Handbook p1 measurements

Agastya International Foundation

Measurements Handbook P1

“I often say that when you can measure what you are speaking about and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind…”

Lord Kelvin

1

Handbook P1 Measurement OVERVIEW OF HANDBOOK ABL

CONCEPT

ABL1 ABL2 ABL 3 ABL 4 ABL 5 ABL 6

Learning to measure Measuring Length Measuring Area Measurement of Volume Measuring Mass and Density Measuring Time TOTAL

NO OF ACTIVITIES 3 2 3 4 2 3 18

TIME (min) 45 60 60 60 30 60 315

ABLs WITH REFERENCE TO STANDARD SERIAL NO. 1 2 3 4 5 6

STANDARD ABL 1 ABL 2 ABL 3 ABL 4 ABL 5 ABL 6

RELEVANT ABL 4, 5, 6 5, 6 5, 6 6, 7 6, 7, 8 6, 7

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PAGE NO 4 15 24 35 43 54

2

LIST OF FIGURES, CHARTS AND WORKSHEETS S. No. Fig/Table No. 1 Fig 1 2 Fig 2 3 4 5

Fig 3 Fig 4 Fig 5

Title Mixed flowers and bunch of pens and pencils Measurement of teacher’s table using different yardsticks Body parts used to measure length in ancient times Measuring length Eye positions and readings

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21

Fig 6 Fig 7 Fig 8 Fig 9 Fig 10 Fig 11 Fig 12 Fig 13 Fig 14 Fig 15 Fig 16 Fig 17 Chart 1 Chart 2 Chart 3 Chart 4 Worksheet 1

Irregular closed figures Types of graph papers Figure with complete squares Figure with complete and incomplete squares Area of irregular figure Net diagram for cube and cuboid Finding volume of irregular object Measuring lung capacity Physical balance Rubber band scale Sand clock Sun dial Images for flip chart Line segments Closed and open figures Difference between mass and weight Measurements

Page No 4 10 11 16 17 27 28 29 29 30 35 37 38 44 46 53 55 5 6 23 42 9

Note to Instructor: All the figures in this handbook are for the Instructor’s reference only. The Charts need to be printed and shown to the learners during the course of the activity. Worksheets need to be printed out in advance for the learners. The number of worksheets required is mentioned in the Material List.

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3

ABL 1: Learning to Measure Activity 1.1

Learning objective What are Physical Quantities?

Key messages  Anything that can be measured and expressed in terms of a number is physical quantity.  Mass, Length and time are termed as fundamental physical quantities. (M, L, T)

1.2

What is measurement?



1.3

What were the methods of measurement for length in ancient times?

TOTAL



Measurement is the determination of quantity of an item or a physical quantity In ancient times, different body parts were used to measure length

Time (min) 15

15

15

45

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4 Time: 15 min

ABL 1.1 LEARNING OBJECTIVE: What are physical quantities?

ADVANCE PREPARATION Material List S. No. 1 2 3

Material Various kinds of flowers A collection of pens and pencils Flip chart of lines, two and three dimensional figures in different sizes – Chart 1

Quantity A bunch/class 20/ class 1/class

Things to do The flowers should be of different sizes and shapes. Collect pencils and pens from the learners themselves so that there is a variety.

Safety Precautions Not Applicable SESSION Link to known information/previous activity Not Applicable Procedure Show the learners the flowers. Ask them what kind of flowers they can see. Ask the learners to segregate the flowers with respect to colour. Then, put the flowers together again and ask them to segregate the flowers with respect to beauty.

Fig 1: Mixed flowers and bunch of pens and pencils1,2

1http://el-p.src-akamai.net/img/p/GEN/lgwt/7703.jpg 2http://thumbs.dreamstime.com/x/pen-holder-916402.jpg

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5 For pens and pencils, ask them to segregate the pens from the pencils. Then put all the pens and pencils together and ask them to put them in two piles.

1. Pens and pencils, which are easy to write with.

2. Pens and pencils, which are difficult to write with.

Next show them the chart - 1 with lines, two and three-dimensional objects drawn on it. Ask them to identify which is smaller and which is bigger.

Chart 1: Images for flip chart

UNDERSTANDING THE ACTIVITY Leading questions 1. If you divide the flowers into two groups of big and small flowers, how many small and big flowers do you have respectively?

2. Which flower is most beautiful?

3. If you divide the pen-pencil collection into two groups of pens and pencils, how many do you have respectively?

4. Which pen or pencil is easy to write with?

5. In the chart which of the two lines is bigger?

6. In the chart which of the two rectangles is bigger?

7. In the chart which of the two boxes is smaller?

Discussion and Explanation  The flowers can be segregated according to their size. There will be a consensus on this in the class.  Answer for the question of the prettiest flower are many and they each learner can have a different answer. .  In case of pens and pencils, segregating them into two groups, one of pens and the other of pencils is easy.  In case of ease of writing, the opinion may vary. Some might like one pencil for its smooth writing while the other may like another.

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6  

In case of lines, length decides the size, in case of plane (i.e. card sheet) area (l x b) decides the size and in case of solid objects (i.e. boxes) volume (l x b x h). So, in the chart, A>B, C<D and E>F. Therefore, anything that can be counted or measured is a physical quantity e.g., no. of flowers, number of pens etc. Things like beauty or the smoothness of writing is not something that can be measured.

Anything that can be measured is called physical quantity.

KEY MESSAGES  

Anything that can be measured and expressed in terms of a number is physical quantity.

Mass, Length and time are termed as fundamental physical quantities. (M, L, T)

LEARNING CHECK 1. Make a list of 5 things in your classroom that can be measured and 5 that cannot be measured.

Time: 15 min

ABL 1.2 LEARNING OBJECTIVE: What is measurement?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6 7

Material Quantity Flipchart of line segments – Chart 2 1/class Bangles, different colours and two of each sizes (they 4/class should be just one size apart) Two glass, same height with different diameter 1/class Water 200 ml/class Food colour A few drops/class Scale 1/class Volume measuring glass 1/class

Things to do Use Chart 2 for activity 1.2 a.

Chart 2: Line segments

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7 Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure 1.2 a. Show the Chart 2 to the learners. Ask them which lines are equal and which are smaller taking any two lines at a time. Then, ask them to measure the lines with help of a scale, and them find out the equal line segments.

UNDERSTANDING THE ACTIVITY Leading questions 1. Of the two lines h and c, which is smaller?

2. Of all the lines on the chart, which are equal?

3. What do you measure the lines in?

Discussion and Explanation  Line h is smaller than c  Lines b and g are equal  When you look at any object, you can compare it with another object of the same type and guess it is bigger or smaller, but if they are almost the same size, only measuring both of them will give you an exact answer. Similarly, in this case, the measurements of the line segments will determine if they are smaller, larger or equal.  The measurements are done in centimeter. The other units of measuring length are meter and kilometer.

Procedure 1.2 b. Show the bangles to the learners ask them which two of them are equal. Then, measure the diameter with the help of a scale and determine which are equal.

Leading questions 1. Which of the four bangles are equal?

2. How can you find out if they are equal?

3. Is there any other way to find out if any two bangles are equal in size?

Discussion and Explanation  Just looking at the bangles, it is not easy to say for sure which bangles are equal in size. So measure the diameter of the two bangles will tell which of them is bigger than the other.

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8 (Another way of finding bangles of equal sizes is to hold the bangles together at one point and see if the other end also has the bangles together. If they do, then they are the same size. If they do not, then they are of different sizes. This is comparing the circumference of the two bangles.)

Procedure 1.2 c. Mix food colour in the water and fill the two glasses with same amount of water in each glass. As the diameter of the glasses is different, the heights of the water in the glasses will be different. Ask the learners which glass has more water. Then, take the measuring glass and measure the water in each glass.

Leading questions 1. Which of the glasses has more water?

2. How do you measure water?

Discussion and Explanation  As the diameter of the glasses is different, the heights of the water in the glasses will be different. But when the volume of the water is measured, it turns out that the water in the glasses is same.  Volume of water is measured here in milliliter. The other unit of measuring volume is liter.  By these experiments we will understand that the exact size of the line segments, the bangles and the volume of the water is known only after measuring it.  The measure - be it measure of length (cm) or of volume (ml) - has two components. One is the number and the other is the unit. So, a line segment measuring 10 cm has 10 as the numerical value and centimeter as the unit. Similarly, if the volume is 50 ml, 50 is the numerical value and milliliter is the unit. With the same unit, the object with a higher numerical value is bigger than that with the smaller value.  Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible.

