Class 5 Mathematics Chapter 8: Weight and Capacity

Anu's list of weights

Anu wrote down the weight of everything in her room. An iron almirah, 40 g. A sofa, 30 g. A refrigerator, 50 g. Her cousin Devi read the list and laughed out loud. Something has gone badly wrong here. Can you spot it too?

Which unit fits?

Grams are for light things. A pencil, a biscuit, a small packet of salt. Kilograms are for heavy things. A bed, a rice bag, a school bag full of books. An almirah is very heavy. So it weighs about 40 kg, not 40 g.

The dial tells the weight

A kitchen dial scale has 0 at the top. The needle turns as you add weight. A 1 kg dial is split into four equal parts. Each part is 250 g. So the big marks read 250 g, 500 g, 750 g and 1 kg.

Read between the marks

Devi puts a packet of sugar on the 1 kg dial. The needle stops halfway between 500 g and 750 g. Halfway between them is 625 g. First count the small lines. Then work out what one small line is worth.

One kilogram is a thousand grams

1 kg = 1,000 g. So 3 kg = 3,000 g. And 7 kg = 7,000 g. To change kilograms into grams, put three zeros after the number. A double number line shows this jump very clearly.

Two units in one weight

Devi buys 3 kg 500 g of flour. The shop scale shows only grams. 3 kg is 3,000 g. Now add the extra 500 g. So the scale must read 3,500 g. In the same way, 2 kg 250 g is 2,250 g.

The small-number trap

A packet of sugar weighs 5 kg 50 g. Is that 5,500 g? No, it is not. 5 kg is 5,000 g. Add only 50 g to it. The answer is 5,050 g. Fifty grams is not five hundred grams.

Grams back into kilograms

Take 10,760 g. Split off the last three digits. Those are the grams, 760. What is left is the kilograms, 10. So 10,760 g = 10 kg 760 g. In the same way, 4,080 g = 4 kg 80 g.

Comparing two weights

Which is more, 1 kg 600 g or 1,700 g? Change both into grams first. 1 kg 600 g becomes 1,600 g. Now compare 1,600 g with 1,700 g. So 1 kg 600 g is the lighter one. Always match the units first.

Tiny weights: the milligram

An ant weighs only 1 mg to 5 mg. A gram is far too big a unit for it. 1 g = 1,000 mg. So 5 g = 5,000 mg. And 4 g 100 mg = 4,100 mg. Medicines are measured in milligrams.

Huge weights: quintal and tonne

A truck full of grain is too heavy for kilograms. So we use bigger units. 100 kg = 1 quintal. 1,000 kg = 1 tonne. That means 10 quintals make 1 tonne. A load of 5,000 kg is 50 quintals, or 5 tonnes.

Remember

• Pick the unit that fits the object.
• 1,000 mg = 1 g and 1,000 g = 1 kg.
• 100 kg = 1 quintal, and 10 quintals = 1 tonne.
• Match the units before you compare.

Scenario:

Anu writes that a pencil weighs 8 kilograms and a sack of rice weighs 25 grams. A class reads it and laughs. Their teacher asks what has gone wrong. The units have been swapped. A pencil is light, so grams suit it. A sack of rice is heavy, so kilograms suit it. The class then reads a dial scale together. It starts at 0, and they work out what one small line is worth before reading anything. Anu rewrites her note: a pencil about 8 grams, a sack of rice about 25 kilograms.

Analysis:

The numbers were fine and the units were swapped. Choosing the unit to suit the object is what stops a weight sounding absurd.

Activity:

Write the weight of six things at home with a sensible unit. Check any that sound silly.

Title:

Guess, then weigh

Safety:

Ask an adult before you use a shop scale or carry anything heavy.

What You Notice:

Light things need grams and heavy things need kilograms. Your guesses get much better after the first two weighings.

An ant weighs only 1 mg to 5 mg, yet it can carry far more than its own weight.

Shops weigh gold in grams and milligrams, because even a tiny bit of gold is costly.

