Download Plainfield Public Schools Mathematics Rigorous Curriculum Design

1
Plainfield Public Schools
Mathematics
Rigorous Curriculum Design
Unit Planning Organizer
Grade/Course
Unit of Study
Pacing
Dates
Geometry
Unit 1 Congruence, Proof, and Construction
7 week / 2 weeks for reteaching or enrichment
September 3 – October 25,2013
Standards for Mathematical Practice
CCSSM Mathematical Practices
 Practices that apply to the unit:
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MP1.
MP2.
MP3.
MP4.
MP5.
MP6.
MP7.
MP8.
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.
Look for and express regularity in repeated reasoning.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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UNIT STANDARDS
G.CO.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.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.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.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.
G.CO.10 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.
G.CO.11 Prove theorems about parallelograms. 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.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
3
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
FOCUS STANDARD:
G.CO.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.
Use
geometric descriptions of rigid
2
motions to transform figures
effect of a given rigid motion on a
Predict
given figure
Apply
definition of congruence in terms
of rigid motions to decide if they
are congruent
4
3
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.CO.7 Use the definition of congruence in terms of rigid motions show
that two triangles are congruent if and only if corresponding pairs of sides
and corresponding pairs of angles are congruent
Use
definition of congruence in terms
2
of rigid motions show that two
triangles are congruent if and only
if corresponding pairs of sides
and corresponding pairs of angles
are congruent
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
4
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and
SSS) follow from the definition of congruence in terms of rigid motions.
Explain
how the criteria for triangle
2
congruence (ASA, SAS, and
SSS) follow from the definition of
congruence in terms of rigid
motions.
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.CO.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.
Prove
theorems about lines and angles
3
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.CO.10 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 triangles
3
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
5
Unit Vocabulary Terms
“Unwrapped” Focus Standards Concepts
● Angle
● Triangle
● Congruent
Figures
● Corresponding
Parts
● Leg of a Triangle
● Hypotenuse
●
●
●
●
●
●
●
●
Circle
Perpendicular Line
Parallel Line
Line Segment
Point
Distance
Arc
Plane
Essential Questions
How may triangles be proven congruent?
How are vertical angles used to prove
triangles congruent?
What is special about a Perpendicular
Bisector?
Supporting Standards
Concepts and
Other Unit-Specific Terms
● Translations
● Transformed Figure
● Sequence of
Transformations
● Transformations
● Rotations
● Reflections
● Image
Corresponding Big Ideas
In unit 1, triangle congruence conditions
are established using analysis of rigid
motion and formal constructions. Various
formats will be used to prove theorems
about angles, lines, triangles and other
polygons
A rigid motion is a transformation of points
in space consisting of a sequence of one
or more translations, reflections, and/or
rotations. Rigid motions are assumed to
preserve distances and angle measures.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.