For example, consider the problem of measuring the time it takes an object to fall a distance of one meter (about 39 in). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one meter. However, many sources of error arise in this case.

Some of them are: o Carelessness o Determining of the exact time at which the object is released and the exact time it hits the ground, o Measurement of the height and the measurement of the time both involve some error, o Air resistance.

Scientific experiments must be carried out with great care to eliminate as much error as possible.

KEY MESSAGES  

Measurement is the determination of quantity of an item or a physical quantity.

Measurement will have always two components, a number and a unit.

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9 Volume is measured in litres. The smaller unit of volume is a milliliter and the larger unit is a kiloliter. The conversion table is given below. The common abbreviations to be used are given in brackets.

10 milliliters (ml) = 1 centiliter (cl) 100 centiliters (cl) = 1 liter (l) 1000 liters (l) = 1 kilo liter (kl)

As in volume, the length is measured in meters. The larger length is measured in kilometer and the smaller in centimeter or millimeter. The conversion table is given below. The common abbreviations to be used are given in brackets.

10 millimeters (mm) = 1 centimeter (cm) 100 centimeters (cm) = 1 meter (m) 1000 meters (m) = 1 kilometer (km)

LEARNING CHECK 1. Measure the length of your Mathematics text book in cm. Convert this information into millimeters.

2. A bottle can hold 2 liter of water. How many bottles of 400 ml can be filled from this one large bottle?

Time: 15 min

ABL 1.3 LEARNING OBJECTIVE: What were the methods of measurement of length in ancient times?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5

Material Scale Cloth Measuring Rod Tailorâ&#x20AC;&#x2122;s measure tape Measure tape used by builders Worksheet 1 â&#x20AC;&#x201C; measurements

Quantity 1/ class 1/ class 1/ class 1/ class 1 per learner

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10

SESSION Link to known information/previous activity Not Applicable Procedure Ask a learner to measure the length of one side of a table using his hand-span. Make a note of the length of the table in number of hand-spans. Ask another learner to do the same. Note this reading too. Next, ask another learner to measure the table using the distance between his elbow and tip of his fingers as a measure.

Then, ask the fourth learner to measure the length of the table using a scale. Put all the reading in a table in figure 2.

Show the learners different types of scales that are used for different purposes, i.e., for measuring cloth in shops, tailor’s measure tape, measure tape used by builders, etc. Let the learners feel these scales and see how they are calibrated. This could be done by passing them around in class.

Figure 2: Measurement of Teacher's table using different yardsticks Student No. 1 2 3 4

What was used to measure?

Hand-span Hand-span Cubit (distance between elbow and tip of the fingers) Scale

No. of units

UNDERSTANDING THE ACTIVITY Leading questions 1. What is a hand span?

2. How will you measure the table with a hand span?

3. Learners 1 and 2 have measured the table with their hand span. Are both the measures same?

4. How is learner 3 measuring the length of the table?

5. What are the different types of measures of length you see around you today?

Discussion and Explanation  Hand span is the distance between the tip of the thumb and the tip of the little finger when your hand is stretched.  To measure with a hand span, start with the tip of the thumb at the starting point and stretch the hand. Mark the place where the tip of the little finger reaches. This is the first mark. This is one hand span. Now, start with the mark as the starting point and make a second mark at the tip of the little finger. This will be the second hand span. Measure like this till the end of the table. The length of the table will be the number of hand spans.

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11   

The length of the table measured by learners 1 and 2 could be different as their hand spans might not be the same.

Learner 3 measured the table with the help of a scale. This is a standardized measurement and does not change.

In ancient times, different body parts were used to measure length. Some of them are shown in fig 3.

Such measurements are non-standard and were only used in ancient times when better tools were not available. However, you will still find the flower seller outside the temple in South India measuring the length of a string of flowers using the “Mozham”, the distance from elbow to fingertips. This is the same as cubit!

Fig 3: Body parts used to measure length in ancient times

   

Measuring length: In our daily life, we now use various types of measuring devices, which are more accurate and standardized. We use a meter scale for measuring length.

A tailor uses a tape, where as a cloth merchant uses a meter rod.

You cannot measure the growth of a tree or the size of your chest using a meter scale, for instance.

Measuring tape is more suitable for this.

For small measurements, such as the length of your pencil, you can use a 15 cm scale from your geometry box.

KEY MESSAGE In ancient times, different body parts were used to measures length like hand span, cubit, fathom, and foot.

LEARNING CHECK Give out worksheet 1 to learners where they need to fill in the blanks in the table. A complete table is provided below for reference.

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12 WORKSHEET 1 â&#x20AC;&#x201C; For Instructor reference LENGTH

METRIC Millimeters mm

Centimeters cm

VOLUME

Meter M

Kilometer Km

METRIC Milliliter ml

WEIGHT

Litre L

METRIC

TEMPERATURE

Grams

Kilograms

G

Kg

Metric tons

METRIC Centigrade oC

TIME

METRIC Second sec.

Minute min.

Hour hr.

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Day D

13

INTERESTING INFORMATION Measurements3 Measuring physical quantities has been going on since ancient times. These measures have been in terms of length, weight, volume time etc. There has been an evolution in the methods of measurements over the centuries. At present, the measurements are standardized and are used all over the world. Let us look at the history of measurements.

Weight For measurements of weight, the human body provides no such easy approximations as for length. But nature steps in. Grains of wheat are reasonably standard in size. Weight can be expressed with some degree of accuracy in terms of a number of grains - a measure still used by jewellers. As with measurements of length, a lump of metal can be kept in the temples as an official standard for a given number of grains. Copies of this can be cast and weighed in the balance for perfect accuracy. But it is easier to deceive a customer about weight, and metal can all too easily be removed to distort the scales.

Therefore, government inspectors check the correctness of the weight measures used by traders and shopkeepers frequently.

Volume A reliable standard of volume is the hard to achieve. Where the exact amount of any commodity in solid form needs to be known, weight is the measure more likely to be relied upon than volume for measurement of solids. For example, 5 Kg rice, 2 tons of Steel etc.

However, for measurement of liquids, volume is very suitable because the liquid takes the shape of the inner space of the measuring jar. For example, one liter of milk.

Time Everything we do revolve around the concept of time. Our schools start at a particular time, we wake up at a particular time and go to sleep at a given time. Trains and busses come and go at specific times everyday so that it is easy for us to catch them. Even when a doctor gives us medicine, he/she might ask us to take it once in the morning and once at night; that is at specific intervals of time. Even when somebody asks you your age, 3

http://www.historyworld.net/wrldhis/plaintexthistories.asp?historyid=ac07

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14 you are telling him or her the amount of time that has passed since you were born. All these examples show that we have to measure time in different ways â&#x20AC;&#x201C; days, minutes, seconds, and years etc. in order for our lives to function smoothly.

TRY IT YOURSELF 1. Measure your friend's height. Make your friend stand against a wall and mark the top of his head with a pencil on the wall. First measure it with your hand span and then with a measuring scale.

2. Invent your own measure and measure the objects in our home.

3. Compare the measurement in the above activity with a measuring scale. Find out which is the measure of your one measure in centimeters.

WEB RESOURCES Measurement of Length: http://resource.npl.co.uk/docs/educate_explore/posters/bg_historyoflength_poster.pdf

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15

ABL 2 Measuring Length Activity 2.1

2.2

Learning objective Key messages How does one get the  Follow correct method of correct measurement of measurement. Start at zero length? mark. If no zero mark, start at (for lower classes only) next whole number and subtract this number from the reading and look at the measurement point from the front.

What are the indirect  It is possible to find the value methods of measuring of small measurements by length? indirect methods like using string, divider.  Large number of similar objects can me measured together and then measure of one is calculated.

TOTAL

Time (min) 10

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50

60

16

ABL 2.1

Time: 15 min

LEARNING OBJECTIVE: How does one get the correct measurement of length?

ADVANCE PREPARATION Material List S. No. 1 2 3 4

Material Scale Scale with broken/uneven ends A book to be measured Pencil

Quantity 1/ group 1/ group 1/ group 1/ group

Things to do Not Applicable Note to Instructors This activity should be done in groups of 4-6. This will allow all the learners to do the activity. The book to be measured should be different for different groups. The learners can use any of their books.

Safety Precautions Not Applicable

SESSION Link to known information/previous activity In the previous section we learnt that now there are standardized units to measure length. Here we will use the centimeter scale to measure the book.