Changing mg to g to kg — Three zeros at every step. — Going from milligrams to grams costs three zeros. Going from grams to kilograms costs three zeros again. Going back the other way, you take three zeros off.

Rice for two reasons

Meher's mother is shopping at the kirana store. She buys 2 kg 500 g of rice for the week. Then she buys 1 kg 750 g more for the festival. Meher wants to know the total. How much rice is going home today?

Add the like parts

Kilograms go with kilograms. Grams go with grams. So 2 kg and 1 kg make 3 kg. Then 500 g and 750 g make 1,250 g. But 1,250 g is 1 kg and 250 g. So the total is 4 kg 250 g.

Add in two columns

Write one column for kilograms and one for grams. Add the gram column first. If it reaches 1,000 or more, carry 1 kg across. Here 500 and 750 give 1,250. Carry the 1 kg and keep 250 g.

Or turn it all into grams

Meher likes another way. She changes both weights into grams. That gives 2,500 g and 1,750 g. Adding them gives 4,250 g. She then splits it back: 4 kg 250 g. Both paths end at the same answer.

Taking weight away

How much more rice is for the week than for the festival? Work out 2 kg 500 g minus 1 kg 750 g. You cannot take 750 g from 500 g. So borrow 1 kg and call it 1,000 g. Now 1,500 g minus 750 g is 750 g.

A path in your head

Meher does the same sum without writing. She takes 500 g off 2 kg 500 g and reaches 2 kg. Then she takes 1 kg off and reaches 1 kg. She still has 250 g to take off. That leaves 750 g.

Many sacks, one weight

A sack of potatoes weighs 10 kg 500 g. The shop has four such sacks. Multiply the kilograms and the grams separately. 4 times 10 kg is 40 kg. 4 times 500 g is 2,000 g, which is 2 kg. The four sacks weigh 42 kg.

Sharing a weight out

A tin holds 4 kg 800 g of groundnuts. It is poured equally into 4 jars. Share the kilograms: 4 kg divided by 4 is 1 kg. Share the grams: 800 g divided by 4 is 200 g. Each jar holds 1 kg 200 g.

Grams first, if you like

The same sharing works in grams. 4 kg 800 g is 4,800 g. Divide 4,800 by 4 and you get 1,200 g. That is 1 kg 200 g again. Pick whichever path feels easier for the numbers.

Weight turns into money

Sugar costs 40 rupees for 1 kg. What will 7 kg 500 g cost? Seven kilograms cost 280 rupees. Half a kilogram costs half of 40, which is 20 rupees. So the bill is 300 rupees.

The double number line

Draw two lines, one above the other. On top mark 5 kg, below it 73 rupees. Double both. Now 10 kg sits above 146 rupees. The two lines always move together.

Remember

• Add and take away like parts: kilograms with kilograms, grams with grams.
• 1,000 g make 1 kg, so carry or borrow in thousands.
• Multiply and divide each part, then join the answers.
• A double number line keeps weight and cost in step.

Scenario:

A shopper buys 2 kg 600 g of potatoes and 1 kg 800 g of onions. A class adds the two. Imran keeps the columns separate and gets 3 kg 1,400 g. His teacher asks how many grams make a kilogram. One thousand. So 1,400 g holds a whole kilogram and 400 grams over. The class carries it across and writes 4 kg 400 g. Imran sees that his columns were right and his answer was not finished. The class checks it a second way, turning everything into grams, and gets 4,400 g, which agrees.

Analysis:

Imran's column work was correct and incomplete. Converting the whole thing to grams is a second route that confirms the carry.

Activity:

Add two weights in kilograms and grams. Then redo it all in grams and check the two answers agree.

Title:

Run a pretend kirana shop

Safety:

Use empty packets only. Do not open sealed food to weigh it.

What You Notice:

Adding is quick when the grams are friendly numbers like 250 or 500. It slows down when you have to carry a whole kilogram.

Shopkeepers often add weights in their heads by rounding to the nearest 500 g first.

A langar kitchen may use over 60 kg of flour in one day of cooking.

