ESD MATH CURRICULUMPresentation by the District Math Committee
December 2, 2010
COMMITTEE MEMBERS
Epping Elementary School
Sandy LandisDeanna Mayne
Epping Middle School
Nancy LehouxKara Reynolds
Epping High School
Kerry McDermottJacqui Pender
District Office
Lyn Healy
LAYERS OF CURRICULUM
Each content area will have: a stated philosophy stated goals a diagram outlining the
important concepts in their discipline
a section on metacognition – “As a mathematicitian this is how I think.”
a sequence from PK-12
LAYERS OF CURRICULUM
Each grade level will have:
a chart of key concepts
vocabulary defined“I can” statements so that students know what they should be able to do!
PHILOSOPHY FOR MATHEMATICSDraft
The Epping School District believes that mathematics can and must be learned by all students.
We strive to offer a learning environment that fosters habits of deliberation, orderliness, analytical thinking, logical reasoning, problem-solving, perseverance and an appreciation for the precision of mathematics.
We show students the real life applications of mathematics so that they will graduate with the mathematical knowledge and skills to be college and career ready.
GOALS FOR MATHEMATICS All students will develop
number sense and computational fluency
basic understanding of key concepts in geometry, algebra, probability, and data analysis while appreciating the interrelationships of all areas of mathematics.
strong problem solving and reasoning abilities.
ability to use appropriate technology to solve mathematical problems.
ability to communicate their understanding of mathematics effectively.
ability to apply mathematics to the 21st century interdisciplinary themes.
Mathematical Processes:
Representing and
Communicating Mathematical
Thinking
Problem Solving
Connections outside of
mathematicsReasoning and
ProofModeling
Mathematical Processes:
Representing and
Communicating Mathematical
Thinking
Problem Solving
Connections outside of
mathematicsReasoning and
ProofModeling
Data Analysis,
Probability and Statistics
Data OrganizationData Analysis
Probability
Data Analysis,
Probability and Statistics
Data OrganizationData Analysis
Probability
Geometry and
Measurement
Geometric Figures
ApplicationsRelationships
Measurement and
Application
Geometry and
Measurement
Geometric Figures
ApplicationsRelationships
Measurement and
Application
Number and Quantity
Number SenseComputational
FluencyEstimation
Number and Quantity
Number SenseComputational
FluencyEstimation
Algebra and Functions
PatternsRelationshipsApplications
Algebra and Functions
PatternsRelationshipsApplications
Number and Quantity
Number SenseUnderstand numbers and
various ways of representing them.
Understand relationships among numbers and
number systems
Computational FluencySolve problems using the
relationships among operations and knowledge about the base
ten system
EstimationUse estimation skills to solve
problems and check reasonableness of
solutions
Number and Quantity
Number SenseUnderstand numbers and
various ways of representing them.
Understand relationships among numbers and
number systems
Computational FluencySolve problems using the
relationships among operations and knowledge about the base
ten system
EstimationUse estimation skills to solve
problems and check reasonableness of
solutions
Algebra and Functions
PatternsRecognize, generate and analyze
patterns
RelationshipsExpress relationships verbally,
symbolically, graphically or as a table of values
Analyze change in various contexts
ApplicationsUse algebraic representations to
solve problems, make predictions, draw conclusions, with and without technology
Algebra and Functions
PatternsRecognize, generate and analyze
patterns
RelationshipsExpress relationships verbally,
symbolically, graphically or as a table of values
Analyze change in various contexts
ApplicationsUse algebraic representations to
solve problems, make predictions, draw conclusions, with and without technology
Geometry and MeasurementGeometric Figures
Analyze characteristics and properties of two and three
dimensional shapes
ApplicationsReason and solve problems with
shapes and their attributes
RelationshipsDevelop mathematical
arguments about geometric relationships
Measurement and Application
Understand measurable attributes of objects
Geometry and MeasurementGeometric Figures
Analyze characteristics and properties of two and three
dimensional shapes
ApplicationsReason and solve problems with
shapes and their attributes
RelationshipsDevelop mathematical
arguments about geometric relationships
Measurement and Application
Understand measurable attributes of objects
Data Analysis Probability and
Statistics
Data OrganizationCollect, organize and display
data using appropriate statistical
and graphical methods
Data AnalysisFormulate questions and analyze data sets to form hypotheses and
make predictions
ProbabilityUnderstand and apply basic
concepts of probability Use probability to make
decisions
Data Analysis Probability and
Statistics
Data OrganizationCollect, organize and display
data using appropriate statistical
and graphical methods
Data AnalysisFormulate questions and analyze data sets to form hypotheses and
make predictions
ProbabilityUnderstand and apply basic
concepts of probability Use probability to make
decisions
Mathematical Processes:
Representing and Communicating Mathematical
ThinkingProblem Solving
Connections outside of mathematics
Reasoning and Proof
Modeling/Representing
Mathematical Processes:
Representing and Communicating Mathematical
ThinkingProblem Solving
Connections outside of mathematics
Reasoning and Proof
Modeling/Representing
HOW DO MATHEMATICIANS THINK? PROBLEM SOLVING
What do I see or visualize when I look at this problem?
