CBSE Class 3 Mathematics Chapter 8: Who is Heavier? NCERT Solutions

Solution: The groundnuts might appear to be more in quantity or volume than the jaggery, but in terms of actual weight, they are not necessarily more. Often, lighter items spread out more, making them look like a larger amount than a denser item of the same weight. So, the groundnuts just look more, but their weight is likely the same as the jaggery.

Solution: When comparing items of the same weight, like 1 kg, the one that is less dense will take up more space and thus require a bigger bag. Items that are fluffy or have a lot of air between them are less dense.

(i) 1 kg popcorn or 1 kg sugar?

Guess: We need a bigger bag for 1 kg of popcorn.

Reasoning: Popcorn is very light and airy, so 1 kg of popcorn will fill up a much larger volume than 1 kg of sugar, which is denser. Therefore, a bigger bag is needed for the popcorn.

(ii) 1 kg peas or 1 kg potatoes?

Guess: We need a bigger bag for 1 kg of peas.

Reasoning: Similar to popcorn, peas are generally less dense than potatoes. This means that 1 kg of peas will occupy more space than 1 kg of potatoes, requiring a larger bag.

Activity Note: The instruction suggests going to the market to check these guesses. This practical activity helps confirm that items with the same weight can have different volumes.

Solution: This question involves estimating the relative weights of a pumpkin and small tomatoes. To lift a pumpkin on a see-saw or balance, the total weight of the tomatoes needs to be comparable to the pumpkin's weight. Based on common sizes, a pumpkin is significantly heavier than a small tomato. The answer suggests that a substantial number of tomatoes are needed.

Estimated Answer: About thirty-five to forty small tomatoes are enough to lift the pumpkin up.

Solution: This is another estimation question comparing the weight of a pumpkin to big mangoes. A pumpkin is generally much heavier than a single mango. To balance the pumpkin, a significant number of big mangoes would be required.

Estimated Answer: About twenty big mangoes may balance the pumpkin.

Solution: This question asks to compare the weight of a person (you) with the weight of pumpkins. A typical pumpkin is quite heavy, often heavier than a young child. To balance a person on a see-saw, multiple pumpkins would likely be needed, depending on the size of the person and the pumpkins.

Estimated Answer: About ten pumpkins can balance me on the see-saw.

Solution: This question requires personal estimation based on observing classmates. Students are asked to think about their own weight and then identify classmates who might weigh similarly, more, or less than themselves. The provided answer gives examples of names for each category.

(a) Almost same as me: Arjun, Saurav, Swarnim.

(b) More than me: Rahul, Rakesh, Ahmad.

(c) Less than me: Ramesh, Suresh, Akhilesh, Shailendra.

Note: These are examples, and actual answers will vary for each student.

Solution: This question assesses a student's strength and ability to lift objects. It asks for an estimation of how many books can be held with one arm extended straight. The answer provided is a personal estimation.

Estimated Answer: I can lift five books on one hand; keeping my arms straight.

Solution: This activity involves matching common food items with typical quantities used in cooking or for a meal. The goal is to associate items with reasonable amounts, understanding different units of measurement like kg, bowl, glasses, spoons, and pinch.

The correct matches are:

Item	Amount
Rice	1 kg
Daal	$1/2\; \backslash text\{\; kg\}$
Peas	1 bowl
Water	8 glasses
Onions	$2$
Mustard seeds	2 spoons
Salt	1 pinch
Red chilli powder	1 spoon

Note: The amount for 'Onions' is listed as '2', which likely implies 2 onions, assuming they are of a moderate size.

Solution: This is a practical activity designed to help students observe and record the quantities of various household items purchased. Students need to look at the packaging or ask their family members about the amounts bought during a single shopping trip. The table below provides examples of items and their typical purchase amounts.

Example List:

Things	Amount	Things	Amount
Rice	5 kg	Sugar	5 kg
Atta	10 kg	Soap	6 pieces
Dal	$2\; \backslash text\{\; kg\}$	Detergent powder	1 kg
Oil	5 litre	Shampoo	200 ml
Tea	1 kg	Salt	500 g
Potato	20 kg	Spices	250 g

Note: Students should fill this table with items and amounts relevant to their own homes. The amounts listed are examples.

Solution: This section requires students to estimate the weight of various objects and then match them with given weight ranges. The goal is to develop an intuitive understanding of how heavy different things are.

Here are the estimated matches:

(i) Brief-case — 10 kg (A briefcase can be heavy if it contains many items, but 10 kg is a high estimate; typically less.)

(ii) Mango - less than 1 kg (A single mango is usually much lighter than 1 kg.)

(iii) Cow - 400 kg (Cows are large animals and weigh several hundred kilograms.)

(iv) Elephant — more than 1000 kg (Elephants are massive animals, weighing thousands of kilograms.)

(v) Wheat - 80 kg (This likely refers to a sack of wheat, which can be quite heavy.)

(vi) Puppy — 2 kg (A young puppy is relatively small and would weigh a few kilograms.)

Solution: Students need to estimate the weight of each item and categorize it as either more than 1 kg or less than 1 kg. This helps in developing a sense of scale for common objects.

Things which weigh more than 1 kg are:

(i) A school bag (can be heavy depending on contents)

(iii) A brick (bricks are dense and typically weigh more than 1 kg)

(iv) A big pumpkin (pumpkins are large and heavy fruits)

Things which weigh less than 1 kg:

(ii) Geometry box (usually light plastic or metal)

(v) Slipper/shoes (a pair of footwear is generally lighter than 1 kg)

Solution: This is a practical activity to verify the weight estimations made in the previous question. By using a physical balance and a known 1 kg weight, students can accurately check if their guesses about which items are heavier or lighter than 1 kg were correct. The provided answer indicates that the student found their guesses to be accurate after checking.

Activity Outcome: On checking by a balance, I found my guess was correct.

Solution: This activity involves direct comparison of weights using a balance. Students are asked to compare pairs of common items and determine which one is heavier. The provided answers are examples of possible outcomes from such comparisons.

(i) A cricket ball is heavier than a water bottle. (Cricket balls are dense rubber, while water bottles can be light plastic or empty.)

(ii) Your shoes or your pencil box. (This depends on the shoes and the pencil box. Typically, a pair of shoes might be heavier than an empty pencil box, but a full pencil box could be comparable.)

(iii) Your Maths book or your Hindi book. (The heavier book depends on the number of pages and paper thickness.)

(iv) Your bag or your friend's bag. (This comparison depends entirely on what each person carries in their bag.)

Note: The specific answers will vary based on the actual items being compared.