Concept 1: Geometric Properties

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 1. Use the words vertex and side when describing simple two-dimensional geometric shapes.

PO 1. Identify two-dimensional shapes by attribute (size, shape, number of sides).

PO 2. Identify two-dimensional shapes by attribute (size, shape, number of sides, vertices).

PO 2. Identify concepts and terms of position and size in contextual situations:

·  Inside/
outside

·  Above/below/between

·  Smaller/
larger

·  Longer/
shorter.

PO 3. Use concepts and terms of position and size in contextual situations:

·  Inside/outside

·  Left/right

·  Above/below/between

·  Smaller/larger

·  Longer/
shorter.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 3. Identify shapes in different environments. (e.g., nature, buildings, classroom, etc.)

PO 4. Name common two-dimensional shapes (square, rectangle, triangle, and circle).

PO 1. Compare attributes of two-dimensional shapes (square, rectangle, triangle, and circle).

PO 1. Build geometric figures with other common shapes. (e.g., tangrams, pattern blocks, geoboards)

PO 1. Identify the properties of two-dimensional figures using appropriate terminology.

PO 1. Recognize regular polygons.

PO 1. Classify polygons by their attributes. (e.g., number of sides, length of sides, angles, parallelism, perpendicularity)

PO 1. Identify the attributes of special triangles. (isosceles, equilateral, right)

PO 5. Draw two-dimensional shapes. (square, rectangle, triangle, circle)

PO 2. Draw two-dimensional figures by applying significant properties of each. (e.g., Draw a quadrilateral with two sets of parallel sides and four right angles.)

PO 2. Draw a geometric figure showing specified properties, such as parallelism and perpendicularity.

PO 1. Draw a geometric figure showing specified properties. (e.g., Draw an obtuse triangle.)

PO 1. Draw a model that demonstrates basic geometric relationships such as parallelism, perpendicu-larity, similarity/

proportionality, and congruence.

PO 2. Identify the hierarchy of quadrilaterals.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 2. Name concrete objects and pictures of three-dimensional solids (cones, spheres and cubes).

PO 2. Identify models or illustrations of prisms, pyramids, cones, cylinders and spheres.

PO 3. Sketch prisms, pyramids, cones, and cylinders.

PO 3. Classify prisms, pyramids, cones, and cylinders by base shape and lateral surface shape.

PO 4. Identify the properties of two- and three-dimensional geometric figures using appropriate terminology and vocabulary.

PO 4. Classify three-dimensional figures by their attributes.

PO 2. Classify three-dimensional solids by their configuration and properties. (e.g., parallelism, perpendicu-larity and congruency)

PO 2. Draw three-dimensional figures by applying properties of each. (e.g., parallelism, perpendicu-larity and congruency)

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 3. Describe relationships between two-dimensional and three-dimensional objects. (squares/
cubes, circles/
spheres, triangles/
cones)

PO 5. Compare attributes of two- dimensional figures with three-dimensional figures.

PO 3. Identify the net (two-dimensional representation) that corresponds to a rectangular prism, cone, or cylinder.

PO 3. Recognize the three-dimensional figure represented by a net.

PO 3. Make a net to represent a three-dimensional object.

PO 4. Distinguish between length, area, and volume, using two- and three-dimensional geometric figures.

PO 4. Represent the surface area of rectangular prisms and cylinders as the area of their net.

PO 4. Make a three-dimensional model from a net.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 3. Draw points, lines, line segments (open or closed endpoints), rays or angles.

PO 5. Draw points, lines line segments, rays, and angles with appropriate labels.

PO 6. Draw triangles with appropriate labels.

PO 5. Draw polygons with appropriate labels.

PO 5. Draw regular polygons with appropriate labels.

PO 5. Draw 2-dimensional and 3-dimensional figures with appropriate labels.

PO 4. Classify angles. (e.g., right, acute, obtuse, straight)

PO 6. Recognize that all pairs of vertical angles are congruent.

PO 7. Identify supplementary or complementary angles.

PO 6. Identify the angles created by two lines and a transversal.

PO 6. Identify the properties of angles created by a transversal intersecting two parallel lines (e.g., corresponding angles are congruent).

PO 6. Solve problems related to complemen-tary, supplemen-tary, or congruent angle concepts.

PO 5. Classify triangles as right, acute, or obtuse.

PO 7. Classify triangles as scalene, isosceles, or equilateral.

PO 7. Recognize the relationship between central angles and intercepted arcs.

PO 7. Recognize the relationship between inscribed angles and intercepted arcs.

PO 7. Solve problems by applying the relationship between circles, angles, and intercepted arcs.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 8. Recognize that a circle is a 360º rotation about a point.

PO 9. Identify the diameter, radius and circumference of a circle.

PO 8. Identify the diameter, radius and circumference of a circle or sphere.

PO 8. Identify arcs and chords of a circle.

PO 8. Identify tangents and secants of a circle.

PO 8. Solve problems by applying the relationship between radii, diameters, chords, tangents or secants.

PO 10. Understand that the sum of the angles of a triangle is 180°.

PO 9. Model the triangle inequality theorem using manipulatives.

PO 9.

Determine whether three given lengths can form a triangle.

PO 9. Solve problems using the triangle inequality property.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 10. Solve problems using special case right triangles.

PO 2. Recognize congruent shapes.

PO 6. Identify congruent geometric shapes.

PO 11. Draw two congruent geometric figures.

PO 10. Identify corresponding parts of congruent polygons as congruent.

PO 11. Determine when triangles are congruent by applying SSS, ASA, AAS or SAS.

PO 4. Recognize similar shapes.

PO 7. Identify similar shapes.

PO 12. Draw two similar geometric figures.

PO 10. Identify corresponding angles of similar polygons as congruent and sides as proportional.

PO 12. Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.

PO 13. Construct a triangle congruent to a given triangle.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 6. Recognize where a line of symmetry divides a two-dimensional shape into mirror images.

PO 3. Recognize line(s) of symmetry for a two-dimensional shape.

PO 5. Identify a line of symmetry in a two-dimensional shape.

PO 8. Draw a two-dimensional shape that has line symmetry.

PO 13. Identify the lines of symmetry in a two-dimensional shape.

PO 9. Draw a two-dimensional shape with a given number of lines of symmetry.

PO 14. Solve contextual situations using angle and side length relationships.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Grade 8

High School

PO 1. Recognize same shape in different positions (slide/
translations).

PO 1. Recognize same shape in different positions (flip/reflection).

PO 1. Recognize same shape in different positions (turn/rotation).

PO 1. Demonstrate translation using geometric figures.

PO 1. Demonstrate reflections using geometric figures.

PO 1. Identify reflections, and translations using pictures.

PO 1. Identify rotations about a point, using pictorial models.

PO 1. Identify the planar geometric figure that is the result of a given rigid transformation.

PO 1. Sketch the planar figure that is the result of two or more transformations.