Teacher
JOYA LAL
Unit title
GEOMETRY ( 3D) – CH 13
Subject
group and
discipline
MYP year
Mathematics
3
Unit
duration 12
(weeks)
Inquiry: Establishing the purpose of the unit
Key concept
Relationship
It refers to the connections between quantities, properties or
concepts and these connections may be expressed as models, rules or
statements. Relationships provide opportunities to explore patterns in
the world.
Related concept(s)
Generalization: A general statement
made on the basis of specific examples.
Space: The frame of geometrical
dimensions describing an entity.
Global context
Scientific and technical innovation
Exploration:
Products, processed and solutions
Statement of
Conceptual Understanding:
Different forms of generalizations of processed and products will help in making relevant connects
and relationships
Statement of Inquiry:
Generalizing relationships between different dimensions of space can help analyze and generate products, processes and solutions.
Inquiry questions
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Factual—
● What are different 2D and 3 D shapes around ?
● How to calculate volumes and surface areas of beakers?
● How is capacity calculated?
● What is the difference between area and surface area of various shapes?
● What is the difference between volume and capacity?
Conceptual—
● How do 2 D shapes generate the 3D prisms ?
● How do we derive the formula of volume of a Pyramid through the volume of a Prism?
● How are the volumes of pyramids , cones and spheres related to corresponding prisms
Debatable—
● How can we use mathematics to aesthetically organise shapes in a given space ?
● To what extent is Mathematics instrumental in designing smart space around us ? (Service as Action connection)
● To what extent surface area of a shape relate to the volume of the shape?
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Objectives
Summative assessment
A: Knowing and understanding
Outline of summative assessment task(s)
including assessment criteria:
i.
select appropriate mathematics when
solving problems in both familiar and
unfamiliar situations
ii.
apply the selected
mathematicssuccessfully when solving
problems iii. Solve problems correctly in a
variety of contexts.
B: Investigating patterns
i.
select and apply
mathematicalproblemsolving techniques to
discover complex patterns
ii.
describe patterns as general
rulesconsistent with findings
iii.
prove, or verify and justify,
generalrules.
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Relationship between summative assessment
task(s) and statement of inquiry:
Sit down assessment
Students will select and apply knowledge
learnt in familiar and unfamiliar situations by
applying relationships using generalisations
and spatial reasoning of 3D shapes
analysing the products in their behaviour with
respect ot surface areas and volumes . They
will use various problem solving
techniques used throughout the unit such as
derivation techniques to solve problems in
different contexts with respect to
Geometry .
Generalizing relationships between different
Students will understand mathematical
relationships using different forms of shapes dimensions of space can help analyze and generate
products, processes and solutions.
and will be able to predict pattern based on
Summative Assessment will assess the
current dimensions . They will discover
different forms of 3D shapes learnt by the
general rules with respect to prisms and
students. It will asses their understanding of
pyramids .
Volume , Surface areas and capacity . It will
as well as capacity through the context
also assess how they generalize the formula
given. They will describe and model
for Prisms and pyramids through the study of
spaces general rules for relationships
respective nets of solid shapes in the real
using formula and simplifications. They
world context . The students will also apply
will justify and verify their findings using
the concept of capacity with respect to various
products .
3
algebraic formulas for surface areas and
volumes.
C: Communicating
i.
use appropriate
mathematicallanguage (notation, symbols
and terminology) in both oral and written
explanations
ii.
use appropriate forms of
mathematical representation to present
information
iii.
move between different forms
ofmathematical representation iv.
communicate complete, coherent and
concise mathematical lines of reasoning
Students will represent real life situations
by modelling relationship to space and
shapes and will be able to generalize rule to
make predictions with respect to nets of solid
shapes . They will be able to explain and
represent using pattern/ products and
designs in a coherent and concise manner
both using algebra and in words the real
life contexts of volumes and surface
areas . They will organize their findings
logically as per context and questions.
v. organize information using a logical
structure
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D: Applying mathematics in real-life
contexts
i.
identify relevant elements of
authenticreal-life situations
ii.
select appropriate mathematical
strategies when solving authentic reallife situations
iii.
apply the selected
mathematicalstrategies successfully to
reach a solution
iv.
justify the degree of accuracy of
asolution
Students will eliminate and accept values
of Shapes in patterns based on their real
life context. They will use algebraic
techniques to solve real life problems. They
will predict future values in case of a real life
situation using the given pattern/
generalisations to 3 D space and will justify
the accuracy of prediction using different
methods. They will also identify and justify
its authenticity with respect to the real life
situation presented in the problem based on
the 1D , 2 D and 3 D concepts of
measurements .
v.
justify whether a solution
makessense in the context of the
authentic real-life situation
Approaches to learning (ATL)
Skill Categories
Skill Cluster
Communication skills
Communication
Skill indicator and description
In order for students to identify and explain pattern and analyse general
rule with respect to 3 D – forumlas .(Objective Ai, B ii, Ci,ii,iii)
They need to make inferences, draw conclusions and make
predictions with respect to shapes & spaces .
