Difference between revisions of "Mensuration"

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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
  
= Concept Map =
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=== Concept Map ===
 
__FORCETOC__
 
__FORCETOC__
<mm>[[Mensuration.mm|flash]]</mm>
 
  
= Textbook =
+
[[File:Mensuration.mm|flash]]
#[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter16.pdf Karnataka text book for Class 10, Chapter 16 - Mensuration]
+
===Additional Resources===
  
#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?jemh1=13-14 NCERT 10 Textbook Chapter 13-Surface Areas and Volumes]
+
==== Resource title ====
 +
[http://www.mathopenref.com/tocs/solidtoc.html Mensuration]
  
=Additional Information=
+
====OER====
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/43064607" |width=450 |height=360 |border=1 }}
+
#Web resources:
 +
##[http://www.primaryresources.co.uk/maths/mathsE1.htm Primary resources] : Website gives printable resources for understanding measurements.
 +
##[http://www.campusgate.co.in/2011/11/areas-and-mensuration.html Campusgate]:  An overview on mensuration is given in this website.
 +
##[[wikipedia:International_System_of_Units#General_rules|Wikipedia]]: For general rules while writing units in measurements is described in this web page.
  
==Useful websites==
+
#Books and journals
#[http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf Download PDF].  This is a good website for interesting activities on mensuration.<br>
+
#Textbooks
#For standard measurements :      [http://www.primaryresources.co.uk/maths/mathsE1.htm click here]
+
##[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?jemh1=13-14 NCERT 10 Textbook Chapter 13-Surface Areas and Volumes]
#[http://www.campusgate.co.in/2011/11/areas-and-mensuration.html click here]
+
#Syllabus documents
#For general rules while writing units :[http://en.wikipedia.org/wiki/International_System_of_Units#General_rules click hre]
+
====Non-OER====
#For teacher reference on dimension. [http://www.britannica.com/EBchecked/topic/163641/dimension click here]
+
#Web resources:
#The metric system is enormously powerful as a standard measurement system.  In this video, you can explore from the very small to the very large and appreciate what a degree of ten means!
+
##[https://www.britannica.com/science/dimension-geometry Encyclopedia Britannica]: Gives a brief on dimensions.
{{#widget:YouTube|id=0fKBhvDjuy0}}
+
##[https://www.sciencehq.com/math-formulas/mensuration-formulas.html Science HQ]: The website lists formulas used in mensuration.
 +
##[https://www.wiziq.com/tutorial/197452-surface-area-of-cylinder-an-activity WizIQ] : An activity on surface area of cylinder.
 +
##[http://www.teachmathematics.net/page/10938/prism-people teachMathematics]: Lesson on understaning prisms with activity.
 +
#Books and journals
 +
#Textbooks
 +
##[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter16.pdf Karnataka text book for Class 10, Chapter 16 - Mensuration]
 +
#Syllabus documents (CBSE, ICSE, IGCSE etc)
 +
{{#widget:YouTube|id=0fKBhvDjuy0}}  
  
==Reference Books==
+
The metric system is enormously powerful as a standard measurement system.  In this video, you can explore from the very small to the very large and appreciate what a degree of ten means!
  
= Teaching Outlines =
+
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/43064607" |width=450 |height=360 |border=1 }}
  
==Concept #1. What is Mensuration ?==
+
Slides with problems and options for solutions.
===Learning objectives===
 
#Recognise units and measurement
 
# Defines mensurstion
 
# Differentiates  standard and non-standard ways of measurements.
 
# Importance of having standardised measurements.
 
# Relates length,breadth,perimeter ,area
 
# Recognise different units 
 
# Classify 2D and 3D figures
 
# They should develop the ability to calculate  the area, perimeter, volume or side  of many different figures.
 
  
===Notes for teachers===
+
===Learning Objectives===
Source: [http://depts.washington.edu/chemcrs/bulkdisk/chem120A_sum06/handout_CH%201-4%20TIMBER.pdf Click here]<br>
+
*Recognizing informal units of measurements
Summary : Measurement are an important part of our everyday life.   Think about your day; you probably made some measurements. Perhaps you checked your weight by stepping on a scale,measuring shoes to fit your feet in the shoe store, or saw measuring up houses when they are doing renovations etc. If you did not feel well, you may have taken your temperature. To make some soup, you added 2 cups of water to a package mix. If you stopped at the Petrol bunk, you watched the petrol pump measure the number of litres of petrol you put in the car.
+
* Differentiating standard and non-standard ways of measurements.
 +
* Understanding importance of having standardized measurements.
 +
* Justifying  accuracy of Standard units of measurements
 +
* Relating length,breadth,perimeter ,area
 +
* Recognizing different units 
 +
* Classifying 2D and 3D figures
 +
* Calculating the area, perimeter, volume or side  of many different figures.
  
