School Administrative District #4

Unity of purpose

CORE CURRICULUM: SCOPE AND SEQUENCE

Department: Mathematics

CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS

 

Performance Indicators: The learner will·

Kindergarten

1.        Review and extend prior learning

2.        Sort and classify objects according to similar attributes

3.        Recognize and extend a variety of patterns

á         Linear, e.g., ABB using Unifix cubes

á         Spatial, e.g., pattern block designs

Grade 1

1.        Review and extend prior learning

2.        Sort and classify objects according to one or more attributes, including color, size, shape, and thickness

3.        Describe and create a variety of patterns

á         Linear

á         Spatial

Grade 2

1.        Review and extend prior learning

2.        Demonstrate an initial understanding of the relationship between

á         Addition and subtraction

Grade 3

1.        Review and extend prior learning

2.        Recognize, describe, and extend a variety of relationships using variables (e.g., if John earns two cents per day, how many days will it take to earn sixteen cents?)

3.        Recognize and describe the relationship between addition and subtraction

4.        Demonstrate an initial understanding of the relationship between

á         Addition and multiplication

á         Multiplication and division

Grade 4

1.        Review and extend prior learning

2.        Recognize and describe the relationship between

á            Addition and multiplication

á            Multiplication and division

3.        Demonstrate an initial understanding of the relationship between

á         Subtraction and division

4.        Use the patterns of numbers, geometry, and/or graphs to solve a problem

Grade 5

1.        Review and extend prior learning

2.        Analyze relationships to explain how a change in one quantity can result in a change in another

3.        Use patterns and multiple representations to solve problems

4.        Recognize and describe the relationship between

á         Subtraction and division

Grade 6

1.        Review and extend prior learning

2.        Demonstrate an understanding of the interrelationships between and among addition, subtraction, multiplication, and division as operations

3.        Investigate, describe, and extend numerical and geometric patterns (e.g., triangular numbers, perfect squares, patterns formed by powers of 10, and arithmetic sequences)

4.        Create a variety of relationships, using variables and expressions

5.        Demonstrate an initial understanding of functional relationships, including the number of sides of a regular polygon and the sum of the measures of the interior angles

Grade 7

1.        Review and extend prior learning

2.        Demonstrate an initial understanding of how to find solutions for unknown quantities in linear equations and in simple equations and inequalities

3.        Investigate and describe functional relationships, including the number of sides of a regular polygon and the sum of the measures of the interior angles

Grade 8

1.        Review and extend prior learning

2.        Investigate and describe functional relationships, including the number of sides of a regular polygon and the maximum number of possible diagonals, expressing the algebraic concept of the number of diagonals of the n^th-sided polygon

Grade 9

1.        Review and extend prior learning

2.        Create a graph to explain a real-life situation and draw inferences from it

3.        Translate and solve a real-life problem using symbolic language

4.        Apply techniques to fit functions (model) to collected data and make predictions from the function of best fit

á         Median-fit line

5.        Identify and use the different types of functions and their descriptions

á         Constant

á         Linear

á         Quadratic

á         Polynomial

Grade 10

1.        Review and extend prior learning

2.        Find the area of non-right triangles when the height is not given

3.        Solve right triangles

á         30-60-90^o

á         45-45-90^o

á         Other right triangles

4.        Identify angles of rotation

á         Degree measure

á         Radian measure

5.        Convert radians to degrees and degrees to radians

Grade 11

1.      Review and extend prior learning

2.      Understand the language of functions

á         Inverse/one-one

á         Function symbolism

á         Composite

á         Piecewise/multi-description

3.        Manipulate with functions

á         Evaluate

á         Add

á         Subtract

á         Multiply

á         Divide

á         Graph

á         Form reciprocals

á         Find inverse

á         Composition

4.        Find the coordinates of end points of the terminal side of a right triangle

5.        Find formula from graph

6.        Identify and use trigonometric functions and their inverses

á         Sine - cosecant

á         Cosine - secant

á         Tangent - cotangent

7.        Determine the signs of the trigonometric functions in the four quadrants

8.        Use laws of sine and cosine to solve oblique triangles

9.        Identify the functions of negative angles

10.    Explain phenomena using a variety of functions (e.g., linear, quadratic, exponential, trigonometric, etc.)

11.    Identify and use the different types of functions and their descriptions

á         Absolute value

á         Exponential

á         Logarithmic

á         Trigonometric (inverse trigonometric)

á         Greatest/least integer

á         Step

12.    Identify a variety of situations explained by the same type of function

13.    Analyze and interpret graphical representations of functions

14.    Calculate combinations and recognize properties of Pascal's triangle

Grade 12

NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).

1.        Review and extend prior learning

2.        Understand the language of functions

á         Even/odd

3.        Identify and use the different types of functions and their descriptions

á         Rational

á         Hyperbolic

á         Recursively defined

á         Symmetrical

á         Circular

4.        Find the values of functions of angles, using tables and a calculator

á         Positive angles

á         Negative angles

á         Angles greater than 360^o

5.        Develop the concept of trigonometric ratio for very large and very small angles

6.        Solve trigonometric equations, using

á         Factoring

á         Radicals

7.        Find remaining trigonometric functions of an angle when given one function

8.        Compute trigonometric functions by

á         Adding

á         Multiplying

9.        Graph circular functions in degree and radian measure

á         Sinusoides y = sin x, y = cos x

á         Change in amplitude

á         Change in period

á         Change in center line

á         Change in frequency

á         Phase shifts

á         Tangent, cotangent, secant, and cosecant

10.    Prove identities

á         Reciprocal

á         Pythagorean

á         Quotient

á         Double angle

á         Sum/difference

á         Half angles

á         Product identities

á         Tangent identities

11.    Apply circular functions to real-world problems

12.    Apply techniques to fit functions (model) to collected data and make predictions from the function of best fit

á         Log-log or semi-log transformation

á         Equation of the tangent to a curve

13.    Locate zeros of functions

á         Rational zeros

á         Decimal approximations

á         Irrational zeros

14.    Apply functions

á         Find the slope of a function at a particular point

á         Find the maximum/minimum values of a function at a particular point

15.    Evaluate functions, using Euler's notation