Procedure Ask the learners to use the scale with proper markings to measure the length of the book. Ask them to make a note of it. Then ask them to use the uneven/broken scale to measure the same length. Ask them to note this reading too. Do they find any difference in the measurements?

Some groups might have the same measurements but some might have it different. Then explain to them how a measurement is taken correctly.

UNDERSTANDING THE ACTIVITY Leading questions 1. How did you use the correct scale?

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17 2. How did you use the broken scale?

3. Are the readings of the lengths different? Why? Discussion and Explanation  When two different scales measure the length of the same book, some groups might have the same measurements but some might have it different.  When using the correct scale, remember to align the zero reading with the starting point of the length to be measured. The reading of the scale at the end point of the scale will be the measure of the length.  When using the broken scale, start at the first full measure. E.g., if 1 on the broken scale is the first full number, start from there. This number should be subtracted from the final reading. In this case, if the final reading is 16 cm, then the actual length is 16 - 1 = 15 cm.

There are three important rules to be followed when measuring any length.

1. Place the scale in contact with the object along its length. The beginning of the object should be on the zero mark of the scale.

Fig 4: Measuring length4

2. In some scales, the ends may be broken. You may not be able to see the zero mark clearly. In such cases, you should avoid taking measurements from the zero mark of the scale. You can use any other full mark of the scale, say, 1.0 cm. Then you must subtract the reading of this mark from the reading at the other end.

3. Correct position of the eye is also important for taking measurement. Your eye must be exactly above or in front of the point where the measurement is to be taken (Fig. 5, (B)). If the position of the eye is to the left or the right of the mark, the reading could be different (Fig. 5, (A) and (C)). This is more so when very small units are being used.

4

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18

Fig 5: Eye positions and readings5

KEY MESSAGES For correct result, the rules of measurements have to be followed: 1. Starting point of length to me measured should be on the Zero reading of the scale.

2. 2. If scale does not have a zero, start at the next full measure and delete the reading of that mark from the observed reading.

3. The eye should be exactly in front of the point where measurement is to be taken.

TRY IT YOURSELF Try to measure a length which is longer than the scale you have. E.g., measure the length of you table with a 30 cm scale. How will you do it?

LEARNING CHECK 1. If the scale you are using has the first full measure is 4 cm. When used correctly, the scale shows 17 cm, what is the actual length of the object?

2. Consider that the scale you are using is proper except between 7 and 8 cm marking where it is uneven. If you are measuring a 12 cm object, is it possible to get the correct measurement using this scale?

ABL 2.2

Time: 50 min

5http://www.ekshiksha.org.in/eContent-Show.do?documentId=54

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19

LEARNING OBJECTIVE: What are the indirect methods of measuring length?

ADVANCE PREPARATION Material List S. No 1 2 3 4 5 6 7 8 9 10

Material Paper Thread/Twine Pencil Pins Scale Ball Divider Wooden blocks Coins/tokens Wire

Numbers required 1/ group 1/ group 1/ group 3/ group 1/ group 1/ group 1/ group 2/ group 10/ group 1/ group

Things to do Not Applicable Note to Instructor As there are five sections to this activity, keep the requirements of all the activities separate. Some items like scale and pencil can be reused. This activity should be done in groups of 4-6 so that all learners get a chance to do it themselves.

Safety Precautions Not Applicable

SESSION Link to known information/previous activity Remember all the points that should be taken into account while measuring a length, which we have learnt in the previous activity.

Procedure The activities are separate and so distribute the material to each group of learners before the start of each activity.

2.2 a. 1: Measuring a curved line with thread Draw a curved line on the paper. Mark one end of the line as A and the other end as B. Take a thread and place it on Point A. Secure this with the help of a pin. Mark the thread at this point with a pencil. Now, take the thread along the curve pressing it down on the curve with your fingers and ending at point B. Mark the Agastya International Foundation. For Internal Circulation only.

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20 thread at point B. Unsecure the thread from point A and measure the distance between the two marked points on the thread using a scale.

UNDERSTANDING THE ACTIVITY Leading questions 1. Should the thread at point A be necessarily the starting of the thread?

2. Why is the thread secured at point A? 3. Why should the thread be marked at points A and B? Discussion and Explanation  The thread need not start at point A, but it is essential the thread at point A be marked, as it is the beginning of the measure of the curved line.  We keep the thread secure at point A so that the measurement along the cured line becomes easy.  The points A and B are marked so that when the thread is removed from the curved line and taken to the scale, the exact positions of the beginning and the end of the line will be known.  The distance between the two marked points on the thread will be the length of the curved line.

2.2 a. 2: Measuring a curved line with divider Draw a curved line on the paper. Mark one end of the line as A and the other end as B. Take the divider and set it so that the distance between the two points is 5 mm. Place one leg of the divider on point A. Now place the other on the curve. Mark it as 'a'. Now, lift the leg at point A and place it on the curve beyond 'a'. Mark this as 'b'. Continue this till you come to point B. Count the number of sections you have made on the curve, i.e., distance between point A and 'a', distance between 'a' and 'b', etc. Multiply the number of sections made by 5mm to get the length of the curved line.

UNDERSTANDING THE ACTIVITY Leading questions 1. Why have we taken the distance between the two legs of the divider as 5 mm?

2. Why should every distance covered by the divider be marked?

3. Can the measurement start from point B? Discussion and Explanation  The principle behind this kind of measurement is that we measure small pieces of the curve, which appear to be straight and then add it up. If we take larger distance, the line, between the two legs will be curved and not straight.  It is important that every distance covered by the divider be marked so that one does not loose count of the smaller sections made by the divider.  In the above activity, if there are 22 smaller parts measured by the divider, the length of the curve will be 22 x 5 mm (distance between two legs of the divider) = 110 mm.  Measurement can start from point B and go towards A. This will give the same measurement.

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21 

If you do not reach the point B exactly with the divider, stop just before B. The remaining length can be measured with a scale and added to the length measured by the divider.

2.2 b Measuring thickness of a wire Wind the wire around the pencil till the length of the wound wire is 2 cm. Ensure that there is no gap or space between two successive turns of the wire. Now count the number of turns. Let us say there are 'n' turns.

Thus, the thickness of the wire = 2 cm / n

UNDERSTANDING THE ACTIVITY Leading questions 1. Why do we wind the wire around the pencil?

2. Why do we not just measure the width with the scale?

3. Why should there be no gap between the turns of the wire?

Discussion and Explanation  The wire is too thin to get the correct measurement of its thickness (diameter) if measured by a scale.

It is impossible to measure the diameter with a scale.  When we wind the wire, the wires touch each other across the diameter (or the thickest part of the wire). Every turn around the pencil increases the length by one diameter (or thickness). So, if we keep winding the wire till its length is 2 cm, it means that the sum of the diameters is 2 cm. But how many diameters have we added? That is given by the number of turns that have been taken. So the thickness of one diameter (or thickness) is 2 cm / no. of turns.  If there is a gap between the turn of the wires, this gap will also be measured. This will give a wrong answer.

2.2 c: Measuring the thickness of a coin Take Re. 1 coins and arrange them in a pile. Take care to see that the coins are of the same size. Measure the height of this pile. Remember that any scale will have a little unmarked portion before the zero mark. Arrange the pile in such a way that proper measurement can be taken.

Let the number of coins be 'n' Let the height of the pile be 'l' Thus, the height (or the thickness) of the pile = l/n

UNDERSTANDING THE ACTIVITY Leading questions 1. Why should the coins be of the same size?

2. What will happen if the coins are of the same diameter but different thickness?

3. What will happen if the coins are of different diameters but same thickness?

Discussion and Explanation  The reason why the coins should be of the same size is that the measure of the thickness of each of the coins will be the same. This will give us the correct thickness of one coin.

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22  

If the coins are of same diameter but different thickness, then the total height of the pile is easy to measure but the thickness of one coin cannot be determined by the formula (l/n). This is because some of the coins are of different thickness.

On the other hand if the thickness of the coins is the same but the diameters are different, it is difficult to make a pile and take the total measurement. If this can be done, the thickness of one coin can be calculated by the formula l/n.

2.2 d Measuring the diameter of a ball Place the ball firmly between two blocks of wood. The ball should not be squeezed, but it should just touch the wooden blocks. Measure the distance between the blocks exactly at the points where the ball touches the blocks. This distance is the diameter of the ball.

UNDERSTANDING THE ACTIVITY Leading questions 1. Why is the distance between the blocks the diameter of the ball?