===Activities===
+
=== Teaching Outlines ===
#[[Mensuration_what_is_mensuration_activity_1| Activity 1 - What and how to measure]]
+
====Concept #1. What is Mensuration ?====
#[[Mensuration_what_is_mensuration_activity_2| Activity 2 - Scale Drawing]]
+
Measurements are an important part of our everyday life.  Think about your day; you probably made some measurements. Perhaps you checked your weight by stepping on a scale,measuring shoes to fit your feet in the shoe store, or saw measuring up houses when they are doing renovations etc. If you did not feel well, you may have taken your temperature. To make some soup, you added 2 cups of water to a package mix. If you stopped at the Petrol bunk, you watched the petrol pump measure the number of litres of petrol you put in the car.
  
==Concept #2.Informal units of measurements ==
+
=====Activities=====
===Learning objectives===
 
#Recognise informal units of measurements
 
#Justify the accuracy of Standard units of measurements
 
  
===Notes for teachers===
+
====== [[What and how to measure]] ======
# The teacher can ask the students to gather information regarding earlier traditional measuring ways from their elders and have an initial discussion in the classroom.
+
Measurement is the act of determining a target's size, length, weight, capacity, or other aspect.  
#  The traditional ways of measurements are a type of measure which uses non-standard units such as hand spans, armlengths, footsteps or pattern blocks to measure length, area, etc.
 
# Non-standard measurements are not always the same but vary from person to person.
 
  
===Activities===
+
====== Concept #2.Informal units of measurements ======
#[[Mensuration_informal_units_of_measurements| Activity 1 - Estimating Distances]]
+
The traditional ways of measurements are a type of measure which uses non-standard units such as hand spans, arm lengths, footsteps or pattern blocks to measure length, area, etc. Non-standard measurements are not always the same but vary from person to person.
  
==Concept #3. Standard units of measurements==
+
===== Activities =====
===Learning objectives===
 
# Develops the ability to obtain accurate measurements and communicate those measurements is a key requirement for progress.
 
# Standardised measuring units ensure uniformity in meaurements.
 
# Recognise The standard unit for length is metre, for weight id kilogram, for time is second, for temperature is Kelvin and for amount of substance it is mole.
 
  
===Notes for teachers===
+
======  [[Estimating distances]] ======
 +
The teacher  asks the students to gather information regarding earlier traditional measuring ways from their elders and have an initial discussion in the classroom
 +
 
 +
====Concept #3. Standard units of measurements ====
 
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.<br>
 
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.<br>
 
For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".<br.
 
For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".<br.
 
The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.
 
The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.
  
===Activities===
+
=====Activities=====
#[[Mensuration_standard_unit_of_measurements| Activity 1 Hunting Treasure and Measuring - Part 1]]
+
 
#[[Mensuration_standard_unit_of_measurements_part_2| Activity 2 Hunting Treasure and Measuring - Part 2]]
+
====== [[Hunting Treasure and Measuring - Part 1]] ======
 +
Measuring things around us by using various instruments for understanding how parameters are measured differently.
 +
 
 +
====== [[Hunting Treasure and Measuring - Part 2]] ======
 +
Exploring various modes of measurements and standard units for them.
 +
 
 +
====Concept # 4. Scale drawing====
 +
A Scale drawing is a drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale).
 +
 
 +
Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car, an airplane, we need scale drawings to represent the size.
 +
 
 +
Drawing to scale is a tool that Engineers use for many different tasks. One key part of every scale drawing is the scaling factor. This number represents the degree to which our scale drawing or scale model has been reduced in size when compared to the original.
 +
 
