| 2.9 Understand and Apply the Space and Dimensionality
Concepts of Geometry |
2.9 Grade 3
(Geometry) |
2.9 Grade 5
(Geometry) |
2.9 Grade 8
(Geometry) |
2.9 Grade 11
(Geometry) |
| A. Shapes and their properties |
A1. Name and label geometric shapes in two and three dimension
(circle/sphere, square/cube, triangle/pyramid, rectangle/prism). |
A1. Give formal definitions of geometric figures. |
A1. Draw, label, measure and list the properties of complementary,
supplementary, and vertical angles. |
A1. Construct figures incorporating perpendicular and parallel
lines, the perpendicular bisector of a line segment and an angle bisector
using computer software. |
|
A2. Build geometric shapes using concrete objects (manipulatives). |
A2. Classify and compare triangles and quadrilaterals according
to sides or angles. |
A2. Classify familiar polygons as regular or irregular up to
a decagon. |
A2. Construct geometric figures using a dynamic geometry tool
(Geometer’s Sketchpad, Cabri Geometre, etc.) |
|
A3. Draw two and three dimensional geometric shapes and construct
rectangles, squares, and triangles on the geoboard and on graph paper satisfying
specific criteria. |
A3. Identify and measure circles, their diameters and radii. |
A3. Identify, name, draw, and list all properties of squares,
cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons,
rectangles, rhombi, circles, spheres, triangles, prisms, and cylinders. |
A3. Prove two triangles or two polygons are congruent or similar
using algebraic and coordinate as well as deductive proofs. |
|
A4. Find and describe geometric figures in real life. |
A4. Construct two and three dimensional shapes and figures using
manipulatives, geoboards, and computer software. |
A4. Construct parallel lines, draw a transversal, measure and
compare angles formed such as alternate interior and exterior angles. |
A4. Identify and prove the properties of quadrilaterals involving
opposite sides and angles, consecutive sides and angles, and diagonals
using deductive proofs. |
|
A5. Identify and draw lines of symmetry in geometric figures. |
|
A5. Distinguish between similar and congruent polygons.
Identify similar triangles and similar polygons. |
A5. Identify corresponding parts in congruent triangles to solve
problems. |
|
A6. Identify symmetry in nature. |
|
|
A6. Solve problems involving inscribed and circumscribed polygons. |
|
|
|
|
A7. Use the properties of angles, arcs, chords, tangents, and
secants to solve problems involving circles. |
| B. Using geometric principles to solve problems |
B1. Fold paper to demonstrate the reflections about a line. |
B1. Create an original tessellation. |
B1. Approximate the value of (pi) through experimentation. |
B1. Solve problems using analytic geometry. |
|
B2. Show relationships between and among figures using reflections. |
B2. Represent and use the concepts of line, point, and plane. |
|
B2. Use simple geometric figures such as triangles and squares
to create, through rotation, transformational figures in three dimensions. |
|
B3. Predict how shapes can be changed by combining or dividing
them. |
B3. Analyze simple transformations of geometric figures and
rotations of line segments. |
|
B3. Construct a geometric figure and its image using various
transformations. |
|
|
B4. Identify properties of geometric figures (i.e., parallel,
perpendicular, similar, congruent, symmetrical). |
|
B4. Generate transformations using computer software. |
|
|
B5. Use simple two dimensional coordinate system to find locations
on a map, and represent points and simple figures. |
|
B5. Model situations geometrically to formulate and solve problems. |
|
|
|
|
B6. Analyze figures in terms of the kinds of symmetries they
have. |
|
|
|
|
B7. Analyze geometric patterns, such as tessellations and sequences
of shapes, and develop descriptions of the patterns. |
| C. Three dimensional geometry |
|
C1. Find familiar solids in the environment and describe them. |
|
C1. Analyze objects to determine if they illustrate tessellations,
symmetry, congruence, similarity, and scale. |
|
|
C2. Estimate areas and volumes as the sums of areas of tiles
and volumes of cubes. |
|
|