Chalkboard
Index
 

Mission Statement
Introduction
Credits


© 2006 by EAST LONGMEADOW PUBLIC SCHOOLS and Scantron Corporation.
All Rights Reserved.

Made with Curriculum Designer
Made with
Curriculum Designer by
Scantron Corporation

EAST LONGMEADOW PUBLIC SCHOOLS
2006 - 2007 DISTRICT CURRICULUM GUIDES
Mathematics - SAT/Trigonometry

Geometry

Problem Solving: Transformations
The learner will be able to apply concepts of the different types of transformations in solving problems.
Strand Scope Source
Problem Solving Reinforce Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.82
  
Geometric Concepts: Apply
The learner will be able to apply the concepts of vectors, phase shift, maxima, minima, points of inflection, and/or exact mathematical descriptions of symmetry to find and/or relate objects and their orientation.
Strand Scope Source
Geometric Concepts Master Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.81
  
Angles/Triangles
The learner will be able to calculate the length of the missing side of a given triangle, know both the meaning and relationship between complementary and supplementary angles, and apply the triangle sum property to find the value of the third angle.
Strand Scope Source
Lines/Angles/Polygons Master East Longmeadow Public School
  
Angles: Complementary/Supplementary
The learner will be able to identify, describe, and apply measures of complementary and supplementary angles.
Strand Scope Source
Angles Master East Longmeadow Public School
  
Angles: Parallel/Transversal
The learner will be able to identify angle relationships created by parallel and transversal lines.
Strand Scope Source
Lines/Angles/Polygons Master East Longmeadow Public School
  
Angles: Properties/Apply
The learner will be able to apply properties of angles in solving both mathematical and real-world problems.
Strand Scope Source
Angles Master East Longmeadow Public School
  
Angles: Right/Real-World
The learner will be able to identify right angles within real-world situations.
Strand Scope Source
Angles Master East Longmeadow Public School
  
Angles: Solve Problems
The learner will be able to obtain solutions to problems with complementary, supplementary, and congruent angles, including vertical angles, angles formed when parallel lines are cut by a transversal, and angles in polygons.
Strand Scope Source
Angles Master East Longmeadow Public School
  
Circle Parts: Apply
The learner will be able to apply the properties of circle parts in real-world situations.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle Parts: Arc/Area
The learner will be able to compute area of sectors of a circle.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle Parts: Pi
The learner will be able to understand the relationship which pi represents.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Arc/Chord/Angle
The learner will be able to apply knowledge of chords, vertical angles, arcs, and circle relationships to determine an unknown angle between intersecting chords.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Diameter/Circumference Problems
The learner will be able to solve a problem in the context of a real world scenario with diameter and circumference.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Real-World Problems
The learner will be able to solve real-world problems applying geometric properties of circles.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Relating Diameter/Circumference
The learner will be able to determine how diameter and circumference are related.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Relationships
The learner will be able to analyze how concentric, congruent, and similar circles are related.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circle: Relationships
The learner will be able to determine the relationships among the radius, diameter, chord, center, and circumference.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circles: Apply Concepts
The learner will be able to apply the various measurements associated with circles (pi, area, circumference, diameter, and radius) within practical contexts.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Circles: Sphere/Problem Solving
The learner will be able to apply spheres to obtain solutions to problems associated with the definition of a sphere and sets of points related to the sphere.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Congruence/Similarity: Apply
The learner will be able to apply the concepts and properties of congruence and similarity.
Strand Scope Source
Congruence/Similarity/Symmetry Master East Longmeadow Public School
  
Diagonals: Polygon/Draw
The learner will be able to draw diagonals of polygons.
Strand Scope Source
Diagonals Master East Longmeadow Public School
  
Diagonals: Rectangle/Story Problem
The learner will be able to determine the length of the diagonals of a rectangle within the context of a real world problem.
Strand Scope Source
Diagonals Master East Longmeadow Public School
  
Figures: Problem Solving/3-D Diagram
The learner will be able to construct a diagram to aid in the solution of a problem involving three-dimensional space.
Strand Scope Source
Three-Dimensional Solids Master East Longmeadow Public School
  
Geometric Concepts: Problem Solving
The learner will be able to solve problems with relationships between geometric concepts and real-world situations.
Strand Scope Source
Geometric Concepts Master East Longmeadow Public School
  
Geometric Probability: Solving
The learner will be able to solve problems involving geometric probability by using areas.
Strand Scope Source
Problem Solving Master East Longmeadow Public School
  
