Tick the question that is the most appropriate for finding the ‘most liked subject’?
Ans:
Why do you think so? Discuss with your friends and teacher.
Ans: Do it Yourself!
Anjali and Rohan recorded the children’s answers (responses) to the above question as follows: They wrote M for Mathematics, L for Languages, T for The World Around Us, A for Arts and P.E. for Physical Education.
Look at the children’s responses above and answer the following questions:
The number of children who like Mathematics the most is _____________ .
The number of children who like Language the most is ____________ .
The number of children who like The World Around Us the most is ___________ .
The number of children who like Physical Education the most is ___________ .
The number of children who like Arts the most is _____________ .
Ans:
The number of children who like Mathematics the most is 10.
The number of children who like Language the most is 8.
The number of children who like The World Around Us the most is 7.
The number of children who like Physical Education the most is 11.
The number of children who like Arts the most is 9
Page No. 205
Let’s fill the above information in this table. Ans:
Q: Now look at the above table and answer the following questions:
What is the most common favourite subject among the children? ________________
What is the least common favourite subject among the children? ________________
Ans:
The most common favourite subject is Physical Education (P.E.) with 11 children choosing it.
The least common favourite subject is The World Around Us with 7 children choosing it.
There are the following two ways to display the information.
Which way of displaying information is easier to understand and why? ____________ Ans: The table (option 2) is easier to understand because it clearly shows the number of children for each subject in an organized way. It is simple to compare the numbers directly, unlike the list (option 1), which requires counting each response.Page No. 206
Colourful Golas
During school lunch break children rush to eat gola of their favourite colour.
Rohan and Anjali record the golas eaten by different children. They want to eat the one that is most eaten by others.
They both start recording the golas eaten by the children.
Look at the information given above. Colour the line drawing of the golas appropriately. Q1: Which colour ice gola do the children eat: (a) the most (b) the least Ans: (a) The most: Yellow colour ice gola (b) The least: Blue colour ice gola How do you know? I counted the golas for each colour. Yellow has the highest count (10), and blue has the lowest count (5).
Q2: Which colour gola would Anjali and Rohan have bought? Ans: Anjali and Rohan would have bought the yellow colour gola because it is the most popular.
Q3: Which colour golas did boys eat the most? Ans: Boys ate the most yellow colour golas.
Q4: Which colour golas did girls eat the most? Ans: Yellow
Q5: Which of the ways of representing data did you use to answer these questions and why? Ans: I used the pictures of golas to count how many of each colour were eaten by Rohan and Anjali. This way was easy because I could see and count the golas directly to find the most and least eaten colours.Page no. 207
Activity – Chess or Cricket
Find out from your classmates how many of them play only chess, only cricket, both or neither.
Now let us organise the above data in the table.
Ans: Example done for students.
Answer these questions based on the data collected from your grade.
Q1: Who plays Chess the most? (Boys/Girls) Ans: Add the number of children who play:
Only Chess and
Both Chess and Cricket
For Girls: 5 (only Chess) + 2 (both) = 7 girls For Boys: 3 (only Chess) + 5 (both) = 8 boys So the answer is: Boys
Q2: Who plays Cricket the most? (Boys/Girls) Ans: Add those who play:
Only Cricket and
Both games
For Girls: 4 + 2 = 6 girls For Boys: 6 + 5 = 11 boys So the answer is: Boys
Q3: How many children play both types of games? Ans: Just add the “Both” row:
Girls: 2
Boys: 5
Total: 2 + 5 = 7 childrenPage No. 208
Bal Mela
Anjali and Rohan have recorded the number of people who ate fruit chaats and sandwiches in the Bal Mela over three days, using a Pictograph.
Let us Do
Q1: Complete the table.
Ans:
Q2: On which day were the most sandwiches sold? Ans: Day 3
Q3: Which item had the highest sale on Day 2? Ans: Sales of fruit chaats on day 2 = 12 Sales of sandwiches on day 2 = 16 The difference in the sales of both items = 16 – 12 = 4. Hence, sandwiches had the highest sale on day 2.
Q4: Complete the table given below. Circle the day that had the highest sales. Ans:
Q:Fill the yellow boxes with 1-digit numbers (multiplicands and multipliers) such that you get the products given in the white boxes.
