Download MEDT 7472 Instructional Design PlanDr. Huett Mary Leigh Sellers

MEDT 7472
Mary Leigh Sellers
Instructional Design Plan
Dr. Huett
Project 3
Storyboard:
Unit Title: Right Triangle Trigonometry
8th Grade Common Core Accelerated Algebra 1
Common Core Standards Addressed:
KEY STANDARDS
Define trigonometric ratios and solve problems involving right triangles.
47.MCC9‐12.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.
48.MCC9‐12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary
angles.
49.MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
Learning objectives:
In this unit students will:
• explore the relationships that exist between sides and angles of right triangles.
• build upon their previous knowledge of similar triangles and of the Pythagorean Theorem to
determine the side length ratios in special right triangles
• understand the conceptual basis for the functional ratios sine and cosine
• explore how the values of these trigonometric functions relate in complementary angles
• use trigonometric ratios to solve problems
• develop the skills and understanding needed for the study of many technical areas
• build a strong foundation for future study of trigonometric functions of real numbers
ENDURING UNDERSTANDINGS
• Similar right triangles produce trigonometric ratios.
• Trigonometric ratios are dependent only on angle measure.
• Trigonometric ratios can be used to solve application problems involving right triangles.
Activities:
1. Vocabulary Building – Frayer Model
Students will use the Frayer Model to create vocabulary cards for terms in the unit. Terms
include right triangle, special right triangle (45/45/90), special right triangle (30/60/90),
trigonometric ratio, tangent of angle, tangent ratio, sine ratio, cosine ratio, inverse
MEDT 7472
Mary Leigh Sellers
Instructional Design Plan
Dr. Huett
trigonometric ratio, inverse tangent, inverse sine, inverse cosine, adjacent side, opposite side,
complementary angles, similar triangles, Pythagorean Theorem. Students can use the following
websites for definitions, examples and practice.
a. http://wvde.state.wv.us/strategybank/FrayerModel.html
b. http://oame.on.ca/main/files/thinklit/FrayerModel.pdf
c. http://www.teachers.ash.org.au/jeather/maths/dictionary.html
d. http://intermath.coe.uga.edu/dictnary/homepg.asp
e. http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/Docu
ments/Vocabulary%20Documents/Vocabulary%20Cards%20Secondary%201%20A%20thru%
20L.pdf
f. http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/Docu
ments/Vocabulary%20Documents/Vocabulary%20Cards%20Secondary%201%20M%20thru
%20Z.pdf
2. Standard: 49.MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Students will review the Pythagorean Theorem, solve for unknowns and use to solve real-life
problems.
Students will access the Investigating Geometry: Right Triangles, Lesson 7.2 – The Pythagorean Theorem
(website hosted by Henrico County Public Schools)
(http://teachers.henrico.k12.va.us/math/igo/07RightTriangles/7_2.html)
a. Warm Up – Algebraic Review, 7.2 Warm Up (answers will be provided on my course page)
b.
c.
d.
e.
f.
g.
1. 10, 2. 2√5, 3. 2√23, 4. 15, 5. 4√3
Lecture Notes – Students will view the Pythagorean PPT, print out a notes copy and
complete the practice problems
Students will view the visual proofs of the Pythagorean Theorem using the Geometers
Sketchpad Link for Lesson 7.2
Students will complete the self-check quiz for immediate feedback on their progress.
Students will use the Pythagorean Theorem to solve real-life problems using the online
applet and the Puzzles and Problems link.
Students will complete the lesson with the Hands-On Activities (Proof A and B) and the
Reducing Radicals Powerpoint.
Students will complete homework/practice problems by completing the Kuta Worksheet for
Pythagorean Theorem (http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/8The%20Pythagorean%20Theorem%20and%20Its%20Converse.pdf and
http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/8-MultiStep%20Pythagorean%20Theorem%20Problems.pdf)
MEDT 7472
Mary Leigh Sellers
Instructional Design Plan
Dr. Huett
3. 49.MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
in applied problems (now applied to Special Right Triangles)
Students will investigate the two special right triangles, 45/45/90 and 30/60/90, solve for unknowns and
solve real-life problems.
a. Students will learn by the Discovery Method using GaDOE “Discovering Special Triangles
Learning Task” activity.
i. Students will complete the activity to determine the relationships of the sides of
special triangles.
ii. Students will access a Wikipage or Discussion Board to post their results and
compare their conclusions with those of two other students.