2. What happens if the ball is squeezed between the blocks?

3. What happens if the ball is not held firmly between the blocks?

Discussion and Explanation  The blocks are kept in such a way that the two opposite ends of the ball touch the blocks. This will happen only when the blocks are parallel to each other. The two ends of the ball means its diameter.

So the distance between the two inner edges of the blocks will be the diameter of the ball.  If the ball is squeezed, the diameter will become smaller (in case of a flexible ball).  If the ball is not held firmly between the blocks, it means that the distance between the blocks is greater than the diameter of the ball.

KEY MESSAGE  

It is possible to find the value of small measurements by indirect methods like using string, divider.

Large number of similar objects can me measured together and then measure of one is calculated.

TRY IT YOURSELF Find the thickness of one paper from a pile of papers (like your notebook). Hint: Find the height of the pile and divide it by the number of papers. This will give the thickness of the paper.

LEARNING CHECK 1. What method will you use to find the height or thickness of the following things: a. Glass (from which you drink water) b. Circumference of a round tiffin box c. Old news paper (hint: pile of news papers will not make a neat pile as they have been bent or crushed) d. The thickest part of a top 2. To measure the thickness of a staple pin, it is better to use a new set of pins than lose pins. Why? Agastya International Foundation. For Internal Circulation only.

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ABL 3: Measuring Area Activity 3.1

Learning objective What is area?

3.2

What is a unit area? How do we measure area?

3.3

How do we use a graph paper to find the area of regular and irregular plane figures?

TOTAL

Key messages  The space inside a figure with a boundary is called its area.  A unit square is the smallest unit of the area.  Areas can be measured in square units like cm2, m2, km2.  Area of a square is measured as the product of its length and breadth.  The area of regular and irregular, plane, closed figures can be calculated by counting the squares that the figure covers on the graph paper.

Time (min) 10 20

30

60

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Time: 10 min

ABL 3.1 LEARNING OBJECTIVE: What is area?

ADVANCE PREPARATION Material List S. No. 1 2 3

Material Flipchart with figures â&#x20AC;&#x201C; Chart 3 Paper Scale

Quantity 1/class 1/ group 1/ group

Chart 3: Closed and open figures

Things to do Not Applicable Safety Precautions Not Applicable

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25 Procedure Show the figures on the flipchart – Chart 3 to the learners. Ask them if they can find the differences between the figures. Ask them to find any similarity between some figures. Use leading questions to help them to notice the open and closed figures.

UNDERSTANDING THE ACTIVITY Leading questions 1. Identify these figures.

2. What are the differences that you can see in the figures?

3. If you want to divide them into two groups how will you do it?

Discussion and Explanation  These figures are two-dimensional. E.g., each one of them has a length and a breadth. The differences seen are the size and the shape. Such 2-dimensional figures are called plane figures. They can be fully drawn in the plane of a paper  We can divide them into groups of spaces contained by straight lines and curved lines.  There is also another way we can divide them - open and closed figures. Closed figures are those which have no starting and ending points. Figures A, C, D, and E are closed figures. Let us take the example of the football field. It is closed on all sides, i.e., it has an inside and an outside. Other examples are a flag, a stamp, the black board etc. The area of these closed surfaces can be calculated as any point is either inside the boundary of this object, outside of this object or on the boundary of the object.  Now, look at figures B and F. These have distinct starting point and ending point. i.e., these points are different. They are figures with open mouths! Here you are not sure which points are in the figure and which are outside. These are called open figures. These figures have no boundary and so it is impossible to find its area.  So it is possible to measure the space contained inside a closed figure, or in other words, it is possible to find the AREA of a figure which has a boundary

KEY MESSAGES The measurement of space inside a figure with a boundary is called its area.

TRY IT YOURSELF Look at the figures in a magazine or a newspaper. Mark the ones whose area can be calculated.

Identify the first two numbers (in Arabic numerals), which are closed figures

LEARNING CHECK 1. Draw 5 open and 5 closed figures.

2. Is it possible to find the area of the floor of your classroom? Why? (Hint: You have to close all doors and windows connecting it to outside.)

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ABL 3.2

Time: 20 min

LEARNING OBJECTIVE: What is unit area? How do we measure area?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6

Material Plain Paper Scale Scissors Square of 2 cm sides in red chart paper Square of 5 cm sides in yellow chart paper Unit squares in centimeter

Quantity 1/ group 1/ group 1/ group 1/ group 1/ group 5/ group

Things to do Not Applicable Note to Instructor This activity will require the Instructor to go around the class to see if the learners have done the activity correctly.

Safety Precautions Not Applicable SESSION Link to known information/previous activity Not Applicable Procedure Ask the learners to measure the unit squares with a scale. Explain to them that the surface inside the square will be the area of the square. As these are of value 1 cm of length and breadth, they are called unit squares.

Ask them to trace these unit squares on the paper and cut them. Make 25 more of these unit squares.

Tell them to take the red square and try and fit as many of these unit squares as they can on it without overlapping.

Now, ask them to try and fit as many unit squares they can on the yellow square given to them without overlapping.

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UNDERSTANDING THE ACTIVITY Leading questions  What is the measure of the small square? Do all sides of this square measure the same?  What is a unit square?  How many unit squares can you accommodate in the red square?  How many unit squares can you accommodate in the yellow square?

Discussion and Explanation 1. The measure of all sides of the small square is 1 cm.

2. A unit square is a square with its sides of one unit. This one unit can be 1 cm, or 1 inch or 1 m, etc. The unit used here is cm, so the value of the area of the unit square is 1 cm square and is written as 1 cm 2.

3. In the red square we have been able to accommodate four unit squares. So the area of this square is 4 cm2. If you measure the sides of the red square you will find that they are 2 cm each, i.e., 2 cm in length and 2 cm in breadth.

So we can say that 2 cm (length) x 2 cm (breadth) = 4 cm2 (area) Therefore area of square = length x breadth 4. In the yellow square we can accommodate 25 unit squares and so its area is 25 cm 2.

As explained in point 3, the area of the yellow square can be written as: 5 cm (length) x 5 cm (breadth) =25 cm2 (area) 5. So, the area of a figure is the number of unit areas that it can accommodate in it.

KEY MESSAGE  A unit square is the smallest unit of the area.  Areas can be measured in square units like cm 2, m2, km2.  Area of a square is measured as the product of its length and breadth.

TRY IT YOURSELF 1. Draw a unit square of any length for its side – say2 cm, 4.5cm, or 10 cm2 or any unknown length. Then try to see how many of these square units can fit into the big square made these sides.

2. What happens if a complete square unit is not accommodated in the figure?

LEARNING CHECK 1. Find the area of a square with its side measuring 6 cm.

2 2. If the area of a square is 16 cm , will the sides always be 4 cm each or can the length be 8 cm and breadth be 2 cm?

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28 Time: 30 min

ABL 3.3

LEARNING OBJECTIVE: How do we use a graph paper to find area of regular and irregular plane figures?

ADVANCE PREPARATION Material List S. No. 1 2 3

Material Different types of graph papers Paper pieces in shapes shown in fig 6 1 cm graph paper

Quantity 1 of each kind /class 1 set / group 1/ group

Things to do Not Applicable Note to Instructors Cut the shapes (figures) shown in the fig 3.3.1 and keep them ready before the class. If each of these figures are in different colours it would be better. Make one set for every group.

Figure 6: Irregular closed figures

Safety Precautions Not Applicable

SESSION Link to known information/previous activity We learnt how to find the area of a square using unit areas. Let us see how we can use this concept to measure the area of other irregular shapes. The same concept is used here. (Irregular shape means that no two sides have equal lengths.)

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29 Procedure 3.3.a Show the learners a graph paper. Explain that each square in the graph paper represents a square unit.

Tell them about different types of graph papers and show theme these. Some are just a grid while there are some with a grid and smaller grid within the bigger grid. Give them a simple graph sheet. Ask them to put the one figure given to them on the graph paper and trace an outline of the figure on the graph paper. Remove the figure and count the number of squares in the outline. Every square of the grid is taken as one square unit.

If only a part of the square is inside the figure, there are two ways of counting these squares. If the area inside the figure is half or more than half of the square, than it is counted as one square unit. If the area inside the figure is less than half, it is ignored. Explain to the learners that 'half' is an approximation and this could lead to error in the final calculation of the area. This will give the area of the figure. Ask them to find the area of all the figures.

Fig 7: Types of graph papers6,7

UNDERSTANDING THE ACTIVITY Leading questions 1. What do you see on this paper?