Explicitly taught skill strategy: Problems solved in the classroom using
various resources
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Critical Thinking
In order for students to complete their formative assessment 1,
assessing criteria A,C,D where they generalize / patterns in 2 D & 3 D
spaces real life relationship and analyse it using different Formulae.
● Formative
assessment 2 assessing criteria A,C,D
(Aiii, Bi, Ciii,iv,v, Dii,iii,iv,v)
Thinking
They need to model relationship of different representation of 3 D
shapes special with respect to surface areas and volumes .
Explicitly taught skill strategy: deriving formulae in the classroom
using various resources
Thinking
Transfer skills
In order for students to find best fittin shape they apply their
knowledge of capacity to various objects in their homes . (Objective
Ai, ii, Ciii, Dii, iii)
Action: Teaching and learning through inquiry
Content
Learning process
Factual Knowledge:
Learning experiences and teaching strategies
- Surface Areas of 3 D
shapes
Week 1:
Acquire:
●
Different Geometry notation using nets of solid shapes (interactive online
activity )
●
Resource #1a
● Students will learn the difference between 2 D & 3 d shapes with respect to Surface areas
volumes .
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Resource#1b
Connect:
● Students will express Surface area of 3 D shapes as the area of all the faces pattern/
generalizations they will notice and summarize rules for how to relate the 2 D bases to the
respective 3 D containers as projections . Calculating their volumes in turn
Resource #2a
Transfer:
International Mindedness:
The students will appreciate the history of Geometry
Euclid the father of geometry
https://www.youtube.com/watch?v=CrIdJKo0whs
https://www.youtube.com/watch?v=WqzK3UAXaHs&list=PL26812DF9846578C3&t=276s
Resource #2b
Throughout the whole unit students will look at discoveries and contributions made by scientific and
technical innovations over time. Student use the information provided and additional research to
communicate an overview of history of Mathematics with respect to Platonic Solids . Students can
create timeline showing major discoveries after Euclid using Adobe spark
Free Timeline Maker with Online Templates | Adobe Spark
Timeline of Mathematics | Mathigon
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Service as Action:
Students can make a gallery walk about contribution of mathematicians from different cultures about
with major contribution to number system.
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(Debatable inquire question #3) (Learning Outcome: Develop international mindedness through global
engagement, multilingualism and intercultural understanding)
Week 2:
Acquire:
● Students learn the connection between Cryosection of prisms & their volumes .
Volumes of 3 D shapes
Conceptual Knowledge:
● Deriving the formulae
For Surface areas
that and identifying pattern
to 3 D shapes
● Students learn to derive the volume of a pyramids through the volume oa corresponding prizm
(Resource #3a)
Connect:
Students solve questions involving surface areas and volume of 3d objects.
Transfer:
Exension: Students try to design their own complex shapes and derive their surface areas &
volumes (Resource # 3b)
(Interdisciplinary connection with DT )
Week 3:
Capacity of beakers / vesicles
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Acquire:
● Students review the concepts of Capacity
● Students are introduced to the concept of capacity Connect:
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● Finding the Volumes of
complex shapes
● Students solve problems based on Surface areas & volumes (Resource #4
● using Nearpod lesson (Resource #4c)
Self Practice (self marking) online exercises :
● Formulae can appear in
different, but equivalent,
forms, or representations,
which can
help us to establish General
patterns in 2D & 3 D space .
Procedural knowledge:
● Modelling real-life situations
with the structure of
Beakers / Rooms / Utensils
and geometric shapes
allows for prediction,
analysis and interpretation.
● Application of Formulae to
complex shapes provide the
means to find best fitting
space to objects which
model real-life situations.
● Patterns in Shapes / Space
in form the development of
Critical and creative tools
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that can be applied to find
unknowns.
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Acquire:
● Students establish deeper understanding of 3 D shapes (using Nearpod lesson Resource #8)
and various types of Prisms & Pyramids Connect:
●
Understanding the difference between Volume & Surface area .
Students research to difference between 1kg of Milk and 1 litre of Milk (ID connection with
Science & Knowledge of BEAKERS OF VARIOUS SHAPES )
Service as Action:
● Students will research in groups / individually about shapes and volumes paced in various
shapes and suggest the best possible packaging for the Diwali gifts for gifting the needy as
part of their joy of giving week .
(Learning Outcome: Creative thinking ) (Debatable question #3)
Formative assessment
Informal feedback:
● Teacher feedback during class based on class observation
● Structured feedback on formative tasks to prepare students for summative assessment
Formative Assessment:
● Formative assessment 2 – Sit down assessment to be taken on Assess prep assessing criteria
A ,C and D
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assessment 1 – Students in group / individually consider your team to be personal
Designer and evaluate from a given set of shapes the best possible option for the client
considering surface areas and volumes and compile it in a presentation (using
PPT/sway/Flipgrid/Adobe Spark)
● Formative
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Differentiation
Content:
Offer ways of customizing the display of information: (As per the UDL guidelines)
● Regular classroom teaching: use of white board (whiteboard.fi) with each individual student
whiteboard, Nearpod open ended questions, Transum self learning exercises to help visualise
and learn using different methods.
