CURRICULUM MAP
Geometry
1st Trimester – 59 Days
Core Standards
Glencoe
Geometry
Additional
resources
Geometry Activities throughout the year, as time permits.
Use and interpret quantities and units correctly in algebraic formulas.
Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Know and use (in reasoning and problem solving) definitions of angles, polygons,
parallel and perpendicular lines, rigid motions, parallelograms, and rectangles.
Rearrange formulas to highlight a quantity of interest. For example, area formulas.
Year Round
Year Round
Year Round
Year Round
Year Round
Chapter 1 - Teach whole Chapter 8 Days
1F
6.
Points Lines and Planes
Find the point on the segment between two given points that divides the segment
in a given ratio.
1.1
1.3
1.2 Precision
and
measurement
Chapter 2 – Sections 1 and 3 through 8 - 13 DAYS
7.
Understand that geometric diagrams can be used to test conjectures and identify
logical errors in fallacious proofs.
Chapter 2
8.
Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; two lines parallel to a third are
parallel to each other; points on a perpendicular bisector of a segment are exactly
those equidistant from the segment’s endpoints.
Inductive Reasoning Processes
Conditional Statements
Deductive Reasoning
Postulates required – Paragraph Proofs Omit
Algebraic Proofs
2.7,2.8
1A
1B
1C
1D
1E
2.1
2.3
2.4
2.5
2.6
MIDTERM
Chapter 3 Sections 1 through 6 – 11 Days
10.
8.
9.
Understand that a linear function, defined by f(x) = mx + b for some constants m
and b, models a situation in which a quantity changes at a constant rate, m, relative
to another.
Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; two lines parallel to a third are
parallel to each other; points on a perpendicular bisector of a segment are exactly
those equidistant from the segment’s endpoints.
Solve algebraically a simple system consisting of one linear equation and one
quadratic equation in two variables; for example, find points of intersection
3.1, 3.2, 3.3,
3.4, 3.6
3.5
3.1, 3.2, 3.3,
3.4, 3.6
Intro to
Proofs
Power Point
Proof Puzzles
11.
12.
between the line y = –3x and the circle x2 + y2 = 3. (draw a picture)
Understand that two lines with well-defined slopes are perpendicular if and only if
the product of their slopes is equal to –1.
Use the slope criteria for parallel and perpendicular lines to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line
that passes through a given point).
3.3
3.4
Chapter 4 Sections 1 through 6 - Days 16
13.
Understand that criteria for triangle congruence are ways to specify enough
measures in a triangle to ensure that all triangles drawn with those measures are
congruent.
4.1, 4.2, 4.3,
4.4, 4.5, 4.6
14.
Understand that criteria for triangle congruence (ASA, AAS, SAS, and SSS) can
be established using rigid motions.
4.4,4.5
15.
Prove theorems about triangles. Theorems include: measures of interior angles of
a triangle sum to q180; base angles of isosceles triangles are congruent; the
triangle inequality; the longest side of a triangle faces the angles with the greatest
measure and vice-versa; the exterior-angle inequality; and the segment joining
midpoint of two sides of a triangle parallel to the third side and half the length.
4.6
Final
Chapter 5 - Sections 1 – 2 & 4 -5 5.3 is Optional – Days 11
13
Understand that criteria for triangle congruence are ways to specify enough
measures in a triangle to ensure that all triangles drawn with those measures are
congruent.
5.1, 5.2, 5.4,
5.5
15.
Prove theorems about triangles. Theorems include: measures of interior angles of
a triangle sum to q180; base angles of isosceles triangles are congruent; the
triangle inequality; the longest side of a triangle faces the angles with the greatest
measure and vice-versa; the exterior-angle inequality; and the segment joining
midpoint of two sides of a triangle parallel to the third side and half the length.
5.1, 5.2, 5.4
17.
Understand that a line parallel to one side of a triangle divides the other two
proportionally, and conversely.
6.1, 6.4
16.
Understand that the assumed properties of dilations can be used to establish the
AA, SAS, and SSS criteria for similarity of triangles.