2. Can you compare this paper (graph paper) to the unit squares that we had made in the previous activity?

3. Can you count the number of squares that are accommodated in each of the figures?

6

http://www.fonerbooks.com/graphing.htm

7http://people.rit.edu/andpph/misc/graph-paper-v-7x9.jpg

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30 Discussion and Explanation  You see squares on the paper. This is called a grid. The grids on the paper can be big or small, but they are equal in length and breadth. So they can be used as unit areas.  Instead of cutting unit areas (as done in the previous activity) we can just place the figure on the graph paper and draw an outline of the figure.  Every square of the grid is taken as one square unit. If only a part of the square is inside the figure, there are two ways of counting these squares. If the area inside the figure is half or more than half of the square, than it is counted as one square unit. If the area inside the figure is less than half, it is ignored. Remember that 'half' is an approximation and this could lead to error in the final calculation of the area.

Look at the figure 8. The figure accommodates 13 complete unit squares. So its area is 13 sq. units.

Fig. 8: Figure with complete squares8

Fig: 9: Figure with complete and incomplete squares 9

Now, look at figure 9. It covers the following: 11 full squares = 11 square units 2 half squares = 2 square units 4 greater than half squares = 4 square units 8

9

http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/areaandperimeterrev4.shtml

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31 1 less than half square = 0 square unit Therefore total area of the figure is 11 + 2 + 4 + 0 = 17 square units.

An example of how the squares are counted is given in the fig 10 Fig 10: Area of irregular figure10

3.3.b Now, suppose you want to find the area of your palm. Take the graph paper and hold your hand, palm down, on the paper. Now draw an out line of the palm. When you lift up the hand, close the figure by joining the end points.

Now, count the complete, half and more than half squares in the outline of the palm. This will be the area of your palm. As the graph paper is a centimeter graph paper, the area of your palm will be in cm2.

UNDERSTANDING THE ACTIVITY Leading questions 1. When you trace your palm on the paper what kind of figure do you see?

2. Why should the end points of the figure be joined?

Discussion and Explanation  The figure seen on the graph paper is an irregular plane figure. In this way area of any irregular closed figure can be calculated.  The end points of the figure have to be joined as we have to find the area of the palm and we know that the area of an open figure cannot be calculated.  Graph sheets are available and are used to measure area. The graph sheets available are in different measures so it is necessary to know the measure of each unit of the graph paper before using it.

KEY MESSAGES The area of regular and irregular plane closed figures can be calculated by counting the squares that the figure covers on the graph paper.

10http://www.poolandspachemicals.co.uk/volcalc.htm

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TRY IT YOURSELF 1. Find the area of a circle using the graph paper method. Compare it with the area calculated by the formula. Area of circle = (pie) r2 (where pie = 22/7, r is the radius of the circle. Take radius in cm; then area will be in cm2 . If the radius is in metres then area will be in metre 2)

INTERESTING INFORMATION Can you hold a million in your hand?

Stick sheets of newspaper together to form a square in which every side is 1 m, fold it and hold it in your hand. You have a million in your hand!!!! How? Area of square with side 1 m = 1 m2 = 10000 cm2 = 1000000 mm2 So you have 1 million square millimeters in you hand!!!!

WEB RESOURCES How to calculate the Area of a given irregular figure using a graph paper? https://www.youtube.com/watch?v=x0NHC0cmKfU

LEARNING CHECK11 Problems to solve

11

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33

ABL 4: Measurement of Volume Activity 4.1

4.2

4.3

Learning objective What is volume?

Key messages  The amount of space occupied by the object in 3 dimensions is its volume.  Solids, liquids and gases all occupy volume.

How is volume of a solid  In solids, whether they are measured? regular or irregular, their volume can be measured by the volume of water they displace.  Only in the case of regular solids, volume can calculated by measuring their dimensions like sides, height or diameter and using formulae.  How do you measure The volume of your lungs can be the volume of your determined by water displacement lungs? method.

TOTAL

Time (min) 10

20

15

45

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Time: 10 min

ABL 4.1

34

LEARNING OBJECTIVE: What is volume?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6 7 8

Material Cardboard carton Compass box Thin book Thick book 1 liter water bottle 1/2 liter water bottle Balloons Measuring jug

Quantity 1/class 1/class 1/class 1/class 1/class 1/class 2/class 1/ class

Things to do Not Applicable Note to Instructors Any other object available in the classroom can also be used to show the concept of volume.

Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure Place the material for the activity one by one on the table so that all the learners can see it clearly. Ask them if all these things can fit into their school bag. The answer will be in the negative. Ask them why. They will say that there is not enough space. Ask them if each of these items needs the same amount of space.

Blow the balloons. One of them should be bigger than the other.

The water bottles must have water in them. Ask a learner to pour water from the smaller bottle into the measuring jug. Note the level of the water in the jug. Empty the jug and ask another learner to pour water from the bigger bottle into the jug. Mark the level of the water again.

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35 Leading questions 1. Can all these things on the table be put into your school bag at the same time?

2. Why? 3. Can the bag hold one of them at a time?

4. Do all of them require the same space?

5. What goes inside the balloon for it to grow bigger?

6. Which of the water bottles holds more water?

Discussion and Explanation  All these items cannot be placed in a school bag at the same time, as there is not enough space in the bag to hold them. Some of them can be placed in the bag. If the carton is too big it might not be able to fit in the bag. So we can say that these things require space. The space that they occupy is called the volume of that item.  Plane objects, like a sheet of paper, cloth or a thin blade, are 2-dimensional objects, which have so little thickness that we can neglect their thickness, and speak only about their area in a plane (or a graph paper which can contain it fully). Most objects are not plane objects. A book, a slate, a door etc – these have thickness also, in addition to length and breadth. They are 3-dimensional objects and they also occupy space and have a volume in addition to the area of their outer surfaces.  Look at the balloons. They were very small and then they became bigger. This is because we blew air in it. So we say that air also occupies the volume inside it.  One of the balloons is bigger and the other is smaller. Do they occupy the same amount of space? No. So the volume of an object can change. Blow more air inside, the volume occupied by the balloon increases. If the air is let out of the balloon the volume of the balloon decreases.  When the volume of water in both the bottles is measured, it will be seen that the bigger bottle holds more volume of water.

KEY MESSAGE  

The amount of space occupied by the object is its volume.

Solids, liquids and gases all occupy space.

LEARNING CHECK 1. Make a list of 5 things that occupy space.

ABL 4.2

Time: 20 min

LEARNING OBJECTIVE: How is volume of a solid measured?

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ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6

Material Cardboard box ( 4 cm x 2 cm x 2 cm) Unit volume box Measuring cylinder Water Thread Stones (should be able to suspend this stone in the measuring cylinder)

Quantity 1/class 16/class 1/class 1/class 1/class 1/class

Things to do The cardboard box (cuboid with sides 4 cm, 2 cm, 2 cm) and the unit volume box (cube with sides 1 cm) can be made from the net diagram given in figure 11. Make these boxes in advance. They should be made of chart paper so that they are not destroyed while handling. Moreover, they can be saved and used later.

Figure 11: Net diagram for cube and cuboid

Safety Precautions Not Applicable

SESSION Link to known information/previous activity We learnt in the previous activity that objects occupy space. Here we will see how much space the object occupies.

Procedure 4.2 a Show the learners the rectangular cardboard box. Ask them if they can measure the volume of the box.

Remind them that the volume is all the space in the box. Then show them the unit box. The volume of each of these unit boxes is 1 cubic cm, or can be called the unit cube. Start placing the unit boxes in the larger box.

Once it is full, ask the learners how many unit boxes have been placed in this box. It will be 16 boxes.

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UNDERSTANDING THE ACTIVITY Leading questions 1. Why is the smaller box called the unit cube?

2. We know that the space in the closed object is its volume. So what is the volume of the bigger box?

3. How many unit cubes can be placed in the larger box?

4. What does the number of unit cubes signify?

Discussion and Explanation  The smaller box is called the unit cube, as the height, the breadth and the length of the cube are 1 cm each.  16 unit cubes can be placed in the bigger box. This shows that the volume of the box is 16 cu cm.  Let us compare this to the sides of the cuboid; Length = 4 cm; Breadth = 2 cm; Height = 2 cm And we have found the volume is 16 cu cm  We have the measure of the sides of the cuboid and the volume. Can you devise a formula to find the volume? (Give the learners a couple of minutes to think of the formula)  Volume of the cuboid = length of cuboid (4 cm) x breadth of cuboid (2 cm) x height of cuboid (2 cm) = 16 cu. cm So, the volume of a cuboid can be calculated by the formula l x b x h 4.2 b Take the measuring cylinder and fill it with water till the halfway mark. Tie the stone with the thread.

