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(4.8) Geometry and spatial reasoning. The student identifies and describes attributes of
geometric figures using formal geometric language.
(4.8.a) Geometry and spatial reasoning. The student identifies and describes attributes
of geometric figures using formal geometric language. The student is expected to identify
and describe right, acute, and obtuse angles.
Clarifying Activity with Assessment Connections
Students construct an angle maker by joining two cardboard strips with a brass fastener
and use it to replicate angles found on real objects, such as the hands on an analog clock
at a specific time, the corner of a room, or an open pair of scissors. Students make a chart
showing the angles they have found, recording the angles with drawings and classifying
them as acute, right, or obtuse.
Assessment Connections
Questioning . . .
Open with . . .
Which type of angle occurs most often in this room? How do you know?
Probe further with . . .
Did you find any right angles in the room? Where? Describe your drawings.
How do you know this is a right angle?
Did you find any obtuse angles in the room? Where? Describe your drawings.
How do you know this is an obtuse angle?
Did you find any acute angles in the room? Where? Describe your drawings.
How do you know this is an acute angle?
Listen for . . .
Does the student use mathematical vocabulary ("right," "acute," and "obtuse") to
describe angles?
Can the student describe what it means for angles to be right, acute, or obtuse?
Look for . . .
Is the student's chart accurate?
Is the student able to self-correct any errors?
Can the student correctly draw right, acute, and obtuse angles?
Does the student recognize the relationship between right, obtuse, and acute
angles?
Does the student recognize that all right angles are the same size?
Does the student recognize that all acute angles are not the same size?
Does the student recognize that all obtuse angles are not the same size?
Can the student create a definition for right, acute, and obtuse angles?
TAKS Connection
© Texas Education Agency. Excerpted from TEA's Released Tests and Interactive
Online Tests, Spring 2001 Mathematics TAAS. Reprinted with permission.
Additional Clarifying Activity
Students trace a right angle using tracing paper, fold a right angle with waxed paper, or
tear off the "square" corner of a piece of paper or cardboard. They compare the right
angles to other angles, such as where a brace is fastened onto a desk or the hands of an
analog clock at a certain time. Students predict whether the angle they have located has a
measure greater than a right angle (obtuse), less than a right angle (acute), or about the
same as a right angle, then use their model of a right angle to test their predictions.
(4.8.b) Geometry and spatial reasoning. The student identifies and describes attributes
of geometric figures using formal geometric language. The student is expected to identify
and describe parallel and intersecting (including perpendicular) lines using concrete
objects and pictorial models.
Clarifying Activity with Assessment Connections
Students identify locations in the room where models of parallel lines occur, such as the
top and bottom of the door, the opposite edges of their notebook paper, or the opposite
edges of the ceiling tiles. They also identify locations where models of perpendicular
lines occur, such as the top and side edges of the chalkboard. As a class, students then
develop a list of both examples and nonexamples of parallel lines and justify each
response.
Assessment Connections
Questioning . . .
Open with . . .
Tell me about the examples you placed in the "parallel line" category.
Probe further with . . .
How do you know lines are parallel?
What do the non-parallel lines have in common?
Can you re-sort into perpendicular lines vs. non-perpendicular lines?
How do you know if the lines are perpendicular?
Can parallel lines also be perpendicular? Why?
Listen for . . .
Does the student use mathematical vocabulary (such as parallel, perpendicular,
intersecting, and right angles) to describe the lines?
Can the student justify his or her choices?
Does the student make and test conjectures about parallel and perpendicular lines?
Does the student develop logical arguments to justify his or her conclusions?
Look for . . .
Can the student identify models of parallel and perpendicular lines?
Does the student understand the relationship between right angles and
perpendicular lines?
Does the student recognize that lines extend?
Does the student recognize that lines that do not intersect in vision may not be
parallel?
Does the student recognize that lines can intersect but not be perpendicular?
Can the student create a definition for parallel lines? Perpendicular lines?
TAKS Connection
© Texas Education Agency. Excerpted from TEA's Educators' Guides to TEKS-Based
Assessment, 1999–2000. Reprinted with permission.
(4.8.c) Geometry and spatial reasoning. The student identifies and describes attributes
of geometric figures using formal geometric language. The student is expected to use
essential attributes to define two- and three-dimensional geometric figures.
Clarifying Activity with Assessment Connections
Students reach into a mystery box, feel a geometric solid that has been placed inside, and
describe the solid to the class one clue at a time, without looking, telling how many faces,
edges, and vertices the solid has. The class tries to guess the solid. (Examples of several
possible solids can be available for students to look at and choose from as the description
is given.)
Assessment Connections
Questioning . . .
Open with . . .
What information does this clue give you?
Probe further with . . .
What solids have you eliminated?
Why did you eliminate those solids?
What are the similarities and differences between the solids that you did not
eliminate?
What would be a good clue to give next? Why?
Listen for . . .
Does the student know the name of the geometric solid?
Does the student use appropriate mathematical vocabulary for critical attributes
(such as vertices, edges, and faces)?
Can the student create a description for three-dimensional solids that includes
mathematical language?
Look for . . .
Does the student know the meaning of vocabulary such as vertices, edges, and
faces?
Can the student use critical attributes to identify geometric solids?
Can the student identify solids that do not fit a particular definition?
TAKS Connection
© Texas Education Agency. Excerpted from TEA's TAKS Information Booklets, January
2002. Reprinted with permission.
Additional Clarifying Activity
Students cut a variety of shapes from paper and arrange them onto a page to form a
picture. Students then write a descriptive paragraph about their picture, using geometric
vocabulary including "vertices," and "edges" or "sides" to describe the shapes used.