Fill the remaining white boxes with appropriate products.
Ans:
Q: The product of the numbers in each row is given in the orange boxes. The product of the numbers in each column is given in the blue boxes. Identify appropriate numbers to fill the blank boxes.
Ans:
Times 10
Q: Match each problem with the appropriate pictorial representation and write the answer. Ans:
Q: How many pebbles are there in this arrangement? _______
This is a 5 × 15 arrangement. There is an easy way to find this product by splitting the arrangement. Ans: Let’s break it down: 5 × 15 can be split as 5 × 10 and 5 × 5. 5 × 10 = 50 5 × 5 = 25 Now add them: 50 + 25 = 75 pebbles. So, the blanks are filled as: 5 × 15 = 5 × 10 and 5 × 5 = 50 + 25 = 75 pebbles.
Page 186
Recall the times-tables that we created in Grade 3. Now construct a times-15 table. You may use the arrangement given below and split the columns into 10 and 5 for ease of counting, as shown on the previous page.
Q1: What patterns do you see in this table? Ans: Each answer is 15 more than the last:
Start at 15, then 30, 45, 60, 75, …
1 × 15 = 15, the number of pebbles in the first row. 2 × 15 = 15 + 15 = 30 i.e., the number of pebbles in the both first and second row 3 × 15 = 15 + 15 + 15 = 45, i.e., the number of pebbles in the first three rows
The last digit alternates between 5 and 0:
15 (5), 30 (0), 45 (5), 60 (0), …
Q2: Compare the times-15 table with the times-5 table. What similarities and differences do you notice?Ans:
Similarity:
1. They follow a pattern:
In the 5-times table, numbers go up by 5 each time.
In the 15-times table, numbers go up by 15 each time.
2. Increae in the difference
The subtraction answers increase by 10 each time:
10, 20, 30, 40, 50…
Difference:
Each successive number in the times-15 table is three times larger than the corresponding number in the times-5 table.
Q3: Construct other times-tables for numbers from 11 to 20, as you did for 15. Ans: To make times-tables from 11 to 20, multiply each number by 1, 2, 3, up to 10. For example:
Q4: As you compared the times-5 table with the times-15 table, compare the times-1 table with the times-11 table, the times-2 table with the times-12 table, and so on. Share your observations. Ans: 1. Times-1 vs. Times-11
2. Times-2 vs. Times-12
3. Times-3 vs. Times-13
…… repeat the same for 14, 15, 16, 17, 18, 19 and 20
Here is an arrangement of wheels. To count the total number of wheels, Tara splits them into two equal groups.
Similarly, 6 × 14 can be obtained by splitting the arrangement into two equal groups.
We have seen how to calculate 3 × 14 and 6 × 14 by splitting and doubling. Can we construct the times-14 table by splitting and doubling? Try! Solution: Yes, we can construct the times-14 table by splitting and doubling.
What other times tables can be constructed by splitting into equal groups and doubling? Give examples. Solution: We can construct 8, 10, 12, 16, 18, 20, etc. times tables by splitting into equal groups and doublings.
Q: A small bus can seat 20 people. How many people can be seated in 12 buses? Now let us do 12 × 20. Solve the following problems. Share your thoughts. Q: 24 × 40 = _______ Ans: First, break 24 into 20 + 4. Then, 20 × 40 = 800 and 4 × 40 = 160. Add them: 800 + 160 = 960. So, 24 × 40 = 960.
Q: 50 × 60 = _______ Ans: 50 × 60 means 5 tens × 6 tens. So, 5 × 6 = 30, then 30 × 100 = 3000. So, 50 × 60 = 3000.
Q: 70 × 80 = _______ Ans: 70 × 80 means 7 tens × 8 tens. So, 7 × 8 = 56, then 56 × 100 = 5600. So, 70 × 80 = 5600.
Page No. 190
A Day at the Transport Museum
Amala, Raahi and Farzan are visiting the “Transport Museum”. This museum has a collection of different modes of transport used by people in India. It includes several vehicles from the olden days. Raahi spots a toy train. She figures out that each coach can seat 14 children. The toy train has 15 coaches.
