Download MLHS-Geometry

Geometry
Topic Outline
Course Description and Philosophy
This course in geometry covers the basic concepts of plane, solid, coordinate, and some analytic geometry stressing
deductive proof and reasoning. Throughout the year, the properties learned in algebra are re-introduced into this course.
Moving towards formal mathematical arguments, the standards presented in this high school geometry course are meant
to formalize and extend middle grades geometric experiences. Transformations are presented early in the year to assist
with the building of conceptual understandings of the geometric concepts. The aims and objectives of the course are to
develop and show the value of the logic of deductive reasoning and to improve and increase the understanding and
application of the terminology, the symbolism, and the structure of mathematics. It is designed to develop the student’s
ability to think creatively and critically in both mathematical and non-mathematical situations. The student will be
shown how the analysis of data collected through the observation and measurement of geometric figures can lead to a
formal statement of a geometric relationship. This course will deepen a student’s understanding of two- and threedimensional figures and their properties and allow them to use these ideas in real-world situations. The course has been
updated to meet the 2010 Common Core Math Standards of High School Geometry
http://www.corestandards.org/Math/Content/HSG/GPE
Teacher Resources:




Illustrative Mathematics Content Standards: High School http://www.illustrativemathematics.org/standards/hs
The Teaching Channel (Common Core Math Channel)
https://www.teachingchannel.org/videos?page=1&categories=subjects_math,topics_common-core&load=1
Flipped Classroom resources including Khan Academy Geometry https://www.khanacademy.org/math/geometry and HippoCampus
Geometry http://www.hippocampus.org/Algebra%20%26%20Geometry
The Mathematics Common Core Toolbox (http://ccsstoolbox.agilemind.com/resources_samples.html) has both sample scope and sequence
documents as well grades 4-12 PARRC assessment tasks.
Text Reference:

Carter, Cuevas, Day, Malloy, and Cummins, Geometry, copyright 2010 by Glencoe/McGraw-Hill, Columbus, OH.
REVISED 2013
1
Unit I: Congruence, Proof, and Construction
Essential Questions: How do the fundamentals of geometry enhance inductive reasoning? How do rigid motion and
formal constructions establish the triangle congruence conditions?
Objectives: Students will be able to:
 Make sense of problems and persevere in solving them.
o SLO 5 Plan a pathway to prove theorems about lines, angles, triangles, and parallelograms.)
 Reason abstractly and quantitatively.
o SLO 4 Know and use properties of rigid transformations in proofs involving lines, angles, triangles, and parallelograms.)
 Construct viable arguments and critique the reasoning of others.
o SLO 5 Build a logical progression of statements to prove conjectures about lines, angles, triangles, and parallelograms.)
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
o SLO 1 Use precise language in the definitions of angles, circles, parallel lines, perpendicular lines and line segments.)
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning
2
Unit I: Topic/Content Skills
Topic 1: Use the undefined
notion of a point, line, distance
along a line and distance around
a circular arc to develop
definitions for angles, circles,
parallel lines, perpendicular lines
and line segments.
Topic 2: Apply the definitions of
angles, circles, parallel lines,
perpendicular lines and line
segments to describe rotations,
reflections, and translations.
Topic 3: Develop and perform
rigid transformations that include
reflections, rotations, translations
and dilations using geometric
software, graph paper, tracing
paper, and geometric tools and
compare them to non-rigid
transformations.
Assessment
Test/Quizzes
Homework
Class Participation
Projects
Resources
Text
Manipulatives
Instructional Method
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Tech Infusion
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
CCS: Unit 1
G.CO.1
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
G.CO.1,
G.CO.4
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Topic 4: Use rigid
transformations to determine,
explain and prove congruence of
geometric figures.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Topic 5: Create proofs of
theorems involving lines, angles,
triangles, and parallelograms.
(Please note G.CO.10 will be
addressed again in unit2 and
G.CO.11 will be addressed again
in unit 4)
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
G.CO.2,
G.CO.3,
G.CO.4,
G.CO.5
BYOD Assessment see
Teaching Channel Video
http://goo.gl/jxPcY
3
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.CO.6,
G.CO.7,
G.CO8
G.CO.9,
G.CO.10,
G.CO.11
Topic 6: Generate formal
constructions with paper folding,
geometric software and
geometric tools to include, but
not limited to, the construction of
regular polygons inscribed in a
circle.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.CO.12,
G.CO.13
Differentiated Learning Activities
Strategic learner: The students will label two index cards with points and lines and cut each halfway. They will then slide the cards together to
model intersections of planes, lines, and coplanar lines. Advanced learner: Using Geometer’s Sketchpad, the students will construct intersecting
lines. They will measure the angles formed and calculate the sum of the adjacent angles. They can move the lines to a different position and
repeat the process. Reteach: If students need extra support, then strategies from this Teaching Channel video, “Discovering the Properties of
Quadrilaterals” may be employed. https://www.teachingchannel.org/videos/geometry-lesson-quadrilaterals?fd=1
Ethical Decision Making/Character Education: Students are given four measures of a music staff. The students determine whether the
combination of notes and/or rests form a frieze pattern. If so, they classify the frieze pattern. The students discuss the importance of music in
schools, and the relationship between music and mathematics.