 +
=====Activities=====
 +
'''[[Scale drawing - Part 1]]'''
 +
 
 +
This activity explores representation of  actual distances on paper using proportional distances. 
 +
 
 +
====== [[Scale drawing - Part 2]] ======
 +
Activity investigates how a blue print represents actual dimensions.
 +
 
 +
==== Concept #5. Measurements in solid figures ====
 +
'''Concept Map'''
 +
 
 +
[[File:measurements_in_solids.mm|Flash|link=http://karnatakaeducation.org.in/KOER/en/index.php/File:Measurements_in_solids.mm]]
 +
 
 +
====Concept #1 - [[Introduction to solid figures]]====
 +
Group activity for children to explore different dimensions in solids.
 +
 
 +
Activity 1- [[Visualising solid shapes]]
 +
 
 +
Activity 2- [[3D shapes model making]]
 +
 
 +
====Concept #2.Cube====
 +
A cube is a 3-dimensional figure having six congruent square faces joined along their edges. The three edges join at each corner to form a vertex. The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids. A cube has all edges the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face.Surface area = <math>6s^2</math>, Where s is the length of any edge of the cube. Volume enclosed by a cube is the number of cubic units that will exactly fill a cube.The volume of a cube is found by multiplying the length of any edge by itself thrice. So if the length of an edge is 's' cm, the volume is <math>s^3</math>
 +
=====Activities=====
 +
======[[Building cubes]]======
 +
This activity explores various methods of making cubes
 +
 
 +
======[[Surface area and volume of a cube]]======
 +
Cube is introduced and analysed to calculate the surface area.
  
==Concept # 4. Scale drawing==
+
====Concept #2.Cuboid====
===Learning objectives===
+
A cuboid is a 3 dimensional solid having 6 rectangular faces. Opposite faces of a rectangle are congruent.
# Represents  actual distances on paper using proportional distances.
+
=====Activities=====
# Recalls  the definition and meaning of scale
+
======[[Surface area of a cuboid]]======
#  learns  about the tools of measuring
+
Cuboid as a shape and its properties are examined.
  
===Notes for teachers===
+
======[[Volume of a cuboid using unit cubes]]======
# A Scale drawing is a drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale).
+
====Concept #3.Cylinder====
# Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car, an airplane, we need scale drawings to represent the size.
+
A cylinder is a closed solid that has two parallel (usually circular) bases connected by a curved surface. It has two ends, called bases, that are usually circular. The bases are always congruent and parallel to each other. On 'unrolling' the cylinder one would find that the side is actually a rectangle when flattened out. The height h is the perpendicular distance between the bases. The radius r of a cylinder is the radius of a base. Axis of the cylinder is a line joining the center of each base. Hollow Cylinder is the one with open top and base. Ex. cylindrical tube.
# Drawing to scale is a tool that Engineers use for many different tasks. One key part of every scale drawing is the scaling factor. This number represents the degree to which our scale drawing or scale model has been reduced in size when compared to the original.  
 
===Activities===
 
#[[Mensuration_scale_drawing_activity_1|Activity 1 - Scale Drawing - Part 1]]
 
#[[Mensuration_scale_drawing_activity_1|Activity 2 - Scale Drawing - Part 2]]
 
  
==Concept #==
+
===== Formulas =====
===Learning objectives===
+
CSA=<math>{2}{\pi}{r^2}{h}</math>
===Notes for teachers===
 
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
 
  
===Activities===
+
Volume of Cylinder=<math>{\pi}{r^2}{h}</math>
#Activity No #1 '''Concept Name - Activity No.'''
 
#Activity No #2 '''Concept Name - Activity No.'''
 
  
 +
TSA of Cylinder=<math>{2}{\pi}{r}{(r+h)}</math>
  
 +
Volume of Cylinder When h=h/2 is<math>{\frac{{\pi}{r^2}{h}}{2}}</math> <math>{\frac{{1}}{3}}{X}{\frac{{22}}{7}}{7^2}{14}</math>
 +
=====Activities=====
 +
======[[Surface area of a cylinder]]======
 +
The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.
  
