Jared Tiffin DeRuyter Central School 2015-2016 School Year
Common Core Geometry Unit Pacing Chart
(Sources: www.geometrycommoncore.com
and AMSCO Text)
Class Introduction and Expectations
Date: Sept. 8rd
Unit 1: Basics of Geometry (14 days)
Dates: Sept. 9 th
– Sept. 28 th
Standards:
Topics:
G. CO. 9, G. Co. 12

Review Radicals

Undefined terms (Points, lines, plane, ray, segment, etc.)

Collinear and coplanar

Intersections of planes, lines, points

Naming lines, planes, points

Ruler Postulate

Measuring segments

Segment addition/subtraction

Distance formula

Simple proofs with segments

Copy segment construction

Ways to name an angle

Adjacent angles

Congruent angles

Classifying angles by their measures

Angle addition postulate/subtraction

Definitions and examples: angle, side, vertex, measure of an angle, acute, obtuse, right, straight congruent, interior points, and exterior points

Simple proofs with angles

Copy angle construction

Segment bisector and midpoint definitions

Angle bisector

Midpoint formula

Adjacent angles, supplementary, complementary, linear pair, vertical angles

Identifying angle pairs

Bisecting a segment

Simple proofs

Linear pair (find missing angles)

Vertical angles (find missing angles)

Complementary and supplementary angles

Bisect an angle construction

Jared Tiffin DeRuyter Central School 2015-2016 School Year
Unit 2: Perpendicular and Parallel Lines (12 days)
Dates: Sept. 29 th
– Oct. 15th
Standards:
Topics:
G. GPE. 5

Definitions: parallel, skew lines, perpendicular lines, perpendicular planes, parallel planes

Proofs

Construct a line perpendicular to a given line through a point not on the line

Construct a line perpendicular to a given line through a point on the line

Construct parallel lines through a point not on a given line

Definitions: vertical angles, corresponding, alternating interior, alternating exterior, same side interior

Finding missing angles along a transversal

Review parallel line theorems

Finding missing angles by drawing an auxiliary line

Proofs

Slope review

Slopes of parallel and perpendicular lines

Writing equations of lines given point and slope
Dates: Oct. 16 th – Nov. 9th
Unit 3: Transformational Geometry (16 days)
Standards: G. Co. 1, G. CO. 2, G. CO. 3, G. CO. 4, G. CO. 5, G. CO. 6, G. SRT. 1, G. GPE.
6
Topics:

Define and use: line symmetry, rotational symmetry, point symmetry

Define: Transformation, pre-image, image, isometry, orientation, invariant, rigid motion

Line of reflection

Properties of line reflections

Point reflections

Properties of point reflections

Reflect over: x-axis, y-axis, y=x, y = -x

Reflection constructions

Angle of rotations, clockwise, counterclockwise

Properties of a rotation

Rotating on a coordinate plane

Rotation construction

Properties and notation of transformations

Find image of a translation

Write a rule for a translation

Finding the pre-image

Translation constructions

Jared Tiffin DeRuyter Central School 2015-2016 School Year

Dilations, scale factors

Properties of a dilation

Finding images

Finding scale factors

Define composition of transformations

Glide reflections and other compositions

Describe two transformations that will map pre-image onto image

Make connection between slope and dilations

Use dilations to partition line segments

Finding the points
Unit 4: Triangle Congruency (10 days)
Dates: Nov. 10 th
– Dec. 1st
Standards:
Topics:
G. Co. 7, G. CO. 8, G. CO. 10, G. CO. 13

Prove and solve triangle sum theorem

Prove and solve problems with isosceles and equilateral traingles

Derive exterior angle theorem

Prove triangles are congruent using rigid motions

Construct an equilateral triangle

Copy a triangle using constructions

Understand that congruence between 2 figures gives rise to a correspondence between parts such that corresponding parts are congruent

Practice using 5 methods of proving triangles congruent
 Prove why SSA and AAA don’t work
Unit 5: Proving Triangles Congruent (10 days)
Dates: Dec. 2nd – Dec. 15th
Standards: G. Co. 7, G. CO. 8
Topics:

Prove triangles are congruent using the 5 congruency criteria

Construct proofs in two columns, paragraph, flowchart
Dates: Dec. 16 h
– Jan. 8th
Unit 6: Advanced Triangle Properties (10 days)
Standards: G. Co. 9, G. CO. 10, G. C. 3
Topics:

Solving problems using the mid-segment property of triangles

Prove and solve problems using the point of concurrency of medians of a triangle

Jared Tiffin DeRuyter Central School 2015-2016 School Year

Construct a mid-segment, centroid, incenter, and circumcenter of a triangle

Understand vocabulary dealing with points of concurrency

Triangle inequality theorem
Unit 7: Similarity (14 days)
Dates: Jan. 11 th – Feb 1st
Standards: G. SRT. 2, G. SRT. 3, G. SRT. 4, G. SRT. 5
Topics:

Set up and solve proportions

Understand the definition of similarity

Dilations again

Similarity ratio

Perimeter and Area ratio

AA, SSS, and SAS

Proofs

Similarity Theorems (Triangle Proportionality theorem)

