Course: Geometry C
Department: Math
Grade(s): 9-12
Unit 7:
LEONA QSI Curriculum Map
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A,B
Essential Questions:
How are figures measured?
Measurement
(16 days)
Area/Perimeter
Measuring
Circles and
Parts of Circles
How do the formulas used to measure a figure relate to what is being
measured?
Core Content
AZCCRS Standards
(High School Standards)
= Major □ = Supporting ○= Additional ★= Modeling
○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.GPE.B.7 Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the
distance formula. (★)
Surface Area
○G.GMD.A.1 Give an informal argument for the formulas
Volume
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.
Density
○G.GMD.A.3 Use volume formulas for cylinders, pyramids,
cones, and spheres to solve problems. (★)
Measurements
with Changing
Parameters
○G.GMD.B.4 Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify three-dimensional
objects generated by rotations of two-dimensional objects.
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). (★)
Mathematical Practices
MP.1-8
Using properties of special
right triangles and trig ratios
to calculate perimeter and
area of regular polygons.
Use distance and midpoint to
compute perimeters and areas
of polygons.
Understand and apply
properties of similarity to the
parts of a circle, which may
include an introduction to
radian measurements
Calculate the arc length and
area of a sector on a circle.
Understand and apply
Cavalieri’s principle which
states that the volume will
stay the same with a right
figure and a non-right figure.
Key Vocabulary: Perimeter, Circumference, Area, Two-Dimensional, ThreeDimensional, Prism, Pyramid, Cube, Cylinder, Cone, Sphere, Hemisphere,
Volume, Surface Area, Lateral Area, Density, Intercepted Arc, Minor Arc,
Major Arc, Length of Arc, Area of Sector, Radian, Cavalier’s Principle,
Dissection, Limits
Tier 3
Assessment
Resources
Support
Identify the
names of
polygons, and
three
dimensional
figures
Formal
Find the area of
irregular shaped
polygons.
In Formal
Use nets to
determine
surface area of 3dimensional
figures.
1.
Pre Test
Quizzes
2.
http://map.mathshell.org/materials/lessons.php?t
askid=213#task213
3.
http://emergentmath.com/2012/11/08/moremath-food-blogging-i-may-need-some-helpfrom-my-southern-friends/
4.
Dan Meyer Obscure Geometry
5.
http://emergentmath.com/2012/01/07/can-wemake-an-even-edgier-brownie-pan-what-aboutthe-perfect-brownie-pan/
6.
http://fivetriangles.blogspot.com/2012/12/40dog-on-lead.html
7.
http://emergentmath.com/2011/02/18/the-pizzacasbah-30-inch-pizza-challenge/
Unit Test
Checking for
Understanding
Questioning
Completion of
Project/Activity/A
ssignments
Summarization of
Learning
Daily Exit Slip
Area and Perimeter
http://map.mathshell.org/materials/lessons.php?t
askid=212#task212
8.
Use principles such as
dissection and Cavalier’s to
derive the formulas for
circumference of a circle,
area of a circle, volume of a
cylinder, pyramid, and cone.
Derive area and volume,
surface area and lateral area
formulas for figures.
http://fawnnguyen.com/don-stewards-completequadrilateral/
Similar in Figures and Ratios of Length,
Perimeter, Area, Volume, Surface Area
9. http://www.tarleton.edu/team/documents/9to12/
geometry/geometry1_5.pdf
10. http://www.nctm.org/standards/content.aspx?id
=33195
11. http://www.nctm.org/standards/content.aspx?id
=25097
12. http://www.mathsisfun.com/geometry/polyhedr
on-models.html
Updated: 2/9/2016
Course: Geometry C
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A,B
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
problems.
Area of Sectors and Arc Length
13. http://map.mathshell.org/materials/lessons.php?t
askid=441#task441
Understand and apply density
formulas to solve problems.
14. http://musingmathematically.blogspot.ca/2012/0
7/bike-trail-task.html
Apply properties of similarity
to solve problems with 3Dimensional figures.
