Difference between revisions of "Mensuration"

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''[http://karnatakaeducation.org.in/KOER/index.php/ಕ್ಷೇತ್ರಗಣಿತ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 
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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 ===
<mm>[[Mensuration.mm|flash]]</mm>
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__FORCETOC__
  
= Textbook =
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[[File:Mensuration.mm|flash]]
To add textbook links, please follow these instructions to:
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===Additional Resources===
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 
  
=Additional Information=
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==== Resource title ====
==Useful websites==
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[http://www.mathopenref.com/tocs/solidtoc.html Mensuration]
1. http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf<br>
 
This is a good website for interesting activities on mensuration.<br>
 
2.For standard measurements :      http://www.primaryresources.co.uk/maths/mathsE1.htm<br>
 
3.For general rules while writing units ://en.wikipedia.org/wiki/International_System_of_Units#General_rules<br>
 
4.For teacher reference on dimension. http://www.britannica.com/EBchecked/topic/163641/dimension<br>
 
  
==Reference Books==
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====OER====
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#Web resources:
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##[http://www.primaryresources.co.uk/maths/mathsE1.htm Primary resources] : Website gives printable resources for understanding measurements.
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##[http://www.campusgate.co.in/2011/11/areas-and-mensuration.html Campusgate]:  An overview on mensuration is given in this website.
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##[[wikipedia:International_System_of_Units#General_rules|Wikipedia]]: For general rules while writing units in measurements is described in this web page.
  
= Teaching Outlines =
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#Books and journals
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#Textbooks
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##[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?jemh1=13-14 NCERT 10 Textbook Chapter 13-Surface Areas and Volumes]
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#Syllabus documents
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====Non-OER====
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#Web resources:
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##[https://www.britannica.com/science/dimension-geometry Encyclopedia Britannica]: Gives a brief on dimensions.
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##[https://www.sciencehq.com/math-formulas/mensuration-formulas.html Science HQ]: The website lists formulas used in mensuration.
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##[https://www.wiziq.com/tutorial/197452-surface-area-of-cylinder-an-activity WizIQ] : An activity on surface area of cylinder.
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##[http://www.teachmathematics.net/page/10938/prism-people teachMathematics]: Lesson on understaning prisms with activity.
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#Books and journals
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#Textbooks
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##[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]
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#Syllabus documents (CBSE, ICSE, IGCSE etc)
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{{#widget:YouTube|id=0fKBhvDjuy0}}
  
==Concept #1. What is Mensuration ?==
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The metric system is enormously powerful as a standard measurement systemIn this video, you can explore from the very small to the very large and appreciate what a degree of ten means!
===Learning objectives===
 
# The students learn that mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume.
 
# Students will learn and understand that it is important to know how to measure things.
 
# They should have a clear distinction of different measuring/calculating parameters
 
# They should understand the characteristics of different figures.
 
# The length of the total boundary of a figure is called its perimeter. The Metric unit of perimeter is same as the unit of length - Metre.
 
# The perimeter of 2D geometrical figures like quadrilaterals can be obtained by calculating the sum of all the sides of the figure.
 
# The amount of surface covered by an object is called it area. The Metric unit of area is square metre.
 
# The capacity of an object to hold is called its volume.
 
# Develop an appreciation towards derivation of formula for calculations.
 
# They should develop the ability to calculate  the area, perimeter, volume or side  of many different figures.
 
  
===Notes for teachers===
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{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/43064607" |width=450 |height=360 |border=1 }}
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.
 
Measurement is an essential part of every aspect of life. The temperature, height, and weight of a patient are measured and recorded.Samples of blood and urine are collected and sent to a laboratory where glucose, pH, urea, and protein are measured by the lab technicians.By learning about measurement, you will develop skills for solving problems.
 
  
===Activity No # Importance of measurements and calculations - a discussion===
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Slides with problems and options for solutions.
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===Learning Objectives===
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Recognizing informal units of measurements
|}
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* Differentiating standard and non-standard ways of measurements.
*Estimated Time :45 minutes
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* Understanding importance of having standardized measurements.
*Materials/ Resources needed : Note book, pen
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* Justifying  accuracy of Standard units of measurements
*Prerequisites/Instructions, if any
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* Relating length,breadth,perimeter ,area
*Multimedia resources
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* Recognizing different units 
*Website interactives/ links/ / Geogebra Applets
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* Classifying 2D and 3D figures
*Process:
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* Calculating the area, perimeter, volume or side  of many different figures.
# Ask the children to make a list of all activities in different areas of life where measurements play an important role.
 