Q:How many children can be seated in the toy train? Ans: 15 × 14 = (10 × 10) + (10 × 4) + (5 × 10) + (5 × 4) = 100 + 40 + 50 + 20 = 210.
Page 191
Q:She wonders how many coaches will be needed for the 324 children from her school. Remember, each coach can seat only 14 children. Ans: 324 ÷ 14
Ans: 23 coaches, 2 children remain (need 24th coach).
Page No. 192
Let Us Solve
Q:Also, identify remainder (if any) in the division problems. (a) 25 × 34 Ans:
(b) 16 × 43 Ans:
(c) 68 × 12 Ans:
(d) 39 × 13 Ans:
(e) 125 ÷ 15 Ans:Thus, when 125 is divided by 15, we get (5 + 3) = 8 with remainder 5.
(f) 94 ÷ 11 Ans: Thus, when 94 is divided by 11, we get (2 + 3 + 3) = 8 with remainder 6.
(g) 440 ÷ 22 Ans:
So, 440 ÷ 22 = 10 + 10 = 20
(h) 508 ÷ 18 Ans: Thus, when 508 is divided by 18, we get (10 + 10 + 5 + 3) = 28 with remainder 4.
Q: Find the answers in Set A. Examine the relationships between the problems and the answers in Set A carefully. Then use this understanding to find the answers in Set B.
Ans:
Ans:
Ans:
Let Us Solve
Q:Also, identify remainder (if any) in the division problems. (a) 237 × 28 Ans:
(b) 140 × 16 Ans:
(c) 389 × 57 Ans:
(d) 807 ÷ 24 Ans: When 807 is divided by 24, we get 10 + 10 + 10 + 2 + 1 = 33, with remainder 15.
(e) 692 ÷ 33 Ans: When 692 is divided by 33, we get 10 + 10 = 20, with remainder 32.
(f) 996 ÷ 45 Ans: When 996 is divided by 45, we get 10 + 10 + 2 = 22, with remainder 6.
Dividing by 10 and 100
Q: A farmer packs his rice in sacks of 10 kg each. (a) If he has 60 kg of rice, how many sacks does he need?
Ans: Each sack holds 10 kg of rice. So we divide:
60 ÷ 10 = 6
⇒ He needs 6 sacks.
(b) If he has 600 kg of rice, how many sacks does he need?
Ans: Each sack holds 10 kg of rice. So we divide:
600 ÷ 10 = 60
⇒ He needs 60 sacks.
Ans: Each sack holds 100 kg of rice. So we divide:
600 ÷ 100 = 6
⇒ He needs 6 sacks.
Ans:
60 ÷ 10 = 6 sacks
600 ÷ 10 = 60 sacks
600 ÷ 100 = 6 sacks
Page No. 198
Q:Find the answers to the following questions. Share your thoughts in grade. 40 ÷ 10 = _________ Ans: 40 ÷ 10 = 4
Think and answer. Write the division statement in each case.
Q1. Manku the monkey sees 870 bananas in the market. Each bunch has 10 bananas. How many bunches are there in the market? Ans: Total bananas in the market = 870 Number of bananas in each bunch = 10 Number of bunches in the market = 870 ÷ 10 = 87 Division statement: 870 ÷ 10 = 87
Q2. Rukhma Bi wants to distribute ₹1000/- equally among her 10 grandchildren on the occasion of Eid. How much money will each of them get? Ans: Number of grandchildren of Rukhma Bi = 10 Amount distributed by Rukhma Bi = ₹ 1000 Amount of money received by each grandchild = ₹ 1000 ÷ 10 = ₹ 100 Division statement: 1000 ÷ 10 = 100
Let Us Solve
Q1: The oldest long-distance train of the Indian Railways is the Punjab Mail which ran between Mumbai and Peshawar. Its first journey was on 12 October 1912. Do you know how many coaches it had on its first journey? It had 6 coaches: 3 carrying 96 passengers and 3 for goods. (a) How many people travelled in each coach on the first journey? (b) This train has been running for 106 years now. It runs between Mumbai, Maharashtra and Ferozepur, Punjab. It has 24 coaches. Each coach can carry 72 passengers. How many people can travel on this train? Ans:(a) Number of coaches carrying passengers in train = 3 Number of peoples in train = 96 People travelled in each coach = 96 ÷ 3
96 ÷ 3 = 10 + 10 + 10 + 2 = 32 Thus, 32 people travelled in each coach. ⇒ 32 people travelled in each passenger coach.