Inductive/Deductive: Conclusions
The learner will be able to form inductive and deductive conclusions within mathematical contexts.
Strand Scope Source
Reasoning Master East Longmeadow Public School
  
Line Segment: Midpoint
The learner will be able to determine the midpoint of a line segment.
Strand Scope Source
Lines Master East Longmeadow Public School
  
Logic: Converse/Inverse/Contrapositive
The learner will be able to identify the truth of an implication, its converse, inverse, and contrapositive.
Strand Scope Source
Logic Master East Longmeadow Public School
  
Logic: Problem Solving
The learner will be able to solve basic logic problems.
Strand Scope Source
Logic Master East Longmeadow Public School
  
Polygons: Problem Solving
The learner will be able to apply the properties, definitions, and/or theorems of polygons to obtain solutions to problems related to the interior and exterior angles of convex polygons.
Strand Scope Source
Polygons Master East Longmeadow Public School
  
Properties: Right Triangles
The learner will be able to use the properties of right triangles to obtain problem solutions using relationships in special right triangles.
Strand Scope Source
Properties of Figures Master East Longmeadow Public School
  
Pythagorean Theorem
The learner will be able to use the Pythagorean Theorem to determine an unknown side length of a right triangle.
Strand Scope Source
Pythagorean Theorem Master East Longmeadow Public School
  
Pythagorean Theorem: Analyze
The learner will be able to identify situations requiring the Pythagorean theorem, and analyze how and why the theorem is used.
Strand Scope Source
Pythagorean Theorem Master East Longmeadow Public School
  
Pythagorean Theorem: Apply
The learner will be able to apply the Pythagorean Theorem.
Strand Scope Source
Pythagorean Theorem Master East Longmeadow Public School
  
Pythagorean Theorem: Triples
The learner will be able to identify Pythagorean triples, such as 3-4-5 and 5-12-13, in right triangles.
Strand Scope Source
Pythagorean Theorem Master East Longmeadow Public School
  
Quadrilaterals: Angle Sum
The learner will be able to understand that the sum of the angles of any quadrilateral equals 360 degrees.
Strand Scope Source
Quadrilaterals Master East Longmeadow Public School
  
Solids: Problem Solving
The learner will be able to solve geometric problems by analyzing three-dimensional solids.
Strand Scope Source
Three-Dimensional Solids Master East Longmeadow Public School
  
Triangles: 30-60-90 Right/Identify
The learner will be able to identify the lengths of the missing sides of a 30-60-90 degree right triangle given the length of one side.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: 45-45-90 Right/Identify
The learner will be able to identify the lengths of the missing sides of a 45-45-90 degree right triangle given the length of one side.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Angle Sum
The learner will be able to understand that the sum of the angles of any triangle equals 180 degrees.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Isosceles/Apply
The learner will be able to apply knowledge of isosceles triangles and the triangle sum theorem in solving for an unknown angle measure.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Isosceles/Sum Theorem
The learner will be able to apply knowledge of isosceles triangles and the triangle sum theorem to solve for the measure of a base angle in an isosceles triangle when the other base angle and the third angle are given in binomial equations of the first degree.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Longest Side
The learner will be able to identify the longest side of a triangle.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Problem Solving
The learner will be able to apply triangle concepts in solving real-world problems .
Strand Scope Source
Triangles Master East Longmeadow Public School
  
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Number Theory

Math Structures: Math Systems
The learner will be able to show that apparently unlike mathematical systems can be similar or identical.
Strand Scope Source
Math Structures Master Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.49
  
Divisibility
The learner will be able to determine which number is evenly divisible by a given number.
Strand Scope Source
Divisibility Master East Longmeadow Public School
  
Ratio/Proportion: Apply
The learner will be able to apply ratio and proportion to everyday scenarios.
Strand Scope Source
Ratio/Proportion Master East Longmeadow Public School
  
Ratio/Proportion: Problem Solving
The learner will be able to obtain problem solutions through the use of ratios and/or proportions.
Strand Scope Source
Ratio/Proportion Master East Longmeadow Public School
  
Ratios/Percents/Decimals/Fractions
The learner will be able to write comparisons as ratios, percents, decimals, and fractions.
Strand Scope Source
Ratio/Proportion Master East Longmeadow Public School
  
Square Roots: Perfect Square/Applying
The learner will be able to identify the square root of numbers which are perfect squares when given in the context of a real-world scenario.
Strand Scope Source
Roots/Radicals Master East Longmeadow Public School
  