==Concept #==
+
======[[Paint and fill the Cylinder]]======
===Learning objectives===
+
The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.
===Notes for teachers===
 
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
 
  
===Activities===
+
====Concept #4. Cone====
#Activity No #1 '''Concept Name - Activity No.'''
+
A cone is a three dimensional solid with a circular base that narrows toward a point, called its vertex. It has a flat circular base, has 1 side which is a curved surface. Shapes which resemble a cone are said to be conical. A cone has a lateral surface area which is the area of its curved surface. It has a total surface area which is the sum of the area of its curved surface and its circular base.
#Activity No #2 '''Concept Name - Activity No.'''
+
=====Activities=====
 +
======[[Surface area of a cone]]======
 +
Areas related to cone are introduced with geogebra sketch.
  
=Assessment activities for CCE=
+
======Concept #6. Sphere======
 +
Sphere is a solid figure where all points are at an equal distance from the center point.It's a ball. It is perfectly symmetrical. It has no edges or vertices (corners). It is not a polyhedron. All points on the surface are the same distance from the center which is the radius "r" of the circular shape. Of all the shapes, a sphere has the smallest surface area for a volume. i.e it can contain the greatest volume for a fixed surface area.
 +
=====Activities=====
 +
======[[Baseball and string activity to find the surface area of a sphere]]======
 +
This activity has been taken from the website  [http://www.ehow.com/info_7838171_classroom-activities-surface-area-sphere.html ehow.com]
 +
====Concept #7. Pyramid====
 +
A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A triangular pyramid with all equilateral triangled faces becomes the regular tetrahedron, one of the Platonic solids. The base of a regular pyramid is a regular polygon and its faces are equally sized triangles. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. A right pyramid has isosceles triangles as its faces and its apex lies directly above the midpoint of the base.
 +
=====Activities=====
 +
======[[Surface area of a pyramid]]======
 +
Investigating areas of surfaces in a pyramid is approached with this activity.
  
= Hints for difficult problems =
+
====Concept #8.Prism====
 +
A prism is a polyhedron for which the top and bottom faces (known as the bases) are congruent polygons, and all other faces (known as the lateral faces) are rectangles. A prism is described by the shape of its base. For instance, a rectangular prism has bases that are rectangles, and a pentagonal prism has bases that are pentagons. When the sides are rectangles, the shape is known as a right prism, indicating that the lateral faces meet the sides of the base at right angles. A rectangular prism can also be called a cuboid. Parts of the prisms - faces, edges and vertices. The characteristics of a prism. Deriving formulae for surface area and volume of a prism..
 +
=====Activities=====
 +
======[[Prism people]]======
 +
This activity has been taken from the website [http://www.teachmathematics.net/page/10938/prism-people teachMathematics].
  
1.Craft teacher of a school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed?
+
[[Difference between Prism and Pyramid]]
Exercise 16.1 Problem 7.[[Mensuration_problems#Problem_1 |solution]]
 
  
2.Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51cm, if the material of which it is made weighs 10gm/ [[Mensuration_problems#Problem_2 |Solution]]
+
=====Solved problems/ key questions (earlier was hints for problems).=====
 +
[[Frustum of Cone]]  
  
3.A Cylindrical container of radius 6cm and height 15cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base , find the radius of the cream cones [[Mensuration_problems#Problem_3 |Solution]]
+
===Projects (can include math lab/ science lab/ language lab)===
 +
*'''Cylindrical Elephant''': Let us make an elephant using only cylindrical objects.
  
= Project Ideas =
+
*'''Project -01-Cylinder'''
 +
**Playing with shuttle cock case**
 +
Materials required:
 +
#Empty cylindrical shuttle cock case
 +
#Scissors
 +
#Instrumental box
 +
#Papers
 +
#Hard board
 +
#Pins/Nails
 +
#Gum
 +
#Glitter pens
 +
*Procedure:Take an empty cylindrical shuttle cock case, measure its height and radius of its base.Calculate its CSA,TSA and volume.Record these calculations in sheets. Separate the lid and then with the help of cutter take out circular base and top.By using scissors cut the cylinder vertically(also the portion attached to lid).Now calculate areas of these four portions separately. Add all the four areas and compare it with your earlier result of TSA of cylindrical shuttle cock case.
 +
===Assessments - question banks, formative assessment activities and summative assessment activities===
 +
Categories will be:  (Subject), (Topic), (Class 8), (Class 9), (Class 9), (Concept Map), (Question banks), (Assessments), Formative, Summative
  
