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Model Mathematics Curriculum
Unit Implementation Plan
UNIT COVER SHEET
Name: Matthew Blair
Grade Level:
Hs Geometery
Unit Title: Math 2 Unit 7 Right Triangles and Trigonometry
Dates of Instruction:
November
Timeframe (Add days as needed)
Unit Timeframe: 2-3weeks
Day 1:
Using Pythagorean Theorem
Lesson/task/assessment
Day 2:
Triangle Similarity and Trig Ratios Lesson/task/assessment Lesson/task
Day 3:
A complements B
Lesson/task/assessment:
Assessment
Lesson
Day 4:
Getting Triggy with It(Day1)
Lesson/task/assessment:Lesson
Day 5:
Getting Triggy with It(Day 2)
Lesson/task/assessment:Lesson/task
Standards Alignment
Content Standards:
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle,
leading to definitions of ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
Standards for Mathematical Practice:
-Makes sense of problems and persevere
-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
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: Math 2 Unit 7
DAY: 1
DAILY LESSON PLAN
Objectives
Students will self assess
Students will use similarity to discover sine, cosine, and tangent.
Content
Standards
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the
angle in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical
Practices
-Makes sense of problems and persevere
-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
Materials
Using Pythagorean theorem worksheet
Preparation
Worksheet needs to be in the hands of the students for homework the night before so
need copies
Lesson
Activities
This a preassessment so students will be given to students the night before,We go over it
as a class discussing where common pitfalls may have been if there were any.
Assessments
This is a preassessment for this unit
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?To intentionally emphasize the development of the
student I will review Pythagoreans theorem and discuss finding missing angles in the triangle this is super
important to understand these basic components to understand the rest of the unit.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: Math 2 Unit 7 DAY: 2
DAILY LESSON PLAN
Objectives
Content
Standards
Mathematical
Practices
Students will
-Recognize the ratios of the sides of right triangles are functions of the acute angles.
-Determine that the sine of an acute angle in a right triangle is equal to the cosine of
that angle’s complement.
-Use trigonometric ratios to solve for unknowns in right triangles.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the
angle 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.
-Makes sense of problems and persevere
-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
Materials
Triangle Similarities and Trig Ratios Worksheets
Preparation
-Making pairs or triads before class, Run off worksheets, Gather up posters and markers
for “DANG” Posters
Lesson
Activities
-Teacher should start by talking about the fact that up to this point we have been
able to find angles given angles, and side lengths given side lengths. Then, present
to the students if they think it is possible to go from knowing angles to knowing
side lengths, or from side lengths to angles. After the discussion, hand out the
“Triangle Similarities and Trig Ratios,” have the students work in pairs or triads to
complete the guided sheet to get to the ratios of sine, cosine, and tangent.
- After students have completed the “Triangle Similarities and Trig Ratios,” have
them check their answers and fill in the self-assessment rubric to see where their
deficiencies are and then have the students find someone in the class that had
gotten what they got wrong and have them explain it to them. If there are concepts
that everyone missed, then teacher should go over it as a class.
-Assign each pair or triad a new problem and have them make a “DANG” poster to
display to the class
Assessments
“Dang” Poster
-Self assessment of worksheet Triangle similarities and Trig Ratio
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? It will be super important to relate find missing angles
and missing sides in the pre assessment to the Trig ratios. Also, we need to emphasize the angle we are
referring to really matters when finding sin, cos, tangent.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: Math 2 Unit 7
DAY:
3
DAILY LESSON PLAN
Objectives
Students will explain and use the relationship between the sine and cosine of
complementary angles.
Content
Standards
G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
Mathematical
Practices
-Makes sense of problems and persevere
-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
Materials
A complements B Worksheet
Preparation
Run of worksheet, set up groups
Lesson
Activities
-Hand out a Complements B assessment, and ask students to complete Exercises 1 and
2 individually. Walk around and monitor student work (check to make sure students are
calculating trigonometric ratios correctly).
- Pair students, and ask them to discuss Exercises 3 through 5. Monitor discussion
between students.
- Ask students to share their findings as a class. Then, discuss Exercise 6.
- Have students complete Exercise 7 individually for independent practice.
Assessments
Observation, and homework problem from number seven on worksheet
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? It is super important to realize how these ratios relate,
to make sure of this I will have students discuss these ratios in small groups, and then have a class discussion
discussing how they relate and why.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: Math 2 Unit 7 DAY: 4
DAILY LESSON PLAN
Objectives
-Students should be able to find missing side lengths or missing angles using
trigonometric ratios.
Content
Standards
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the
angle in the triangle, leading to definitions of trigonometric ratios for acute angles.
Mathematical
Practices
G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
-Makes sense of problems and persevere
-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
Materials
Getting triggy with it worksheet and activity
Preparation
-Run off worksheet part one(finding third side of triangle)
-Discussion questions
Lesson
Activities
-As an introductory exercise, ask students to find a missing side of a right triangle
with two given sides. Students should use the Pythagorean Theorem.
- Discuss what would happen if only one side was given. What other information
would need to be known in order to find the length of a missing side? Remind
students of the trigonometric ratios.
- Present the following problem to students.
12
x
49°
Assessments
- Discuss which sides are given with respect to the given angle. Ask students what
trigonometric ratio involves these sides. Demonstrate solving for the missing side
using sine.
- Repeat examples using cosine and tangent to find a missing side of a right
triangle.(Work in groups)
-Each group present a problem
-observation
-Group presentations and discussion
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? Very rarely in math do we see a triangle given where
each with all the information given. I really want to show and convey to students you have to refer to what
information is given and how it relates whether through Pythagorean Theorem or trig ratios. Because deciding
what is given makes the problems do able. As the teacher I will hammer home you have to digest what you are
given before starting.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: Math 2 Unit 7 DAY: 5
DAILY LESSON PLAN
Objectives
- Use trigonometric ratios to solve for unknowns in right triangles.
Content
Standards
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the
angle in the triangle, leading to definitions of ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
Mathematical
Practices
-Makes sense of problems and persevere
-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
Materials
Getting triggy with it worksheet and posterboard for presentation
Preparation
Run of worksheets and decide on how to group
Lesson
Activities
1. - Present the following right triangle to students.
15
x°
8
Ask students what is the different here. They should recognize that the angle is
the unknown this time. Explain that if two sides are known, then the angle may
be found using trigonometric ratios and their inverses.
Ask what trigonometric ratio could be written for this unknown angle.
Demonstrate solving for the missing angle. Explain the inverse trigonometric ratio
used to find the solution.
- Discuss definitions of angle of elevation and angle of depression.
2. - Complete the following word problems requiring students to apply
trigonometric ratios to real life situations:
a.
A flagpole creates a 16 foot shadow on the ground. The angle of elevation
from the tip of the shadow to the sun is 67°. To the nearest foot, how tall is
the flagpole?
An airplane traveling 25,000 feet above the ground begins a landing. The pilot
spots his landing zone on the ground at an angle of depression of 4°. How far will
the airplane travel to arrive at his landing zone?
Assessments
- Hand out Getting Triggy With It(part 2) assessment. Monitor students as they
complete exercises.
Getting triggy with it assessment and observation
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? To solve any of these elevation or depression
problems you have to draw the problems and refer to the picture which will be required. Secondly we will
discuss how angles of elevation and depression relate and what is which but I think to understand and make the
relation to previous material students must and I mean must draw a picture to solve.