15. http://jdevarona.wordpress.com/2012/07/13/letthe-random-problem-ideas-begin/
Volume
16. http://map.mathshell.org/materials/lessons.php?t
askid=216#task216
17. http://mrpiccmath.weebly.com/blog/3-actsmmm-juice
18. http://mrpiccmath.weebly.com/blog/3-acts-popbox-design
19. http://mrmeyer.com/threeacts/youpourichoose/
20. http://threeacts.mrmeyer.com/popcornpicker/
21. https://s3.amazonaws.com/threeacts/dollarwall.z
ip
22. http://threeacts.mrmeyer.com/coincarpet/
23. http://threeacts.mrmeyer.com/carcaravan/
24. http://threeacts.mrmeyer.com/besttriangle/
25. https://s3.amazonaws.com/threeacts/applemothe
rship.zip
Cavalier’s Principle for Volume
26. http://education.ti.com/en/us/activity/detail?id=
0CB018E255D84C3D88F156B16F39752B&ref
=%2Fcalculators%2Fdownloads%2FUS%2FAc
tivities%2FSearch%2FSubject%3Fs%3D5022%
26sa%3D5024%26t%3D5054%26d%3D1008
27. Density
Updated: 2/9/2016
LEONA QSI Curriculum Map
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A,B
Course: Geometry C
Department: Math
Grade(s): 9-12
http://www.yummymath.com/wpcontent/uploads/cows-global-warming.pdf
28.
Unit 8:
Essential Questions:
How can figures and their measurements be used to model real objects?
Modeling
How can modeling be used to solve problems?
(14 days)
Modeling
Relationship
between Twoand ThreeDimensional
Objects
Applied
Geometry and
Design
AZCCRS Standards
= Major □ = Supporting ○= Additional ★= Modeling
○G.GMD.B.4 Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify three-dimensional
objects generated by rotations of two-dimensional objects.
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.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). (★)
Mathematical Practices
MP.1-8
Core Content
(High School Standards)
Key Vocabulary: Perimeter, Circumference, Area, Two-Dimensional, ThreeDimensional, Prism, Pyramid, Cube, Cylinder, Cone, Sphere, Hemisphere,
Volume, Surface Area, Lateral Area, Density, Intercepted Arc, Minor Arc, Major
Arc, Length of Arc, Area of Sector, Radian, Similarity, Model, Approximation,
Assumption, Net, Cross-Section, Revolution, BTU, Population Density,
Topography
Tier 3
Assessment
Resources
Support
Use technology to identify
the shapes of 2-dimensional
cross-sections of 3dimensional objects.
Lateral area
versus surface
area.
Use technology to Identify 3dimentional objects created
by revolving 2-dimensional
objects.
Identify nets for
polyhedrons,
cylinders, and
cones.
Apply surface area and
volume in a context to solve a
problem with given
constraints.
Calculate basic
surface areas
using nets
Solve problems in a context
to maximize or minimize the
dimensions of a figure.
Apply concepts of density
based on area and volume in
modeling situations (e.g.,
persons per square mile,
BTUs per cubic foot).
Formal
Pre Test
1.
2.
Quizzes
Unit Test
3.
In Formal
4.
Checking for
Understanding
Questioning
5.
Cross Sections
https://tube.geogebra.org/student/b248823
http://nlvm.usu.edu/en/nav/frames_asid_126_g_
3_t_3.html?open=instructions&from=topic_t_3.
html
http://www.shodor.org/interactivate/activities/C
rossSectionFlyer/
http://www.learner.org/courses/learningmath/ge
ometry/session9/part_c/index.html
Modeling between 2 and 3 Dimensional Objects
http://map.mathshell.org/materials/lessons.php?t
askid=428#task428
Completion of
Project/Activity/A
ssignments
6.
http://map.mathshell.org/materials/lessons.php?t
askid=439#task439
Summarization of
Learning
7.
http://www.korthalsaltes.com/
8.
http://math.arizona.edu/~models/
9.
http://mathworld.wolfram.com/topics/SolidGeo
metry.html
Daily Exit Slip
10. http://www.andrewlipson.com/mathlego.htm
Apply geometric methods to
solve design problems (e.g.,
designing an object or
Applied Geometry Models
11. http://highered.mheducation.com/sites/0072532947/st
Updated: 2/9/2016
Course: Geometry C
Department: Math
Grade(s): 9-12
LEONA QSI Curriculum Map
Teacher:
Course Group: Geometry A,B,C
Pre-Requisites: Geometry A,B
structure to satisfy physical
constraints or minimize cost;
working with typographic
grid systems based on ratios).
udent_view0/chapter9/cross-sections_of_a_cube.html
12. http://illuminations.nctm.org/Lesson.aspx?id=2
788
13. Interactive 2D Figures Rotation to form 3D
solids
http://www.shodor.org/interactivate/activities/3
DTransmographer/
Updated: 2/9/2016