What information do I have? What information do I need? How do I get that information?
What strategy do I use to solve the problem? What strategies do others use? What strategy would be best?
What do I do when I get stuck? What common mistakes do
people make when working with this type of problem? What is the misunderstanding that causes the mistake?
HOW DO MATHEMATICIANS THINK? CONNECTIONS
Have I seen this before? How does that connection help?
Where do I recognize and apply mathematics in my life?
HOW DO MATHEMATICIANS THINK? REASONING AND PROOF
Does my answer or solution make sense? How do I prove it?
Is there a pattern or rule? What is it? Does it always work?
HOW DO MATHEMATICIANS THINK? REPRESENTATION
How do I best show my thinking?
LEARNER STRATEGIES
Draw a diagram Make a table or t-chart Look for patterns Solve a simple similar problem Write and solve an equation Make connections to prior
knowledge Use literacy skills of determining
importance, questioning, making inferences, making predictions
Conduct experiments Conjecture (generalizing or
educational guessing) and check guesses
Estimate
GRADES K-5 TOPIC SEQUENCE
K 1 2 3 4 5Number – Counting and Cardinality
Number NamesCounting to tell the number of objectsComparing and ordering numbers
Number-Operations and the Problems They Solve
Composing and decomposing numbers; addition and subtraction
Addition and subtractionDescribing situations and solving problems with addition and subtraction
Addition and subtractionDescribing situations and solving problems with addition and subtraction
Multiplication and divisionDescribing situations and solving problems with multiplication and division
Multiplication and divisionProblem solving with the four operations
Number – Base Ten
Two digit numbersComposing and decomposing ten
Numbers up to 100Adding and subtracting in base ten
Numbers up to 1,000Adding and subtracting in base ten
Numbers up to 10,000Adding and subtracting in base tenMultiplying and dividing in base ten
Numbers up to 100,000Multiplying and dividing in base ten
Whole numbers in base tenDecimal conceptsOperations on decimals
Number -- Fractions
Fractions as representations of numbersFractional quantities
Operations on fractionsDecimal concepts
Fraction equivalenceOperations on fractions
Measurement and Data
Direct measurementRepresenting and interpreting data
Length measurementTime measurementRepresenting and interpreting data
Length measurementTime and moneyRepresenting and interpreting data
The number line and units of measurePerimeter and areaRepresenting and interpreting data
The number lines and units of measurePerimeter and areaAngle measurementRepresenting and interpreting data
Units of measureVolumeRepresenting and interpreting data
Geometry Shapes, their attributes, and spatial reasoning
Shapes, their attributes, and spatial reasoning
Shapes, their attributes, and spatial reasoning
Properties of 2-dimensional shapesStructuring rectangular shapes
Lines and anglesLine symmetry
CoordinatesPlane figures
GRADES 6-8 TOPIC SEQUENCE
6 7 8 Ratios and Proportional Relationships
Ratios Unit Rates
Analyzing proportional relationships Percents
The Number System
Operations The system of rational numbers
The system of rational numbers The system of real numbers
The system of real numbers
Expressions and Equations
Expressions Quantitative relationships and the algebraic approach to solving problems
Expressions Quantitative relationships and the algebraic approach to solving problems
Slope of lines in the coordinate plane Linear equations and systems
Functions Function concepts Functional relationships between quantities
Geometry Properties of area, surface area and volume
Congruence and similarity angles
Congruence and similarity The Pythagorean Theorem Plane and solid geometry
Statistics and Probability
Variability and measures of center Summarizing and describing distributions
Situations involving randomness Random sampling to draw inferences about a population Comparative inferences about two populations
Patterns of association in bivariate data
SAMPLE SEQUENCE: NUMBER OPERATIONS
K – composing and decomposing numbers; addition and subtraction
1 – addition and subtraction 2 – addition and subtraction 3 – multiplication and
division 4 – multiplication and
division 5- using operations on
decimals
SAMPLE GRADE LEVEL INFORMATION: GRADE SIX – RATIOS AND PROPORTIONALRELATIONSHIPS Key Concepts:
Ratio Concept Ratio Reasoning
Vocabulary: Ratio Rate Equivalent ratios Tape diagram Double number line diagram Equation Table Coordinate plane Measurement units (e.g. inches,
centimeters)
GRADE SIXRATIOS AND PROPORTIONAL RELATIONSHIPS
I Can…Describe a ratio using ratio
languageDescribe a rate that is
associated with a ratioSolve real-world ratio/rate
math problems that involve:Making tablesPlotting pairs on coordinate planes
Converting between different units
Converting between percent and rate
NEXT STEPS FOR THE COMMITTEE AND FOR OUR TEACHERS
High School Teachers are discussing their options as CCSS provide two different pathways to learning mathematics.
Middle School Teachers are working to develop key concepts, vocabulary and I can statements which lead to unit design.
Teachers in PreK- 2 will be looking at CCSS to plan their trajectories (units).