Download Suggested Unit Pacing (# of days): 12 - Alamance

Alamance-Burlington School System
Math III Unit Plan
Priority standards are highlighted in yellow.
Unit 1: Geometry and Proofs
Mathematical
Practices
Conceptual
Overview
Essential
Understandings
G.CO.9
Common Core Standards
G.CO.10
G.CO.11
G-CO.12
G-SRT.2
G.SRT.3
The Mathematical Practices are
K-12 standards and together with
the content standards prescribe
that students experience
mathematics as a coherent, useful,
and logical subject. Teachers of
mathematics should intentionally
provide daily opportunities for
students to develop these
mathematical habits of mind.
Suggested Unit Pacing (# of days): 12
P4
P5
P6
P7
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
P8
Look for and express regularity in repeated reasoning.
P1
P2
P3
Students will be able to understand basic geometric concepts and complete proofs.
In this unit students will start by learning basic geometric definitions such as vertical
angles, and complementary angles. Students will then explore the angles that are formed
when two parallel lines are cut by a transversal. After mastering these concepts student
will transition into investigating segments found in triangles. Finally student will learn
how to complete basic proofs involving various shapes.
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; points on a perpendicular bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle
sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle
meet at a point.
Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
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.
Given two figures, use the definition of similarity in terms of similarity transformations to
decide if they are similar; explain using similarity transformations the meaning of similarity for
triangles as the equality of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides.
Use the properties of similarity transformations to establish the AA criterion for two triangles
to be similar.
G.SRT.4
G.SRT.5
Learning
Targets
Essential
Terminology
Literacy
Integration
Technology
Integration
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle
divides the other two proportionally, and conversely; the Pythagorean Theorem proved using
triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships
in geometric figures.
These suggested learning targets were determined based on the intentions of the CCSS and/or NCES. Teachers
will need to add the criteria for success in order to create outcome-based targets.
The learner will…
 define angle, circles, perpendicular lines, parallel lines, and line segments.
 apply properties to prove lines parallel.
 make geometric Constructions (copying a segment, copying an angle, bisecting an
angle, constructing a line parallel to a given line through a point not on line) with a
variety of tools and methods.
 identify congruent figures, prove triangles congruent by ASA, AAS, SSS, SAS, HL

identify and apply the properties of parallelograms.
 identify, prove theorems and apply midsegments, concurrent lines, altitudes, perpen
dicular bisectors, and medians of triangles.
 solve ratios and proportions, identify similar polygons, prove triangles similar, ratio
nalize denominators, apply properties of special right triangles and use congruence and
similarity to prove relationships in geometric figures.
Vertical angles
Alternate interior angles
Corresponding angles
Same-side interior angles
Perpendicular bisector
Equidistant
Isosceles triangle
Base angles
Vertex angle
Legs of an isosceles triangle
Midsegment of a triangle
Median of a triangle
Concurrent lines
Parallelogram
Opposite angles
Consecutive angles
Diagonals
Rectangles
Squares
Literacy
Standards
Literature
Connections
Technology
Standards
Technology
Resources
Proof resources

Additional
Resources

http://ahs.arabcityschools.org/ourpages/auto/2013/1/14/57509334/Triangle%20Proofs%20R
eview%201_14_13.pdf
http://www.letspracticegeometry.com/wp-content/uploads/2011/11/proofs-involvingcongruent-triangles.pdf

http://basic-geometry.wikispaces.com/Chapter+3+Lessons
Cross
Curricular
Integration
Assessment
Pre-/Postassessment
On-going/
Formative
Assessment
Summative
Teachers determine the learning plan while reflecting on the range of abilities, styles, interests and needs of
students. How will the work be personalized and differentiated in order to achieve the desired learning targets?
Considerations
for the Learning
Plan
Re-teaching
Enrichment