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Sequence of Concepts
Trigonometry
 Identifying sides, defining ratios in terms of
similarity, solving right triangles
 Variety of tasks in applying trigonometry
Geometry Year-Long Curriculum Guide
Third Quarter
Rationale for Sequence
Nearly three weeks are allowed for
development of trigonometry. Activity 22 is
supplemented by rich tasks in applied contexts
(angles of elevation/depression, indirect
measurement, etc.). Law of Sines and Law of
Cosines are not included in the TNCore
Geometry standards.
Area of plane figures builds on prior
knowledge in the middle grades and will be
followed by three dimensional geometry.
Prior Knowledge
Math 8: Pythagorean Theorem
Math 6: Area of triangles/quads/composite figures
Area of Plane Figures
Math 7: Circle formulas, area problem solving
 Area of triangles, quadrilaterals, and circles
(includes sector area, arc length, and radian
measure)
 Regular polygons: area, interior/exterior angles
Circles unit will be studied in Quarter Four.
Math 6: Prism volume
Three Dimensional Geometry
Book order is otherwise followed up to
Math 7: 3-D problem solving, composite solids,
 Introducing prisms, cylinders, cones, pyramids,
omitting spherical geometry lesson (36-3).
cross sections
and spheres: including nets, cross sections and
Supplemental tasks allow for deeper
Math 8: Cone, cylinder, sphere volume formulae
revolution
application in real-world problem solving.
 Volume, surface area of each solid: explaining
and using formulas, applying density
 Effects on area and volume from changing
dimensions
HCDE Math Website: Task Arcs, Tasks, and other teacher resources referenced on the pacing guide may be found at www.hcde.org.
Website Directions:
1) Log in using username and password in top right hand corner of webpage (HCDE email & password).
2) Select 6-HS Math/Teacher Resources/Geometry
Springboard Login: Textbook resources can be accessed online at http://hamiltontn.springboardonline.org
Website Directions:
1) Log in
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 1
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
2) Select Algebra 2
Teacher Notes:
Tasks, CRAs, and Assessments that previously appeared on TNCore are now located on EduTOOLBOX.org, which is a free website. Many of these tasks do not
require a user account to access. You just go to EduTOOLBOX.org. For tasks or resources in this pacing guide which show an * beside them, a user account is
necessary. To create a user account:
1. Go to EduTOOLBOX.org
2. Click on Login in the right hand corner
3. Select the Tab: Create a New Account
4. Complete the information which includes a username that you create, a password of your choice, and other additional information.
5. Once you log in with your username and password, resources with the * will be unlocked and available to the user
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 2
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
Dates
1/4 – 1/6
(3 days)
Tennessee State Standards
G-SRT.C.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.C.7: Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
in applied problems. ★
G-MG.A.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). ★
Core Material
L 22-1, L 22-2
Additional Resources
Useful Ratios
1/9 – 1/13
G-SRT.C.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.C.7: Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
in applied problems. ★
L 22-2, L 22-3,
L 22-4,
Skate Park Task*
Proving Pythagorean
Th.
1/17 – 1/20
(4 days)
G-SRT.C.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.C.7: Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
TV Size Task*
Unknown Angles
in applied problems. ★
Grade of Interstate
Task
L 30-1, L 30-2,
L 30-3
1/23-1/27
1/30-2/3
G-GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and
rectangles, e.g., using the distance formula. ★
G-MG.A.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.A.2: Apply concepts of density based on area and volume in modeling situations
(e.g., persons per square mile, BTUs per cubic foot). ★
G-CO.C.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.
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 3
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Making Right
Triangles
Evaluating
Statements about
Length and Area
Composite Area
L 31-1, L 31-2,
L 31-3
Revised
Area of Octagon and
Circle
5/29/16
Dates
2/6-2/10
Tennessee State Standards
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
G-C.A.1: Prove that all circles are similar.
G-C.B.5: 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 the constant of
proportionality; derive the formula for the area of a sector.
G-GMD.A.1: Give an informal argument for the formulas for the circumference of a circle,
area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
G-GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and
Core Material
L 32-1, L 32-2,
L 32-3,
EA 1Unit 5 p. 477
Additional Resources
Circle Pattern
Gerrymandering
rectangles, e.g., using the distance formula. ★
2/13-2/17
G-GMD.B.4: Identify the shapes of two‐dimensional cross‐sections of three dimensional
objects, and identify three‐dimensional objects generated by rotations of two‐dimensional
objects.
2/21-2/24
(4 days)
G-GMD.A.1: Give an informal argument for the formulas for the circumference of a circle,
area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
G-GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve
Review and Reteach
Day,
L 33-1, L 33-2,
L 33-3
L 34-1, L 34-2,
L 35-1
Popcorn Anyone?
Fruit Boxes
Prisms and Cyl
problems. ★
G-MG.A.1: Use geometric shapes, their measures, and their properties to describe objects
2/27-3/3
(e.g., modeling a tree trunk or a human torso as a cylinder). ★
G-MG.A.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).
G-GMD.A.1: Give an informal argument for the formulas for the circumference of a circle,
area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
G-GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve
L 35-2, L 35-3,
EA 2 Unit 5 p. 549,
L 36-1, L 36-2
Fishing for the Best
Prism
Pyramid and Cone
problems. ★
G-GMD.B.4: Identify the shapes of two‐dimensional cross‐sections of three dimensional
objects, and identify three‐dimensional objects generated by rotations of two‐dimensional
objects.