6.3, 6.5
1G
Similar Polygons
6.2
17.
Understand that a line parallel to one side of a triangle divides the other two
proportionally, and conversely.
Prove theorems about triangles. Theorems include: measures of interior angles of
a triangle sum to q180; base angles of isosceles triangles are congruent; the
triangle inequality; the longest side of a triangle faces the angles with the greatest
measure and vice-versa; the exterior-angle inequality; and the segment joining
midpoint of two sides of a triangle parallel to the third side and half the length.
Use triangle similarity criteria to solve problems and to prove relationships in
geometric figures. Include a proof of the Pythagorean theorem using triangle
similarity.
STEM Introduce simple trigonometric equations formally using inverse
trigonometric functions and evaluate the solutions numerically using technology.
Solving trigonometric equations by means of the quadratic formula is optional.
7.1
20.
Understand that by similarity, side ratios in right triangles are properties of the
angles in the triangle, leading to definitions of sine, cosine, and tangent.
7.2, 7.3, 7.4
21.
Use sine, cosine, tangent, and the Pythagorean Theorem to solve right triangles in
7.2, 7.3, 7.4,
Chapter 6 –Sections 1 through 5 - 6.6 Optional -- 10 DAYS
Chapter 7 Sections 1 though 5 – 10 Days
15.
18.
19.
7.3
7.1, 7.2
7.1, 7.2, 7.3,
7.4, 7.5
Proofs
Involving
Triangles
Worksheet
22.
applied problems. Angels of Elevation and Depression
Use and explain the relationship between the sine and cosine of complementary
angles.
7.5
7.4
Chapter 9 – 1 through 5 ( Optional 9-4 as a hands on Activity) – 5 Days
26.
Use two-dimensional representations to transform figures and to predict the effect
of translations, rotations, and reflections.
9.1, 9.2, 9.3
28.
Use two-dimensional representations to transform figures and to predict the effect
of dilations.
Understand that dilating a line produces a line parallel to the original. (In
particular, lines passing through the center of the dilation remain unchanged.)
9.5
Understand that the dilation of a given segment is parallel to the given segment
and longer or shorter in the ratio given by the scale factor. A dilation leaves a
segment unchanged if and only if the scale factor is 1.
Understand that dilations can be used to show that all circles are similar.
9.5
29.
30.
31.
9.5
9.5 and find
supplementary
material.
MIDTERM
Chapter 8 Sections 1 through 7 – 8 Days
23.
Use and prove properties of and relationships among special quadrilaterals:
parallelogram, rectangle, rhombus, square, trapezoid and kite.
24.
Characterize parallelograms in terms of equality of opposite sides, in terms of
equality of opposite angles, and in terms of bisection of diagonals; characterize
rectangles as parallelograms with equal diagonals.
25.
Use coordinates to prove simple geometric theorems algebraically. For example,
prove or disprove that a figure defined by four given points in the coordinate plane
is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at
the origin and containing the point (0, 2).
Prove theorems about triangles. Theorems include: measures of interior angles of
a triangle sum to q180; base angles of isosceles triangles are congruent; the
triangle inequality; the longest side of a triangle faces the angles with the greatest
measure and vice-versa; the exterior-angle inequality; and the segment joining
midpoint of two sides of a triangle parallel to the third side and half the length.
15.
8.2, 8.3, 8.4,
8.5, 8.6
8.2, 8.3, 8.4,
8.5, 8.6
8.7
8.1
Chapter 10 Sections 1 through 8 -- 18 Days
9.
Solve algebraically a simple system consisting of one linear equation and one
quadratic equation in two variables; for example, find points of intersection
between the line y = –3x and the circle x2 + y2 = 3. (draw a picture)
10.3, 10.5,
10.6, 10.7
32.
Understand that there is a unique circle through three non-collinear points, and
four circles tangent to three non-concurrent lines.
10.1, 10.5,
10.6,
33.
Identify and define radius, diameter, chord, tangent, secant, and circumference.
