EDCP 342A Unit planning:
Rationale and overview for planning a 3 to 4 week unit of work in secondary
school mathematics
Your name: Amandeep Buttar
School
Topic of unit: Circle Geometry
Preplanning questions:
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(1) Why
do we teach this unit to secondary school students? Research and talk about the
following: Why is this topic included in the curriculum? Why is it important
that students learn it? What learning do you hope they will take with them
from this? What is intrinsically interesting, useful, beautiful about this
topic? (150 words)
The
circle geometry is added in the secondary school curriculum with the aim of
developing students’ previous geometry knowledge further up to higher level.
Studying circle properties would increase their logical thinking and
deduction skills. Also, students are required to have the knowledge of circle
geometry for learning the future mathematics such as, the applications in
algebra and the study of calculus etc.
Importance of topic: After learning circular properties, students
would be able to deeply realize the role of circular shape in their daily
life. With this learning, they would not only be able to create an attractive
and beautiful circular design, but also determine the missing lengths of line
segments of those designs.
In
terms of attractiveness, the circular figure is unique and perfect design as
compared to other shapes. It can also be connected to the cycles of nature
such as the seasons, day and night, birth and death.
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(2) What
is the history of the mathematics you will be teaching, and how will you
introduce this history as part of your unit? Research the history of your
topic through resources like Berlinghof & Gouvea’s (2002) Math through the
ages: A gentle history for teachers and others and Joseph’s (2010)
Crest of the peacock: Non-european roots of mathematics, or equivalent
websites. (100 words)
The
date of invention of circle is unknown or not recorded in the history.
Euclidean used circle as a sample space in constructing the geometry. He is
also known as the "father of geometry.” The concept of circles and
sphere was extremely used in the Greek Astronomy too. Greeks were the ones
who first observed that the earth’s size is similar to circular
shape. The invention of wheel turned out to be one of the greatest
revolutions on earth, which is derived from a circle. I will use history in
making the hook of my lesson interested. I will engage students by asking
that,” How our life would have affected if circle based inventions were not
made”?
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(3) The
pedagogy of the unit: How to offer this unit of work in ways
that encourage students’ active participation? How to offer multiple entry
points to the topic? How to engage students with different kinds of
backgrounds and learning preferences? How to engage students’ sense of logic
and imagination? How to make connections with other school subjects and other
areas of life? (150 words)
As
this chapter is very visual, I will have at least two different and
interesting activities in each lesson in order to encourage the students’
participation in learning. The topic would be presented to students through
many entry points. Firstly, in the beginning of the lesson, student would be
provided real images showing properties on the projector. Students would also
be asked to provide other examples of object that travel in circular
pathways. Secondly, I will include some outdoor activities in order to have
student actively participate in learning. For example, I would ask students
to form shapes that would show circle properties by standing in the hallway
or school ground accordingly. It will also help students with different
backgrounds to visualize the property clearly. Furthermore, students would be
given the examples of circular shapes used in every other academic subjects.
The vocabulary such as, pathways, model airplane, satellite, circular, orbit,
compass etc. would also be discussed for ELL students.
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(4) A
mathematics project connected to this unit: Plan and describe a student
mathematics project that will form part of this unit. Describe the topic,
aims, process and timing, and what the students will be asked to produce.
(100 words)
Topic: Circle Geometry Properties
Time: 2-4 hours
Objective: Student would be able to identify and
describe features of their design that display circle geometry concepts.
Introduction: Students would be asked to sketch a design for
a corporate or team logo independently. The design must be based on circles
including tangents and chords.
Guidelines:
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Using geometry tool or
computer tools, draw your design.
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Measure and label all
angles and lengths that demonstrate the circle properties.
Students’ work should show:
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Sketches of their
design.
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A detailed, labeled
copy of their design that shows circle geometry properties.
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Written explanations of
the circle properties they used in their design.
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A final colored copy of
their design with an explanation of its purpose, if necessary.
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(5) Assessment
and evaluation: How will you build a fair and well-rounded assessment and
evaluation plan for this unit? Include formative and summative, informal/
observational and more formal assessment modes. (100 words)
My
overall assessment would depend upon the following three key points:
1. Conceptual
understandings: How do students show their understanding of circle properties
by explaining and illustration?
2. Procedural
understanding: How do students calculate the angles and length of line
segments in circle diagram?
3. Problem
solving skills: How do students select and apply their learning to solve
problems?
Formal assessment: I would be observing students’ learning
throughout the lesson. To assess students’ understanding, I would use fist of
five and exit slips techniques. Students would also be assessed on their
participation in learning activities.
Summative assessment: There will be unit test at the end of
unit. Students would receive marks out of 40.
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Elements of your unit plan:
a) Give a numbered list of the topics of the 10-12 lessons
in this unit in the order you would teach them.