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 4
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
Dates
Tennessee State Standards
G-MG.A.1: Use geometric shapes, their measures, and their properties to describe objects
Core Material
Additional Resources
(e.g., modeling a tree trunk or a human torso as a cylinder). ★
G-MG.A.2: Apply concepts of density based on area and volume in modeling situations
3/6-3/10
3/13-3/16
(4 days)
(e.g., persons per square mile, BTUs per cubic foot). ★
G-MG.A.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).
G-MG.A.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-GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems. ★
G-GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems. ★
L 37-1, L 37-2,
EA 3 Unit 5 p. 549,
Glasses
(accompanying
lesson)
3D in 2D,
Propane Tank
Modeling with
Geometry
Ice Cream Puddle
End of Third Quarter
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 5
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
Geometry Year-Long Curriculum Guide
Fourth Quarter
Rationale for Sequence
Return to Activity 24 for circles unit to close
out the year. Suggest revisiting 32-3 for arc
length/sector area/radians. Activity 26 is
omitted given its focus on lines. Activity 28 is
omitted as parabolas are not a geometry
standard. Lessons 29-1 and 29-2 were
addressed in Quarter 1. Probability (Unit 6) is
not a tested geometry standard.
Sequence of Concepts
Prior Knowledge
Math 7: Circle circumference formula
Circles
Algebra I: Completing the square, vertex form
 Basic vocabulary of circles’ lines and segments
and their relationships
 Relationships among lines, arcs, and angles:
central, inscribed, and circumscribed angles,
inscribed triangles and quadrilaterals
 Equations of circles on the coordinate plane,
including completing the square for standard
form
 Constructing the incircle and circumcircle of a
triangle
Input from Algebra II teachers on key concepts Revisiting Algebra 1 concepts in preparation for
Algebra II Preparation
motivated discussion on which gap topics to
Algebra 2.
 Simplifying radicals, including rational
emphasize
during
post-EOC
time.
exponents
 Solving a linear system of equations
 Solving a quadratic equation (factoring,
completing the square, graphing)
HCDE Math Website: Task Arcs, Tasks, and other teacher resources referenced on the pacing guide may be found at www.hcde.org.
Website Directions:
1) Log in using username and password in top right hand corner of webpage (HCDE email & password).
2) Select 6-HS Math/Teacher Resources/Geometry
Springboard Login: Textbook resources can be accessed online at http://hamiltontn.springboardonline.org
Website Directions:
1) Log in
2) Select Algebra 2
Teacher Notes:
Tasks, CRAs, and Assessments that previously appeared on TNCore are now located on EduTOOLBOX.org, which is a free website. Many of these tasks do not
require a user account to access. You just go to EduTOOLBOX.org. For tasks or resources in this pacing guide which show an * beside them, a user account is
necessary. To create a user account:
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 6
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
1.
2.
3.
4.
5.
Go to EduTOOLBOX.org
Click on Login in the right hand corner
Select the Tab: Create a New Account
Complete the information which includes a username that you create, a password of your choice, and other additional information.
Once you log in with your username and password, resources with the * will be unlocked and available to the user
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 7
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Revised
5/29/16
Dates
3/20-3/24
3/27-3/31
4/3-4/7
4/10-4/13
(4 days)
4/17-4/21
4/24-4/28
5/1-5/5
Tennessee State Standards
Spring Break
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
G-C.A.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.
Core Material
Spring Break
L 24-1, L 24-2,
L 24-3
L 25-1, L 25-2
G-C.A.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.A.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
G-GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean
Theorem; complete the square to find the center and radius of a circle given by an equation.
G-GPE.B.4: Use coordinates to prove simple geometric theorems algebraically: prove or
disprove that the point (1,√3 ) lies on the circle centered at the origin and containing the point
(0, 2).
L 25-3, L 25-4,
EA 1 Unit 4 p. 371
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 8
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
L 32-3
(arc/sector/radian)
Secants and Tangents
(Lessons 11-16)
G-C.A.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.A.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle. Find arc lengths and areas of sectors of circles.
G-CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
Algebra II Prep: Topics include:
- simplifying radicals including rational exponents
Additional Resources
Circles in Triangles
Folding Circles
Central and Inscribed
Angles
Arc Length/Sector
Cyclic Quadrilaterals
L 27-1, L 27-2
Writing the Equation of
a Circle
Comp the Square
L 29-3,
EA 2 Unit 4 p.429,
Review and Reteach
Day
Revised
Equations of Circles and
Their Tangents
Hospital Locator
5/29/16
Dates
5/8-5/12
5/15-5/19
5/22-5/26
Tennessee State Standards
- solving a linear system of equations
solving quadratic equations (by factoring, by completing the square, and by graphing)
Alg II Prep continued
Alg II Prep continued
Alg II Prep continued
Hamilton County Department of Education
2016-2017 Geometry Year-Long Curriculum Guide
Page 9
Key:
L – Lesson (SpringBoard)
ST – Supplemental Task
EA – Embedded Assessment (SpringBoard)
Core Material
Additional Resources
End of Fourth
Quarter
Revised
5/29/16