Download UBD Lesson Plan Template – Stage 3 Learning Plan

UBD Lesson Plan Template – Stage 3 Learning Plan
Back Design Template
Task: (Describe briefly)
Instructional Process:
WHERE are we going? WHY? WHAT? is expected?
Goals:
To have student’s begin thinking about the applications of basic trigonometry and Geometry to
other mathematics as well as the real world.
For the students to understand the Essential Questions of UBD stage 1:
 What is the importance of math in the world today?
 How can we apply the information in the unit to the real world?
 How does the information in the unit enable us to enter higher mathematics?
For the students to understand or know how to:
 Identify special right triangles and use their properties to find information about them.
 Find sine, cosine, and tangent of right triangles.
 Understand the properties and aspects of circles and how to use them along with
trigonometry to find information about the circle.
 Use their knowledge of circles to help them compute the measures of spheres.
Expectations:
In order to gain understanding of the goals students will:
 Complete homework assignments for each day of classroom instruction. This will give the
students practice and experience in using the ideas learned in class. I will give the
students an opportunity during the first ten minutes of class to ask questions concerning
the homework.
 Complete a web quest that enables the students to apply the information learned in class
to real world situations in a fun and exciting adventure. They will answer questions
concerning the web quest and complete a poster project describing one of the steps in
the web quest.
(Logical/Quantitative & Narrative Windows)
 Answer the Essential Questions in essay format upon completion of the unit. After
completing the unit exam, they will answer the questions and we will discuss their
answers in an open-classroom discussion. This will enable the students to see the point
of learning the information in the unit
(Foundational Window)
Relevance and Value:
To set up the basis of knowledge necessary for entering higher mathematics:
 The students will develop a source of information within their minds that is necessary to
every future math class the students take.
 The basic ideas of trigonometry and geometry learned in the unit are essential to all
mathematics.
Prerequisite Skills:
 Understand what a triangle is
 Know that the three angles in a triangle add up to 180 degrees
 Understand similar triangles and what makes triangles similar.
 Understand what complementary angles are.
Evaluate if students know and understand what defines a shape as a triangle. Also, determine if
they understand that the three angles in any triangle add up to 180 degrees. This will be done
by means of a Smart board activity. Also, evaluate the student’s knowledge of similar
triangles. This is done by means of a group activity where they review what a similar triangle
is.
How will we HOOK and HOLD student interest?
MM2G1 (Special Right Triangles):
The smart board activity to evaluate prerequisite skills will be on the smart board at the beginning
of class. Begin by asking the students general questions concerning triangles. Then, ask
volunteers to come to the front of the classroom to participate in the activity of deciding if a
shape is a triangle or not. The next aspect of the Hook and Hold step is the other part of the
evaluation that determines and exercises knowledge about the sum of the three angles of
triangles.
MM2G2 (Sine, Cosine, and Tangent to Special Right Triangles):
(After ten-minute homework review) Have students divide into groups of 3-4 students. Pass out
worksheet that has an activity and questions concerning similar triangles. The students will
be given 5-7 minutes to complete this, and then we will discuss their answers. I will then start
my lecture about the new topic for the day.
(Narrative Window)
The next portion of the new topic deals with trig ratios of complementary angles. In order to Hook
and Hold my students’ attention, I will have a smart board activity that gives them a visual
representation and participation in the activity.
(Aesthetic Window)
MM2G3 (Properties of Circles):
The first portion deals with chords, tangents, and secants. In order to hook and hold my students I
will have my acoustic guitar in class that day and begin by telling them we will be learning
about chords today. I will play a few chords on my guitar, and then ask them if they know of
any other types of chords that exist in the world. I will then use the hole in the guitar and a
string that crosses it to describe the mathematical chord. This will then lead into discussion of
secants and tangents of circles as an application of triangle symmetry.
(Aesthetic Window)
The next portion deals with properties of central, inscribed, and related angles. In order to Hook
and Hold the students’ attention, I will allow the students to come up to the smart board and
select which images display central and inscribed angles.
