Download Copy of Plainfield Public Schools Math Curriculum UNIT 1 v2.docx

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Plainfield Public Schools
Mathematics
Rigorous Curriculum Design
Unit Planning Organizer
Grade/Course
Unit of Study
Pacing
Geometry
Trigonometry
7 week ,
Standards for Mathematical Practice
●
MP1.
MP2.
MP3.
MP4.
MP5.
MP6.
MP7.
MP8.
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.
●
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
2
UNIT STANDARDS
G.GPE.6 Find the point on a directed line segment between two given points that partitions
the segment in a given ratio.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures
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.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.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
3
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
Focus Standard:
G.GPE.6 Find the point on a directed line segment between two given
points that partitions the segment in a given ratio.
Find
Line segment
1
ratio
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
Focus Standard:
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to
one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
Prove
Triangle
4
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
Focus Standard :
G.SRT.5 Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures
Use
congruence and similarity
2
Solve
problem
3
Prove
relationship
4
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4
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
Focus Standard:
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.
Understand
Right triangle
1
Trigonometric ratios
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
Explain and use
sine and cosine of complementary 2
angles.
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve
right triangles in applied problems.★
Use
trigonometric ratios and the
Pythagorean Theorem
2
“Unwrapped” Skills
“Unwrapped” Concepts
DOK
(students need to be able to do)
(students need to know)
Levels
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.
4
Derive
area of a triangle
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
5
“Unwrapped” Focus Standards Concepts
Laws of Cosine
Laws of Sines
Area of Triangle
Cosecant
Secant
Cotangent
Angle of elevation
Angel of depression
Pythagorean Theorem
Trigonometric Ratios
Perpendicular Lines
Right Angles
Congruent
Similarity
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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Essential Questions
When a tv picture is forced to fill a screen
why may the picture be distorted?
Corresponding Big Ideas
Proportions are used to identify similar
polygons
How can a coordinate grid be used to model Properties of similar polygons may be used
and describe trigonometric ratios?
to solve problems.
How do the angles of two similar triangles
compare?
You may determine triangles similar using
AA, SSS and SAS.
Proportional relationships of corresponding
angle bisectors, altitudes and medians in
similar triangles may be used to solve
problems.Scale factors are used to interpret
and solve problems
How do you find a side length or angle
measure in a right triangle?
Certain right triangles have properties that
allow their side lengths to be determined
without using the Pythagorean Theorem
The angles of elevation and depression are
the acute angles of right triangles formed by
a horizontal distance and a vertical height
How are the Pythagorean Theorem and
special right triangle rules used to find the
lengths of the sides of right triangles?
The Pythagorean Theorem and special right
triangle rules are used to find the lengths of
the sides of right triangles.
How do trigonometric ratios relate to similar There are three trigonometric functions that
are used to find the lengths and angle
right triangles?
measures of right triangles.
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7
Engaging the Learner
The Hopewell people were Native Americans whose culture flourished in the central Ohio
Valley about 2000 years ago. They constructed earthworks using right triangles. The bestsurviving features of the Hopewell Tradition era are mounds built for uncertain purposes.
Great geometric earthworks are one of the most impressive Native American monuments
throughout American prehistory. Eastern Woodlands mounds have various geometric
shapes and rise to impressive heights. The function of the mounds is still under debate. Due
to considerable evidence and surveys, plus the good survival condition of the largest
mounds, more information can be obtained. Earthworks were built for various purposes by
heaping earth in piles and shaping them. Some of the earthworks were large burial mounds,
others served as platforms for structures such as temples, and still others served as
defensive walls. Mounds were usually cone-shaped, oval, or formed into the shape of an
animal."
Which standard(s) (priority/supporting) will the task address?
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures
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
What essential Question(s) and corresponding Big Idea(s) will this task target?
How do the angles of two similar triangles compare?
Proportional relationships of corresponding angle bisectors, altitudes and medians in similar
triangles may be used to solve problems. Scale factors are used to interpret and solve
problems. You may determine triangles similar using AA, SSS and SAS.
