
and the equation for a conic section• Use coordinates to prove simple geometric
theorems algebraically Statistics and Probability
Using Probability to Make Decisions• Calculate expected values / use them to solve
problems• Use probability to evaluate outcomes of
decisions
AppendixGrade Level
Strand: Operations and Algebraic Thinking
Modeling Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.