EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4 week unit of work in secondary school
mathematics
Your name: Ian Mak
School, grade & course: King George Secondary, 8 & Mathematics
School, grade & course: King George Secondary, 8 & Mathematics
Topic of unit: Algebra
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, beautiful about this topic? (150 words)
Without algebra, calculations and formulae from many
different fields would not be possible. When Einstein theorized that E =
mc^2, he was using algebra. When a business order is calculating inventory,
deciding how much he needs to buy to meet expected sales for the month, he is
using algebra. Moreover, this material is incredibly applicable to everyday
life as well. When you calculate tips after dinner, you are using algebra!
When you calculate how much time to dedicate to homework tonight and how much
time to spend with friends, you’re using algebra!
I hope that students not only learn the elementary
operations and concepts of the unit (opposite operations, operations applied
to one side must be done to the other etc), but understand the practicality
of the material. I hope that they understand how pervasive these simple
calculations are in our lives that are dominated by consumerism and currency
exchange.
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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)
Algebra eliminated the necessity of approximation. Before
algebra, mathematicians had to approximate many of the calculations they
could now conduct WITH algebra. Algebra allowed Newton to calculate the
acceleration due to gravity, and allowed Archimedes to discover the value of
pi when looking at the ratios of radius to its circumference.
I would use facts like these in my hooks to get students
interested. I could also design worksheets in which students would, using
algebra, figure out constants that have already been derived so they can
understand what each philosopher had to do. For example, a worksheet centered
around physics principles could have multiple questions which have the
solution of -9.81, student just figured out acceleration due to gravity!
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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)
It’s important to emphasize the real life applications of
algebra in my examples (calculating tips, calculating tax/income percentages,
cooking etc). Moreover, to emphasize the versatility of algebra as a skill to
help solve almost any problem such as how much furniture you can fit in one
room, how many hours you paid for in parking, or how long a pipeline needs to
be to stretch from Canada to Mexico. This versatility is how I would offer
multiple entry points to the topic: I can cater examples to students’ general
interests so it is more personalized and directly applicable to their lives. For
example, if a student loves snowboarding and is struggling, I can give them
an algebra question that uses snowboarding as an illustration.
For different ethnic backgrounds, I could emphasize the
algebraic origins that their home country has, since algebra has history in
many countries. I need to make sure, for any unit, that none of the examples
are exclusionary to any person of any particular socio-economic status,
religion etc.
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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)
The project will be a summative assessment on lessons 1-6.
Students will be placed in a heist scenario where they need to locate vaults individually
by solving various one and two variable equations, both written in words and
mathematically, and finally graphing the equation and answering some analysis
questions about their graph.
This class is a 120 minute block; they have the whole time
to work on it. The process is 2 parts: first part they complete individually
with the same problems, second part is individually with different problems.
Students will produce a graph and two filled-out answer
sheets.
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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)
I will have small formative assessments after lesson 2,
lesson 5, and lesson 10 to make sure students are understanding these
critical components of the unit. Throughout the classes though there will be
informal assessment going on as homework is completed, class discussions are
had, and different activities are completed. This will include written and
verbal confirmation of understanding.
There will be one summative assessment toward the end of
the unit that will test comprehension/communication/application of the
material.
Retest/corrections will be allowed for all assessments,
but there will be a cap of how much higher a student’s grade can increase.
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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
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Introduction to Ian
and Classroom Expectations
Introduction to
Expressions (written to variable, variable to written, what are variables?)
Evaluating
algebraic expressions (substitution into equations)
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2
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Distributive Law
(feeding the chickens!)
- Dress up like a farmer and bring a
chicken and a toy tractor
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3
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Formative
Assessment on Lessons 1 and 2
Definition/terminology
of polynomials
Adding/Subtracting
Polynomials
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4
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Addition and
Subtraction Equations
- I’m thinking of a number…
Multiplication and
Division Equations
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5
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Combined Operations
Equations
containing Brackets
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6
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Formative
Assessment on lessons 3-5
Linear Relation
(Ordered Pairs)
- I’m thinking of an ordered pair…
Solution to Two
Variable Equations
Be a wizard!