Comparing difference sized objects

Modeling

Right Triangle Similarity

Geometric Mean
Unit 8: Radicals/Pythagorean Theorem/Right Triangle Trig (14 days)
Dates: Feb. 2nd – Feb.26
th
Standards: G. SRT. 6, G. SRT. 7, G. SRT. 8
Topics:

Add, subtract, multiply, and divide radicals

Pythagorean theorem to find a missing side

Converse of Pythagorean theorem

Prove Pythagorean theorem using similar triangles

30-60-90 and 45-45-90 special right triangles (find missing sides)

Trig. Ratios using sin, cos, tan

State exact trig values (0, 30, 45, 60, 90)

SOHCAHTOA

Find missing angle using inverse SOHCAHTOA

Label sides of triangle given trig ratio

Cofuction property between sin and cos (complements)

Non-right triangle trig

Tangent ratio and angle of elevation and depression

Tangent is slope

Modeling

Jared Tiffin DeRuyter Central School 2015-2016 School Year
Unit 9: Polygons and Quadrilaterals (10 days)
Dates: Feb.29
th
– March 11 th
Standards: G. CO. 3, G. CO. 11, G. CO. 13
Topics:

Find the sum of the interior angles of any polygon

Find the sum of the exterior angles of any polygon

Find the measure of one interior angle of a regular polygon

Find the measure of one exterior angle of a regular polygon

Applications

Solve proportions given similar polygons

Work with the properties of a parallelogram, rectangle, rhombus, square, trapezoid, and isosceles trapezoid

Describe rotations and reflections that will carry rectangle, parallelogram, trapezoid, or regular polygon itself

Construct all quadrilaterals, inscribed squares, and hexagon
Unit 10: Quadrilateral Proofs (8 days)
Dates: March 14 rd
– March 23 th
Standards: G. CO. 11
Topics:

Prove that a quadrilateral is a parallelogram, rhombus, rectangle, square, trapezoid, or isosceles trapezoid

Use given parallelograms to prove that triangles and their corresponding parts are congruent

Transversal lines theorems
Unit 11: Coordinate Geometry Proofs (10 days)
Dates: March 24 th
– April 7th
Standards: G. GPE. 4, G. GPE. 7
Topics:

Write out coordinate proofs using slope, distance and midpoint formulas

Prove right triangles, parallelograms, squares, rhombus, rectangle, trapezoid, isosceles trapezoid, parallelism
Unit 12: Finding Numerical Values of Circles (13 days)
Dates: April 8 th
– May 3rd
Standards: G. C. 2, G. C. 5
Topics:

Identify and describe relationships within a circle: inscribed angles, radii, chords, central angles, circumscribed angles, inscribed angles to a diameter, the radius of a circle is perpendicular to the tangent, secants, major arc, minor arc

Construct a tangent line from a point outside a given circle to the circle

Jared Tiffin DeRuyter Central School 2015-2016 School Year

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius

Review circumference and area of circles and part over whole

Defined the radian measure of the angle as the constant of proportionality

Derive the formula for the area of a sector, length of a sector
Unit 13: Circle Proofs and Equation of Circles and Systems of Equations (10 days)
Dates: May 4 th – May 18 th
Standards: G. GPE. 1 G. GPE. 4, G. C. 1, G. C. 3
Topics:

Prove whether or not a coordinate point lies on a circle

Derive the equation of a circle of given center and radius using the
Pythagorean Theorem

Write the equation of a circle given center and radius

Complete the square to find the center and radius of a circle given by an equation

Prove that all circles are similar

Prove properties of angles for a quadrilateral inscribed in a circle

Use coordinates to prove simple geometric theorems
Dates: May 19 th
– May 31 th
Unit 14: Surface Area and Volume (8 days)
Standards: G. MG. 1, G. MG. 2, G. MG. 3, G. GMD. 1, G. GMD. 3, G. GMD. 4
Topics:

Compute areas of shapes that are not formed by unit squares or simple parts of unit squares

Approximate the area of curved regions using rectangles and triangles (Jordan measure)

Study the basic properties of area using set notation

Give in informal argument for the formulas for the circumferences of a circle, area of a circle, volume arguments

State the scaling principle for 2D objects and 3D objects

Using volume formulas for cylinders, pyramids, cones, and spheres to solve problems

Identify the shapes of 2D cross sections of 3D objects and vice versa

Identify cross sections of solids as similar or congruent

Work with 3D relationships (two planes perpendicular to the same line are parallel)

Derive the volume formulas for cone, cylinder, pyramid

Compute volumes of cylinders, pyramids, cones, and spheres

Use cross sections of 3D shapes to identify different 2D shapes (conic sections)

Identify 3D shapes generated by rotating 2D objects

Use geometric shapes and their properties to model real life situations

Jared Tiffin DeRuyter Central School

Use geometry to solve design problems
Review For Regents (9 days)
Dates: June 1 st
– June 13 th
(teach multiple choice)
2015-2016 School Year