School Administrative District #4
Unity of purpose
CORE CURRICULUM:
PRIORITIES FOR IMPLEMENTATION, 1998-99
Department: Mathematics
To implement the newly written curriculum in mathematics will take three to five years. During this time teachers at all grade levels must carefully assess what in-coming students know and can do and plan lessons that move those students as far as possible along the learning continuum. Deciding which performance indicators to emphasize at given levels (K-4, 5-8, 9-12) at various stages of implementation (1998-99, 1999-2000, etc.) requires teachers to establish priorities. Although every student is expected to know and do more than what is indicated below, the following priorities should focus discussion as teachers at all grades and levels meet to plan and review lessons during the 1998-99 academic year. For the complete list of performance indicators for a given grade or level, teachers should consult the scope-and-sequence guide.
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Grades K- 4 |
Performance Indicators: The learner will·
á Read, write, order, and compare numbers through six digits
á Read, write, and use money notation through four digits
á Demonstrate a basic understanding of fractions through tenths
á Use age-appropriate language to communicate mathematical concepts related to numbers and number sense
á Compute whole numbers in all four operations with ever-increasing ease
á Memorize basic facts related to
á Addition up to 9 + 9
á Subtraction up to 18-9
á Multiplication up to 5 x 10
á Use age-appropriate language to communicate mathematical concepts related to computation
CONTENT STANDARD: MEASUREMENT
á Count and exchange equivalent quantities of money
á Tell time to the nearest minute, using an analog and a digital clock
á Name the months and days of the week in sequence and locate any given month and/or day
á Use appropriate tools and units to measure length
á Use age-appropriate language to communicate mathematical concepts related to measurement
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
á Recognize and describe the relationship between
á Addition and subtraction
á Addition and multiplication
á Multiplication and division
á Use patterns to solve problems
á Use age-appropriate language to communicate mathematical concepts related to patterns, relations, and functions
á Use lists, charts, graphs, etc. to solve problems
á Use age-appropriate language to communicate mathematical concepts related to discrete mathematics
CONTENT STANDARD: MATHEMATICAL REASONING
á Distinguish between "important" and "unimportant" mathematical information
á Draw logical conclusions about mathematics by answering questions such as What do you think the answer is? Why do you think that is a good answer? Why isn't that a good answer?
á Use age-appropriate language to communicate mathematical concepts related to mathematical reasoning
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
á Collect, organize, display, and interpret data, using various types of graphs, charts, and tables
á Use age-appropriate language to communicate mathematical concepts related to data analysis and statistics
CONTENT STANDARD: PROBABILITY
á Investigate and describe the concept of probability as chance, and list possible results of a given situation
á Use age-appropriate language to communicate mathematical concepts related to probability
CONTENT STANDARD: ALGEBRA
á Use language and symbols to express numerical relationships
á Recognize and use algebraic properties
á Identity property
á Multiplication
á Division
á Zero property
á Addition
á Subtraction
á Multiplication
á Division
á Commutative property for
á Addition
á Multiplication
á Use age-appropriate language to communicate mathematical concepts related to algebra
á Recognize, describe, and analyze plane and solid geometric figures
á Identify and describe objects in his/her environment that depict geometric figures
á Use age-appropriate language to communicate mathematical concepts related to geometry
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Grades 5-8 |
Performance Indicators: The learner will·
á Read, write, order, and compare numbers through twelve digits and decimals through thousandths
á Use numbers in a variety of equivalent and interchangeable forms
á Integers
á Fractions
á Decimals
á Percents
á Memorize basic facts related to
á Multiplication up to 12 x 12
á Division up to 144 ü 12
á Using correct terminology, compute and model all four operations with integers, fractions, decimals, and percents
CONTENT STANDARD: MEASUREMENT
á Use appropriate tools and units to measure length, weight, area, volume, time, and temperature
á Read and use the scale of a drawing
á Design and construct a model to scale
á Recognize, understand, and use equivalent measures within both U.S. customary units and the metric system
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
á Demonstrate an understanding of the interrelationships between and among addition, subtraction, multiplication, and division as operations
á Use tables, networks, and schedules to solve problems
CONTENT STANDARD: MATHEMATICAL REASONING
á Follow logical arguments