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Probability/Statistics

Statistical Experiments
The learner will be able to study a problem, establish the information needed to solve the problem, devise an experiment, carry it out, collect the data, draw conclusions based on the data, and communicate the results to others.
Strand Scope Source
Statistics Reinforce Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.96
  
Predictions: Curve Fitting
The learner will be able to make predictions from data using curve fitting.
Strand Scope Source
Predictions Introduce Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.96
  
Venn Diagrams: Apply
The learner will be able to apply Venn diagrams that use two or three overlapping categories to obtain solutions to logic problems.
Strand Scope Source
Venn Diagram Master East Longmeadow Public School
  
Average
The learner will be able to understand the effect of additional data on the average.
Strand Scope Source
Average/Median/Mode/Range Master East Longmeadow Public School
  
Average: Weighted Average
The learner will be able to solve problems that involve the calculation of a weighted average.
Strand Scope Source
Average/Median/Mode/Range Master East Longmeadow Public School
  
Chance: Apply
The learner will be able to apply concepts of chance.
Strand Scope Source
Chance Master East Longmeadow Public School
  
Combinations/Permutations: Illustrate
The learner will be able to illustrate all permutations and combinations four items or less.
Strand Scope Source
Combinations Master East Longmeadow Public School
  
Complementary Events: Probability
The learner will be able to calculate the probability of complementary events.
Strand Scope Source
Independent/Dependent/Mutually Exclusive Master East Longmeadow Public School
  
Counting Methods: Apply
The learner will be able to apply counting methods.
Strand Scope Source
Counting Methods Master East Longmeadow Public School
  
Counting Methods: Problem Solving
The learner will be able to solve real-world problems by applying counting methods.
Strand Scope Source
Counting Methods Master East Longmeadow Public School
  
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Trigonometry

Triangles: Problem Solving
The learner will be able to solve real-world triangle problems using trigonometric concepts.
Strand Scope Source
Triangles Reinforce Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.67
  
Periodic Phenomena: Sine/Cosine
The learner will be able to investigate real-world phenomena which is periodic using the sine and cosine functions.
Strand Scope Source
Periodic Phenomena Master Massachusetts Curriculum Frameworks, January 1996, Grade 12, p.67
  
Angle Measure: Converting
The learner will be able to convert between angle and radian measure.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Angle Measure: Degree/Radian
The learner will be able to interchangeably use degrees and radians to illustrate angle measure and describe the advantages and/or disadvantages of their choice.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Angle Measure: Degree/Radian
The learner will be able to comprehend the relationship between measure in radians and degrees.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Angle Measure: Relating Degree/Radian
The learner will be able to determine the relationship between measure in radians and degrees.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Angle Measures: Relating Degree/Radian
The learner will be able to evaluate how degrees and radians are related.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Angles: Degrees/Equations
The learner will be able to solve an equation involving determining trigonometric values by substituting degree measures.
Strand Scope Source
Radians/Angles Master East Longmeadow Public School
  
Circle: Unit/Sine/Cosine
The learner will be able to comprehend the idea of sine and cosine being defined as the x and y coordinates of points on the unit circle.
Strand Scope Source
Circles Master East Longmeadow Public School
  
Connecting: Across Forms
The learner will be able to solve a given problem for the appropriate trigonometric ratios, radian measures, and angle measures.
Strand Scope Source
Connecting Master East Longmeadow Public School
  
Connecting: Graphing/Trig. Functions
The learner will be able to use basic methods of graphic representation on trigonometric functions.
Strand Scope Source
Connecting Master East Longmeadow Public School
  
Polar Coordinates: Define
The learner will be able to give a definition of polar coordinates.
Strand Scope Source
Polar Forms/Equations/Graphs Master East Longmeadow Public School
  
Polar Coordinates: Graph
The learner will be able to graph different points in the polar coordinate system.
Strand Scope Source
Polar Forms/Equations/Graphs Master East Longmeadow Public School
  
Polar Equations: Graph
The learner will be able to represent polar equations in graphical form.
Strand Scope Source
Polar Forms/Equations/Graphs Master East Longmeadow Public School
  