Offer alternatives for visual information: (As per the UDL guidelines)
● Provide auditory cues for key concepts using Math tool in one note where auditory notes will be
provided.
●
GeoGebra to visualise solid shapes & their measurements
Provide options for language, mathematical expressions, and symbols(As per the UDL
guidelines)
● Pre-teach vocabulary ( Geometry ) and symbols, especially in ways that promote connection
to the learners’ experience and prior knowledge
● Highlight how ID , 2 D & 3 D shapes relate to measurements
● Highlight patterns, critical features, big ideas, and relationships (As per the UDL
guidelines) ●
Use multiple examples of cubes cuboids , prisms & pyramids to emphasize
critical features of capacity . Learning extension:
● Extra challenging questions provided in task sheets and in the class
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● Students can research on various puzzles originated on various parts of world based on
properties of 3 D shapes and Platonic solids .
Process:
Increase mastery-oriented feedback (As per the UDL guidelines)
● Provide feedback that is frequent, timely, and specific
Provide options for self-regulation (As per the UDL guidelines)
● Support activities that encourage self-reflection and identification of personal goals
Facilitate personal coping skills and strategies (As per the UDL guidelines)
● Additional help to be provided outside classroom during zero lesson
● Class recordings available for students to pace their learning
● Extra time provided in assessments for learning support students
● Additional time provided for submissions to enable self paced learning Product:
● All students will learn to identify pattern and establish real life relationships using shapes
around us .
● Students will be able to use the logic of shapes to generalise pattern to solve for surface
areas and volumes of complex shapes .
Resources
Textbooks:
●
Oxford Mathematics
●
Haese Mathematics
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Online Graphing and interactive activity software’s:
●
Transum
●
Nearpod
●
Geogebra
●
Desmos:
Resource #1a Surface Areas
https://www.transum.org/Software/SW/Starter_of_the_day/Students/Surface_Area.asp?Level=2
Resource #1aa Volumes
https://www.transum.org/Software/SW/Starter_of_the_day/Students/Volume.asp
Resource #1b ( difference between Surface Areas & volumes
https://www.youtube.com/watch?v=muw-MQeIkO4
Resource # 2a PROPANE TANK
https://www.map.mathshell.org/download.php?fileid=828
Resource # 2b Capacity & volumes
https://www.youtube.com/watch?v=GKCE8ohIBqE
Resource #3a
https://nearpod.com/t/math/6th/surface-area-volume-part-b-L720020
Resource #3b
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Geometric-Solids/
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Resource#4a GeoGebra
https://www.geogebra.org/m/avkgxbea#material/rCxXxFhE
Resource #4b DESmos
https://teacher.desmos.com/activitybuilder/teacherguide/5e6931dfc628310c3b172700
https://www.transum.org/Maths/Activity/Volume/default.asp?Level=2
https://www.pbslearningmedia.org/resource/mkcpt.math.g.triangularprism/finding-the-volume-of-a-triangular-prism/#.WlaXkK6nHIU
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Resource # 5a
https://www.youtube.com/watch?v=qJwecTgce6c
Resource #6
https://www.youtube.com/watch?v=G_51PEKRItU
Resource #7
https://docs.google.com/spreadsheets/d/1MNdYC_MSebo37_8rejnyE6cjG3EnDfBr9QK5t1L5sk4/edit#gid=0
Resource #8
https://nearpod.com/t/math/7th/volume-of-prisms-pyramids-68-L69925765
Other Resources:
1.
2.
3.
4.
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/geometric-solids/e/identify-parts-of-3d-shapes
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/geometric-solids/e/identify-geometric-solids--3d-fig
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-volume-with-fractions/e/find-volume-by-mult
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-surface-area/v/surface-area-word-problem-ex
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Reflection: Considering the planning, process and impact of the inquiry
Prior to teaching the unit
During teaching
After teaching the unit
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Students are already well versed with the
concept of Areas and perimeters of
standard shapes and their formulas .
This unit will further enhance their
understanding of the dimensions in real
life , difference between surface areas
and volumes and capacity . They will be
able to understand the different types of
sphapes and spaces in rela life . They will
explore the application capacity in real life
. In line with the IB learner profile, in this
unit students will strive to be:
Knowledgeable: By understanding and
applying logic ( not memorise just the
formulas to detife the volumes )
Thinkers: By recognising and applying
their knowledge and conceptual
understanding to real life and unfamiliar
contexts. They will able to make
predictions based on given information
about the best shape fitting in the given
space .
Communicators: By
learning to
communicate mathematically in a logical
and coherent manner and by
communicating using different forms of
shapes and its application in the correct
manner with respect to the given context .
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Inquirers: Students will learn to inquire
more about concepts and how they can
be related to real life situations.
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