= Math Fun =
+
[[Category:Class 8]]
 +
[[Category:Mensuration]]

Revision as of 10:53, 15 June 2022

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]

Additional Resources

Resource title

Mensuration

OER

  1. Web resources:
    1. Primary resources : Website gives printable resources for understanding measurements.
    2. Campusgate: An overview on mensuration is given in this website.
    3. Wikipedia: For general rules while writing units in measurements is described in this web page.
  1. Books and journals
  2. Textbooks
    1. NCERT 10 Textbook Chapter 13-Surface Areas and Volumes
  3. Syllabus documents

Non-OER

  1. Web resources:
    1. Encyclopedia Britannica: Gives a brief on dimensions.
    2. Science HQ: The website lists formulas used in mensuration.
    3. WizIQ : An activity on surface area of cylinder.
    4. teachMathematics: Lesson on understaning prisms with activity.
  2. Books and journals
  3. Textbooks
    1. Karnataka text book for Class 10, Chapter 16 - Mensuration
  4. Syllabus documents (CBSE, ICSE, IGCSE etc)

The metric system is enormously powerful as a standard measurement system. In this video, you can explore from the very small to the very large and appreciate what a degree of ten means!

Slides with problems and options for solutions.

Learning Objectives

  • Recognizing informal units of measurements
  • Differentiating standard and non-standard ways of measurements.
  • Understanding importance of having standardized measurements.
  • Justifying accuracy of Standard units of measurements
  • Relating length,breadth,perimeter ,area
  • Recognizing different units
  • Classifying 2D and 3D figures
  • Calculating the area, perimeter, volume or side of many different figures.

Teaching Outlines

Concept #1. What is Mensuration ?

Measurements are an important part of our everyday life. Think about your day; you probably made some measurements. Perhaps you checked your weight by stepping on a scale,measuring shoes to fit your feet in the shoe store, or saw measuring up houses when they are doing renovations etc. If you did not feel well, you may have taken your temperature. To make some soup, you added 2 cups of water to a package mix. If you stopped at the Petrol bunk, you watched the petrol pump measure the number of litres of petrol you put in the car.

Activities
What and how to measure

Measurement is the act of determining a target's size, length, weight, capacity, or other aspect.  

Concept #2.Informal units of measurements

The traditional ways of measurements are a type of measure which uses non-standard units such as hand spans, arm lengths, footsteps or pattern blocks to measure length, area, etc. Non-standard measurements are not always the same but vary from person to person.

Activities
Estimating distances

The teacher asks the students to gather information regarding earlier traditional measuring ways from their elders and have an initial discussion in the classroom

Concept #3. Standard units of measurements

A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.
For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".<br. The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system.

Activities
Hunting Treasure and Measuring - Part 1

Measuring things around us by using various instruments for understanding how parameters are measured differently.

Hunting Treasure and Measuring - Part 2

Exploring various modes of measurements and standard units for them.

Concept # 4. Scale drawing

A Scale drawing is a drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale).

Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car, an airplane, we need scale drawings to represent the size.

Drawing to scale is a tool that Engineers use for many different tasks. One key part of every scale drawing is the scaling factor. This number represents the degree to which our scale drawing or scale model has been reduced in size when compared to the original.

Activities

Scale drawing - Part 1

This activity explores representation of actual distances on paper using proportional distances.

Scale drawing - Part 2

Activity investigates how a blue print represents actual dimensions.

Concept #5. Measurements in solid figures

Concept Map

[maximize]

Concept #1 - Introduction to solid figures

Group activity for children to explore different dimensions in solids.

Activity 1- Visualising solid shapes

Activity 2- 3D shapes model making

Concept #2.Cube

A cube is a 3-dimensional figure having six congruent square faces joined along their edges. The three edges join at each corner to form a vertex. The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids. A cube has all edges the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face.Surface area = , Where s is the length of any edge of the cube. Volume enclosed by a cube is the number of cubic units that will exactly fill a cube.The volume of a cube is found by multiplying the length of any edge by itself thrice. So if the length of an edge is 's' cm, the volume is

Activities
Building cubes

This activity explores various methods of making cubes

Surface area and volume of a cube

Cube is introduced and analysed to calculate the surface area.