# Have a discussion in the classroom regarding importance of measurements and how difficult life would be without measurements.
 
Developmental Questions:
 
# Why measure ?
 
# How do we measure ?
 
*Evaluation:
 
# What are the measuring modes and units seen at the market, Hospital, Chemist laboratories, Gold shop, Tailors, Bakeries, Petrol bunks, water tankers, milk vendors, contractors, kitchen, airport, and so on.?
 
*Question Corner:
 
# What were the early crude measuring modes used. Find out from your elders.
 
# Why do you think certain measuring standards are needed ?
 
# Who formulates the standards
 
  
==Concept #2.Informal units of measurements ==
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=== Teaching Outlines ===
===Learning objectives===
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====Concept #1. What is Mensuration ?====
#  The students understand that informal 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.  
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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.
# They comprehend that estimate and informal measurement are interchangeable terms.
 
# They realise that informal measurements are not always the same but vary from person to person.
 
  
===Notes for teachers===
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=====Activities=====
# The teacher can ask the students to gather information regarding earlier informal measuring ways from their elders and have an initial discussion in the classroom.
 
===Activity No # 1. Estimating distances===
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time :1 hour
 
*Materials/ Resources needed : Sticks, ropes, writing pad, pencil.
 
*Prerequisites/Instructions, if any
 
# The students should have been introduced to different forms of informal measurements.
 
# They should have the ability to measure and document their findings accurately.
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process:
 
# The teacher can ask the students to determine the distances of library, principal's room, playground, dining hall, entrance gate from their classroom using various informal measuring methods.
 
# The children can decide which method to use - whether foot, sticks or ropes.
 
# The task can be done in groups of 3 children.
 
# Document and compare the results.
 
# Discuss regarding the length of distance.
 
# Reiterate that it is very important to use same measuring modes to facilitate comparisons.
 
*Developmental Questions:
 
# Which point would we mark as the point of reference for measuring our classroom.
 
# Similarly what are the points of reference for other places.
 
# How do we mark them.
 
# Which measuring unit have you chosen ?
 
# How will you document the findings ?
 
# How can we tabulate our findings on board for comparisons ?
 
# What would be our report back time ?
 
# What are our findings ?
 
# What conclusions can we draw ?
 
*Evaluation:
 
# What have we learnt so far about measuring object?
 
*Question Corner:
 
# How can we measure curves?
 
# What are the problems with informal measuring units?
 
# Can we think of methods to measure so that measures taken by anyone would always be same for a given object or distance.
 
  
===Activity No # ===
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====== [[What and how to measure]] ======
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Measurement is the act of determining a target's size, length, weight, capacity, or other aspect.  
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
==Concept #3. Standard units of measurements==
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====== Concept #2.Informal units of measurements ======
===Learning objectives===
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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.
# They should understand that there is no natural unit for the measurement of surfaces. It is necessary to fix upon an artificial unit and that , that artificial unit is a square. To find the area  of a surface is to find how many times this measuring unit can be applied to or is contained times in the given figure.
 
# It is essential for students to have an understanding of the units used to measure .
 
# The students should understand that no matter what field of science they enter, they will need to take measurements, understand them, communicate them to others, and be able to repeat them. In other words, all have to speak the same basic language.
 
# The ability to obtain accurate measurements and communicate those measurements is a key requirement for progress.
 
# These are the seven basic units in the SI system: the kilogram (kg) (mass), the second (s) (time), the Kelvin (K) (temperature),  the ampere (A) (electric current), the mole (mol) (amount of a substance), the candela (cd) (luminous intensity), and the meter (m), (distance).
 
# A unit is any measurement that there is 1 of.
 
  
===Notes for teachers===
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===== Activities =====
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".
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======  [[Estimating distances]] ======
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The teacher  asks the students to gather information regarding earlier traditional measuring ways from their elders and have an initial discussion in the classroom
  
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====Concept #3. Standard units of measurements ====
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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.
 
