CHALKDUST’S
CORRELATION TO
|
The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. |
Chalkdust Chapter/ Section |
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1.0 Students demonstrate
understanding by identifying and giving examples of undefined terms, axioms,
theorems, and inductive and deductive reasoning. |
2.1, 2.2, 2.6, 2.1, 6.2 |
|
2.0 Students write
geometric proofs, including proofs by contradiction. |
2.5, 3.1, 3.4, 4.5, 5.5 |
|
3.0 Students construct and
judge the validity of a logical argument and give counterexamples to disprove
a statement. |
3.3, 5.5 |
|
4.0 Students prove basic
theorems involving congruence and similarity. |
4.1, 4.2, 8.4, 8.5, 8.6 |
|
5.0 Students prove that
triangles are congruent or similar, and they are able to use the concept of
corresponding parts of congruent triangles. |
4.1, 4.3, 8.5 |
|
6.0 Students know and are
able to use the triangle inequality theorem. |
5.4, 5.5 |
|
|
8.6, 6.7, 10.2 -10.6, 13.6 |
|
8.0 Students know, derive,
and solve problems involving the perimeter, circumference, area, volume,
lateral area, and surface area of common geometric figures. |
1.6, 4.4, 8.3, 11.4 -11.7, 12.1- 12.7 |
|
9.0 Students compute the
volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres;
and students commit to memory the formulas for prisms, pyramids, and
cylinders. |
Chapter 12 |
|
10.0 Students compute areas
of polygons, including rectangles, scalene triangles, equilateral triangles,
rhombi, parallelograms, and trapezoids. |
11.1, 11.2, 11.3, 11.4 |
|
11.0 Students determine how
changes in dimensions affect the perimeter, area, and volume of common
geometric figures and solids. |
Chapter 12 |
|
|
4.2, 6.2 |
|
13.0 Students prove
relationships between angles in polygons by using properties of
complementary, supplementary, vertical, and exterior angles. |
2.6, 3.5, 3.6, 4.2 |
|
14.0 Students prove the
Pythagorean theorem. |
9.2 |
|
15.0 Students use the
Pythagorean theorem to determine distance and find missing lengths of sides
of right triangles. |
9.2 |
|
16.0 Students perform basic
constructions with a straightedge and compass, such as angle bisectors,
perpendicular bisectors, and the line parallel to a given line through a
point off the line. |
1.7, 4.5, 4.7, |
|
17.0 Students prove
theorems by using coordinate geometry, including the midpoint of a line
segment, the distance formula, and various forms of equations of lines and
circles. |
1.4, 2.3, 2.3., 4.4, 5.3, 10.7, 13.4 |
|
18.0 Students know the
definitions of the basic trigonometric functions defined by the angles of a
right triangle. They also know and are
able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2
+ (cos(
x )) 2 = 1. |
9.5, 9.6, 10.2, 11.4, 11.6, 13.6 |
|
19.0 Students use
trigonometric functions to solve for an unknown length of a side of a right
triangle, given an angle and a length of a side. |
9.5, 9.6 |
|
20.0 Students know and are
able to use angle and side relationships in problems with special right
triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90°
triangles. |
9.4 |
|
21.0 Students prove and
solve problems regarding relationships among chords, secants, tangents,
inscribed angles, and inscribed and circumscribed polygons of circles. |
10.1, 10.2, 10.4, 10.5, 11.5, |
|
22.0 Students know the
effect of rigid motions on figures in the coordinate plane and space,
including rotations, translations, and reflections. |
7.1, 7.2, 7.3, 7.4, 7.5 |
This is the only standard that does not have a section on in the textbook:
18.0 … They also know and are able
to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2
+ (cos( x )) 2
= 1.
The book does have sin/cos/tan relationships, but they are not used as in the above formula.