Concept #2.Cuboid

A cuboid is a 3 dimensional solid having 6 rectangular faces. Opposite faces of a rectangle are congruent.

Activities
Surface area of a cuboid

Cuboid as a shape and its properties are examined.

Volume of a cuboid using unit cubes

Concept #3.Cylinder

A cylinder is a closed solid that has two parallel (usually circular) bases connected by a curved surface. It has two ends, called bases, that are usually circular. The bases are always congruent and parallel to each other. On 'unrolling' the cylinder one would find that the side is actually a rectangle when flattened out. The height h is the perpendicular distance between the bases. The radius r of a cylinder is the radius of a base. Axis of the cylinder is a line joining the center of each base. Hollow Cylinder is the one with open top and base. Ex. cylindrical tube.

Formulas

CSA=

Volume of Cylinder=

TSA of Cylinder=

Volume of Cylinder When h=h/2 is

Activities
Surface area of a cylinder

The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.

Paint and fill the Cylinder

The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.

Concept #4. Cone

A cone is a three dimensional solid with a circular base that narrows toward a point, called its vertex. It has a flat circular base, has 1 side which is a curved surface. Shapes which resemble a cone are said to be conical. A cone has a lateral surface area which is the area of its curved surface. It has a total surface area which is the sum of the area of its curved surface and its circular base.

Activities
Surface area of a cone

Areas related to cone are introduced with geogebra sketch.

Concept #6. Sphere

Sphere is a solid figure where all points are at an equal distance from the center point.It's a ball. It is perfectly symmetrical. It has no edges or vertices (corners). It is not a polyhedron. All points on the surface are the same distance from the center which is the radius "r" of the circular shape. Of all the shapes, a sphere has the smallest surface area for a volume. i.e it can contain the greatest volume for a fixed surface area.

Activities
Baseball and string activity to find the surface area of a sphere

This activity has been taken from the website ehow.com

Concept #7. Pyramid

A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A triangular pyramid with all equilateral triangled faces becomes the regular tetrahedron, one of the Platonic solids. The base of a regular pyramid is a regular polygon and its faces are equally sized triangles. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. A right pyramid has isosceles triangles as its faces and its apex lies directly above the midpoint of the base.

Activities
Surface area of a pyramid

Investigating areas of surfaces in a pyramid is approached with this activity.

Concept #8.Prism

A prism is a polyhedron for which the top and bottom faces (known as the bases) are congruent polygons, and all other faces (known as the lateral faces) are rectangles. A prism is described by the shape of its base. For instance, a rectangular prism has bases that are rectangles, and a pentagonal prism has bases that are pentagons. When the sides are rectangles, the shape is known as a right prism, indicating that the lateral faces meet the sides of the base at right angles. A rectangular prism can also be called a cuboid. Parts of the prisms - faces, edges and vertices. The characteristics of a prism. Deriving formulae for surface area and volume of a prism..

Activities
Prism people

This activity has been taken from the website teachMathematics.

Difference between Prism and Pyramid

Solved problems/ key questions (earlier was hints for problems).

Frustum of Cone  

Projects (can include math lab/ science lab/ language lab)

  • Cylindrical Elephant: Let us make an elephant using only cylindrical objects.
  • Project -01-Cylinder
    • Playing with shuttle cock case**

Materials required:

  1. Empty cylindrical shuttle cock case
  2. Scissors
  3. Instrumental box
  4. Papers
  5. Hard board
  6. Pins/Nails
  7. Gum
  8. Glitter pens
  • Procedure:Take an empty cylindrical shuttle cock case, measure its height and radius of its base.Calculate its CSA,TSA and volume.Record these calculations in sheets. Separate the lid and then with the help of cutter take out circular base and top.By using scissors cut the cylinder vertically(also the portion attached to lid).Now calculate areas of these four portions separately. Add all the four areas and compare it with your earlier result of TSA of cylindrical shuttle cock case.

Assessments - question banks, formative assessment activities and summative assessment activities

Categories will be: (Subject), (Topic), (Class 8), (Class 9), (Class 9), (Concept Map), (Question banks), (Assessments), Formative, Summative