Download 2015-2016 Geometry 2nd Quarter Mathematics Scope and Sequence

2015-2016 Geometry 2nd Quarter Mathematics Scope and Sequence
Unifying Concept: Triangles and Quadrilaterals
Mathematics Content Focus:
Mathematical Practice Focus
(Chapters 2,3,4, 5)
Mathematically Proficient Students…
Students will use inductive and deductive reasoning to 1. Make sense of problems and persevere in solving
prove theorems about lines and angles
them.
2. Reason abstractly and quantitatively.
Students will investigate angles formed by parallel
3. Construct viable arguments and critique the reasoning
lines and transversals. Students will also learn the
of others.
criteria for parallel and perpendicular lines and use
4. Model with mathematics.
them to solve geometric problems.
5. Use appropriate tools strategically.
6. Attend to precision.
Students will also prove theorems about triangles
7. Look for and make use of structure.
involving interior angles and bisectors of triangles.
8. Look for and express regularity in repeated reasoning.
Students use logic to identify the criteria for triangles
to be congruent.
Students will prove and apply theorems about
perpendicular bisectors, angle bisectors, medians,
and triangle midsegment theorem.
Target Standards
G.CO.B.6
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid
motions to decide if they are congruent.
G-CO.B.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent
if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G-CO.B.8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G-CO.C.9
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.
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, √3) lies on the circle centered at the origin and containing the point (0, 2).
G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them 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).
Quarter Major Clusters
Arizona considers Major Clusters as groups of related standards that require greater emphasis than some of the
others due to the depth of the ideas and the time it takes to master these groups of related standards.
G-CO.B Understand congruence in terms of rigid motions
Essential Concepts
Essential Questions
 A rigid motion is a transformation of points in space
 How do you determine if two figures are
consisting of a sequence of one or more translations,
congruent?
reflections, and/or rotations.
 What has to be true in order for two triangles to
 Rigid motions are assumed to preserve distances and
be congruent?
angle measures.
 How do the criteria for triangle congruence
 Congruent triangles have corresponding sides and
(ASA, SAS, and SSS) follow from the definition
corresponding angles that are congruent.
of congruence in terms of rigid motions?
 The criteria for triangle congruence (ASA, SAS, and
 Why does SSA not work to prove triangle
SSS) follow from the definition of congruence in terms
congruence?
of rigid motions.
8/28/2015 9:56 AM
Curriculum Instruction and Professional Development Math Department
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G-GPE.A.4
2015-2016 Geometry 2nd Quarter Mathematics Scope and Sequence
G-CO.C Prove geometric theorems
Essential Concepts:
Essential Questions:
 A theorem is a statement that can be proven from
 How is a theorem different from an axiom?
previously known facts, including postulates, axioms
 What is the difference between an axiom and a
and definitions.
postulate?
 A proof is a logical argument that shows that a
 How do you know when a proof is complete and
theorem is true based on given information.
valid?
 Properties of the sides and angles of geometric figures
can be stated as theorems and proven. Several
examples are listed in the standards.
G-GPE.B Use coordinates to prove simple geometric theorems algebraically
Essential Concepts
Essential Questions
 Coordinate geometry can be used to solve simple
 How do you determine if two lines are parallel,
geometric theorems algebraically.
perpendicular or neither?
 Coordinate geometry can be used to prove that
 Given an equation of a line and a point not on the
parallel lines have the same slope and perpendicular
line, how do you write the equation of a line that
lines have opposite reciprocal slopes.
is parallel to the given line and through the given
point? Perpendicular?
 How are geometry and algebra related to each
other?
8/28/2015 9:56 AM
Curriculum Instruction and Professional Development Math Department
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