(b) Number of coaches in train = 24 Number of passengers in each coach = 72 Number of people travel in the train = 24 × 72
⇒ 1728 people can travel on this train now.
Page No. 199
Q2: Amala and her 35 classmates, along with 6 teachers, are going on a school trip to Goa. They are using the double-decker “hop on hop off” sightseeing bus to explore the city.
(a) 2 people can sit on every seat of the bus. There are 15 seats in the lower deck and 10 in the upper deck. How many seats will they need to occupy? Are there enough seats for everyone?
(b) Find the total cost of the tickets for all children.
(c) What is the cost of the tickets for all teachers?
Ans: (a) Total people: 35 Students + 6 Teachers = 41 people.
Seats needed: 41 ÷ 2 = 20 (1 extra person needs 1 seat).
Total seats: 15 (lower) + 10 (upper) = 25
Yes, there are enough seats for everyone. Since, the total number of seats is more than the required number of seats occupied.
(b) Ticket price for each child = ₹ 359 Total cost of the tickets for all children = 36 × ₹ 359
Total coat of tickets for all children = ₹ 12,924
(c) Ticket price for adult = ₹ 899 Total cost of the tickets for all teachers = 6 × ₹ 899
Q3: Kedar works in a brick kiln. (a) The kiln makes 125 bricks in a day. How many bricks can be made in a month? (b) Each brick is sold in the market for ₹9. How much money can they earn in a month? Ans: (a) Assume 30 days Number of bricks made in a day = 125 So, number of pricks can be made in a month = 30 × 125
⇒ Therefore, 3750 bricks can be made in a month
(b) Price of each brick = ₹ 9 Money earned in a month = ₹ 9 × 3750
Q4: Chilika lake in Odisha is the largest saltwater lake in India. It is famous for the Irrawaddy dolphins. Boats can be hired to go see the dolphins. The trip from Puri includes a bus ride followed by a boat ride. Eight people will be going on the trip.
A bus ticket from Puri to Satapada costs ₹60.
A two-hour boat ride for 8 people costs ₹1200.
How much money do we need to spend on each person?
Q5: Find the multiplication and division sentences below. Shade the sentences. How many can you find?
Ans:
250 × 4 = 1000
50 × 20 = 1000
5 × 22 = 110
52 × 20 = 1040
104 × 6 = 624
30 × 15 = 450
50 × 19 = 950
1000 × 6 = 6000
55 × 101 = 5555
99 × 7 = 693
200 × 16 = 3200
35 × 9 = 315
931 ÷ 10 = 93
4 × 26 = 104
Q6: Solve
(a) 35 × 76
Ans:
(b) 267 × 38 Ans:
(c) 498 × 9 Ans:
(d) 89 × 42 Ans:
(e) 55 × 23 Ans:
(f) 345 × 17 Ans:
Following above table method, we can solve below questions as well.
(g) 66 × 22 Ans:
(h) 704 × 11 Ans:
(i) 319 × 26 Ans:
(j) 459 ÷ 3 Ans:
Thus, when 459 is divided by 3, we get 100 + 50 + 3 = 153 with no remainder.
(k) 774 ÷ 18 Ans:
So, 774 + 18 = 10 + 10 + 10 + 10 + 3 = 43
(l) 864 ÷ 26 Ans:
Thus, when 864 is divided by 26, we get (10 + 10 + 10 + 3 = 33) with remainder 6.
In a similar manner, we can solve remaining questions also.
(m) 304 ÷ 12
Ans: Thus, when 304 is divided by 12, we get (10 + 10 + 5 = 25) with remainder 4.
(n) 670 ÷ 9 Ans:
Thus, when 670 is divided by 9, we get (50 + 20 + 4 = 74) with remainder 4.
(o) 584 ÷ 25 Ans: Thus, when 584 is divided by 25, we get (10 + 10 + 2 + 1 = 23) with remainder 9.
