Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

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STANDARD 4.2     (GEOMETRY AND MEASUREMENT)     ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.

A.     Geometric Properties

By the end of Grade 2, students will:

 1.         Identify and describe spatial relationships among objects in space and their relative shapes and sizes.

·        Inside/outside, left/right, above/below, between

·        Smaller/larger/same size, wider/ narrower, longer/shorter

·        Congruence (i.e., same size and shape)

 2.         Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes.

·        Vertex, edge, face, side

·        3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid

·        2D figures – square, rectangle, circle, triangle

·        Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape)

 3.         Describe, identify and create instances of line symmetry.

 4.         Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Identify and describe spatial relationships of two or more objects in space.

·        Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)

·        Relative shapes and sizes

 2.         Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.

·        Vertex, edge, face, side, angle

·        3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid

·        2D figures – square, rectangle, circle, triangle, pentagon, hexagon, octagon

 3.         Identify and describe relationships among two-dimensional shapes.

·        Same size, same shape

·        Lines of symmetry

 4.         Understand and apply concepts involving lines, angles, and circles.

·        Line, line segment, endpoint

 5.         Recognize, describe, extend, and create space-filling patterns.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Identify and describe spatial relationships of two or more objects in space.

·        Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)

·        Relative shapes and sizes

·        Shadows (projections) of everyday objects

 2.         Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.

·        Vertex, edge, face, side, angle

·        3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid

·        2D figures – square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon

·        Inclusive relationships – squares are rectangles, cubes are rectangular prisms

 3.         Identify and describe relationships among two-dimensional shapes.

·        Congruence

·        Lines of symmetry

 4.         Understand and apply concepts involving lines, angles, and circles.

·        Point, line, line segment, endpoint

·        Parallel, perpendicular

·        Angles – acute, right, obtuse

·        Circles – diameter, radius, center

 5.         Recognize, describe, extend, and create space-filling patterns.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Understand and apply concepts involving lines and angles.

·        Notation for line, ray, angle, line segment

·        Properties of parallel, perpendicular, and intersecting lines

·        Sum of the measures of the interior angles of a triangle is 180°

 2.         Identify, describe, compare, and classify polygons.

·        Triangles by angles and sides

·        Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

·        Polygons by number of sides

·        Equilateral, equiangular, regular

·        All points equidistant from a given point form a circle

 3.         Identify similar figures.

 4.         Understand and apply the concepts of congruence and symmetry (line and rotational).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Understand and apply concepts involving lines and angles.

·        Notation for line, ray, angle, line segment

·        Properties of parallel, perpendicular, and intersecting lines

·        Sum of the measures of the interior angles of a triangle is 180°

 2.         Identify, describe, compare, and classify polygons and circles.

·        Triangles by angles and sides

·        Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

·        Polygons by number of sides.

·        Equilateral, equiangular, regular

·        All points equidistant from a given point form a circle

 3.         Identify similar figures.

 4.         Understand and apply the concepts of congruence and symmetry (line and rotational).

 5.         Compare properties of cylinders, prisms, cones, pyramids, and spheres.

 6.         Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.

 7.         Identify a three-dimensional shape with given projections (top, front and side views).

 8.         Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.         Understand and apply properties of polygons.

·        Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

·        Regular polygons

 2.         Understand and apply the concept of similarity.

·        Using proportions to find missing measures

·        Scale drawings

·        Models of 3D objects

 3.         Use logic and reasoning to make and support conjectures about geometric objects.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Understand and apply concepts involving lines, angles, and planes.

·        Complementary and supplementary angles

·        Vertical angles

·        Bisectors and perpendicular bisectors

·        Parallel, perpendicular, and intersecting planes

·        Intersection of plane with cube, cylinder, cone, and sphere

 2.         Understand and apply the Pythagorean theorem.

 3.         Understand and apply properties of polygons.

·        Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

·        Regular polygons

·        Sum of measures of interior angles of a polygon

·        Which polygons can be used alone to generate a tessellation and why

 4.         Understand and apply the concept of similarity.

·        Using proportions to find missing measures

·        Scale drawings

·        Models of 3D objects

5.         Use logic and reasoning to make and support conjectures about geometric objects.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.         Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use Pythagorean Theorem to decide whether an object can fit through a doorway).

 2.         Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets or projective views).

 3.         Apply the properties of geometric shapes.

·        Parallel lines – transversal, alternate interior angles, corresponding angles

·        Triangles

a.      Conditions for congruence

b.      Segment joining midpoints of two sides is parallel to and half the length of the third side

c.      Triangle Inequality

·        Minimal conditions for a shape to be a special quadrilateral

·        Circles – arcs, central and inscribed angles, chords, tangents

·        Self-similarity

 4.         Use reasoning and some form of proof to verify or refute conjectures and theorems.

·        Verification or refutation of proposed proofs

·        Simple proofs involving congruent triangles

·        Counterexamples to incorrect conjectures