21st Century Skills: Collaboration & Communication. Have students form collaborative groups that rotate station to station learning geometric
transformations. Use the Teaching Channel video Carousel Activity: Rotating through Geometry Stations to see how this strategy increases
student engagement and productivity. https://www.teachingchannel.org/videos/carousel-activity-math-lesson
4
Unit II: Similarity and Proof
Essential Questions: How are proportions used to solve geometric problems? How will the understanding of dilations and proportional
reasoning help to develop a formal understanding of similarity?
Objectives: Students will be able to:
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
o SLO 1 Proof of the similarity of specific circles used to reason about the similarity of all circles.
 Construct viable arguments and critique the reasoning of others.
o SLO 5 Construct proofs about triangles using assumptions, definitions, and previously established theorems.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
o SLO 3 Use the definition of rigid transformations to determine if two figures are similar.
 Look for and express regularity in repeated reasoning.
5
Unit II: Topic/Content Skills
Topic 1: Generate proofs that
demonstrate that all circles are
similar.
Assessment
Test/Quizzes
Homework
Class Participation
Projects
Resources
Text
Manipulatives
Instructional Method
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Tech Infusion
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
CCS: Unit 2
G.C.1
Topic 2: Justify the properties of
dilations given by a center and a
scale factor. A dilation takes a line
not passing through the center of
the dilation to a parallel line, and
leaves a line passing through the
center unchanged (the dilation of a
line segment is longer or shorter in
the ratio given by the scale factor).
Topic 3: Given two figures, use
the definition of similarity in terms
of similarity transformations to
decide if they are similar; explain
using similarity transformations
the meaning of similarity for
triangles as the equality of all
corresponding pairs of angles and
the proportionality of all
corresponding pairs of sides.
Topic 4: Use the properties of
similarity transformations to
establish the AA criterion for two
triangles to be similar.
Topic 5: Prove theorems about
triangles.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.SRT.2
Test/Quizzes
Homework
Class Participation
Projects
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
G.SRT.3
G.SRT.1
Exit Cards: see video
http://goo.gl/JcPAo
Text
Manipulatives
6
G.CO.10,
G.SRT.4
Differentiated Learning Activities
Strategic learner: The students can use Geometer’s Sketchpad to determine if a biconditional statement is true or false by testing both the
statement and its converse. Advanced learner: Students design a hole of a mini-golf course that requires the ball to hit one or two walls. The
students draw at least one possible path to the hole using similar triangles that would result in a hole-in-one.
Ethical Decision Making/Character Education: Students find conditional statements in the school’s honor code and write the converse of each
statement. The students will determine if the conditional statement and the converse are biconditional. The teacher will review the importance of
the honor code and academic integrity.
21st Century Skills: ICT (Information Communication technology) Provide more time for students to reason with dynamic 3D geometry
software. Use the Teaching Channel video Using Technology for Hard-to-Teach Concepts to learn how the master teacher differentiates for 3
different groups; uses Geometry software to increase efficiency and allow more time to address reasoning skills; and inspires to students use
concrete objects in conjunction with calculators to explore quadratics. https://www.teachingchannel.org/videos/technology-and-geometry?fd=1
Unit III: Trigonometry
Essential Questions: How does similarity apply to right triangles? What is right triangle trigonometry? How can we calculate the
missing measures in all triangles – not just right triangles? How is trigonometry used to solve real-life problems?
Objectives: Students will be able to:
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique the reasoning of others.
o SLOs 3 Justify solutions to problems involving side lengths and angle measures using triangle congruence and similarity criteria.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
o SLO 4 Demonstrate the need for precision when deriving definitions.
 Look for and make use of structure.
o SLO 8 Look for hidden structures to prove and apply the law of Sines and Cosines.
 Look for and express regularity in repeated reasoning.
7
Unit III: Topic/Content Skills
Topic 1: Find the point on a directed
line segment between two given
points that partitions the segment in a
given ratio.
Topic 2: Prove theorems about
triangles.
