Idaho Department of Education
Content Standards |
Objective |
Sub Objectives |
Task Analysis |
Essential Vocabulary |
Sample Assessment |
Resources |
| Standard 4: Concepts and
Principles of Geometry |
| Goal 4.1: Apply concepts of size,
shape, and spatial relationships. |
8.M.4.1.1 Describe and classify
relationships among types of one-, two-, and three- dimensional
geometric figures, using their defining properties.
CL: C, D
Calc: CN
Content Limit: Classify only. Figures may include triangles and
quadrilaterals. Triangles may be classified by angles (acute,
equiangular, obtuse, or right) or by sides (equilateral, isosceles, or
scalene) or both (e.g., an obtuse isosceles triangle). Quadrilaterals
may be classified according to number and position of parallel sides as
well as angle measure (square, trapezoid, paralle logram , rectangle, or
rhombus). Three-dimensional figures can include cubes, rectangular
prisms, spheres, pyramids, cones, and cylinders. ‘Describe’ to be
assessed in the classroom, not on the ISAT. |
• Describe and classify relationships
among types of two- and three- dimensional geometric figures, using
their defining properties |
• Identify two- and three-dimensional
figures according to their defining characteristics
• Compare characteristics of two- and three-
dimensional figures |
acute • equiangular • obtuse • right
• equilateral • isosceles • scalene • parallel • trapezoid •
parallelogram • rhombus • cube • prism • sphere • pyramid • cone •
cylinder • quadrilateral |
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8.M.4.1.2 Draw and measure various
angles and shapes using appropriate tools.
CL: C
Calc: YES
Content Limit: Measure only using superimposed protractor. ‘Draw’ to be
assessed in the classroom, not on the ISAT. |
• Draw and measure various angles and
shapes using appropriate tools |
• Recall properties of angles and
shapes • Make use of tools to create or
measure angles and shapes |
compass • protractor |
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| 8.M.4.1.3 Apply the fundamental
concepts, properties, and relationships among points, lines, rays,
planes, and angles.
CL: C
Calc: CN
Content Limit: Items may include parallel, intersecting and
perpendicular lines including two parallel lines cut by a transversal
and the congruent and supplementary angles formed. Angles may include
acute, right, obtuse, and straight. Angle relationships may include
complementary, supplementary, and congruent. Symbols used may include:
capital letter for points, two-headed arrow above two capital letters
for lines, line segment above two capital letters for line segments,
one-headed arrow above two capital letters for rays, angle symbol with
one capital letter or angle symbol with three capital letters for
angles, and symbols for parallel, perpendicular, and right angle. |
• Apply the fundamental concepts,
properties, and relationships among points, lines, rays, planes, and
angles |
• Name lines, rays, planes and angles
using points • Identify parallel,
intersecting, perpendicular lines
• Name acute, obtuse, right and straight angles
• Identify and calculate compliments and
supplements
• Show congruence among corresponding and vertical
angles |
point • line • segment • ray • plane
• complementary • supplementary • congruent • transversal • intersect •
perpendicular • corresponding angles • vertical angles |
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| 8.M.4.1.4 Identify and model the
effects of reflections, translations, rotations, and scaling on various
shapes.
CL: D, E
Calc: CN
Content Limit: When using three-dimensional shapes: Transformations may
include reflections, rotation and translations. Items are limited to one
transformation per item. Rotations occur in increments of 90º. When
using two-dimensional shapes: Transformations may include reflections,
rotation, translations, and change of scale . Items are limited to two
transformations per item. Rotations occur in increments of 45º.
Algebraic rules limited to translations and reflections when the figure
is shown on a coordinate grid . No algebraic rules are required for items
involving more than one transformation. Rotations must indicate
clockwise or counterclockwise. |
• Identify and model the effects of
reflections, translations, rotations, and scaling on various shapes |
• Use coordinate geometry to
re present and examine the properties of geometric shapes
• Describe sizes, positions, and orientations of
shapes under transformations such as: reflections, rotations,
translations and dilations |
clockwise/counterclockwise •
reduction /enlargement • reflection • rotation • translation • dilation •
scale factor |
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| 8.M.4.1.5 Identify congruence,
similarities, and line symmetry of shapes.
CL: E
Calc: CN
Content Limit:Shapes limited to two-dimensional figures. |
• Identify congruence, similarities,
and line symmetry of shapes |
• Explain and illustrate the
congruence, similarity and line symmetry of objects |
symmetry • congruent • similar |
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| 8.M.4.1.6 Explain the concept of
surface area and volume (capacity). CL:
Calc:
Content Limit: Assessed in the classroom, not on the ISAT. |
• Explain the concept of surface area
and volume (capacity) |
• Compare and contrast the concepts
of area, surface area and volume of figures |
surface area • volume • capacity •
square units • cubic units |
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| 8.M.4.1.7 Use appropriate vocabulary
and symbols. CL:
Calc:
Content Limit: Assessed in the classroom, not on the ISAT. |
• Use appropriate vocabulary and
symbols |
• See content limit of 8.M.4.1.3 for
correct figure symbols -communicate using
correct mathematical terminology |
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| Goal 4.2: Apply the geometry of right
triangles. |
No objectives at this grade level. |
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| Goal 4.3: Apply graphing in two
dimensions. |
8.M.4.3.1 Identify and plot points on
a coordinate plane.
CL: C
Calc: CN
Content Limit: Points limited to integer ordered pairs. Points may
appear in any of the four quadrants or on either axis. |
• Identify and plot points on a
coordinate plane |
• List ordered pair for given point
• Plot given points in coordinate plane
• Name 4 quadrants |
x-axis • y-axis • origin • coordinate
plane • ordered pair • quadrants |
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