Download Unit Map 2012-2013 - The North Slope Borough School District

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Unit Map 2012-2013
North Slope Borough School District
Collaboration / Geometry* (District Macro)
/ Grade 10 (North Slope Borough School District)
Monday, September 17, 2012, 4:48PM
Quarter 4 (Week 28, 10 Weeks)
Unit Description
Type Author Name:
Michael Lancaster
Robbin Stockton
Samantha Leavitt
Stage 1: Desired Results
ILF Overarching Understandings/Essential Questions
ILF Performance Expectations
Alaska State Standards
State Standards & GLEs
2012 ELA and Math Standards
Mathematics (2012), HS: Geometry, Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to
develop in their students.
1.
2.
3.
4.
5.
6.
7.
8.
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.
Mathematics (2012), HS: Geometry, Congruence
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G - CO Experiment with transformations in the plane.
G-CO.1. Demonstrates understanding of key geometrical definitions, including angle, circle, perpendicular line, parallel line,
line segment, and transformations in Euclidian geometry. Understand undefined notions of point, line, distance along a line, and
distance around a circular arc.
G - CO Make geometric constructions.
G-CO.13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Mathematics (2012), HS: Geometry, Similarity, Right Triangles, and Trigonometry
G - SRT Prove theorems involving similarity.
G-SRT.5. Apply congruence and similarity properties and prove relationships involving triangles and other geometric figures.
G - SRT Define trigonometric ratios and solve problems involving right triangles.
G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
G - SRT Apply trigonometry to general triangles.
G-SRT.9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
G-SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G-SRT.11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and
non-right triangles (e.g., surveying problems, resultant forces).
Mathematics (2012), HS: Geometry, Circles
G - C Understand and apply theorems about circles.
G-C.1. Prove that all circles are similar.
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central,
inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to
the tangent where the radius intersects the circle.
G-C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
G-C.4. (+) Construct a tangent line from a point outside a given circle to the circle.
G - C Find arc lengths and areas of sectors of circles.
G-C.5. Use and apply the concepts of arc length and areas of sectors of circles. Determine or derive using similarity the fact
that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as
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the constant of proportionality; derive the formula for the area of a sector. Expressing Geometric Properties with Equations
Mathematics (2012), HS: Geometry, Geometric Measurement and Dimension
G - GMD Explain volume formulas and use them to solve problems.
G-GMD.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid
figures.
Mathematics (2012), HS: Geometry, Modeling with Geometry
G - MG Apply geometric concepts in modeling situations.
G-MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).*
G-MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per
cubic foot).*
G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios).*
Content Area Understandings & Essential Questions
Content Area OUs & EQs
Topical Understandings & Essential Questions
Knowledge
Student will know...
Skills
Students will be able to...
Stage 2: Assessment Evidence
Transfer Task(s) (Performance Assessments)
At least one assessment in GRASPS form.
Evaluative Criteria
Other Evidence (Graded)
Stage 3: Learning Plan
Learning Experiences (in order of implementation)
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Checking for Understanding (Ungraded)
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Resources and Preparation Materials
Last Updated: Thursday, August 9, 2012, 2:35PM
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