Carrying and borrowing weight — A thousand grams is one kilogram, both ways. — Going up, 1,000 g becomes 1 kg and is carried. Coming down, 1 kg becomes 1,000 g and is borrowed.

Multiplying a weight — Split, times, join. — Split the weight into kilograms and grams. Multiply each part. Then join the two answers into one weight.

How much water for two cups?

Ramiz is watching tea being made at home. He wonders how much water goes into two cups. Is one whole litre enough? Is it far too much? His grandmother smiles and hands him a measuring jug. Let us find out with him.

What capacity means

Capacity is how much a container can hold. A bucket holds a lot. A spoon holds very little. We measure capacity in litres and millilitres. A litre is the bigger unit. A millilitre is the smaller one.

Which unit fits?

Someone writes that a bucket holds 20 ml. That cannot be right. Twenty millilitres is about four spoonfuls. A bucket holds about 20 l instead. Medicine and eye drops are measured in millilitres. Buckets, cans and drums are measured in litres.

Reading the jars

Ramiz lines up three containers. A jug marked 1 l. A jar marked 500 ml. A small cup marked 100 ml. He fills all three. Together they hold 1,600 ml, which is 1 l 600 ml.

One litre is a thousand millilitres

1 l = 1,000 ml. The milkman leaves 2 l of milk every morning. The family vessel is marked only in millilitres. So they must look for the 2,000 ml mark on it.

Two bottles at school

Ramiz carries a 500 ml bottle to school. He empties it twice in the day. That is 500 ml and 500 ml, which comes to 1,000 ml. So he drinks exactly 1 l of water at school.

A mixed measure in millilitres

A bottle holds 1 l 400 ml. Mary says that is 1,400 ml. Daisy says it is 1,040 ml. Mary is right. One litre is 1,000 ml, and 400 ml is added to it.

Careful with small numbers

Now take 3 l 40 ml. It is not 3,400 ml. Forty is not four hundred. Write 3,000 ml for the litres. Then add just 40 ml. The answer is 3,040 ml.

Millilitres back into litres

Take 7,250 ml. Split off the last three digits. Those are the millilitres, 250. What is left is the litres, 7. So 7,250 ml = 7 l 250 ml. In the same way, 14,075 ml = 14 l 75 ml.

Adding two amounts

Tina buys 2 l 500 ml of petrol. Sam buys 2 l 800 ml. Add the millilitres: 500 and 800 make 1,300. That is 1 l and 300 ml. So together they buy 5 l 300 ml.

Taking away and sharing

Sam's tank shows 9 l after filling. He put in 5 l 300 ml. So it held 3 l 700 ml before. A juice seller has 6 l and pours 250 ml glasses. He can fill 24 glasses.

Remember

• Capacity is how much a container holds.
• 1,000 ml make 1 l, so carry and borrow in thousands.
• Millilitres suit spoons and drops. Litres suit buckets and cans.
• Match the units before you add or compare.

Scenario:

Class five at a school in Bhuj keeps a water diary for a week. Each child brings a 500 ml bottle and fills it three times a day. There are forty children in the class. Ravina, the class monitor, writes the amounts on the board every evening. On Wednesday she also notices a tap near the hand pump that will not shut. It drips steadily into a mug she has placed below it. The mug takes in about 200 ml of water every minute. The teacher asks the class to work out the numbers before they report the leak to the head teacher.

Analysis:

Capacity sums answer a real question about school water use, and they show why a small leak matters.

Activity:

Place a mug under a dripping tap at home for ten minutes, then measure what it caught.

Title:

Make your own measuring jar

Safety:

Use water only, and wipe up spills so nobody slips.

What You Notice:

Most cups hold between 150 ml and 250 ml. It takes four to six cups to fill one litre.

A teaspoon holds about 5 ml, so two hundred spoonfuls would fill one litre.

A petrol pump in India measures fuel in litres and shows the amount to three decimal places.

Changing litres to millilitres — Litres and kilograms behave the same way. — Both jump by a thousand. 3 kg 40 g is 3,040 g, and 3 l 40 ml is 3,040 ml. Learn one and you know the other.