Download Unit 3 - Cabarrus County Schools

Unit #: 3
Subject(s): Math 3
Grade(s): 9-12
Designer(s): Megan Bell, Karen Mullins, Kristen Fye, Ashley Pethel,
Christy Bentley, Elizabeth Smith
PREAMBLE
This unit will allow students to build on their knowledge of triangle congruence from Math 2 by discussing and proving if objects are parallelograms, and then
rectangles. Students will explore points of concurrency. Students will build on their knowledge of geometric proof, and extend to flow and paragraph proof.
Note – a conscious decision was made to not put all of the geometry units together as it was thought this would not be an integrated approach. Only Honors
will explore the orthocenter as a point of concurrency. Teachers will need discuss two column proofs in Math 3 for the 2016-2017 school year as they were
not covered previously in Math 2.
Note: Similarity is in Math 2.
STAGE 1 – DESIRED RESULTS
Unit Title: Modeling with Geometry
Transfer Goal(s): Students will be able to independently use their learning to recognize patterns in two dimensional and three dimensional figures.
Enduring Understandings:
Students will understand that…
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All parallelograms share common properties.
Two triangles can be proved congruent with only 3 congruent pieces
in a valid way.
Points of concurrency create specific properties for the triangles they
are created for.
An object can be sliced vertically, horizontally, and diagonally to
create 2D cross-sections.
Proofs are a way to demonstrate valid mathematical reasoning.
Students will know:
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Lines and point of concurrency vocabulary: medians (centroid),
perpendicular bisector (circumcenter), angle bisector (incenter)
Properties of parallelograms: opposite sides and angles are congruent,
diagonals bisect each other, if diagonals are congruent then it is a
rectangle
Methods of proving triangles congruent
Special angles created by parallel lines cut by a transversal
Density is a proportional unit of measure
Essential Questions:
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Why is it important to include every logical step in a proof?
What is the best way to write a proof?
Where is the point of concurrency in a triangle?
How do geometric relationships and applications of measurements
help us solve real world problems?
Why are units important?
Students will be able to:
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Write a flow proof and/or paragraph proof proving a quadrilateral as a
parallelogram.
Model problems with geometry.
Explore the lines of concurrency and their points of concurrency.
Prove two figures are congruent with mathematical reasoning.
Recognize repeated patterns for geometric figures.
Use density for decision making in real world situations.
Identify cross-sections of 3D figures as 2D objects.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
1
Unit #: 3
Subject(s): Math 3
Grade(s): 9-12
Designer(s): Megan Bell, Karen Mullins, Kristen Fye, Ashley Pethel,
Christy Bentley, Elizabeth Smith
STAGE 1– STANDARDS
Common Core State Standards
NC.M3.G-CO.10
Verify experimentally properties of the centers of triangles (centroid, incenter,
and circumcenter).
NC.M3.G-CO.11
Prove theorems about parallelograms.
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Opposite sides of a parallelogram are congruent.
Opposite angles of a parallelogram are congruent.
Diagonals of a parallelogram bisect each other.
If the diagonals of a parallelogram are congruent, then the parallelogram
is a rectangle.
NC.M3.G-CO.14
Apply properties, definitions, and theorems of two-dimensional figures to prove
geometric theorems and solve problems.
NC.M3.G-GMD.3
Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to
solve problems.
NC.M3.G-GMD.4
Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
NC.M3.G-MG.1
ACT Standards
Apply geometric concepts in modeling situations
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Use geometric and algebraic concepts to solve problems in modeling
situation:
Use geometric shapes, their measures, and their properties, to model
real-life objects.
Use geometric formulas and algebraic functions to model relationships.
Apply concepts of density based on area and volume.
Apply geometric concepts to solve design and optimization problems.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
2