School Administrative District #4
Unity of purpose
CORE CURRICULUM: SCOPE AND SEQUENCE
Department: Mathematics
CONTENT STANDARD: NUMBERS AND NUMBER SENSE
Students will understand and demonstrate a sense of what numbers mean and how they are used. Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
CONTENT STANDARD: COMPUTATION
Students will understand and demonstrate computation skills. Computation involves understanding the fundamental operations of and relationships between and among addition, subtraction, multiplication, and division. Proficiency in computational skills requires that students learn to evaluate the reasonableness of an answer and to obtain accuracy in calculations with ever-increasing ease and confidence, with and without technological tools.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
2. 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
Students
will understand and demonstrate measurement skills. Measurement
is valuable as an integrating skill throughout the curriculum and in
everyday life. The use of estimation is vital in determining the reasonableness
of measurement. Measurement attributes (e.g., length, volume, time),
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
2. Use measurement tools and units appropriately and recognize limitations in the precision of the measurement tools
á Protractor
á Compass
á Vernier caliper
á Graphing calculator
CONTENT STANDARD: PATTERNS, RELATIONS, AND FUNCTIONS
Students will understand that mathematics is the science of patterns, relationships, and functions. Relationships are central to mathematical understanding. A study of patterns often reveals regularity, indicating the presence of a mathematical relationship. Studying relationships allows students to make generalizations and predictions about phenomena and occurrences.
Performance Indicators: The learner will·
|
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 30-60-90o
á 45-45-90o
á Other right triangles
4. Identify angles of rotation
á Degree measure
á Radian measure
5. Convert radians to degrees and degrees to radians
CONTENT STANDARD: DISCRETE MATHEMATICS
Students will understand and apply concepts in discrete mathematics. Discrete mathematics studies discrete processes (e.g., all possible bus routes in a school district). This study includes the exploration of diagrams, networks, and flowcharts that students construct to model situations or use for planning, scheduling, and decision making. Three main concerns of discrete mathematics are existence (Is there a solution?), counting (How many solutions are there?), and efficiency (What is the best solution?).
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
2. Given a property of points and lines, determine the truth of that property in graph theory
CONTENT STANDARD: MATHEMATICAL REASONING
Students will understand and apply concepts of mathematical reasoning. Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct and evaluate valid arguments in problem settings and to evaluate the arguments of others.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
2. Follow logical arguments
á Judge the validity of arguments
3. Construct simple valid arguments
4. Construct proofs for mathematical assertions, including indirect proofs and proofs by mathematical induction
CONTENT STANDARD: DATA ANALYSIS AND STATISTICS
Students will understand and apply concepts of data analysis. Individuals are faced with massive quantities of information which must be selected, sorted, and analyzed to reach conclusions. Sound decision making requires the ability to collect data effectively, organize data, discover patterns, summarize trends, make inferences, draw conclusions, and make predictions. The ethical use of statistics is a paramount concern in the Information Age.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
CONTENT STANDARD: PROBABILITY
Students will understand and apply concepts of probability. Probability is the study of uncertainty. Informed consumers of information understand the basic principles of probability. People need to understand the uncertainties and limitations involved when drawing conclusions from data.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
CONTENT STANDARD: ALGEBRA CONCEPTS
Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
CONTENT STANDARD: GEOMETRY
Students will understand and apply concepts from geometry. Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which people live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.
Performance Indicators: The learner will·
|
Grade 10 |
1. Review and extend prior learning
2. Use the appropriate geometric devices to compute
á Perimeter/circumference
á Triangle
á Square
á Rectangle
á Parallelogram
á Rhombus
á Trapezoid
á Miscellaneous n-gons
á Circle
á Area
á Triangle
á Square
á Rectangle
á Parallelogram
á Rhombus
á Trapezoid
á Miscellaneous n-gons
á Circle
á Sectors
á Total surface area
á Prism
á Pyramid
á Cube
á Cylinder
á Sphere
á Cone
á Lateral area
á Prism
á Pyramid
á Cone
á Right circular cylinder
á Volume
á Prism
á Pyramid
á Cube
á Cylinder
á Sphere
á Cone
á Degree measure
á Polygon angles
á Minor arcs
á Major arcs
3. Use theorems about complementary, supplementary, and vertical angles to work with transversals and intersections
4. Investigate triangles by
á Finding angle measure, using
á Angle Sum Theory
á Exterior Angle Corollary
á Identifying and constructing altitudes and medians
á Comparing exterior and remote interior angles
5. Investigate quadrilaterals by
á Understanding the properties of quadrilaterals with respect to
á Sides
á Angles
á Diagonals
á Medians
6. Investigate polygons (excluding triangles and quadrilaterals) by
á Classifying polygons as
á Equilateral
á Equiangular
á Regular
á Concave
á Convex
á Finding the sum of the interior and exterior angles of regular and non-regular polygons
7. Investigate circles by
á Identifying points and lines related to circles
á Chord
á Central angles
á Inscribed angles
á Arc
á Segment
á Secant
á Tangent
á Identifying corresponding parts of congruent circles
á Applying theorems about tangents to circles
á Applying measurement properties of inscribed angles
á Applying measurement properties for angles formed by
á Two secants
á A secant and a tangent
á Two tangents
á Two chords
á A chord and a tangent
á Finding ratios and products of lengths of segments related to circles
á Applying inequality relationships to circles
8. Write and solve proportions to find missing corresponding parts of similar or congruent polygons
9. Investigate coordinate planes by
á Finding the midpoint of a segment
á Identifying parallel and perpendicular lines, using slope
á Using coordinates in space
10. Write conditional statements
á If·then
á If and only if
11. Write inverse and contrapositives
12. Use postulates of equality to draw conclusions about geometric figures
á Addition
á Subtraction
á Multiplication
á Division
á Substitution
13. Use a variety of methods to perform geometric proofs
á Two column
á Paragraph
á Indirect
á Analytical
á Coordinate geometry
14. 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
15. Demonstrate an initial understanding of how to apply matrices to geometric transformations
á Size change
á Scale change
16. Use geometry to solve real-life problems and justify the solutions to those problems
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Developed 07/17/97 Revised 07/08/98 |
curr-math-scope-10.doc |