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.
===Activity No # Hunting treasure and measuring===
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time : 1 hour
 
*Materials/ Resources needed:
 
# Weighing pan with measures of 1 kg, 500gm, 250gm and 100gm and 50gm.
 
# Digital scale
 
# Postal scale.
 
# Measuring cans of 1 litre, 500ml, 250 ml, 100ml,
 
# Measuring tape, Ruler.
 
# Watch or stop clock.
 
# Paper and pen.
 
*Prerequisites/Instructions, if any
 
# The students should have been introduced to the concept of formal measurements.
 
# They should be well versed with standard units and subunits.
 
# They should know unit conversions.
 
# They should have the skill of measuring and recording accurately.
 
# They should be aware that comparisons can be made only between similar measuring units.
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process:
 
# The idea here is to inculde several measuring units for practise.
 
# Initially instruct the students regarding the activity and its purpose.
 
# Group students into 3 in each.
 
# The teacher shall make packets of things as treasure and hide them in the school premises.
 
# The students shall pick chits containing clues to hunt and find the packets.
 
# 30 minutes is given to search.
 
# The students search packets and come back to classroom.
 
# The packets may contain cloth, ribbons, ropes, water, fruits, ingredients , vegetable , books , juice, stamps,envelops or any such measurable items.
 
# The students have to quickly decide which measuring mode they are going to use, measure and record their findings.
 
# They also have to measure the distance at which they found each and record the time taken to search.
 
*Developmental Questions
 
# What measuring apps can you see here ?
 
# Can you list the purpose of each ?
 
*Evaluation
 
  
*Question Corner:
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=====Activities=====
# What are standard the units of length ?
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# What are the standard units of weight ?
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====== [[Hunting Treasure and Measuring - Part 1]] ======
# How are liquids measured ?
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Measuring things around us by using various instruments for understanding how parameters are measured differently.
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 +
====== [[Hunting Treasure and Measuring - Part 2]] ======
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Exploring various modes of measurements and standard units for them.
  
===Activity No # ===
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====Concept # 4. Scale drawing====
{| style="height:10px; float:right; align:center;"
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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).
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
*Estimated Time
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
==Concept #4. Scale drawing==
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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.
===Learning objectives===
 
# The students should comprehend that 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.
 
# Maintaining as constant a scaling factor throughout the sketches.
 
# Students should be able to read and understand a scaling factor.
 
# They should be able to find a scaling factor and create a scale drawing.
 
===Notes for teachers===
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
  
[[File:Scale drawing activity.jpeg|300px|left]]
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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=====
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'''[[Scale drawing - Part 1]]'''
  
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This activity explores representation of  actual distances on paper using proportional distances. 
  
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====== [[Scale drawing - Part 2]] ======
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Activity investigates how a blue print represents actual dimensions.
  
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==== Concept #5. Measurements in solid figures ====
 +
'''Concept Map'''
  
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[[File:measurements_in_solids.mm|Flash|link=http://karnatakaeducation.org.in/KOER/en/index.php/File:Measurements_in_solids.mm]]
  
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====Concept #1 - [[Introduction to solid figures]]====
 +
Group activity for children to explore different dimensions in solids.
  
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[https://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_2D_and_3D_shapes?venotify=created Introduction to 2D and 3D shapes]
  
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Activity 1- [[Visualising solid shapes]]
  
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Activity 2- [[3D shapes model making]]
  
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====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=====
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======[[Building cubes]]======
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This activity explores various methods of making cubes
  
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======[[Surface area and volume of a cube]]======
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Cube is introduced and analysed to calculate the surface area.
  
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====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.
  
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======[[Volume of a cuboid using unit cubes]]======
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====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=<math>{2}{\pi}{r^2}{h}</math>
  
 +
Volume of Cylinder=<math>{\pi}{r^2}{h}</math>
  
 +
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.
  
 +
======[[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  [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.
  
*Estimated Time
+
====Concept #8.Prism====
*Materials/ Resources needed
+
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..
*Prerequisites/Instructions, if any
+
=====Activities=====
*Multimedia resources
+
======[[Prism people]]======
*Website interactives/ links/ / Geogebra Applets
+
This activity has been taken from the website [http://www.teachmathematics.net/page/10938/prism-people teachMathematics].
*Process/ Developmental Questions
 
*Evaluation
 
*Question Corner
 
  
= Hints for difficult problems =
+
[[Difference between Prism and Pyramid]]
  
= Project Ideas =
+
=====Solved problems/ key questions (earlier was hints for problems).=====
 +
[[Frustum of Cone]]  
  
= Math Fun =
+
===Projects (can include math lab/ science lab/ language lab)===
 +
*'''Cylindrical Elephant''': Let us make an elephant using only cylindrical objects.
  
'''Usage'''  
+
*'''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
  
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
+
[[Category:Class 8]]
 +
[[Category:Mensuration]]

Latest revision as of 06:59, 10 August 2023

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.

Introduction to 2D and 3D shapes

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