Transcript ESD Math Curriculum

ESD MATH
CURRICULUM
Presentation by the District Math
Committee
December 2, 2010
COMMITTEE MEMBERS

Epping Elementary School
 Sandy
Landis
 Deanna Mayne

Epping Middle School
 Nancy
Lehoux
 Kara Reynolds

Epping High School
 Kerry
McDermott
 Jacqui 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
MATHEMATICS
Draft
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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
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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.
Algebra and
Functions
Number and
Quantity
Patterns
Relationships
Applications
Number Sense
Computational
Fluency
Estimation
Mathematical
Processes:
Representing and
Communicating
Mathematical
Thinking
Data Analysis,
Probability and
Statistics
Data Organization
Data Analysis
Probability
Problem Solving
Connections outside
of mathematics
Reasoning and
Proof
Modeling
Geometry and
Measurement
Geometric Figures
Applications
Relationships
Measurement
and
Application
Number and Quantity
Number Sense
Understand numbers and various ways
of representing them. Understand
relationships among numbers and
number systems
Computational Fluency
Solve problems using the relationships
among operations and knowledge about
the base ten system
Estimation
Use estimation skills to solve problems and
check reasonableness of solutions
Algebra and Functions
Patterns
Recognize, generate and analyze patterns
Relationships
Express relationships verbally, symbolically,
graphically or as a table of values
Analyze change in various contexts
Applications
Use algebraic representations to solve
problems, make predictions, draw
conclusions, with and without technology
Geometry and
Measurement
Geometric Figures
Analyze characteristics and properties of
two and three dimensional shapes
Applications
Reason and solve problems with shapes
and their attributes
Relationships
Develop mathematical arguments about
geometric relationships
Measurement and Application
Understand measurable attributes of
objects
Data Analysis
Probability and Statistics
Data Organization
Collect, organize and display data
using appropriate statistical
and graphical methods
Data Analysis
Formulate questions and analyze data sets
to form hypotheses and make predictions
Probability
Understand and apply basic
concepts of probability
Use probability to make decisions
Mathematical Processes:
Representing and
Communicating
Mathematical Thinking
Problem 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
Composing and
decomposing
numbers;
addition and
subtraction
Addition and
subtraction
Describing
situations and
solving
problems with
addition and
subtraction
Addition and
subtraction
Describing
situations and
solving
problems with
addition and
subtraction
Multiplication
and division
Describing
situations and
solving
problems with
multiplication
and division
Multiplication
and division
Problem solving
with the four
operations
Two digit
numbers
Composing and
decomposing
ten
Numbers up
to 100
Adding and
subtracting in
base ten
Numbers up
to 1,000
Adding and
subtracting in
base ten
Numbers up to
10,000
Adding and
subtracting in
base ten
Multiplying and
dividing in base
ten
Numbers up to
100,000
Multiplying and
dividing in base
ten
Whole
numbers in
base ten
Decimal
concepts
Operations on
decimals
Fractions as
representations
of numbers
Fractional
quantities
Operations on
fractions
Decimal
concepts
Fraction
equivalence
Operations on
fractions
Number –
Counting and
Cardinality
Number Names
Counting to tell
the number of
objects
Comparing and
ordering
numbers
NumberOperations and
the Problems
They Solve
Number – Base
Ten
Number -Fractions
3
4
5
Measurement
and Data
Direct
measurement
Representing
and interpreting
data
Length
measurement
Time
measurement
Representing
and
interpreting
data
Length
measurement
Time and
money
Representing
and
interpreting
data
The number line
and units of
measure
Perimeter and
area
Representing
and interpreting
data
The number
lines and units
of measure
Perimeter and
area
Angle
measurement
Representing
and
interpreting
data
Units of
measure
Volume
Representing
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
shapes
Structuring
rectangular
shapes
Lines and
angles
Line symmetry
Coordinates
Plane figures
GRADES 6-8 TOPIC SEQUENCE
6
7
Ratios and
Proportional
Relationships
The Number System
Ratios
Unit Rates
Analyzing proportional
relationships
Percents
Operations
The system of rational
numbers
Expressions and
Equations
Expressions
Quantitative relationships
and the algebraic
approach to solving
problems
The system of rational
numbers
The system of real
numbers
Expressions
Quantitative relationships
and the algebraic
approach to solving
problems
8
The system of real
numbers
Slope of lines in the
coordinate plane
Linear equations and
systems
Function concepts
Functional relationships
between quantities
Functions
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 PROPORTIONAL
RELATIONSHIPS
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Key Concepts:
Ratio Concept
 Ratio Reasoning
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Vocabulary:
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Ratio
Rate
Equivalent ratios
Tape diagram
Double number line diagram
Equation
Table
Coordinate plane
Measurement units (e.g. inches, centimeters)
GRADE SIX
RATIOS AND PROPORTIONAL
RELATIONSHIPS

I Can…
 Describe a ratio using ratio
language
 Describe a rate that is associated
with a ratio
 Solve real-world ratio/rate math
problems that involve:
 Making tables
 Plotting pairs on coordinate
planes
 Converting between different
units
 Converting between percent
and rate
NEXT STEPS FOR THE
COMMITTEE AND FOR OUR
TEACHERS
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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).