EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4 week unit of work in secondary school
mathematics
Your name: Deeya
School, grade & course: Elgin Park Secondary School, Grade 9, Mathematics
School, grade & course: Elgin Park Secondary School, Grade 9, Mathematics
Topic of unit: Powers and Exponents
Preplanning questions:
(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, and beautiful about this topic? (150
words)
Powers is a way to represent repeated
multiplication. This topic is included in the curriculum as often very large
or small numbers are more easily expressed in exponential form. Not only do
they appear in Chemistry and Physics but in economics, social sciences, and
many other disciplines. It is important for students to learn it as they can
connect it with everyday connections – when calculating area of his/her room,
to measure large distances (for ex distance from the moon to the earth), when
counting things that grow very quickly (for ex: bacteria). Exponents are also
used to represent to describe a computer’s memory, in computer games,
investing and finance and population growth. I hope that from this topic,
students will know how use and read a calculator, use it in other subjects,
simplify their answer and use it in their everyday life. What makes it
fascinating is the magical way of expressing a very large number in a
shorthand expression.
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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)
It was interesting to read the
history of powers and I would definitely share it with my students. The term power was used by the Greek mathematician Euclid for the
square of a line and afterwards was discovered by Archimedes who proved the
law of exponents, 10a 10b = 10a+b. Some mathematicians (e.g., Isaac Newton) used exponents only for
powers greater than two, preferring to represent squares as repeated
multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d.
To incorporate the history as part of my unit, I would talk about Euclid who is referred to as
the “father of geometry” and they could even turn to Pg93 to see how he
ressembled. POWER appears in English in 1570 in Sir Henry Billingsley's
translation of Euclid's Elements: "The power of a line is the square of
the same line." - http://mathforum.org/library/drmath/view/58247.html
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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)
To encourage students’
active participation, I will introduce the topics with a variety of hook –
(songs on powers and exponents, history) so that they find it interesting in
the beginning itself. Throughout this unit manipulatives and visual aids
(posters) will be used and games as well (puzzles, kahoot, beach ball
activity, spinning the wheel) will be played. This will provide multiple opportunities
for students with different learning styles to gain understanding, possibly
even subconsciously during the games.
I will also encourage group
work as students can learn from each other. They will even get the chance to
create their own game, and activities where they
can mix skills they have learned in other subjects, for instance art, social
studies and language, with their mathematical knowledge and discover
connections for themselves.
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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)
Time : 2 period / math
class
Title: Powers and
Exponents
Objective: To provide
learning environment that stimulates and enhances effective learning
Instructions : Students will have
to submit a creative project in two days with the following requirements and
they may choose a real life application of exponents from the following list
·
Light years
·
computers
·
bacterial growth
·
radioactive half-life
·
engineering
·
medicine
·
scientific notation
Requirements :
a)
What is the application of exponents you
researched?
b)
Describe its connection to the real world.
c)
What is the impact of your area of research on science and/or
mathematics?
d)
How would your area of research find it more difficult to work/study if
exponents weren’t used?
e)
Why is your area of research important/significant to your life, your
community, and the world?
Formats: comic strip,
song, video, skit, Prezi, PowerPoint, song, brochure , or others (but need to
be discussed with me first)
NOTE: You may choose to work alone or with a
partner.
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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)
Formative assessment
Since formative
assessment process provides information needed to adjust teaching and
learning while they are still happening, I will often observe group interactions
and individual work, do 2-3 quizzes every week, check classwork and homework,
do exit- admit slip so that I can understand and quickly determine which students have it, which ones
need a little help, and which ones are going to require much more instruction
on the concept.
Summative assessment
The
tests, assignments, and projects are used to determine whether and to what degree students have
learned the material they have been taught.
The
rubric for the project will be as shown below.
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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.
Lesson
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Topic
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1
-3.1
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Using
exponents to describe numbers
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Represent repeated multiplication with exponents
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Describe how powers represent repeated multiplication
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2-3.2
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Powers
of tens and zero exponents
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3-3.3
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Exponent
laws
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4-3.4
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Order
of operations
-
Use the order
of operations on expressions with powers
-
Apply the laws of exponents
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5-3.5
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Using
exponents to solve numbers
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Solve problems that require combining powers
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6-3.6
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Using
exponents to solve difficult numbers (surface area)
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Use powers to solve problems that involve repeated
multiplication
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7
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Project
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8
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Project
+ Revision
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9
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Presentation
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10
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Chapter
3 review
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11
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Unit
test
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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.
Title:
Powers
and Exponents
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Duration:
1h15mins
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Grade Level:
Grade
9
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Rationale:
Students
will be familiar with the laws of exponents and able to apply the Order of Operations for expressions involving
addition, subtraction, multiplication, and division with grouping symbols.
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SWBAT:
-
solve a given problem by applying the order of
operations without the use of technology
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solve a given problem by applying the order of
operations with the use of technology
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identify the error in applying the order of operations
in a given incorrect solution
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Objective
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Time
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Activity
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Materials
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Attendance
Review
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10 minute
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Welcome
the students and review a bit what we did in the previous classes.
Students
will play the jeopardy game for a quick revision.
http://www.math-play.com/Exponents-Jeopardy/Exponents-Jeopardy.html
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Laptop,
smart board, buzzer for the jeopardy game
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Introduction/
hook
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5 minutes
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Imagine you are
about to get your L license. How ugly would that be if everybody decided to
drive on any side of the road they wanted to? Crash, collision!!
So for Math too
there are rules that we need to obey – Recap : BEDMAS
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Laptop, L sign
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Lesson
notes & practice
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20
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Will
explain, using examples, the exponent laws of powers with integral bases
(excluding base 0) and whole number exponents:
I
will solve some examples on the board and afterwards the students will be
encouraged to come and solve it on the board
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Worksheet, laptop, smart board
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CW
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20
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Students
will be given some CW Pg 111 no 5-13
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Book,
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Activity
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15
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Spinning
the wheel
The
students will be sitting in group of 4. Each color represents a number. The
group who gets the correct answer will get the chance to spin the wheel
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Spinning
wheel, paper, pen
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Closure
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5
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Recap
on the rules of powers
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