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Line 26: + + + + − + − ##[http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf Download PDF]. This is a good website for interesting activities on mensuration.+ − + − + − + − ##For teacher reference on dimension. [http://www.britannica.com/EBchecked/topic/163641/dimension click here] − ##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! Line 39:
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Line 93: + − * 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. − + − # 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. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − + + − + − * Represents actual distances on paper using proportional distances.+ − * Recalls the definition and meaning of scale+ − * learns about the tools of measuring+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
no edit summary
[[File:Mensuration.mm|flash]]
[[File:Mensuration.mm|flash]]
===Additional Resources===
===Additional Resources===
==== Resource title ====
[http://www.mathopenref.com/tocs/solidtoc.html Mensuration]
====OER====
====OER====
#List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
#Web resources:
##[http://www.primaryresources.co.uk/maths/mathsE1.htm Primary resources] : Website gives printable resources for understanding measurements.
##For standard measurements : [http://www.primaryresources.co.uk/maths/mathsE1.htm click here]
##[http://www.campusgate.co.in/2011/11/areas-and-mensuration.html Campusgate]: An overview on mensuration is given in this website.
##[http://www.campusgate.co.in/2011/11/areas-and-mensuration.html click here]
##[[wikipedia:International_System_of_Units#General_rules|Wikipedia]]: For general rules while writing units in measurements is described in this web page.
##For general rules while writing units :[http://en.wikipedia.org/wiki/International_System_of_Units#General_rules click here]
#Books and journals
#Books and journals
#Textbooks
#Textbooks
#Syllabus documents
#Syllabus documents
====Non-OER====
====Non-OER====
#List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
#Web resources:
##[https://www.britannica.com/science/dimension-geometry Encyclopedia Britannica]: Gives a brief on dimensions.
##[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
#Books and journals
#Textbooks
#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]
##[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)
#Syllabus documents (CBSE, ICSE, IGCSE etc)
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/43064607" |width=450 |height=360 |border=1 }}{{#widget:YouTube|id=0fKBhvDjuy0}}
{{#widget:YouTube|id=0fKBhvDjuy0}}
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!
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/43064607" |width=450 |height=360 |border=1 }}
Slides with problems and options for solutions.
===Learning Objectives===
===Learning Objectives===
*Recognizing informal units of measurements
*Recognizing informal units of measurements
* Differentiates standard and non-standard ways of measurements.
* Differentiating standard and non-standard ways of measurements.
* Understanding importance of having standardized measurements.
* Understanding importance of having standardized measurements.
* Justifying accuracy of Standard units of measurements
* Justifying accuracy of Standard units of measurements
====== [[What and how to measure]] ======
====== [[What and how to measure]] ======
Measurement is the act of determining a target's size, length, weight, capacity, or other aspect.
====== [[Scale drawing]] ======
====== 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.
====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, armlengths, footsteps or pattern blocks to measure length, area, etc.bNon-standard measurements are not always the same but vary from person to person.
===== Activities =====
===== Activities =====
====== [[Hunting Treasure and Measuring - Part 1]] ======
====== [[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]] ======
====== [[Hunting Treasure and Measuring - Part 2]] ======
Exploring various modes of measurements and standard units for them.
====Concept # 4. Scale drawing====
====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 #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=<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=====
=====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.
====== [[Scale drawing - Part 1]] ======
======[[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.
====== [[Mensuration_scale_drawing_activity_1|Scale drawing - Part 2]] ======
====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.
====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].
[[Difference between Prism and Pyramid]]
=====Solved problems/ key questions (earlier was hints for problems).=====
=====Solved problems/ key questions (earlier was hints for problems).=====
[[Frustum of Cone]]
===Projects (can include math lab/ science lab/ language lab)===
===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:
#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===
===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
Categories will be: (Subject), (Topic), (Class 8), (Class 9), (Class 9), (Concept Map), (Question banks), (Assessments), Formative, Summative
[[Category:Class 8]]
[[Category:Mensuration]]