Note the reading of the level of the water in the cylinder. Let this be V1 ml (or cu cm). Now suspend the stone in the cylinder. The water level will rise. Note the reading of the water level now. Let this be V2 ml.

UNDERSTANDING THE ACTIVITY Leading questions 1. Why can the volume of the stone not be calculated by the formula lxbxh?

2. When noting down the level of the water in the cylinder why do we use the unit ml?

3. Why does the water level rise when the stone is suspended in the cylinder?

Discussion and Explanation  The volume of the stone cannot be calculated by the formula lxbxh as it is not a regular shape and these measurements cannot be taken.  The water in the cylinder also occupies space so its volume can be measured. The cylinder measures volume of liquids and so is marked in ml.  Now, the level of water initially is V1 ml. The level of the water after the stone is suspended is V2 ml.

The increase is because the stone is also occupying some space in the cylinder along with the water.

This is why the level of water has increased.  The volume of the stone can be calculated by the difference of these levels.  Therefore, volume of stone = V2 ml - V1ml = (V2- V1) ml.

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38 

Note: millilitre (ml) is the same as cubic centimeter (cc).

1 cc = 1cm x 1cmx1 cm; 1000cc = 1 litre Fig 12: Finding volume of irregular object12

Metric Volume Units A liter is the basic unit of volume. It id denoted as 'l' 1 l = 1000 ml (milliliter)

KEY MESSAGES  

In regular solids, volume is measured by calculating it by a formula.

In irregular solids volume is measured by the volume of water it displaces.

LEARNING CHECK 1. I have a container of length 4 cm, breadth 2 cm and height 10 cm. If I fill the container with water till the

height of 5 cm, what is the volume of the water in the container?

2. I have one big box with sides 5m, 3 m, and 2 m. I have some smaller boxes which measure 6 cm, 4 cm and 10 cm. How many smaller boxes can I fit in one big box?

ABL 4.3

Time: 15 min

LEARNING OBJECTIVE: How do you measure the volume of your lungs?

ADVANCE PREPARATION Material List S. No. 12

Material

Quantity

https://www.google.co.in/search?q=Measuring+irregular+objects

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39 1 2 3 4

Plastic tube Large plastic marked bottle Large water basin/ tub Water

1/class 1/class 1/class 1/class

Things to do Not Applicable Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure Fill the tub with water till 10 cm in height. Fill the marked water bottle till the top. (Note the water bottle has markings in milliliters along its side), Close the bottle tightly at its mouth with your hand and turn the bottle upside down. The water from the bottle should not spill. Place the mouth of the bottle below the water level in the tub before you remove your hand. You will see that there is no air in the bottle. Without tilting the bottle insert one end of the tube into the bottle. The other end should be outside the tub as shown in fig 13.

Take a deep breath and breathe out as much as you can through the tube. Note the water level in the tub will rise and the water level in the bottle will fall, Note the decrease in water volume from the markings in the bottle

Fig 13: Measuring lung capacity13

13

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UNDERSTANDING THE ACTIVITY Leading questions 1. What happens if the bottle opening is not covered before it is inserted in the water?

2. What happens when you breathe out into the tube?

3. Where does the air go?

Discussion and Explanation  If the bottle opening is not covered before it is inserted in the water, some of the water will spill and air will enter the bottle. This will give wrong value of the capacity of the lungs.  What you will observe is that the air that you breathe out into the tube will pass through the tube into the bottle and pushes the water out of the bottle through the gap between the tube and the bottle mouth. If this activity is done correctly, i.e., you have taken a deep breath and breathed out all the air fully from your lungs, then the volume of water you pushed out from the bottle into the tub is equivalent to how much air your lungs can hold.  The volume or the capacity of your lungs can be measured from the level of the water displaced in the bottle as the bottle is marked.  Having a large air capacity in your lungs means you can distribute oxygen around your body at a faster rate. The capacity of the lungs increases as children grow but can be also increased by doing breathing exercises regularly.

KEY MESSAGE 

The volume of your lungs can be determined by water displacement method

INTERESTING INFORMATION 

The total capacity (volume) of the lungs of an average adult is 6 litres.

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41

ABL 5: Measuring Mass and Density Activity 5.1

5.2

5.3

5.4

Learning objective Key messages What is mass and  Mass is the amount of matter weight? present in a body.  Mass is a constant and does not change.  Weight is the force exerted by gravity on a given object/body.  Weight is dependent on mass and gravity and will change if the gravitational force changes.

How do you  The common balance is based construct a on the principle that the mass common balance? of an object can be determined by equating it with standard weights How do you  The principle of the rubber band construct a rubber scale is that the every weight band scale? will pull the rubber band to a certain extent. The amount of pull will give the weight of the object.

What is the density  Density of an object is how of a substance? close the smallest particles of How is it the object are packed together. measured?  Density can be measured by the formula: density = Mass/Volume TOTAL

Time (min) 10

15

15

15

55

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ABL 5.1

Time: 10 min

LEARNING OBJECTIVE: What is mass and weight?

ADVANCE PREPARATION Material List S. No. 1

Material Chart â&#x20AC;&#x201C; Difference between Mass and Weight

Quantity 1 per class

Things to do Not Applicable

Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure Start with this introductory discussion. Everyday we see people buying vegetables from a vendor. What will you ask a vendor if you want to buy some vegetables? I would ask for one Kg or two kgs of vegetables. What is this Kg measuring? (Most learners will say weight of the vegetable).

Once you have taken answers from learners, explain that this measure is actually called mass. Mass is the amount of matter/substance in a body or object. This always remains constant wherever the object is. (One potato will have the same amount of matter if it is taken to any part of India and even on the moon!)

If this is mass, then what is weight? Weight is the force exerted by the earth on a mass. The force acting on everything in the earth is gravity. Gravity exerts a pull on an object based on its mass. This is called weight and is normally measured in Newton or Kgf (Kilogram force).

Therefore weight on Earth (W) = m x g; Where m is mass and g is the gravity on Earth.

To make our daily lives easy, we use the words weight and mass interchangeably as 1Kgf = 1 Kg. Scientifically, there are differences between mass and weight. Let us try to answer some questions to see if we understood mass and weight correctly.

Call out statements from columns in the table below and ask learners to identify if you are talking about mass or weight. Once you are done, put up the chart for learners to observe.

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CHART 4 – Difference between mass and weight S. No Mass Weight 1 It is the measure of the amount It is the measure of the amount of force acting on a of matter in a body. mass due to the acceleration due to gravity.

2 It is a property of matter. The It depends on the effect of gravity. mass of an object is the same everywhere.

3 It can never be zero.

It can be zero if no gravity acts upon an object, as in outer space.

4 It does not change according to It varies according to location, as gravity is different location at different locations e.g., it is less on top of a mountain.

5 It usually is measured in grams It often is measured in newton or Kgf, a unit of force. and kilograms.

UNDERSTANDING THE ACTIVITY Leading questions 1. Will your mass be the same on the earth and the moon?

2. Will your weight be the same on the earth and the moon?

Discussion and Explanation  Mass remains the same at all times and does not change with respect to location. Therefore, our mass is the same on the earth and the moon.  Weight depends on gravity. The gravity on the moon is 1/6th that on the earth and hence or weight will not be the same on the Earth and the moon. We will weight much lesser on the moon!

 When we make common measurements in shops etc. we are always measuring weight. Various methods of measuring weight are – Common 2–pan balance, spring balance etc. used by street vendors and shops, weighing scales in hospitals to measure the weight of people, more modern electronic balances based on principles other than gravity etc.

KEY MESSAGES    

Mass is the amount of matter present in a body.

Mass is a constant and does not change.

Weight is the force exerted by gravity on a given object/body.

Weight is dependent on mass and gravity and changes from one location to another.

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LEARNING CHECK Ask learners to list the key things they have learnt. Guide them to the key messages listed and then put up the chart of key messages. If you have time during the class, make up a small game, quiz or match the following as a learning check. This may have to be done as part of advance preparation.