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7
(Double Block)
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Summative
Assessment
- Heist Mission
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8
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Linear Models 1
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9
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Linear Models 2
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10
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Formative
Assessment on Linear Models
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(11)
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(12)
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(13)
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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 for Summative Assessment Linear Relations
Subject: Mathematics
Grade: 8
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Lesson Number: 8 of
10
Time: 120 minutes
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Big Idea or Question for the Lesson:
Can
students recollect and show comprehension and understanding of Ch 5.1-5.6?
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PLO foci for this lesson:
All of the combined PLO from 5.1 to 5.6
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Objectives: Students will be able
to (SWBATs)
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Individually recall material from Ch 5.1-5.6
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Content and Language Objectives:
- Show written understanding of the
material
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Skills/Strategies required:
- Everything from 5.1 to 5.6
- All of the required skills from 5.1 to 5.6
lesson plans
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Materials/resources:
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“Heist” Blank Part 1 and Part 2 sheets for students
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Three 4-digit number locks for lockers
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Masking tape for grid
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Black light/ markers/ some glue
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Highlighter/yellow fluorescent paper with prewritten
equations on them and names of students
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Dress up in a black outfit, black toque, black pants,
black sweater, black gloves
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Alpha, Bravo, and Charlie Signs for each group of desks
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Assessment Plan:
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Students must complete two summative assessment sheets
with their individual solutions to problems and equations required to pull
off the “Heist”
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Adaptations: [ for EALs]
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Maybe need to explain what a heist is and explain some of
the questions, but everything should be accessible
Modifications: [for slower
processers]
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No modifications
Extensions: [ for the ‘quick study’
folk]
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If student’s finish early, they can work on other class
work quietly
Hook
and Introduction
(5-7 min) (__:__ - __:__)
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Student’s
desks should be oriented in three groups, with a wide open space in the
middle of the class
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Students are
assigned to one of the three groups: Alpha, Bravo, or Charlie.
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In the open
section of the class, use the masking tape to create a 12 x 12 grid with
origin in the center for a graph (x goes from -6 to 6, y goes from -6 to 6)
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Set up the
two black lights at the back of the room for later
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Students! You
have been recruited to break into three separate vaults that are located
somewhere on this grid which is a blueprint of a bad guy’s house. The
location of these vaults are located in three lockers somewhere in this
school. To find the location of these lockers, you have to answer the
following questions and find the clues.
Development (about 100 min) (__:__ - __:__)
- Teacher-led (15 min)
(__:__ - __:__)
Students! You must individually
complete the first section before you can search for the locker. As you can
see, solving the questions will help you find the floor of the locker, locker
number, and the four digit combination to get into the locker. Inside you
will find the clue to the location of your team’s vault. Once everyone in
your group has handed in the first section to me, I will tell you the
location of your team’s locker, whether your whole group got it right or not.
This is not a race. You must be quiet in the hallways. There are guards that
if they see you, you lose. In other words, if we catch you screaming or
running, you lose marks.
- Independent Work (__:__ - __:__)
Students now have to fill out Part
1 of the Summative Assessment. This has more of the equation based questions
from Lessons 1-5. (30-40 mins)
Once they fill out the assessment
and handed in part 1 to you, you give them the instructions and each group
can now go search for their locker, open it, and find their code. When they
come back, with a seemingly blank piece of paper, tell them to figure out how
to read it and point them to a table with a black light, some other markers
to mislead them, and some glue. (10-15
mins)
Say, “OH NO, it looks like we’ve
been duped! There are way more than 3 vaults! Alpha Bravo and Charlie need to
all split up individually to locate your own vaults!” They should find their
own personalized equations to continue on with their assessment (each student
has their name beside an equation).
Now that they have their code
(equation) they have to answer part 2 of the summative assessment. This
contains a lot of graphing questions from Lesson 6. Once they have found
their vault, they can tape an x where their vault is. (30 mins)
- Class/Group Activity (__:__ - __:__)
Finding the lockers and figuring out
how to find their personal codes (use the black light!)
- Independent Work (__:__ - __:__)
Part 1 and Part 2 of Summative
Assessment
Closing (5 min) (__:__
- __:__)
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Alpha, Bravo, and Charlie, you have all successfully found
the vaults! Now we have all we need to locate the treasures inside! Perhaps
next class will be entirely focusses on figuring out how to GET to the vaults
(Linear Modelling lesson)
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No homework! Thanks for participating everyone!
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