(p) 900 ÷ 15 Ans: Thus, when 900 is divided by 15, we get (10 + 10 + 10 + 10 + 10)
(q) 658 ÷ 32 Ans:
Thus, when 658 is divided by 32, we get (10 + 10 = 20) with remainder 18.
(r) 974 ÷ 9 Ans:
Thus, when 974 is divided by 9, we get (100 + 5 + 2 + 1 = 108) with remainder 2.
Page No. 201
Chinnu’s Coins
Q1: Five friends plan to visit an amusement park nearby. Each of them uses different notes and coins to buy the ticket. The cost of the ticket is ₹750.
Bujji has brought all notes of ₹ 200.
And Munna has brought all notes of ₹50.
Whereas Balu has brought all notes of ₹20.
And guess what, Chinnu has all coins of ₹5.
And Sansu has all coins of ₹2.
(a) Find out how many notes/coins each child has to buy the ticket. Ans: Bujji: ₹750 ÷ ₹200 = 3 notes and ₹150 left → Needs 4 notes (₹800), will get ₹50 back.
Munna: ₹750 ÷ ₹50 = 15 notes
Balu: ₹750 ÷ ₹20 = 37 notes and ₹10 left → Needs 38 notes (₹760), will get ₹10 back
Chinnu: ₹750 ÷ ₹5 = 150 coins
Sansu: ₹750 ÷ ₹2 = 375 coins
(b) Which of these children will not receive any change from the cashier? Ans: Munna, Chinnu, and Sansu will not receive any change from the cashier.
(c) How long would the cashier take to count Chinnu’s coins? Ans: 150 coins at ~2 seconds each = 150 × 2 = 300 seconds = 5 minutes.
Q2: Observe the following multiplications. The answers have been provided. In each case, do you see any pattern in the two numbers and their product? For what other multiplication problems will this pattern hold? Find 5 such examples. Ans: We observe that, the ones digit of the product is the product of ones digits of the multiplicand and multiplier, and the tens digit of the product is the sum of ones digit of the multiplicand and multiplier.
Other such examples are
Page No. 202
Q3: Assume each vehicle is travelling with full capacity. How many people can travel in each of these vehicles? Match them up. Ans:
Q1: Notice the number of days in February in the years 2024 and 2025.
Number of days in Feb 2024 = _____________
Number of days in Feb 2025 = _____________
Ans:
Number of days in Feb 2024 = 29 Days
Number of days in Feb 2025 = 28 Days
Page No. 176
Q2: Fill in the blanks with consecutive leap years before and after 2024. Ans: A leap year occurs every 4 years. 2016, 2020, 2024, 2028, 2032, 2036
Q3: We know that most years have 365 days. How many days would a leap year have? Ans: Leap year: 365 + 1 = 366 days.
Q4: Write the names of the months when you celebrate your favourite festivals.Ans: Example festivals:
Q5: Answer the following questions by writing the appropriate days of the week: (a) Today: ___________ (b) Yesterday: ___________ (c) Tomorrow: ___________ (d) Day after tomorrow: ___________ (e) Day before yesterday: ___________ Ans: Assume today is Friday, April 25, 2025: (a) Today: Friday (b) Yesterday: Thursday (c) Tomorrow: Saturday (d) Day after tomorrow: Sunday (e) Day before yesterday: Wednesday
Q6: July 1 is a Monday. Write the dates for the next two Mondays. Ans: July 1: Monday.
Each day of a week comes exactly 7 days after the previous occurrence of the same weekday. So, the dates for the next two Mondays will be
Next Monday: July 1 + 7 = July 8. Following Monday: July 8 + 7 = July 15.
Q7: Laali is born on 04/07/2014 and Chotu is born on 04/12/2019. Who is older among the two and how much? Ans: Laali: Born 04/07/2014. Chotu: Born 04/12/2019. Compare: 2014 < 2019, Laali is older. Difference: From 04/07/2014 to 04/12/2019. Years: 2019 − 2014 = 5 years. Months: July to December = 5 months. Days: Same day (4th), so 0 days. Laali is older by 5 years, 5 months.