Triangle: Area/Trigonometric Properties
The learner will be able to solve for the area of a triangle using trigonometric properties.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Apply Trigonometry
The learner will be able to apply trigonometry in finding the unknown sides and/or angles of right triangles.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Develop Trigonometry Relation
The learner will be able to use a right triangle to develop the following trigonometric relationships: sine, cosine, and tangent.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Oblique/Problem Solving
The learner will be able to solve real-world oblique triangle problems using trigonometric concepts.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Pythagorean Triples
The learner will be able to use the relationships between Pythagorean triples to calculate the sine, cosine, and tangent values of angles.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Right/Problem Solving
The learner will be able to solve real-world right triangle problems using trigonometric concepts.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Solving General
The learner will be able to use trigonometric ratios to solve general triangles.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Solving Oblique
The learner will be able to use trigonometric ratios to solve oblique triangles.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Solving Right
The learner will be able to use trigonometric ratios to solve right triangles.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Solving Right
The learner will be able to solve right triangles.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Solving Right
The learner will be able to find the measure of each unknown side (to the nearest tenth or hundredth) or angle (to the nearest degree), solve real-world trigonometry problems, and include the angle of depression or elevation in calculations.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: SSA Case
The learner will be able to discern whether 0,1, or 2 triangles exist, and what they are in an SSA (side, side, angle) case.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Triangles: Trigonometric Ratios/30-60-90
The learner will be able to apply an understanding of the 30-60-90 Triangle Theorem to calculate the values of sine, cosine, and tangent of 30 and 60 degree angles.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Trigonometric Ratios/45-45-90
The learner will be able to apply an understanding of the 45-45-90 Triangle Theorem to calculate the values of sine, cosine, and tangent of a 45 degree angle.
Strand Scope Source
Right Triangles Master East Longmeadow Public School
  
Triangles: Trigonometric Relationships
The learner will be able to apply trigonometric relationships in order to solve problems.
Strand Scope Source
Triangles Master East Longmeadow Public School
  
Trig Concepts: Law of Sines and Cosines
The learner will be able to apply the Law of Sines and the Law of Cosines to solve oblique triangles.
Strand Scope Source
Trigonometric Concepts Master East Longmeadow Public School
  
Trig. Equations: Amplitude
The learner will be able to identify the amplitude of a given trigonometric equation.
Strand Scope Source
Trigonometric Equations Master East Longmeadow Public School
  
Trig. Equations: Period
The learner will be able to identify the period of the graph of a given trigonometric equation.
Strand Scope Source
Trigonometric Equations Master East Longmeadow Public School
  
Trig. Equations: Solutions
The learner will be able to determine possible solutions for trigonometric equations.
Strand Scope Source
Trigonometric Equations Master East Longmeadow Public School
  
Trig. Identities
The learner will be able to identify and use the trigonometric identities.
Strand Scope Source
Trigonometric Identities Master East Longmeadow Public School
  
Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Law of Sines/Derive
The learner will be able to develop the Law of Sines by working with triangles, their angles, and their side lengths.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Negative Angle
The learner will be able to find the trigonometric value of a negative angle measure.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Positive/Negative
The learner will be able to use given knowledge of trigonometric values to determine in what quadrant an unknown angle lies.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Problem Solving
The learner will be able to use the trigonometric ratios of angle measure to solve problems.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Quadrants
The learner will be able to list the signs of each of the trigonometric equations in all four quadrants.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Quadrantal Angles
The learner will be able to determine the values of the trigonometric ratios of the quadrantal angles (0, 90, 180, etc.).
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Sine/Cosine/Tangent
The learner will be able to determine the numerical values for the sine, cosine, and/or tangent of a given angle within a right triangle from an illustration where the side lengths are given.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Sine/Cosine/Tangent
The learner will be able to find the sine, cosine, and tangent given angle degrees.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Standard Position
The learner will be able to determine the trigonometric ratios of an angle in standard position.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Trigonometric Tables
The learner will be able to find either the sine, cosine, or tangent of right triangles by utilizing a table of trigonometric ratios.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trig. Ratios: Understand
The learner will be able to understand basic trigonometric ratios.
Strand Scope Source
Trigonometric Ratios Master East Longmeadow Public School
  
Trigonometric Identities: Knowledge
The learner will be able to know the following trig identity: cosine squared + sine squared = 1.
Strand Scope Source
Trigonometric Identities Master East Longmeadow Public School
  
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Algebraic Concepts

Algebraic Concepts: Problem Solving
The learner will be able to use algebraic methods to solve real-world problems.
Strand Scope Source
Algebraic Concepts Master East Longmeadow Public School
  
Algebraic Concepts: Slope
The learner will be able to find and/or calculate slopes.
Strand Scope Source
Algebraic Concepts Master East Longmeadow Public School
  
Algebraic Expressions: Factor
The learner will be able to determine the factors of algebraic expressions.
Strand Scope Source
Expressions Master East Longmeadow Public School