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).