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Lesson
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Topic
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1
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Exploring Angles in a circle (central and Inscribed angles)
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2
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Angles part 2
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3
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Chord Properties (review Pythagoras theorem )
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4
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Chord properties part 2
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5
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Tangent to a circle
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6
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Tangents part 2
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7
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Review
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8
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Review
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9
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Unit Test
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10
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(11)
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(12)
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b) Write a detailed lesson plan for one of the lessons
which will not be in a traditional lecture/ exercise/ homework format. Be sure to include your pedagogical goals, topic of the
lesson, preparation and materials, approximate timings, an account of what the
students and teacher will be doing throughout the lesson, and ways that you
will assess students’ background knowledge, student learning and the overall
effectiveness of the lesson. Please use a template that you find helpful, and that
includes all these elements.
Lesson Plan -
Properties of Chords in a Circle
Unit:
Circle Geometry Subject: Mathematics
Grade:
9 Time:
73 minutes
Big Idea or Question
for the Lesson:
·
Describe the relationship among the center
of a circle, a chord, and the perpendicular bisector of the chord?
PLO foci for this
lesson:
- At the end of lesson, students should be able to solve
problems and justify the solution strategy using circle properties,
including the perpendicular from the center of a circle to a chord bisects
the chord
Objectives
(SWBATs):
It
is expected that students will:
1. Learn about
the perpendicular from the center of circle to a chord bisects the chord.
2. Learn about
the line segment that joins the center of a circle to midpoint of a chord is
perpendicular to the chord and its length is the shortest distance of the chord
from the center of the circle.
Assessment
Plan:
- Formative:
Checking
understanding throughout the lesson (Observation/ fist of five) Students
would also be assessed on their participation; how well they work together
in a group.
- Exit
slips – check for understanding of key concepts, not for marks.
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Material
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Equipment
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Fire
game activity instructions sheets
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Adaptations
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For ESL students or students with a less
extensive vocabulary, key words would be defined.
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During the power point
presentation, instructions will be given on key terms to focus on, as well as
terms being written on the board and circled throughout as they are covered.
Vocabulary words:
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Chord
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Arc
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Central Angle
·
Perpendicular Bisector
The adaptations will also help other students who
may have trouble following along. For those students appear unable to write
and understand at the same time, they would be given written handouts so that
they can focus on the lesson rather than filling words in.
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Contingency Plan for Early Finishers
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Students who finish early will be given
an additional question to add to their exit slips, asking them to answer the
“what are three important properties of perpendicular bisectors of chords in
circles?” In the future, if students are bored or need something to do, they
may be given the topic related interesting puzzle.
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Time
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Teacher will
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Student will
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5 Minutes
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Introduction:
·
Showing
students a sequence of pictured on the overhead projector.
  
·
Asking
students to observe.
·
Introducing
topic with questions such as,
·
What
could we call the horizon?
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How
is the center of the sun related to horizon?
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·
Listen to
introduction and observing the pictures.
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10 Minutes
20 Minutes
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Activity:
Goal: Investigation of relation between
the center of a circle and a line segment that joins two points on the
circle.
Explaining the procedure:
Think-Pair-Share
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Construct
then cut out a large circle. Label the Centre of the circle.
·
Choose
two points A and B on the circle. Join these points to form line segment AB.
Make sure AB does not go through the Centre of the circle.
·
Fold
the circle so that A coincides with B. Crease the fold, open the circle, and
draw a line along the fold. Mark the point C where the fold line intersects
AB.
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Repeat
the steps above for two other points D and E on the circle.
·
What
do you notice about line segments AC and CB?
·
Compare
your results with another pair of classmates.
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What
appears to be true about each line segment and its related fold line?
·
What
name could you give each fold line?
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Through
which point do both fold lines appear to pass?
Teaching Chord properties with
examples:
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Discussion
of activity questions.
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Example
worksheets handout.
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The
teacher solves examples by engaging students in the discussion.
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Reinforcing
the correct application of the Pythagorean Theorem.
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· Turn to the person(s) next to them and perform the activity
Write down answers in their notes handout and compare with
another pair of students.
·
Provide
answers for the teacher to write on the board
·
Listen to
teacher’s definitions and answers
·
Answer
any additional questions
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15 Minutes
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Practice: Asking students to Solve questions p.389
#1, 2, 4, 5, 6,
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Students solve questions independently.
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15 Minutes
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Activity: Sticks on a Fire Game:
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Dividing
students into pairs.
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Handing
out activity instructions and Fire circles sheets.
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Monitoring
the activity.
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Play games in pairs
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8 Minutes
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Closing the lesson: Exit Slip
·
Hand out exit slip
·
In your own words,
define the following questions:
·
Describe how you know
that the diameter of the circle forms a right angle with the chord at their
point of intersection.
·
What is perpendicular
bisector of a Chord?
Home work: They would also be assigned to solve
questions 7-9, 12, 13 on page 389 from the textbook. Unfinished
questions from practice would also be added in the homework.
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Record key points of the lesson.
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Reflection
/ Follow Up / Next Steps:
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Do students have a good
understanding of the key terms? Does this provide a solid foundation on which
to build further discussion of circle geometry?
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Were students engaged?
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Were they able to keep
up with the speed of the presentation?
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Were they more willing
to discuss with their partners than with the class?
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Were there students who
were visibly confused or bored?
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Were students more or
less able to grasp the key points of the presentation or was it too
sophisticated/fast?
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