Assessment
Test/Quizzes
Homework
Class Participation
Resources
Text
Manipulatives
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Topic 3: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
Topic 4: Derive the definitions for
trigonometric ratios using similarity
of right triangles.
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Topic 5: Explain and use the
relationship between the sine and
cosine of complementary angles.
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Topic 6: Use trigonometric ratios
and the Pythagorean Theorem to
solve right triangles in applied
problems.
Topic 7: Derive and use the formula
for the area of an oblique triangle
(A = 1/2 ab sin (C)).
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Topic 8: Prove and apply the Laws
of Sines and Cosines to solve
problems involving both right and
oblique triangles.
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
8
Instructional Method
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Tech Infusion
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
CCS: Unit 3
G.GPE.6
G.SRT.4
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
G.SRT.9
G.SRT.10,
G.SRT.11
Differentiated Learning Activities
Strategic learner: A triangle is drawn over a map of Honduras. Using the measurements of the triangle, students approximate the area of
Honduras. Advanced learner: Students use Geometer’s Sketchpad to solve a real-life problem involving vectors. For example, the students are
given the coordinate of a boat’s starting point, the speed of the boat, and the speed and direction of the wind. The students find the boat’s new
speed and the angle at which the boat has been blown off course.
21st-Century Skills: Students learn about the use of mathematics in other cultures. They recognize the contributions to mathematics from a
variety of cultures and the needs that led to those contributions. EXAMPLE: Students create a website about the history of trigonometry,
focusing on how advancements emerged from practical interests, such as the quest for astronomical measurements, the need to find ways of telling
time, and the importance of cartography and navigation tools. Working in groups, each team of students focuses on a different part of the website:
One group prepares a report on the development of sine, cosine, and versine in India and how these concepts developed from Indian astronomy.
Another group focuses on the further development of trigonometry in the Islamic world and the contributions of Abu Wafa in the 10th century
C.E. A third group focuses on work of Al-Biruni the 11th century, including his demonstration of the tangent formula. A fourth group reports on
how the work of Jabir Ibn Aflah helped spread trigonometry to Europe in the 13th century.
Unit IV: Circles and Expressing Geometric Properties through Equations
Essential Questions: How are circles connected to other geometric properties and figures? How can the rectangular coordinate system be
used to verify geometric properties and solve geometric problems? How is similarity used to establish the relationship among segments
on chords, secants and tangents as well as to prove basic theorems about circles?
Objectives: Students will be able to:
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
 Use the slope criterion for parallel and perpendicular lines to create symbolic representations and manipulate the symbols to solve
geometric problems.
 Construct viable arguments and critique the reasoning of others.
 Model with mathematics.
o SLO 7 Use the coordinate plane to draw models of figures used in proofs.
o SLO 8 Present visual models of polygons on the coordinate plane prior to applying the distance formula.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning
9
Unit IV: Topic/Content Skills
Topic 1: 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.
Assessment
Test/Quizzes
Homework
Class Participation
Projects
Resources
Text
Manipulatives
Instructional Method
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Tech Infusion
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
CCS: Unit IV
G.C.2
Topic 2: Prove the properties of
angles for a quadrilateral
inscribed in a circle and construct
inscribed and circumscribed
circles of a triangle, and a tangent
line to a circle from a point
outside a circle, using geometric
tools and geometric software.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.C.3, G.C.4
Topic 3: Use similarity to show
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.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.C.5
Topic 4: 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.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.GPE.1
10
Topic 5: Prove the slope criteria
for parallel and perpendicular
lines and use them to solve
geometric problems (e.g. find the
equation of a line parallel or
perpendicular to a given line that
passes through a given point.)
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
G.GPE.5
Topic 6: Construct formal proofs
using theorems, postulates, and
definitions involving
parallelograms.
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
G.CO.11
Topic 7: Use coordinates to
prove simple geometric theorems
algebraically.
Test/Quizzes
Homework
Class Participation
Projects
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources
Topic 8: Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula.
Text
Manipulatives
G.GPE.4
G.GPE.7
Differentiated Learning Activities
Strategic learner: The students make an origami figure out of a square piece of graph paper. The students then unfold the paper and find the
slope of each fold. Advanced learner: Students are given a passage to read about the Apollo 13 spacecraft mission. The students are also given a
diagram of the relationship between the Apollo 13 capsule and the Earth labeled with important points and angles. The students use the diagram
to find various arc and angle measures such as the angle of reentry that brought the crew home safely on that unforgettable day.
21st-Century Skills: Students identify and ask significant questions about mathematics and engage in analyzing each others’ answers.
