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Mensuration (view source)

Revision as of 07:14, 5 June 2021

7,039 bytes added ,  07:14, 5 June 2021
→‎Concept #1 - Introduction to solid figures
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[[File:Mensuration.mm|flash]]
 
[[File:Mensuration.mm|flash]]
 
===Additional Resources===
 
===Additional Resources===
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==== Resource title ====
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[http://www.mathopenref.com/tocs/solidtoc.html Mensuration]
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====OER====
 
====OER====
 
#Web resources:
 
#Web resources:
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##[https://www.britannica.com/science/dimension-geometry Encyclopedia Britannica]: Gives a brief on dimensions.
 
##[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.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.
 
#Books and journals
 
#Books and journals
 
#Textbooks
 
#Textbooks
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This activity explores representation of  actual distances on paper using proportional distances.   
 
This activity explores representation of  actual distances on paper using proportional distances.   
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====== [[Scale drawing - Part 1|Scale drawing - Part 2]] ======
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====== [[Scale drawing - Part 2]] ======
 
Activity investigates how a blue print represents actual dimensions.
 
Activity investigates how a blue print represents actual dimensions.
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==== Concept #5. Measurements in solid figures ====
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'''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]]====
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Group activity for children to explore different dimensions in solids.
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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====
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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>
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=====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====
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A cuboid is a 3 dimensional solid having 6 rectangular faces. Opposite faces of a rectangle are congruent.
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=====Activities=====
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======[[Surface area of a cuboid]]======
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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====
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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.
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===== Formulas =====
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CSA=<math>{2}{\pi}{r^2}{h}</math>
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Volume of Cylinder=<math>{\pi}{r^2}{h}</math>
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TSA of Cylinder=<math>{2}{\pi}{r}{(r+h)}</math>
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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>
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=====Activities=====
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======[[Surface area of a cylinder]]======
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The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.
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======[[Paint and fill the Cylinder]]======
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The shape can be thought of as a circular prism. Cylinder could be closed or open. Surface areas for a cylinder is investigated.
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====Concept #4. Cone====
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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.
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=====Activities=====
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======[[Surface area of a cone]]======
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Areas related to cone are introduced with geogebra sketch.
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======Concept #6. Sphere======
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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.
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=====Activities=====
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======[[Baseball and string activity to find the surface area of a sphere]]======
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This activity has been taken from the website  [http://www.ehow.com/info_7838171_classroom-activities-surface-area-sphere.html ehow.com]
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====Concept #7. Pyramid====
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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.
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=====Activities=====
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======[[Surface area of a pyramid]]======
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Investigating areas of surfaces in a pyramid is approached with this activity.
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====Concept #8.Prism====
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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..
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=====Activities=====
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======[[Prism people]]======
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This activity has been taken from the website [http://www.teachmathematics.net/page/10938/prism-people teachMathematics].
    
=====Solved problems/ key questions (earlier was hints for problems).=====
 
=====Solved problems/ key questions (earlier was hints for problems).=====
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[[Frustum of Cone]]  
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===Projects (can include math lab/ science lab/ language lab)===
 
===Projects (can include math lab/ science lab/ language lab)===
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*'''Cylindrical Elephant''': Let us make an elephant using only cylindrical objects.
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*'''Project -01-Cylinder'''
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**Playing with shuttle cock case**
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Materials required:
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#Empty cylindrical shuttle cock case
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#Scissors
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#Instrumental box
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#Papers
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#Hard board
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#Pins/Nails
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#Gum
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#Glitter pens
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*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
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[[Category:Class 8]]
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[[Category:Mensuration]]
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