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+ 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. |
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B.
Transforming Shapes |
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By the end of Grade
2, students will: |
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1.
Use simple
shapes to make designs, patterns, and pictures. |
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2.
Combine and
subdivide simple shapes to make other shapes. |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 3, students will: |
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1.
Describe and
use geometric transformations (slide, flip, turn). |
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2.
Investigate
the occurrence of geometry in nature and art. |
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Building
upon knowledge and skills gained in preceding grades, by the end of
Grade 4, students will: |
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1.
Use simple
shapes to cover an area (tessellations). |
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2.
Describe and
use geometric transformations (slide, flip, turn). |
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3.
Investigate
the occurrence of geometry in nature and art. |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 5, students will: |
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1.
Use a
translation, a reflection, or a rotation to map one figure onto another
congruent figure. |
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2.
Recognize,
identify, and describe geometric relationships and properties as they
exist in nature, art, and other real-world settings. |
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Building
upon knowledge and skills gained in preceding grades, by the end of
Grade 6, students will: |
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1.
Use a
translation, a reflection, or a rotation to map one figure onto another
congruent figure. |
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2.
Recognize,
identify, and describe geometric relationships and properties as they
exist in nature, art, and other real-world settings. |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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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 |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 8, students will: |
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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 |
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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) |
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Building
upon knowledge and skills gained in preceding grades, by the end of
Grade 12, students will: |
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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. |
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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. |
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3.
Determine
whether two or more given shapes can be used to generate a tessellation. |
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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 |