MM2G4 (Find and Compare Measures of Spheres):
In order to Hook and Hold the attention of my students, I will hand out Styrofoam balls and flexible
tape measures. I will then give them specific instructions to measure the circumference and
give them a formula that will allow them to determine the diameter of the sphere with that
information. I will then begin the lesson on how to use previously known/gained information to
discover the surface area and volume of a sphere.
(Experiential Window)
How will we EQUIP students for expected performances?
Every day I will explain each new segment of the standards within the Geometry Unit. The
students will be strongly encouraged to take detailed notes. If they are absent, I will print a
copy of my Smart Board Notebook for that day to give to them (I will write all the lecture notes
and example problems on the Smart Board).
With every lesson, I will incorporate specific Smart Board activities and visual representations in
order to give the students visual representations of the ideas.
(Aesthetic Window)
I will reserve a computer lab or a mobile lab one day during the unit so the students can complete
an activity with Geometer’s Sketchpad (by KCP Technologies).
(Experiential Window)
Hand out several sheets that summarize the main topics and ideas within the unit
Students will complete the group assignment worksheet for similar triangles.
During the lesson concerning the area of a sector of a circle, I will order pizza for the class and
we will have a math lab concerning the area of a slice of pizza
(Experiential Window)
How will we help students RETHINK and REVISE?
Each night, the students will be given about 15-30 problems of homework to practice the new
topics. We will take the first ten minutes of every class session to answer any questions
concerning the previous night’s homework assignment.
Students will keep a math journal where each night they will summarize what they learned in
class that day.
Students will grade each other’s daily quizzes. I will read the answer aloud, and the students will
mark right or wrong. If they know the answer, they can explain it to their classmate(s).
How will students self-EVALUATE and reflect on their learning?
Quizzes of 2-3 questions will be given each day. They will cover the topic(s) that were on the
homework. Students will trade quizzes and grade each other.
An exam will be given at the end of the unit. It will cover all topics in the unit. When I return the
tests to the students, they can come to me before or after school to ask questions concerning
the test.
The Web Quest “National Treasure: The Geometer’s Key” will evaluate the student’s learning.
They will answer questions throughout the Web Quest and turn them in to me.
The students must also generate a poster explaining one of the steps within the Web Quest and
present to the class.
The students will answer the Essential Questions of the unit in paragraph form (after the unit
exam). This enables them to realize the enduring understandings of the unit and for me to
analyze their learning.
(Foundational Window)
How will we TAILOR learning to varied needs, interests, styles?
Visual Learners: The Smart Board applications will equip their learning style
Auditory Learners: They will learn best by listening to the lectures.
Attention Deficit Students (ADD/ADHD): By breaking the class in to segments of 1)Homework
review 2) Hook and Hold (which has various hands-on/involvement activities) 3) Lecture (which is
also broken into different topics and also has various activities and visual aids scattered
throughout). One complete day will be spent in the computer lab working on the Web Quest. Part
of another day will be spent in the computer lab working with Geometer’s Sketch Pad.
Hearing Impaired Learners: I will give them a copy of my notes for the day prior to class, as well
as a copy of the lecture notes and examples I worked on the Smart Board. Basically everything I
say in reference to the lesson will be written on the Smart Board.
Visual Impaired Learners: They can utilize a tape recorder in class so they can review the
lecture as many times as possible. I can also set the smart board to display large text.
Slow Learners: Copies of the lecture notes will be given to them. The math journal will help them
to recall what they learned and analyze it without actually working math problems.
How will we ORGANIZE and sequence the learning?
Day 1: MM2G1 & First Part of MM2G2
Day 2: MM2G2
Special Right Triangles & Sine, Cosine, and
Tangent Ratios to Similar Right Triangles:
Specific: Length of the sides of 30,60,90 triangles
Length of the sides of 45,45,90 triangles
Relationship of Trigonometry ratios for similar
triangles
Sine, Cosine, and Tangent Ratios to Similar
Right Triangles
Specific: Relationship between trigonometric
ratios of complementary angles.
