Content Area: Math
Index: 4.2A Grade 12 CPI 3
Standard: 4.2 - Geometry and Measurement
Strand: A - Geometric Properties
Cumulative Progress Indicator: 3 - The student will apply
the properties of geometric shapes
·
Parallel lines –
transversal, alternate interior angles, corresponding angles
·
Triangles
a.
Conditions for congruence
b.
Segment joining midpoints of two
sides is parallel to and half the length of the third side
c.
Triangle Inequality
·
Minimal conditions
for a shape to be a special quadrilateral
·
Circles –
arcs, central and inscribed angles, chords, tangents
·
Self-similarity
Grade: 12
Sample Activities:
·
Students make tessellations with an assortment of
different triangles, noting the variety of geometric patterns that are formed,
including parallel lines, congruent angles, congruent triangles, similar
triangles, parallelograms, and trapezoids.
·
Students identify congruent angles on a parallelogram
grid, and use their results to develop conjectures about alternate interior
angles, corresponding angles of parallel lines, and opposite angles of a
parallelogram.
·
Working together, students review geometric vocabulary
by sorting words written on index cards into groups and explaining their reasons
for creating the groups they did. For example, they might place
"parallelogram," "rhombus," "square," and
"rectangle" in one group (since they are all parallelograms) and
place "kite" and "trapezoid" in another group (since they
are not parallelograms).
·
Students find a variety of strategies for demonstrating
that the sum of the measures of the angles of a triangle is 180 degrees. Some
use protractors and measure a pencil-and-paper figure, others create a triangle
with Geometer's Sketchpad software and post the measures of the angles before
dragging it from a vertex to notice that the sum always remains the same, and
still others use a method that requires tearing each of the corners from an
oaktag triangle and then fitting them together to make a line.
· Fluid
Power/Robotics