á Use models, known facts, properties, and relationships to explain his/her thinking
á Demonstrate and justify that multiple paths to a conclusion may exist
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
á Collect, organize, display, and interpret data in a variety of graphical forms
á Find the mean, median, mode, and range of a set of data
CONTENT STANDARD: PROBABILITY
á Determine the probability of a given sample event and express that probability as a ratio, decimal, or percent
CONTENT STANDARD: ALGEBRA
á Recognize and use algebraic properties
á Distributive property
á Associative property for
á Addition
á Multiplication
á Multiplicative inverse property
á Inverse property of addition
á Addition property of equality
á Multiplication property of equality
á Create and solve problems using formulas
CONTENT STANDARD: GEOMETRY
á Distinguish between and use appropriate geometric symbols
á Find the perimeter/circumference, area, surface area, and volume of given circles, polygons, and geometric solids
á Identify, classify, describe, and draw various angles, circles, polygons, and geometric solids
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Grades 9-12 |
Performance Indicators: The learner will·
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
á Describe the structure of the real number system and identify its appropriate applications and limitations
á Use numbers in a variety of equivalent and interchangeable forms in problem solving
CONTENT STANDARD: COMPUTATION
á Use a variety of materials, strategies, and symbols to manipulate
á Real numbers
á Use various techniques to approximate solutions to real-life and abstract problems, determine the reasonableness of answers to those problems, and justify the results
CONTENT STANDARD: MEASUREMENT
á Convert from one measurement system to another, using unit multipliers
á Metric to U.S. customary units
á U.S. customary units to metric
á Use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
á Create a graph to explain a real-life situation and draw inferences from it
á Solve right triangles
á 30-60-90o
á 45-45-90o
á Other right triangles
á Manipulate with functions
á Identify and use trigonometric functions and their inverses
á Analyze and interpret graphical representations of functions
CONTENT STANDARD: DISCRETE MATHEMATICS
á Analyze and solve problems
á Follow logical arguments
á Formulate counterexamples
á Derive properties and other mathematical models
á Judge the validity of arguments
á Analyze situations where more than one logical conclusion can be drawn from data presented
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
á Manipulate large, realistic sets of data
CONTENT STANDARD: PROBABILITY
á Distinguish between probability of simple, independent, dependent, inclusive, and mutually exclusive events
á Find the probability of a
á Simple event
á Compound event, using
á A sample space
CONTENT STANDARD: ALGEBRA CONCEPTS
á Distinguish and compute between the various sets of complex numbers
á Real numbers
á Compute with integers, using
á Absolute value
á Exponents
á Solve quadratic equations by
á Factoring
á Using the Quadratic Formula
á Finding the nature of roots using the discriminant
á Graphing (e.g., calculator, computer, graph paper)
á Solve multi-step linear equations
á Solve linear systems of equations and inequalities by
á Graphing
á Substitution
á Solve linear and non-linear systems of equations and inequalities by using
á Multiplication/addition method, i.e., elimination method
á Matrices/determinants
CONTENT STANDARD: GEOMETRY
á Use formulas for perimeter, area, surface area, and volume of many types of figures; and apply the appropriate unit labels (i.e., units, square units, cubic units)
á Understanding the properties of quadrilaterals
á Investigate circles
á Demonstrate the ability to prove
á Triangles similar using
á Angle-angle
á Side-angle-side
á Proportional sides
á Side splitting
á Triangles congruent showing
á Triangles similar
á Angle-side-angle
á Side-side-angle
á Hypotenuse-leg
á A one-to-one correspondence between corresponding sides
á Corresponding parts of congruent triangles congruent
á Arcs congruent
á Chords congruent
á Line segments in proportion
á Line segments in a triangle unequal in length
á Lines parallel
á Lines perpendicular
á Angles complementary
á Angles supplementary
á Angles in a triangle unequal in measure
á Triangles isosceles
á Quadrilateral a parallelogram
á Quadrilateral a rectangle
á Quadrilateral a rhombus
á Quadrilateral a square
á Quadrilateral a kite
á Theorems about angles formed by parallel lines and a transversal
á Corresponding angles congruent
á Alternate interior/exterior angles congruent
á Same side interior supplementary
á Theorem for the sum of angles of a triangle
á Theorem for the sum of sides of a triangle
á Theorems about bisectors, altitudes, and medians of various geometric figures, especially the triangle
á Relationships among arcs, chords, central angles, inscribed angles, and exterior angles
á Inequality Theorem for triangles
á Overlapping triangles
á Intersecting chords, secants, and tangents
á Apply matrices to geometric transformations
á Demonstrate an understanding of how to apply matrices to geometric transformations