Solve application problems using trigonometric
ratios.
Steps in Lesson:
1. (No homework questions necessary, no
homework assigned prior to class)
2. Smart Board activity to hook and hold
attention, as well as to recall prerequisite
skills.
3. Instruction time: I teach the new topic,
while using the Smart Board for visual
representations.
4. When finished with Special Right
Triangles, use the group activity about
similar triangles to transition into
trigonometry ratios to similar right
triangles
5. Assign homework
Steps in Lesson:
1. First ten minutes of class, allow for
questions concerning homework.
2. 2-3 Question quiz concerning the
homework. Students trade quizzes and
grade for one another.
3. Smart Board Activity to hook and hold
attention, as well as recall the idea of
complementary angles.
4. Instruction Time: I teach the new topic,
describing how trigonometry ratios and
complementary angles are related. (I will
also use a smart board application
concerning the unit circle). I will then
teach the students how to use the
information to solve application
problems.
5. Assign Homework
Day 3: MM2G3
Day 4: MM2G4 (Pizza Lab Day)
Properties of Circles
Specific: Properties of chords, tangents, and
secants as an application of triangle symmetry
Properties of central, inscribed, and related angles
Properties of Circles
Specific: Use properties of circles to solve
problems involving length of an arc and the
area of a sector
Steps in Lesson:
1. Ten minutes for homework questions
2. 2-3 Question quiz concerning the
homework
3. Hook and Hold: Use my acoustic guitar to
show musical chords. Transition
discussion to mathematical chords.
4. Instruction time: Utilize the Smart Board to
display what a chord, secant, and tangent
line are. Then explain the triangles
created by each of them and the
symmetry of those triangles. Transition to:
discussion of central, inscribed, and
related angles (They are created by
chords, secants, and tangents). Discuss
their properties.
5. Assign Homework
Steps in Lesson:
1. Ten minutes for homework questions
2. 2-3 Question quiz concerning the
homework
3. Hook and Hold: Use description of a pizza
(and picture of one on Smart Board) to
describe a slice of pizza as the area of a
sector of a circle. (If possible/permitted by
the school, I will have pizza waiting on the
class)
4. Instruction: Explain the formulas/
processes of finding the arc length and
area of a sector of a circle. The students
will then measure the pizza and use the
formulas to discover the area of their
slice.
5. Assign Homework
Day 5: MM2G3
Properties of Circles
Specific: Justify measurements and
relationships in circles using geometric and
algebraic properties
Steps in Lesson:
1. Ten minutes for homework questions
2. 2-3 Question quiz over the homework
3. Hook and Hold: Use a real-life
application problem concerning a
circular object (possibly the rotunda in
the Capitol). Get the students to
guess the angle (on the unit circle)
that a certain object would be at.
4. Transition from the hook and hold
step into the actual Lesson. Show
them that it is possible to use
geometry and algebraic properties to
find the exact location.
5. Assign homework
Day 7: Web Quest Day
Steps in Lesson
1. Homework Questions
2. No Quiz Today
3. Go to computer labs to complete the
Web Quest
Day 6: MM2G4
Find and Compare Measures of Spheres
Specific: Use and apply Surface Area and
Volume of a sphere
Determine the effect on surface area and
volume by changing the radius or
diameter of a sphere
Steps in Lesson:
1. Ten minutes for homework questions
2. 2-3 Question quiz concerning the
homework
3. Hook and Hold: Distribute Styrofoam
balls to the classroom for the activity
mentioned in the UBD Hook and hold
section
4. Teach the lesson concerning volume
and surface area of spheres
5. Go to the computer lab to use
Geometer’s Sketchpad.
6. Assign homework
Day 8: Unit Exam Day
Steps in Lesson
1. Students begin examination upon
entering the room
2. When they finish the test they will
begin working on answering the
Essential Questions
Resources/Materials: (List items)






References:
Adapted/formatted from Understanding by Design by Grant Wiggins and Jay McTighe