Mensuration

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

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Additional Information

Useful websites

1. http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf

- This is a good website for interesting activities on mensuration.

Teaching Outlines

Concept #1. What is Mensuration ?

Learning objectives

1. The students learn that mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume.
2. They should understand the need for measuring objects.
3. They should have a clear distinction of different measuring/calculating parameters
4. They should understand the characteristics of different figures.
5. 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.
6. The perimeter of 2D geometrical figures like quadrilaterals can be obtained by calculating the sum of all the sides of the figure.
7. The amount of surface covered by an object is called it area. The Metric unit of area is square metre.
8. The capacity of an object to hold is called its volume.
9. Develop an appreciation towards derivation of formula for calculations.
10. They should develop the ability to calculate the area, perimeter, volume or side of many different figures.

Notes for teachers

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. 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 # Understanding the importance of measurements and calculations

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• Estimated Time :45 minutes
• Materials/ Resources needed : Note book, pen
• Prerequisites/Instructions, if any
• Multimedia resources
• Website interactives/ links/ / Geogebra Applets
• Process:

1. Ask the children to make a list of all activities in different areas of life where measurements play an important role.
2. Have a discussion in the classroom regarding importance of measurements and how difficult life would be without measurements.

Developmental Questions:

1. Why measure ?
2. How do we measure ?
3. 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.?

• Evaluation:

1. Do you agree taht measures are actually expressing quantity in numbers.

• Question Corner:

1. What were the early crude measuring modes used. Find out from your elders.
2. Why do you think certain measuring standards are needed ?
3. Who formulates the standards

Activity No # Tangram

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• Estimated Time : 40 minutes.
• Materials/ Resources needed: Chart papers, scissors, pencil, scale.
• Prerequisites/Instructions, if any

1. The students should have understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.
2. They should be able to draw mentioned shapes accurately and cut exactly on boundaries.

• Multimedia resources
• Website interactives/ links/ / Geogebra Applets
• Process:

1. This is a very old Chinese puzzle known as a tangram.
2. Cut out the square below into 7 shapes.
3. Cut out the 7 shapes and rearrange them to form:

(a) a square from two triangles, and then change it to a parallelogram; (b) a rectangle using three pieces, and then change it into a parallelogram; (c) a trapezium with three pieces; (d) a parallelogram with four pieces; (e) a trapezium from the square, parallelogram and the two small triangles; (f) a triangle with three pieces; (g) a rectangle with all seven pieces.

1. Finally, put the pieces back together to form the original square.

• Developmental Questions:

1. Were you all able to read and follow the instructions.
2. Name and point the different shapes in the figure.
3. Name the dimensions of each shape.

• Evaluation:

1. Analyse how much space each shape is occupying.
2. What can you refer to the space occupied by each shape.

• Question Corner:

1. What are the characteristic properties of each shape: square, rectangle, triangle, parallelogram and trapezium ?
2. What type of two triangles would you need to form a square ?
3. What did you learn from this activity ?

Concept #2.Informal units of measurements

Activity No #

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Activity No #

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Concept #3. Standard units of measurements

Learning objectives

1. 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.
2. It is essential for students to have an understanding of the units used to measure .

Activity No #

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Activity No #

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• Evaluation
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Concept #4. Scale drawing

Activity No #

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