10.1, 10.5,
10.6
34.
Identify and describe relationships among angles, radii, and chords. Include the
relationship between central, inscribed and circumscribed angles; inscribed
10.2, 10.3,
10.4, 10.5,
Tessellation
Hands on
Activity 9-4
angles on a diameter are right angles; the radius of a circle is perpendicular to the
tangent where the radius intersects the circle.
10.6
35.
Determine the arc lengths and the areas of sectors of circles, using proportions.
10.2
36.
STEM Construct a tangent line from a point outside a given circle to the circle.
10.5 activity
37.
STEM Prove and use theorems about circles, and use these theorems to solve
problems involving:
a. Symmetries of a circle
b. Similarity of a circle to any other
c. Tangent line, perpendicularity to a radius
d. Inscribed angles in a circle, relationship to central angles, and equality of
inscribed angles
e. Properties of chords, tangents, and secants as an application of triangle
similarity.
10.2, 10.3,
10.4, 10.5,
10.6, 10.7
38.
Understand that the equation of a circle can be found using its definition and the
Pythagorean Theorem.
10.8
39.
Decide whether a point with given coordinates lies on a circle defined by a given
equation
10.8
40.
Decide whether a point with given coordinates lies on a circle defined by a given
equation.
10.8
Final
Chapter 11 Sections 1 through 5 -- 15 Days
19.
STEM Introduce simple trigonometric equations formally using inverse
trigonometric functions and evaluate the solutions numerically using technology.
Solving trigonometric equations by means of the quadratic formula is optional.
Apply concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).
11.3
35.
42.
Determine the arc lengths and the areas of sectors of circles, using proportions.
Use coordinates to compute perimeters of polygons and areas for triangles and
rectangles, e.g. using the distance formula.«
11.3
11.1, 11.2
43.
Find areas of polygons by dissecting them into triangles
11.3
44.
STEM Use the behavior of length and area under dilations to show that the
circumference of a circle is proportional to the radius and the area of a circle is
proportional to the square of the radius. Identify the relation between the constants
of proportionality.
11.3
41.
Chapters
11,12,13
45.
Understand that the area of a decomposed figure is the sum of the areas of its
components and is independent of the choice of dissection.
11.4
27.
Understand that models of objects and structures can be built from a library of
standard shapes; a single kind of shape can model seemingly different objects.
Chapter 11
Chapter 12 Sections 1 through 7 -- 15 Days
46
19.
47.
Apply formulas and solve problems involving volume and surface area of right
prisms, right circular cylinders, right pyramids, cones, spheres and composite
figures.
STEM Introduce simple trigonometric equations formally using inverse
trigonometric functions and evaluate the solutions numerically using technology.
Solving trigonometric equations by means of the quadratic formula is optional.
Use geometric shapes, their measures and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a cylinder).
Chapter 12
12.3, 12.5
Chapter 12
MIDTERM
Chapter 13 Sections 1 through 5 --- 15 Days
19. STEM Introduce simple trigonometric equations formally using inverse
trigonometric functions and evaluate the solutions numerically using
technology. Solving trigonometric equations by means of the quadratic
formula is optional.
25. Use coordinates to prove simple geometric theorems algebraically. For
example, prove or disprove that a figure defined by four given points in the
coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies
on the circle centered at the origin and containing the point (0, 2).
46. Apply formulas and solve problems involving volume and surface area of
right prisms, right circular cylinders, right pyramids, cones, spheres and
composite figures.
49. Explain why the volume of a cylinder is the area of the base times the
height, using informal arguments.
50
13.1, 13.2,
13.4
13.5
Chapter 13
13.1
For a pyramid or a cone, give a heuristic argument to show why its volume is 13.2
one-third of its height times the area of its base.
48. STEM Understand that Cavalier's principle allows one to understand volume
formulas informally by visualizing volumes as stacks of thin slices.
(Introduce, mastery not expected)
13.1, 13.2
47. Use geometric shapes, their measures and their properties to describe
objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Chapter 13