b. Students will access the Investigating Geometry: Right Triangles, Lesson 7.3 – Special Right
Triangles (website hosted by Henrico County Public Schools)
(http://teachers.henrico.k12.va.us/math/igo/07RightTriangles/7_3.html)
c. Warm Up – Algebraic Review (immediate feedback given online),
d. Lecture Notes – Students will view the Special Right Triangles PPT, print out a notes copy
and complete the practice problems
e. Students will practice using the 45/45/90 and 30/60/90 relationships using the Geometers
Sketchpad Link for Lesson 7.3.
f. Students will complete the self-check quiz for immediate feedback on their progress.
g. Students will complete homework/practice problems using the Kuta Worksheets for Special
Right Triangles (http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/8Special%20Right%20Triangles.pdf)
4. 47.MCC9‐12.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.
Students will discover the trigonometric relationships in right triangles, use these to solve for unknowns
and solve real-life problems using trigonometric relationships.
a. Students will learn by the Discovery Method using GaDOE “Create Your Own Triangles
Learning Task” activity.
i. Students will complete the activity to determine the relationships of the sides of
special triangles.
ii. Students will access a Wikipage or Discussion Board to post their results and
compare their conclusions with those of two other students.
iii. Students will practice determining these ratios using the Kuta Practice Sheet
(http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9Trigonometric%20Ratios.pdf )
iv. Students will practice determining inverse trig relationships using the Kuta Practice
Sheet (http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9Inverse%20Trigonometric%20Ratios.pdf)
MEDT 7472
Mary Leigh Sellers
Instructional Design Plan
Dr. Huett
b. Students will access the Investigating Geometry: Right Triangles, Lesson 7.4 – Right Triangle
Trigonometry (website hosted by Henrico County Public Schools)
(http://teachers.henrico.k12.va.us/math/igo/07RightTriangles/7_4.html)
c. Warm Up – Algebraic Review (immediate feedback given online), Current Lesson (students
can use a calculator to determine these values) Answers will be given on my website.
d. Lecture Notes – Students will view the Right Triangle Trigonometry PPT, print out a notes
copy and complete the practice problems
e. Students will see a visual representation of the angle of elevation and how this relates to
right triangles and trigonometric relationships using the Geometers Sketchpad link for
Lesson 7.4.
f. Students will complete the self-check quiz for immediate feedback on their progress.
g. Students will use the Applet to see a visual representation of how the angles and
trigonometric relationships change as angle measures change.
h. Students will complete the Hands-On Activities to explore sine, cosine, and tangent.
i. Students will complete the calculator practice to ensure mastery of this needed skill.
j. Students will get immediate feedback as they practice two online quizzes prior to
completing homework.
k. Students will practice solving right triangles by completing the Kuta Practice Worksheets
(http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9Solving%20Right%20Triangles.pdf and
http://www.kutasoftware.com/FreeWorksheets/GeoWorksheets/9-MultiStep%20Trig%20Problems.pdf)
5. Students will complete a Partner Summative Performance Task by completing the “Find That Side or
Angle Learning Task” by accessing a Wikipage. Students will complete questions, compare results,
discuss commonalities and differences and complete and submit the Learning Task.
6. Students will complete a Summative Multiple Choice Unit Test.
Assessments:
Assessments are embedded in each lesson for the unit. There are warm up assessments, formative
assessments in the form of practice problems with keys and online ‘checks’ and summative assessments
in the form of a paper/pencil test and GaDOE learning tasks.
Module design:
This module will be set up as a unit with lessons based on topics. Modules will contain all necessary
links, pdfs, embedded videos and powerpoints (where possible).
Interactivity and collaboration:
Many of the lessons involve animations and are interactive in this manner. Two learning tasks are
completed collaboratively, one using a discussion board and the other a wikipage.
MEDT 7472
Mary Leigh Sellers
Instructional Design Plan
Dr. Huett
Use of technology:
Students use applets, animation, videos, and online practice quizzes. Students also
Learner support:
A “How To Do This Online Course” sheet will be developed with tips and reminders.
Additional website such as Purplemath (http://www.purplemath.com/), SOSmathematics
(http://www.sosmath.com/ ), and others will be given for sources of additional practice.
Teacher contact information will be given along with ‘office hours’ where the teacher will be available
for immediate help.
A “HELP” tab on the discussion board will be developed so students can ask for help from each other.
Any support given by other students is encouraged up to the Unit Online Test and Partner Summative
Performance Task.