ABL 5.2

Time: 15 min

LEARNING OBJECTIVE: How do you construct a common balance?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5

Material Wooden beam (50 cm long) Two identical plastic lids Standard weights of small denomination Twine Stone, pencil, duster

Quantity 1/ class 1 pair/ class 1 set / class 4 m / class 1 each /class

Things to do Not Applicable Note to Instructor This activity is done as a demonstration but it can be made more interactive if the learners are asked to help.

Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure Take the wooden beam and balance it on your finger. The point at which the finger lies when the beam is perfectly balanced is the center of the beam. Mark this point.

Tie a thread at the point marked on the wooden beam. This system acts as a beam of balance. Make three holes on the edge of each lid. These holes should be such that the distance between any two holes is the same. Suspend the lids with the help of thread as shown in the figure. When there are no weights in the pans, beam should stand in a perfectly horizontal position.

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45 Now, ask a learner to place a stone on the left pan and then lift the apparatus. What happens? Now, add standard weights to the right pan till the beam becomes horizontal again. Note the reading of the weights on the right pan.

Get some more learners to weight other objects.

Fig 14: Physical balance

UNDERSTANDING THE ACTIVITY Leading questions 3. If the beam is not suspended from the center, what will happen?

4. Why should the holes be equidistant?

5. What happens when an object is kept on the left pan and the apparatus is lifted?

6. Can the objects be kept on the right pan and the known weights on the left?

Discussion and Explanation  If the beam is not suspended from the center, the beam will not be horizontal to the ground as the mass of the beam on one side will be more than the other. So, the beam should be suspended from its center.  The holes, if equidistant, will help to balance the lids horizontal so that the objects kept in them will not slide off them.

When an object is kept on the left pan and the apparatus is lifted, it tilts to the left as this side of the beam becomes heavier. To counter this, weights are put in the other pan. Now, when the object is kept in one pan and the weights on the other, and if the beam is horizontal then the mass of the object is equal to the sum of the weights.  Yes, the weights and the objects can be interchanged and there will be no change in the results.

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KEY MESSAGES The common balance is based on the principle that the mass of an object can be determined by comparing it with a combination of standard weights like 1000gm (1 kg), 500 gm, 250 gm, 100 gm & 50 gm.

TRY IT YOURSELF Sometimes you see vegetable vendors do not use standard weights but different sizes of stones. Find out how this works.

Time: 15 min

ABL 5.3 LEARNING OBJECTIVE: How do you construct a rubber band scale?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6 7 8

Material Cardboard box Rubber bands Paper clips Standard weights Twine Duct tape Small plastic cup 3 cm wide strip of paper

Quantity 1/class 5/class 5/class 1 set /class 1/class 1/class 1/class 1/class

Things to do Not Applicable Note to Instructor This activity is done as a demonstration but it can be made more interactive if the learners are asked to help.

Safety Precautions Not Applicable

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SESSION Link to known information/previous activity Not Applicable Procedure Remove the top of the cardboard box and turn it on its side. This will allow the learners to see inside the box.

Put a 5 cm piece of tape on the center of the top of the box. Punch two holes in the tape about 3 cm apart. Put the twine through the holes and tie it, making a loop. Put another piece of duct tape over the holes and twine to make it stronger.

Now, take two paper clips and bend them to form an "S" shape. Hang one of these from the string inside the box. On this clip hang a rubber band. On the other end of the rubber band hang the second paper clip. Take the plastic cup and punch two holes on its edge. Tie the string through these holes. Hang this cup from the second paper clip.

Take the strip of paper and paste it right behind the cup. With the cup empty, mark the position of the cup on the paper. Mark it "0". Start adding small quantities of known weight to the cup and mark the position of the cup on the paper. Suppose the known weights are 100 g and 200 g. Mark the position of the cup when these weights are in the cup. Then remove the paper and divide the space between the marks into equal distances.

These will be the 25 g, 50 g, 75 g, etc. marks. Put the paper back in its original place. The rubber band scale is ready for use.

Then take the other objects of unknown weights and put them in the cup. Note the reading of the top of the cup after it has come to rest. This will be the weight of the unknown object. Ask the learners to some things that they have like sharpeners, erasers pens, etc.

Fig 15: Rubber band Scale14

14http://science-notebook.com/measure03-mass.html#Making_a_Rubber_Band_Scale

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UNDERSTANDING THE ACTIVITY Leading questions 1. Why are the tapes used?

2. What happens when the weights are put in the cup?

3. Which weight will pull the rubber band more?

4. Why are known weights used initially?

5. If the rubber band breaks during this activity, what does it mean?

Discussion and Explanation  The balance is suspended from the roof of the cardboard box. The tape makes the place stronger and also stops the string from moving.  When the weights are put in the cup, the rubber band stretches. The more the weight more will be the stretch of the rubber band.  The heavier object will pull the rubber band more.  When the marking is done on the paper when known weights are put in the pan, the scale is calibrated.

Now unknown weights can be placed in the pan and their weight known.  If the rubber band breaks in this activity it means that the rubber band is not strong enough to take the weight in the pan. A stronger rubber band has to be used.

KEY MESSAGES The principle of the rubber band scale is that the every weight will pull the rubber band to a certain extent.

The amount of pull will give the weight of the object.

INTERESTING INFORMATION Types of balances There are different types of balances. For regular use there is spring balance, kitchen weighing scale, bathroom scales, electronic balance, etc. For accurate measurement of mass of a body, a physical balance is used. It works on the same principle as that of beam balance. It is used to weigh chemicals in laboratory and small amount of gold in jewelers shop.

Different types of balances

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Time: 15 min

ABL 5.4

LEARNING OBJECTIVE: What is the density of a substance? How is it measured?

ADVANCE PREPARATION Material List S. No. 1 2 3 4 5 6

Material Cork block Stone Measuring cylinder Scale to measure length Weighing scale to measure small quantities String

Quantity 1/class 1/class 1/class 1/class 1/class 1/class

Things to do Not Applicable

Note to Instructor Ensure that the two objects whose density has to be found should be roughly of the same size and volume.

Only then will the difference in weight and density be understood properly Safety Precautions Not Applicable

SESSION Link to known information/previous activity You have learnt how to find the volume of an object, or the space it occupies. We will use this property to find another property of a substance.

Procedure Ask the learners what difference they find between the cork block and the stone. The learners will answer that one is hard while the other is softer. The other comparison is that the look is different. They will also say that the weights are different. This is when you tell the learners that we will be looking at the weights of the two objects Ask the learners that even though the two objects look to be of the same size why are their weights different?

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50 This is because the molecules of the stone are more tightly packed than those of the cork. This could be found out by comparing their density. To find the density, we need the volume and the mass of the objects.

Find the volume of the cork block by measuring the sides and using the formula for the volume (volume = Length x breadth x height). Let us assume that the volume of the cork block is V 1. Use a weighing scale and find the mass of the block. Let us call it M1. .

Use the water displacement method to find the volume of the stone (as explained in 4.2 b). Let us mark it V 2.

Find the mass of the stone using the weighing scale and Mark it as M 2.

UNDERSTANDING THE ACTIVITY Leading questions 1. The two objects are almost the same size but their weights are different. Why? 2. What is density?

Discussion and Explanation  The two objects appear to be the same size so it is expected that they weigh the same. But it is not so.

The reason is that the molecules in the stone are closer than those in the cork. So for the same size, there are more number of molecules in stone than the cork.  Density of a substance (or an object) is how close the molecules of the substance are packed together.  Density of an object is the ratio of the mass of the object and its volume Therefore, Density = Mass / Volume So, density of cork block= Mass of block / Volume of the block = M1 / V1  Similarly, the density of the stone will be: Density (stone) = M2/V2  Now, compare the densities of the two objects. We will find that the density of the stone is more than that of the cork. Thus it is heavier than the cork.

KEY MESSAGE:  

Density of an object is how close the smallest particles of the object are packed together.

Density can be measured by the formula: density = Mass/Volume

INTERESTING INFORMATION What weighs more - A Kg of Iron or a Kg of Feathers?

Many of us will instantly say “feathers” but when you come to think of it, the weight is exactly the same. Then why do they look different? This is because of their densities! The Iron occupies very little space while the feathers occupy a lot of space. This means that the volume of the feathers is much more than that of the Iron.

We know that density is mass/volume. The density of feathers is much lesser than that of Iron. So there can be many more Iron molecules in a small space than feathers

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51 1. Find the Volume: Take a transparent container of about 1 liter. Fill it with water till the halfway mark.

Mark it with a marker. Then take the things from your kitchen whose volume you want to find. E.g., take a potato. Drop it in the container and see how much the water rises. Mark this. Remove the potato and drop a tomato in the container. Mark this too. To differentiate the marks name them appropriately. Do you think you can find the density of each? How will you do that?

