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

+ or -

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.

E.     Measuring Geometric Objects

By the end of Grade 2, students will:

 1.         Directly measure the perimeter of simple two-dimensional shapes.

 2.         Directly measure the area of simple two-dimensional shapes by covering them with squares.

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

 1.         Determine the area of simple two-dimensional shapes on a square grid.

 2.         Determine the perimeter of simple shapes by measuring all of the sides.

 3.         Measure and compare the volume of three–dimensional objects using materials such as rice or cubes.

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

 1.         Determine the area of simple two-dimensional shapes on a square grid.

 2.         Distinguish between perimeter and area and use each appropriately in problem-solving situations.

 3.         Measure and compare the volume of three–dimensional objects using materials such as rice or cubes.

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

 1.         Use a protractor to measure angles.

 2.         Develop and apply strategies and formulas for finding perimeter and area.

·        Square

·        Rectangle

 3.         Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa.

 4.         Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one’s foot).

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

 1.         Use a protractor to measure angles.

 2.         Develop and apply strategies and formulas for finding perimeter and area.

·        Triangle, square, rectangle, parallelogram, and trapezoid

·        Circumference and area of a circle

 3.         Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders.

 4.         Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa.

 5.         Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one’s foot).

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

 1.         Develop and apply strategies for finding perimeter and area.

·        Geometric figures made by combining triangles, rectangles and circles or parts of circles

·        Estimation of area using grids of various sizes

 2.         Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).

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

 1.         Develop and apply strategies for finding perimeter and area.

·        Geometric figures made by combining triangles, rectangles and circles or parts of circles

·        Estimation of area using grids of various sizes

·        Impact of a dilation on the perimeter and area of a 2-dimensional figure

2.         Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).

 3.         Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.

·        Volume - prism, cone, pyramid

·        Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)

·        Impact of a dilation on the surface area and volume of a three-dimensional figure

 4.         Use formulas to find the volume and surface area of a sphere.

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

 1.         Use techniques of indirect measurement to represent and solve problems.

·        Similar triangles

·        Pythagorean theorem

·        Right triangle trigonometry (sine, cosine, tangent)

 2.         Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures.

·        Approximation of area using grids of different sizes

·        Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given conditions using graphing calculators, dynamic geometric software, and/or spreadsheets

·        Estimation of area, perimeter, volume, and surface area