Last year I taught out of the McDougal Littell 2004 edition of Geometry Concepts and Skills. It was pretty watered down for a geometry course. This year I'm looking at the 2010 Glencoe Geometry book and it's a big jump. I will definitely be taking out a lot of these standards/sections.
Last year I did not teach similarity and one geometry class missed out on surface area and volume while the other missed out on circles and trig ratios. I don't want to talk about it. Anyway, I've never used this book before but so far I like the sequencing and for Illinois folk there are tons of PSAE problems, which is a plus.
I spent a few hours typing out these standards to build a concept list from and now my twitter friends are kind of talking me out of it. So, I may pull out my last year's Geo text and do those as well and combine. Or something.
Anyway, the list is huge and I made some notes and such along the way. So check them out and let me know what you're thinking.
All standards in red are ones I plan on chopping unless you say otherwise!
What should I eliminate, combine, rewrite, or rearrange?
I don't like how often it just says use, apply, recognize. Those words are somewhat vague. If I am a student how do I know that I used it right, applied the right thing, and recognized what I'm supposed to? It seems like they should be written differently in order to clearly assess.
Actually there are quite a few that I would really like to break down even more, but there's already 166 standards! That's ridiculous!
Geometry Glencoe Objectives
1 Identify and model points, lines, and planes
2 Identify intersecting lines and planes
3 Measure segments.
4 Calculate with measures
5 Determine precision of measurements
6 Determine accuracy of measurements
7 Find the distance between two points.
8 Find the midpoint of a segment.
9 Measure and classify angles.
10 Identify and use congruent angles and the bisector of an angle.
11 Identify and use special pairs of angles.
12 Identify perpendicular lines.
13 Identify and name polygons
14 Find perimeter, circumference, and area of two-dimensional figures.
15 Identify and name three-dimensional figures.
16 Find surface area and volume.
17 Make conjectures based on inductive reasoning.
18 Find counterexamples.
19 Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams.
20 Find counterexamples.
21 Analyze statements in if-then form.
22 Write the converse, inverse, and contrapositive of if-then statements.
23 Use the Law of Detachment
24 Use the Law of Syllogism.
25 Identify and use basic postulates about points, lines, and planes.
26 Write paragraph proofs.
27 Use algebra to write two-column proofs.
28 Use properties of equality to write geometric proofs.
29 Write proofs involving segment addition.
30 Write proofs involving segment congruence.
31 Write proofs involving supplementary and complementary angles.
32 Write proofs involving congruent and right angles.
33 Identify the relationships between two lines or two planes.
34 Name angle pairs formed by parallel lines and transversals.
35 Use theorems to determine the relationships between specific pairs of angles.
36 Use algebra to find angle measurements.
37 Find slopes of lines.
38 Use slope to identify parallel and perpendicular lines.
39 Write an equation of a line given information about the graph.
40 Solve problems by writing equations.
41 Recognize angle pairs that occur with parallel lines.
42 Prove that two lines are parallel using angle relationships.
43 Find the distance between a point and a line.
44 Find the distance between parallel lines.
45 Identify and classify triangles by angle measures.
46 Identify and classify triangles by side measures.
47 Apply the Triangle Angle-Sum Theorem.
48 Apply Exterior Angle Theorem.
49 Name and use corresponding parts of congruent polygons.
50 Prove triangles congruent using the definition of congruence.
51 Use the SSS Postulate to test for triangle congruence.
52 Use the SAS Postulate to test for triangle congruence.
53 Use the ASA Postulate to test for triangle congruence.
54 Use the AAS Postulate to test for triangle congruence.
55 Use properties of isosceles triangles.
56 Use properties of equilateral triangles.
57 Identify reflections, translations, and rotations.
58 Verify congruence after congruence transformation.
59 Position and label triangles for use in coordinate proofs.
*Never done this before*
60 Write coordinate proofs.
*Never done this before*
61 Identify and use perpendicular bisector in triangles.
62 Identify and use special bisectors in triangles.
63 Identify and use medians in triangles.
64 Identify and use altitudes in triangles.
65 Recognize and apply properties of inequalities to the measures of the angles of a triangle.
*Not sure about this at all!*
66 Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.