EXAMPLE: The class divides into two groups. In one group, students use a piece of string and a ruler to measure the circumference (c) and
diameter (d) of circular objects, such as the lid of a jar, the face of a clock, or a pie plate. For each object measured, they calculate c/d. Then they
calculate the average of each result to come up with an approximate value for pi. In the other group, students use the method developed by
Archimedes, using inscribed and circumscribed polygons. Students compare the two groups’ results. They recognize that pi is an irrational
number, so it cannot be measured precisely. Then they research how people in different cultures have tried to calculate pi from ancient to modern
times.
11
Unit V: Extending to Three Dimensions
Essential Questions: How are two-dimensional objects used to explain, visualize, and apply geometric concepts to threedimensional objects? Where are volume and surface area used in real-life?
Objectives: Students will be able to:
 Make sense of problems and persevere in solving them.
o SLO 2 Use concrete models to solve problems involving volume formulas.
o SLO 6 Analyze givens, constraints, relationships and goals presented in a design problem.
 Reason abstractly and quantitatively.
o SLO 1 Using informal arguments related to a specific circle to justify the general statement given as formula for all circles.
 Construct viable arguments and critique the reasoning of others.
 Model with mathematics.
o SLO 3 Use models of 3-D objects to examine the characteristics of their 2-D cross-sections.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.
12
Unit V: Topic/Content Skills
Topic 1: Develop informal
arguments to justify 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).
Topic 2: Solve problems using
volume formulas for cylinders,
pyramids, cones, and spheres.
Assessment
Test/Quizzes
Homework
Class Participation
Projects
Resources
Text
Manipulatives
Instructional Method
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Tech Infusion
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
CCS: Unit V
G.GMD.1
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
G.GMD.3
Topic 3: Identify the shape of a
two-dimensional cross-section of a
three-dimensional figure and
identify three-dimensional objects
created by the rotation of twodimensional objects.
Topic 4: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling
a tree trunk or a human torso as a
cylinder).
Topic 5: Use density concepts in
modeling situations based on area
and volume. (e.g., persons per
square mile, BTUs per cubic foot).
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
G.MG.1
Test/Quizzes
Homework
Class Participation
Projects
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Topic 6: Solve design problems
using geometric methods. (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios).
Test/Quizzes
Homework
Class Participation
Text
Manipulatives
Lectures
Hands-On Activities
Lab Work
Group Collaboration
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Geometer’s Sketchpad
Scientific Calculator
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Project: NCSM Great
Task The Tipi -
Geometry
13
G.GMD.4
G.MG.2
G.MG.3
Differentiated Learning Activities
Strategic learner: The students will read a passage on The Great Pyramid in Giza. They will use the geometric formulas and procedures learned
in this unit to solve problems based on this passage. Advanced learner: The students will each bring in a box from home. They will find the
measurements, surface area, and volume of the box. The students will divide the measurements in half and create a box with these measurements.
They will then find the surface area and volume of their new box. This activity will shows that when the measurements of a prism are cut in half,
it does not necessarily mean the surface area and volume will also be cut in half. Using technology: This video, Using Technology for Hard-toTeach Concepts, demonstrates how teachers can provide more time for reasoning with dynamic 3D geometry software.
https://www.teachingchannel.org/videos/technology-and-geometry
21st-Century Skills: Students make sense of applied mathematical problems through analysis and synthesis of evidence, and persevere in solving
problems. EXAMPLE: Students read about the mathematics of three-dimensional maps that a team of researchers has designed for measuring the
environmental value of open space areas with no roads (http://www.sciencenews.org/view/generic/id/8519/title/Math_Trek__Miles_from_Nowhere). Students
then explore current policies pertaining to conserving roadless areas, such as the controversial “Roadless Rule” and determine how the
mathematical maps could be used to improve policies for conserving open space. They craft a letter to their congressional representative or
another policymaker explaining their analysis.
Possible PBL Assessment: What will schools look like in 2050? Students in Eeva Reeder's math class apply geometry to find out!
According to the Edutopia website, "Every spring at Mountlake Terrace High School, near Seattle, students in Eeva Reeder's geometry classes
work feverishly to complete an architectural challenge: Design a 2,000-student high school to meet learning needs in 2050, fitting it on a given
site. In a period of six weeks, students must develop a site plan, a scale model, floor plans, a perspective drawing, a cost estimate, and a written
proposal. They must then make an oral presentation to local school architects who judge the projects and 'award' the contract -- all making use of
geometric and mathematical concepts. (Read this Edutopia.org outline of the project, which includes several Edutopia videos that profile studentarchitect teams.)" YOUTUBE CLIP: https://www.youtube.com/watch?feature=player_embedded&v=hxufdpcfpJY
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