2. Using the measuring cylinder how will you find the volume of a peanut in a shell?

3. Guess the volume of liquid that the following items can hold. Then check them against the actual measures. E.g., Teacup, teaspoon, tablespoon, glass, and water jug.

4. How will you find the density of a liquid?

LEARNING CHECK 1. A block of wood has a mass of 180 grams. It is 10 cm long, 6 cm wide, and 4 cm thick. What is its volume and density?

2. What is the density of an object with a mass of 120 g and a volume of 7 ml?

3. We have an object with a density of 620g/cm3 and a volume of 75 cm3. What is the mass of this object?

WEB RESOURCES 1. Air occupies: spacehttps://www.youtube.com/watch?v=H3PxZfJPrpE 2. Measuring Irregularly Shaped Objects: https://www.youtube.com/watch?v=7HcoVawJiVU

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ABL 6: Measuring Time Activity Learning objective Key messages 6.1 What is time? Why  Time is measured so that we can carry do we measure time? out our day-to-day activities easily.  Time can be measured in various units like seconds, minutes, hours, days, months, years etc.

6.2

How is the sand clock  constructed?

6.3

How does the sun  dial work?

The sand clock is constructed on the principle that the time required for the flow of a certain quantity of sand is the same at all times.

It works on the principle of the regular movement of the sun and formation of shadows.

TOTAL

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Time (min) 10

20

20

50

ABL 6.1

Time: 10 min

53

LEARNING OBJECTIVE: Why and how do we measure time?

ADVANCE PREPARATION Not Applicable Material List Not Applicable Things to do Not Applicable

Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure Start by asking a learner what the time is. Now ask him/her what that means? (For example: What does it mean when you say it is 2 ‘o’ clock?). This is nothing but a way of measuring time. Why do we measure time?

Ask the learners a set of leading question so that they understand the importance of time.

UNDERSTANDING THE ACTIVITY Leading questions 1. How old are you? What do we mean when we say we are ____________ years old?

2. When did you eat breakfast? When will you eat dinner?

3. How do we decide who comes first in a running race?

Discussion and Explanation  When we tell our age, we are actually stating a measure of the time that has passed since we were born.

We normally measure age in Years.  We eat specific meals at specific times. Time also helps us explain things that we do or did. Since we finished eating breakfast, it becomes the past. What we are doing now is the present. Since we will eat dinner later it is the future. Time is thus, divided into past, present and future. These events are all a few hours apart. Therefore we see time can be measured in hours also!

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54  

In a race, the person who takes the least amount of time to finish is the winner. This person may win by just a few seconds. This time can also be measured in seconds.

Time can be measured in various units like seconds, minutes, hours, days, months, years etc. Measuring time helps us carry out our day-to-day activities smoothly.

KEY MESSAGES  

Time is measured so that we can carry out our day-to-day activities easily.

Time can be measured in various units like seconds, minutes, hours, days, months, years etc.

LEARNING CHECK Give three examples where measuring time makes life easier.

Time: 20 min

ABL 6.2 LEARNING OBJECTIVE: How is the sand clock constructed?

ADVANCE PREPARATION Material List S. No. 1 2  3  4  5  6

Material Plastic 500 ml bottles Sand Duct tape Square of thick aluminum foil (1 inch by 1 inch) Sharpened pencil Stopwatch

Quantity 2/group 1 cup /group 12" /group 1/group 1/group 1/group

Things to do Not Applicable Safety Precautions Not Applicable

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55 Procedure Fill one of the bottles with one cup of fine sand. Cover the top of this bottle with the aluminum foil and secure it with the duct tape on the side of the bottle. Make a neat hole with the help of a pencil. Attach the neck of the second bottle to the first at the neck. Invert the bottle and note the time taken for all the sand to fall into the empty bottle.

Fig 16: Sand clock15

The time taken can be adjusted by increasing or decreasing the amount of sand in the bottle.

UNDERSTANDING THE ACTIVITY Leading questions 1. Why is the apparatus called the sand clock?

2. Why should the hole in the aluminum foil have neat edges?

3. When will the sand start falling into the bottle below?

4. How can the time be adjusted for one complete displacement of sand from one bottle to the other?

Discussion and Explanation  The apparatus is called a sand clock as the time is measured by the flow of sand from one bottle to the other.  The hole in the aluminum foil must have neat edges so that the sand does not get stuck in it and disturb the smooth flow of the sand.  When the bottle is turned upside down, the sand will start falling into the bottle below.  If the time has to be increased for one complete displacement, the amount of sand in the bottle should be increased. If the time has to be decreased some sand has to be removed from the bottle.

15

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56 ď&#x201A;ˇ ď&#x201A;ˇ

The sand clock has been used for a long time but it has its disadvantages. It cannot measure very small or very large time span.

The picture of a sand clock (called icon) is used in modern computers to indicate that you are waiting for the computer to complete some activity.

KEY MESSAGE The sand clock is constructed on the principle that the time required for the flow of a certain quantity of sand is the same at all times.

ABL 6.3

Time: 10 min

LEARNING OBJECTIVE: How does the sun dial work?

ADVANCE PREPARATION Material List S. No. 1 2 3

Material Sundial Compass Watch

Quantity 1/class 1/class 1/class

Things to do Not Applicable Safety Precautions Not Applicable

SESSION Link to known information/previous activity Not Applicable Procedure On a sunny day, take the learners out in the playground. Place the sundial in an elevated place (like on a stool) so that the learners can see the shadow cast by the dial clearly. Give one of the learners the compass and ask him to find the North direction. Ask another learner to place the sundial's elevated portion facing the North.

Now, the sundial is set up for use.

Look at the shadow that is formed by the elevated portion of the dial. The time of the day will be where the shadow points. Verify this by using the watch.

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UNDERSTANDING THE ACTIVITY Leading questions 1. Why is the apparatus called the sundial?

2. What do you see on the disc of the dial?

3. How does the sundial work?

4. Why should the sundial be kept in the open?

5. Will the sundial show time at night?

Discussion and Explanation     

Sundials were used to tell the time of the day in olden times and are based on the principle that the position of the sun changes continuously during the day.

The disc of the sundial has calibrations, which will tell the time.

As the sun moves across the sky, the central post on the sundial casts a shadow on its circular plate. It is just like reading a clock – the marks or calibrations on the plate tell you what time it is.

The sundial has to be kept in the open, as there should be no other shadow falling on the dial. This could interfere with reading of the correct time.

As there is no sun at night, there is no shadow formed. So the sundial does not tell the time at night.

Fig 17: Sundial16

KEY MESSAGES It works on the principle of the regular movement of the sun and formation of shadows.

LEARNING CHECK 1. Is it possible to use the sundial if it is kept in a balcony?

2. If the sky is clear at night is it possible to tell time using moonlight?

16

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TRY IT YOURSELF You can make a sundial at home!  Materials you will need:  Plastic cup with a lid (like the ones used for takeaway food)  Compass  Straw  Permanent Marker  Pencil  Tape  Watch  Sand This is how you put it together?

Making: Using a pencil, make a hole on the side of the cup about 2 inches below the rim. Place some sand in the cup so that it stays firm and upright. Then cover the cup with the lid. Make a hole in the middle of the lid.

Put the straw through the two holes. The end of the straw that comes out of the side of the cup should be about 3 cm and should be secured to the cup with a duct tape. The larger part of the straw comes out of the lid and is at an acute angle with the lid.

Setting up the dial: Identify where the sundial will be kept. It should be a flat surface large enough to hold the apparatus and should also get sunshine throughout the day. Now, using the compass, find the North direction.

Place the apparatus in such a way that the straw points towards the North. Mark the position of the dial by drawing an outline with a permanent marker so that the position is not changed.

Marking the dial: Use the permanent marker, and your watch, to mark the shadow of the straw on the rim of the lid. Mark every hour of the sunlight hours on the lid.

Your Sundial is ready for use!

Remember that calibrating the sundial will take a day.

WEB RESOURCES How to make a sundialhttps://www.youtube.com/watch?v=lcL2f-KInWI

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MEASUREMENTS Fill in the blank boxes in the table given below: LENGTH

METRIC mm

cm

m

________________________

km

METRIC Milliliter

Litre

WEIGHT

METRIC Metric tons g

kg

METRIC

_______________________________________

Centigrade

TIME

METRIC sec.

min.

hr.

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d