*Not sure about this at all!*
67 Write indirect algebraic proofs
. *NERVOUS!*
68 Write indirect geometric proofs.
*NERVOUS!*
69 Use the Triangle Inequality Theorem to identify possible triangles.
70 Prove triangle relationships using the Triangle Inequality Theorem.
71 Apply the Hinge Theorem or its converse to make comparisons in two triangles. *NERVOUS!*
72 Prove triangle relationships using the Hinge Theorem or its converse. *NERVOUS!*
73 Find and use the sum of the measures of the interior angles of a polygon.
74 Find and use the sum of the measures of the exterior angles of a polygon.
75 Recognize and apply properties of the sides and angles of parallelograms.
76 Recognize and apply properties of the diagonals of parallelograms.
77 Recognize the conditions that ensure a quadrilateral is a parallelogram.
78 Prove that a set of points forms a parallelogram in the coordinate plane.
79 Recognize and apply properties of rectangles.
80 Determine whether parallelograms are rectangles.
81 Recognize and apply the properties of rhombi and squares.
82 Determine whether quadrilaterals are rectangles, rhombi, or squares.
83 Apply properties of trapezoids.
84 Apply properties of kites.
85 Write ratios.
86 Write and solve proportions.
87 Use proportions to identify similar polygons.
88 Solve problems using the properties of similar polygons.
89 Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorem.
90 Use similar triangles to solve problems.
91 Use proportional parts within triangles.
92 Use proportional parts with parallel lines.
93 Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles.
94 Use the Triangle Bisector Theorem.
*Never done this before*
95 Identify similarity transformations.
*Never done this before*
96 Verify similarity after a similarity transformation.
*Never done this before*
97 Interpret scale models.
*Never done this before*
98 Use scale factor to solve problems.
*Never done this before*
99 Find the geometric mean between two numbers.
100 Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse.
101 Use the Pythagorean Theorem.
102 Use the Converse of the Pythagorean Theorem.
103 Use the properties of 45-45-90 triangles.
104 Use the properties of 30-60-90 triangles.
105 Find trigonometric ratios using right triangles.
106 Use trigonometric ratios to find angle measures in right triangles.
107 Solve problems involving angles of elevation and depression.
108 Use angles of elevation and depression to find the distance between two objects.
109 Use the Law of Sines to solve triangles.
110 Use the Law of Cosines to solve triangles.
111 Find magnitudes and directions of vectors. *Not happy about this!!*
112 Add and subtract vectors. *Not happy about this!!*
113 Draw reflections.
114 Draw reflections in the coordinate plane.
115 Draw translations.
116 Draw translations in the coordinate plane.
117 Draw rotations.
118 Draw rotations in the coordinate plane.
119 Draw glide reflections and other compositions of isometries in the coordinate plane.
120 Draw compositions of reflections in parallel and intersecting lines.
121 Identify line and rotational symmetries in two-dimensional figures.
122 Identify line and rotational symmetries in three-dimensional figures.
123 Draw dilations.
124 Draw dilations in the coordinate plane.
125 Identify and use parts of circles.
126 Solve problems involving the circumference of a circle.
127 Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.
128 Find arc lengths .
129 Recognize and use relationships between arcs and chords.
130 Recognize and use relationships between arcs, chords, and diameters.
131 Find measures of inscribed angles.
132 Find measures of angles of inscribed polygons.
133 Use properties of tangents.
134 Solve problems involving circumscribed polygons.
135 Find measures of angle formed by lines intersecting on or inside a circle.
136 Find measures of angles formed by lines intersecting outside the circle.
137 Find measures of segments that intersect in the interior of a circle.
138 Find measures of segments that intersect in the exterior of a circle.
139 Write the equation of a circle.
140 Graph a circle on a coordinate plane.
141 Find perimeters and areas of parallelograms.
142 Find perimeters and areas of triangles.
143 Find areas of trapezoids.
144 Find areas of rhombi and kites.
145 Find areas of circles.
146 Find areas of sectors of circles.
147 Find areas of regular polygons.
148 Find areas of composite figures.
149 Find areas of similar figures by using scale factors.
150 Find scale factors or missing measures given the areas of similar figures.
151 Draw isometric views of three-dimensional figures. *This made me cry in college (the unhappy kind, not
the Jesse Johnson kind)*
152 Investigate cross sections of three-dimensional figures.
153 Find lateral areas and surface areas of prisms.
154 Find lateral areas and surface areas of cylinders.
155 Find lateral areas and surface areas of pyramids.
156 Find lateral areas and surface areas of cones.
157 Find volumes of prisms.
158 Find volumes of cylinders.
159 Find volumes of pyramids.
160 Find volumes of cones.
161 Find surface areas of spheres.
162 Find volumes of spheres.
163 Describe sets of points on a sphere.
164 Compare and contrast Euclidean and spherical geometries.
165 Identify congruent or similar solids.
166 Use properties of similar solids.
There is one more chapter on probability and measurement but I really doubt I will even make it through these previous 12 chapters!