How do you find a side length or angle measure in a right triangle?
The angles of elevation and depression are the acute angles of right triangles formed by a
horizontal distance and a vertical height. Certain right triangles have properties that allow
their side lengths to be determined without using the Pythagorean Theorem
How are the Pythagorean Theorem and special right triangle rules used to find the lengths
of the sides of right triangles?
The Pythagorean Theorem and special right triangle rules are used to find the lengths of the
sides of right triangles.
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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How do trigonometric ratios relate to similar right triangles?
There are three trigonometric functions that are used to find the lengths and angle measures
of right triangles.
Proportional relationships of corresponding angle bisectors, altitudes and medians in similar
triangles may be used to solve problems. Scale factors are used to interpret and solve
problems
Which “unwrapped specific concepts and skills will this task target?
Prove theorems about triangles
Use congruence and similarity
Solve problems and prove relationships in geometric figures
Use the relationship between the sine and cosine of complementary angles
Use trigonometric ratios and the Pythagorean Theorem
How will the students apply the concepts and skills? What will they do and/or
produce?
Students will study the history of the Hopewell people( Native Americans) and their
contribution to mathematics
Apply Pythagorean Theorem to solve for length of the hypotenuse
Proportional relationships of angle bisectors, altitudes and medians in similar triangles and
scale factors to interpret and solve problems
Use trigonometric functions to solve problems
What resources, instruction, and information will students need in order to complete
the task?
Appendix 1 : Hopewell Geometry Task
What evidence of learning will I look for to show that I know all of my students have
conceptually learned the concepts and skills – the standard(s)? Completion of tasks
with data table and analysis.
Appendix 2 : Hopewell Geometry Task Rubric
How can I differentiate the application and/or evidence to meet the varying needs of
my students?
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Give a personal cue to begin work
Give work in smaller units
Provide immediate reinforces and feedback
Make sure the appropriate books and materials are available
Introduce the assignment in sequential steps
Check for student understanding of instructions
Check on progress often in the first few minutes of work
Provide time suggestions for each task
Provide a checklist for long detailed tasks
Use technological resource
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Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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Advanced or Exemplary
 All “Goal” criteria plus:
Goal ( 7 – 10 points)
 All answers are correct
 Use Pythagorean Theorem
 Use trigonometric functions
 Apply and use scale factor to justify reasoning
 Gives a correct explanation such as finds the lengths of all three sides and shows
lengths don’t satisfy the Pythagorean Rule.
Progressing
 Meets _3-4__ of the “Goal” criteria
 Provides partially correct explanation
Beginning
 Meets fewer than 4 of the “Goal” criteria
 Provides an incorrect explanation
 Task to be repeated after re-teaching
 Comments:
Interdisciplinary Connections and Related
Focus Standards
Specific to Task
CCSS.ELA-Literacy.RST.9-10.7 Translate
quantitative or technical information
expressed in words in a text into visual
form (e.g., a table or chart) and translate
information expressed visually or
mathematically (e.g., in an equation) into
words
CCSS.ELA-Literacy.RH.9-10.4 Determine
the meaning of words and phrases as they
are used in a text, including vocabulary
describing political, social, or economic
aspects of history/social science
21st Century Learning Skills
Specific to Task #1
those that apply for each task:
❑ Teamwork and Collaboration
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
❑ Critical thinking and Problem Solving
❑ Flexibility and Adaptability
❑ Effective Oral and Written
Communication
❑ Accessing and Analyzing Information
❑ Other
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Instructional Strategies/Resources
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Task /Activities that solidifies mathematical concepts
Use questioning techniques to facilitate learning
Reinforcing Effort, Providing Recognition
Practice , reinforce and connect to other ideas within mathematics
Promotes linguistic and nonlinguistic representations
Cooperative Learning
Setting Objectives, Providing Feedback
Varied opportunities for students to communicate mathematically
Use technological and /or physical tools
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Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.