Standard 4:Mathematics

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.

 

B.     Transforming Shapes

 

By the end of Grade 2, students will:

 

 1.         Use simple shapes to make designs, patterns, and pictures.

 

 2.         Combine and subdivide simple shapes to make other shapes.

 

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

 

 1.         Describe and use geometric transformations (slide, flip, turn).

 

 2.         Investigate the occurrence of geometry in nature and art.

 

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

 

 1.         Use simple shapes to cover an area (tessellations).

 

 2.         Describe and use geometric transformations (slide, flip, turn).

 

 3.         Investigate the occurrence of geometry in nature and art.

 

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

 

 1.         Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

 

 2.         Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

 

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

 

 1.         Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

 

 2.         Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

 

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

 

 1.         Understand and apply transformations.

·        Finding the image, given the pre-image, and vice-versa

·        Sequence of transformations needed to map one figure onto another

·        Reflections, rotations, and translations result in images congruent to the pre-image

·        Dilations (stretching/shrinking) result in images similar to the pre-image

 

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

 

  1.         Understand and apply transformations.

·        Finding the image, given the pre-image, and vice-versa

·        Sequence of transformations needed to map one figure onto another

·        Reflections, rotations, and translations result in images congruent to the pre-image

·        Dilations (stretching/shrinking) result in images similar to the pre-image

 

  2.         Use iterative procedures to generate geometric patterns.

·        Fractals (e.g., the Koch Snowflake)

·        Self-similarity

·        Construction of initial stages

·        Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski’s Triangle)

 

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

 

  1.         Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic object, and, conversely, determine whether and how one object can be transformed to another by a transformation or a sequence of transformations.

 

 2.         Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.

 

 3.         Determine whether two or more given shapes can be used to generate a tessellation.

 

 4.         Generate and analyze iterative geometric patterns.

·        Fractals (e.g., Sierpinski’s Triangle)

·        Patterns in areas and perimeters of self-similar figures

·        Outcome of extending iterative process indefinitely