School Administrative District #4

Unity of purpose

CORE CURRICULUM: SCOPE AND SEQUENCE

Department: Mathematics

CONTENT STANDARD: GEOMETRY

 

Performance Indicators: The learner will·

Kindergarten

1.        Review and extend prior learning

2.        Identify and describe representations of plane geometric figures (e.g., circle, triangle, square, rectangle)

3.        Compare the size and shape of plane geometric figures

4.        Use positional words to describe the proximity of objects in space (e.g., near, far, up, down, beside)

Grade 1

1.        Review and extend prior learning

2.        Identify, describe, and draw representations of plane geometric shapes according to the number of sides, corners, and square corners

3.        Identify and describe objects in his/her environment that depict geometric figures

Grade 2

1.        Review and extend prior learning

2.        Identify representations of three-dimensional geometric shapes (e.g., sphere, cylinder, cone, pyramid, cube, rectangular prism), when presented a model

3.        Identify and create figures, symmetric along a line, using manipulatives

4.        Compare and contrast plane and solid geometric shapes

á         Circle/sphere

á         Square/cube

á         Triangle/pyramid

á         Rectangle/rectangular prism

5.        Demonstrate an initial understanding of

á         Perimeter

á         Area

á         Volume

Grade 3

1.        Review and extend prior learning

2.        Analyze plane geometric figures and identify relevant properties, including the number of angles, square angles, and segments

3.        Given appropriate drawings or models, identify and describe congruent, symmetrical, and similar two-dimensional figures, using tracing procedures

Grade 4

1.        Review and extend prior learning

2.        Analyze solid geometric figures and identify relevant properties, including the number of faces, vertices, and edges

3.        Distinguish between and use the appropriate symbols for

á         Points

á         Segments

á         Rays

á         Lines

á         Parallel lines

á         Perpendicular lines

á         Angles

á         Right

4.        Investigate and describe the relationship between and among points, lines, line segments, and rays

5.        Identify and draw representations of

á         Points

á         Lines

á         Line segments

á         Rays

á         Angles

6.        Use transformations such as slides, flips, and rotations

7.        Use the properties of shapes and figures to describe the physical world

8.        Find the perimeter of polygons, given the lengths of sides

á         Triangles

á         Squares

á         Rectangles

Grade 5

1.      Review and extend prior learning

2.      Identify lines which illustrate intersection, parallelism, and perpendicularity

3.      Distinguish between and use the appropriate symbols for

á         Angles

á         Acute

á         Obtuse

á         Straight

á         Planes

á         Second dimension

á         Third dimension

4.        Identify and classify angles as

á         Acute

á         Right

á         Obtuse

á         Straight

5.        Measure and draw right, acute, obtuse, and straight angles and triangles, using appropriate tools

6.        Construct the perpendicular bisector of a line segment and an angle bisector, using a compass and straightedge

7.        Demonstrate an initial understanding of how to determine congruence or noncongruence of segments, angles, and polygons by direct comparison, given their attributes

8.        Find the area of polygons, given the lengths of sides

á         Triangles

á         Squares

á         Rectangles

9.        Find the diameter, radius, and circumference of a circle, given a center point

10.    Differentiate between area and perimeter and know when to apply the concepts of perimeter and area to given situations

11.    Investigate and predict the results of combining, dividing, and changing two-dimensional shapes

12.    Investigate triangles by

á         Identifying corresponding parts of congruent triangles

13.    Investigate quadrilaterals by

á         Identifying corresponding parts of congruent quadrilaterals

Grade 6

1.        Review and extend prior learning

2.        Identify and classify angles as

á         Complementary

á         Supplementary

3.        Identify, classify, describe, and draw polygons (e.g., pentagon, hexagon, heptagon, octagon, nonagon, and decagon - two dimensional shapes)

4.        Determine congruence or noncongruence of segments, angles, and polygons by direct comparison, given their attributes

5.        Sketch, construct models, and classify rectangular prisms, cones, cylinders, and pyramids

6.        Investigate circles by

á         Identifying points and lines related to circles

á         Center point

á         Radius

á         Diameter

7.        Find the area of a circle, given the diameter or the radius

8.        Investigate, create, and solve problems requiring him/her to find

á         Perimeter/circumference

á         Area

9.        Investigate triangles by

á         Classifying triangles according to their angle measure

á         Acute

á         Right

á         Obtuse

á         Isosceles

á         Equilateral

á         Scalene

10.    Verify the Pythagorean Theorem by measuring and then applying the Pythagorean Theorem to find the missing length of a side of a right triangle when the lengths of the other two sides are given

Grade 7

1.        Review and extend prior learning

2.        Identify and classify angles as

á         Adjacent

á         Vertical

3.        Use inductive and deductive reasoning to compare and contrast quadrilaterals (e.g., parallelogram, rectangle, square, rhombus, trapezoid)

4.        Determine if geometric figures (triangles and quadrilaterals) are similar and write proportions to express the relationships between corresponding parts of similar figures

5.        Construct a three-dimensional model, using cubes, given the top, side, and/or bottom views; and determine the volume and surface area of the model

6.        Inscribe equilateral triangles, squares, and hexagons in circles, using a compass and a straightedge

7.        Given appropriate dimensions, estimate and find the area of a polygon by sub-dividing that polygon into rectangles and right triangles

8.        Investigate, create, and solve problems involving the volume and surface area of

á         Rectangular prisms

á         Cylinders

9.      Find the volume and surface area of rectangular prisms and cylinders, given the appropriate dimensions

Grade 8

1.        Review and extend prior learning

2.        Compare, classify and draw three dimensional shapes

3.        Apply transformations (rotate or turn, reflect or flip, translate or slide, dilate or scale) to geometric figures represented on graph paper

4.        Identify real-life applications of transformations (e.g., tiling, fabric design, art, scaling)

5.        Describe, classify, and construct plane and solid figures, using the appropriate geometric tools

6.        Investigate, create, and solve problems involving the volume and surface area of

á         Cones

á         Pyramids

7.        Find the volume and surface area of cones and pyramids, given the appropriate dimensions

Grade 9

1.        Review and extend prior learning

2.        Derive and 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)

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

Grade 11

1.        Review and extend prior learning

2.        Solve locus problems

á         Set of points equidistant from

á         A given point (circle)

á         Two points (line)

á         A point and a line (parabola)

á         Set of points such that

á         The sum of the distance from two fixed points is constant (ellipse)

á         The difference of the distances from two fixed points is constant (hyperbola)

3.        Apply matrices to geometric transformations with respect to

á         Size change

á         Scale change

4.        Demonstrate an initial understanding of how to apply matrices to geometric transformations with respect to

á         Reflections

á         Rotations

á         Translations

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.      Apply matrices to geometric transformations with respect to

á         Reflections

á         Rotations

á         Translations