Download Unit 3 - Middletown Public Schools

Middletown Public Schools
Mathematics Unit Planning Organizer
Grade/Course Geometry
16 instructional days (+4 reteaching/extension)
Duration
Subject
Unit 3
Mathematics
Polygons
Big Idea
One can draw reasonable conclusions from repeated observations, and it may be necessary to justify those conclusions using a logical
argument.
Logical arguments require a bank of pre-requisite concepts, skills and definitions and the ability to link them together, such that if one
thing is true, another must be true.
How does one make and support a reasonable conclusion regarding a problem?
How do previous understandings impact the process of making a logical argument?
Essential
Question
Mathematical Practices
Practices in bold are to be emphasized in the unit.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Domain and Standards Overview
Prove geometric theorems.
Make geometric constructions.
Geometry, Unit 3 Polygons
2014
1
Revised November 18,
Priority and Supporting Common Core State Standards
Bold Standards are Priority
CC.9-12.G.CO.10 Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle sum to 180 degrees;
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.
Explanations and Examples
Students may use geometric simulations (computer software or graphing
calculator) to explore theorems about triangles.
(See GSP Triangle Sum Lab)
CC.9-12.G.CO.11 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.
Students may use geometric simulations (computer software or graphing
calculator) to explore theorems about parallelograms.
CC.9-12.G.CO.13 Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
Students may use geometric software to make geometric constructions.
(See Proving Quadrilateral Properties (1))
(See GSP Lab – Constructing Regular Polygons)
Concepts
What Students Need to Know
● theorems about triangles
Skills
What Students Need to Be Able to Do
● PROVE
● theorems about parallelograms
● PROVE
Geometry, Unit 3 Polygons
2014
Bloom’s Taxonomy Levels
Depth of Knowledge Levels
5
5
2
Revised November 18,
Standard
Learning Progressions
The standards below represent prior knowledge and enrichment opportunities for standards in this unit.
Pre-requisite Skills
Accelerated Learning
CC.9-12.G.CO.10 Prove theorems
about triangles. Theorems include:
measures of interior angles of a
triangle sum to 180 degrees; 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.
CC.9-12.G.CO.11 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.
CC.9-12.G.CO.13 Construct an
equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
Geometry, Unit 3 Polygons
2014
Understand and apply the Pythagorean Theorem.
8.G.6-8
Use coordinates to prove simple geometric theorems
algebraically. G.GPE.4-7
Draw, construct, and describe geometrical figures
and describe the relationships between them.
7.G.1-3
Use coordinates to prove simple geometric theorems
algebraically. G.GPE.4-7
Draw, construct, and describe geometrical figures
and describe the relationships between them.
7.G.1-3
3
Revised November 18,
Unit Assessments
Performance Task
Common Formative Assessment
Geometry, Unit 3 Polygons
2014
G.CO.11
4
Revised November 18,