Vertical Alignment
Geometry
Prince William County Public Schools/ Mathematics
K-5
NCTM Process Standards:
ü Problem Solving
ü Reasoning and Proof
ü Communication
ü Connections
ü Representation / Big Ideas:
· Shapes, both two and three-dimensional, exist in great variety. There are many different ways to see and describe similarities and differences among shapes. The more ways that one can classify and discriminate shapes, the better one understands them.
· Shapes have properties that can be used when describing and analyzing them. Properties can be explored and analyzed in a variety of ways.
· An analysis of geometric properties leads to deductive reasoning in a geometric environment.
K.11A Identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle).
K.11B Compare the size (larger, smaller) and shape of plane geometric figures(circle, triangle, square, and rectangle).
K.12 Describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. /
1.12 Identify and trace, describe, and sort plane geometric figures (triangle, square, rectangle, and circle) according to number of sides, vertices, and right angles.
1.13 Construct, model, and describe objects in the environment as geometric shapes (triangle, rectangle, square, and circle) and explain the reasonableness of each choice.
/
2.15A Draw a line of symmetry in a figure.
2.15B Identify and create figures with at least one line of symmetry.
2.16 Identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).
3.14 Identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
3.15 Identify and draw representations of points, line segments, rays, angles, and lines.
3.16 Identify and describe congruent and noncongruent plane figures. /
4.10A Identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices.
4.10B Identify representations of lines that illustrate intersection, parallelism, and perpendicularity.
4.11A Investigate congruence of plane figures after geometric transformations, such as reflection, translation, and rotation, using mirrors, paper folding, and tracing.
4.11B Recognize the images of figures resulting from geometric transformations, such as translation, reflection, and rotation.
4.12A Define polygon.
4.12B Identify polygons with 10 or fewer sides. /
5.11 Measure right, acute, obtuse, and straight angles.
5.12A Classify angles as right, acute, obtuse, or straight.
5.12B Classify triangles as right, acute, obtuse, equilateral, scalene, or isosceles.
5.13A Using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), develop definitions of these plane figures.
5.13B Using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), investigate and describe the results of combining and subdividing plane figures.
Vertical Alignment
Geometry
Prince William County Public Schools/ Mathematics
6 – 8
NCTM Process Standards:
ü Problem Solving
ü Reasoning and Proof
ü Communication
ü Connections
ü Representation / Big Ideas:
· Spatial reasoning skills are essential to formal inductive and deductive reasoning skills required in subsequent mathematics learning.
· Geometric relationships can be determined by visualizing, comparing, constructing, sketching, measuring, transforming, and classifying geometric figures.
· Plane and solid figures can be described, classified, and compared according to their attributes.
· Transformations are used in a variety of ways including: modeling, tiling, fabric design, etc.
· The surface area and volume of prisms, cylinders, pyramids, and cones can be developed conceptually.
· Visualization, measurement, and proportional reasoning skills are used to understand the effect of scale change on distance, area, and volume, and in the study of similar figures.
· The Pythagorean Theorem is applicable to life experiences.
6.11A Identify the coordinates of a point in a coordinate plane a coordinate plane.
6.11B Graph ordered pairs in a coordinate plane.
6.12 Determine congruence of segments, angles, and polygons.
6.13 Describe and identify properties of quadrilaterals. /
7.6 Determine whether plane figures (quadrilaterals and triangles) are similar and write proportions to express the relationships between corresponding sides of similar figures.
7.7 Compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.
7.8 Given a polygon in the coordinate plane, represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. /
8.6A Verify by measuring and describe the relationship among vertical angles, adjacent angles, supplementary angles, and complementary angles.
8.6B Measure angles of less than 360˚.
8.8A Apply transformations to plane figures.
8.8B Identify applications of transformations.
8.9 Construct a three-dimensional model given the top or bottom, side and front views.
8.10A Verify the Pythagorean Theorem.
8.10B Apply the Pythagorean Theorem.
Revised July 20, 2011