EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4 week unit of work in secondary school
mathematics
Topic of unit: SI
measurements, Surface Area and Volume
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)
SI measurement is an
important topic because it is useful for changing units as different things have different kinds of measurements in life. Instead of simply
using a unit converter, through this topic, students learn techniques to convert
between Imperial and SI units by using proportions. This topic assists them
in making connections between units and having a better understanding of
ratios and proportions in mathematics. Eventually, students will be able to
learn more than one way of approaching a problem.
Volume & surface are is also
an important topic to be included in the curriculum, because it is useful to know when students
have to think visually about different 3-D objects to figure out their volume and
surface area. For example, when making 3-D geometric shapes or
filling a container with liquid, students should know the formula for the
area and volume of various 3-D shapes and understand the different
measurement units.
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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 geometry is about lengths, angles, areas, and volumes
of objects. Ideas in geometry first appeared in the ancient Indus Valley and
ancient Babylonia from around 3000 BC. As the ancient Egyptions found the
area of a circle, they could figure out that the area of the cylinder had to
do with the base and the height. Similarly, students can find the
relationship between the volumes of water in cylinder and cone or volumes of
water in pyramid and prism. Moreover, by measuring the diameter of circular
objects, students can identify the relationship between the diameter and the
circumference of a circle.
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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)
Since students of different
backgrounds are used to different measurements, they should
present the measurements, which they are familiar with, to the class. In this case, students will understand the international measuring
system of units by country, and this activity will attract some students’
attention and help them engaged with learning measurements. Moreover, in order to enhance student self-efficacy and their learning, students
should be encouraged to discuss with partners and present their ideas to the
class orally as well as in writing on the board, since they learn more from watching others solving the problem. Especially
for ESL students it is a very important part of learning, because they can
practice oral skills as much as their writing skills. SI measurements and
surface area & volume are useful in science as well when students do the
experiments and calculate the density and the volume of geometric objects.
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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 topic is the surface area & volume, and it
aims to help students familiarize themselves with 3-D objects by creating solid
3-D geometric shapes. They have to create patterns for each 3-D objects and
make the actual shapes. Then, students need to find their surface areas &
volumes and show their reasoning in their reports with the picture of their objects.This
project should last about two weeks, and they should make a project in a
group of three people. Through this project, students are able to organize
their thoughts about 3-D objects, which are found in real life.
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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)
For formative assessment, I will give students a
quiz every three classes. The quiz should include some multiple choice
problems and short answer questions, and this is to check for students’ understanding.
For summative assessment, students make the unit project and the unit test at
the end of the unit of measurement and surface area & volume. For informal/
observational assessment, each group of three walk from station to station,
where they make different geomeric shapes with the given 3-D math nets and
measure the side lengths to calculate the surface area. They have to write
the answers in different units.
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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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SI Measuremet: Introducing SI units
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2
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Imperial Measurement
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3
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Conversion between SI & Imperial Units
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4
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-Quiz on Measurement: Using Unit Analysis and
proportional reasoning to verify the conversion.
-Units of Surface Area
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5
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Surface Area of Sphere: Orange activity
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6
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Surface Area of a Pyramid, Prism, Cylinder, Cone: Create
3-D objects
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7
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-Quiz on Surface Area of 3-D objects
- Units of Volume
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8
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Volume of a Cone, Pyramid, and Sphere: Comparing the
volumes of liquid in different 3-D objects (models in plastic)
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9
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Surface Area and Volume of a Composite Figure
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10
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Quiz on both Surface Area and Volume of 3-D objects
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11
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Review Day
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12
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-Unit Test on Measurement, Surface Area &
Volume,
-Unit Project due: Reports about surface area & volume of 3-D objects
created by students
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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.
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Lesson Plan
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Subject: Mathematics
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Lesson #6
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Grade: 10
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Time: 80 minutes
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Topic: Surface Area of a Pyramid,
Prism, Cylinder, Cone: Create 3-D objects
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Big
ideas: Students will understand how to
solve problems, using SI and imperial units, that involve the surface area of 3-D
objects.
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Objectives:
3.2 Determine the surface area of a right cone, right cylinder, right prism, right pyramid or sphere, using an object or its labelled diagram. 3.4 Determine an unknown dimension of a right cone, right cylinder, right prism, right pyramid or sphere, given the object’s surface area and the remaining dimensions. 3.5 Solve a problem that involves surface area, given a diagram of a composite 3-D object. |
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Content: What students will know
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Language Objectives
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Curricular Competencies
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- (Key
vocabulary) Different shapes of 3-D objects.
- The total
area of the surface of a 3-D object.
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- Students
will be able to orally describe the properties of 3-D objects
(number of each surface, different shapes of each surface, and the area of each surface). |
- Students
work in pairs in
Think/Pair/Share to figure out the total area of the surface of a 3-D object. - Students calculate the unknown dimension of the object, with its surface area and the remaining dimensions given. |
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Materials/equipment needed: (powerpoint and
nets in the “Materials” file in the email)
powerpoint, calculators, rulers, nets
(3-D models: cylinder, prism, pyramid, cone)
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Introduction
(10 mins):
(10 mins) Introduce real-life examples of 3-D object using power point presentation and make students figure out which one has which shape. |
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Body (60 mins):
(5 mins) Recap: Check for students’ understanding
Draw the sphere on the board and let students
solve for its surface area in different units.
(20 mins) Students in groups move from station to station to figure out the total surface area of the 3-D figures. Using the given 3-D math nets, they have to build 3-D object. Through this process, they will be able to familiarize themselves with the properties of different 3-D objects. Each station has a different net for 3-D model (pyramid, prism, cylinder, cone).
(20 mins) As students orally explain how
they have got the solution, a teacher goes over the process of calculating
the total surface area of each 3-D shape.
(15 mins) Students individually write write the answer on their mini-boards. They are asked to calculate the surface area of any 3-D object that I show on the board. Also, they calculate the unknown dimension of the 3-D object with its surface area given. |
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Closing (10
mins):
Students discuss about the real life situation where people have to calculate surface area of the objects. |
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Assessment
Plan: (Infomative assessment at the end of
the lesson)
Students individually write the answer on their mini-boards. |
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Adaptations:
For check-in on learners’ prior knowledge, students can take a short
quiz on the surface area of the sphere at
the beginning of the lesson.
- key vocabulary: diameter, radius, length, width, height, apex, base, face, cone, cylinder, prism, pyramid, sphere Modifications: - Instead of introducing mini-board activity as informative assessment, make students discuss and write down the solution of the 3-D object given in the problem on the big paper. - Instead of letting students in groups move from station to station, give each group of students only one 3-D object to figure out the surface area of the object and present their solution to the class. Extensions: - For homework assignment, students are asked to bring any 3-D object with the calculated surface area of the object.
- Students
have to create their own 3-D
objects and calculate its surface area.
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