Download 3rd 9 weeks

2016.17, Geometry, Quarter 3
The following practice standards will be used throughout the quarter:
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.
Ongoing Standards
Note to Teachers: The following ongoing and fluency standards will be practiced all year long and embedded into your instruction instead
of being taught in isolation.
G.WCE.1 I can use correct notation to describe and name all geometric figures.
G.WCE.2 Correctly interprets geometric diagrams and determines what can and cannot be assumed.
G.WCE.3 I can explain the meaning of the symbols in the formulas.
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
*Unless otherwise noted, all resources are from the HMH Geometry 2015 edition.
Standards
Student Friendly “I Can” Statements
Unit 5 Trigonometry
G.SRT.6 Understand that by similarity, side ratios in right
I can use properties of similar right triangles to form the definitions of
triangles are properties of the angles in the triangle, leading to
trigonometric ratios for acute angles.
definitions of trigonometric ratios for acute angles.
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G.SRT.7 Explain and use the relationship between the sine and
cosine of
complementary angles.
I can calculate sine and cosine ratios for acute angles in a right triangle
when two side lengths are given.
I can explain and use the relationship between the sine of an acute angle
and the cosine of its complement.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem
to solve right triangles in applied problems.
I can use the Pythagorean Theorem to solve for unknown side length of a
right triangle.
I can draw right triangles that describe real world problems and label the
sides and angles with their given measures.
WCE.G.16 Apply the geometric mean to right triangles.
WCE.G.17 Prove the Pythagorean Theorem using triangle
similarity
WCE.G.18 Make use of the converse of the Pythagorean
Theorem, Pythagorean triples and special right triangles and use
them to solve problems.
I can solve application problems involving right triangles, including angle of
elevation and depression, navigation and surveying, using the Pythagorean
Theorem and trigonometry.
I can use the geometric mean to find parts of a right triangle with an
altitude drawn to the hypotenuse.
I can prove the Pythagorean Theorem using triangle similarity.
I can use the converse of the Pythagorean Theorem to determine if a
triangle is acute, obtuse, or right.
I can list the common Pythagorean triples.
I can solve right triangles including special right triangles (such as 30-60-90
and 45-45-90) by finding the measures of all sides and angles in the
triangles.
Unit 7- Measurement and Modeling in Two and Three Dimensions
G.GMD.1 Give an informal argument for the formulas for the
I can define 𝜋 as the ratio of a circle’s circumference to its diameter.
circumference of a circle, area of a circle, volume of a cylinder,
I can use algebra to demonstrate that because 𝜋 is the ratio of a circle’s
pyramid, and cone. Use dissection arguments, Cavalieri’s
circumference to its diameter that the formula for a circle’s circumference
principle, and informal limit arguments.
must be C = 𝜋 ∙ d.
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G.GMD.3 Use volume formulas for cylinders, pyramids, cones,
and spheres to solve problems.
I can develop formulas to calculate the volumes of 3-D figures including
spheres, cones, prisms, and pyramids.
WCE.G.21 Use the similarity ratio between two solids to find the
volume.
I can use the similarity ratio between two solids to find the volume.
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).
I can use geometric shapes, their measures and their properties to
describe objects.
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).
I can apply the concept of density when referring to situations involving
area and volume.
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).
I can apply geometric methods to solve design problems.
WCE.G. 8 Find the lateral area and surface area of threedimensional figures.
I can find the surface area of prisms, cylinders, pyramids, spheres and
cones.
I can describe the difference between lateral and surface area.
Honors Addendum
Note for Teachers of Honors: Do not teach this Honors
Addendum at the end of the quarter. Embed the Honors
Addendum within the regular Scope & Sequence.
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.
I can derive the formula, A = ½ absin(C), for the area of a triangle.
I can calculate the area of a triangle using the formula A=1/2absin(C)
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G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them
to solve problems.
I can derive the Law of Sines.
I can use the Law of Sines to solve real world problems.
I can derive the Law of Cosines.
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).
I can use the Law of Cosines to solve real world problems.
I can distinguish between situations that require the Law of Sines or the
Law of Cosines.
I can represent real world problems with diagrams of right and non-right
triangles and use them to solve for unknown side lengths and angle
measures.
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