(a) Laali will turn 5 years old on ______________. Ans: Born: 04/07/2014. 5 years old: 04/07/2014 + 5 years = 04/07/2019.
(b) Chotu’s 10th birthday will be celebrated on Ans: Born: 04/12/2019. 10th birthday: 04/12/2019 + 10 years = 04/12/2029.
Q8: Check the manufacturing and expiry dates on the wrapper of any biscuit packet. (a) How old is the packet of biscuits? Ans: Example: Manufacturing: 01/01/2025, Today: 25/04/2025. Duration: From 01/01/2025 to 25/04/2025.
Q9: Notice the day on which July 15 falls in your calendar. Now find out what day is August 15? September 15? October 15? What pattern do you notice? Share in grade. Ans: Assume July 15, 2024, is a Monday (calendar check). August 15: 31 days later (July 15 to August 15). 31 ÷ 7 = 4 weeks, 3 days. Monday + 3 = Thursday. September 15: 31 days later (August 15 to September 15). Thursday + 3 = Sunday. October 15: 30 days later (September 15 to October 15). 30 ÷ 7 = 4 weeks, 2 days. Sunday + 2 = Tuesday. Pattern: Days shift by 2–3 days per month (30–31 days).
Now choose a date and look up the day on which it falls. Challenge your friends to guess what day will the same date fall in the following month. Ans: Do it Yourself!
Page No. 177 (Let Us Explore)
Q1: Find out when the year begins in each of these calendars. Ans:
Hindu Calendar – Starts with Chaitra (March/April)
Islamic Calendar – Starts with Muharram (Moves each year; in 2025, it starts in July/August)
Sikh Calendar (Nanakshahi) – Starts with Chet (March/April)
Q2: Check how the names of the months in these calendars correspond to the months in the English calendar. Ans:
Hindu Calendar:
Chaitra ≈ March/April
Vaishakha ≈ April/May
And so on…
Islamic Calendar:
Muharram, Safar, etc.
These months move about 10 days earlier every year because it follows the moon.
Sikh Calendar:
Chet ≈ March/April
Vaisakh ≈ April/May
And so on…
Q3: Identify the months from the Hindu/Islamic/Sikh or any other calendar in which some of the important festivals of the community fall. Ans:Hindu Festivals:
Diwali – Kartika (October/November)
Holi – Phalguna (February/March)
Islamic Festivals:
Eid al-Fitr – Shawwal (April/May in 2025)
Eid al-Adha – Dhu al-Hijjah (June/July in 2025)
Sikh Festivals:
Vaisakhi – Vaisakh (April)
Guru Nanak Jayanti – Kartik (November)
Q4: Identify the dates of the new moon and full moon in your community’s calendar every month. Do you notice any pattern? Ans: In the Hindu calendar,
Purnima means full moon
Amavasya means new moon
These come about 15 days apart
In the Islamic calendar,
The new moon marks the start of a new month
The lunar cycle (from new moon to next new moon) is about 29.5 days, so there is a clear pattern.
Q5: How are the full moon or new moon days named in your community’s calendar? Ans:Hindu Calendar:
Purnima – Full Moon
Amavasya – New Moon
Islamic Calendar:
The new moon starts each month (e.g., 1st Muharram)
Sikh Calendar:
The new month begins on Sangrand
Special days like full moons are observed during religious occasions
Page No. 178
Look at the picture below. It shows the time spent on different activities by a doctor. Write the number of hours spent on each activity in the space provided. Then, find the total number of hours between 6 o’clock morning to 6 o’clock evening and 6 o’clock morning of the next day.The total number of hours is ________ . Ans:
Total: 6 AM to 6 PM = 12 hours.
Full day: 6 AM to next 6 AM = 24 hours.
Page No. 180
Fill in the blanks by writing time in the appropriate format.Ans:
Page No. 181
Raghav leaves home at 8:20 AM and returns back at 8:35 AM. How much time has he taken?Ans: From 8:20 AM to 8:35 AM.
Minutes: 35 − 20 = 15 minutes.
Let Us Do
Q1: Show the appropriate times on the clock as per instructions. (a) Raghav started doing his homework at 10:20 AM. He took 25 minutes to finish it. Show the time that he finished his homework.Ans:
(b) Muneera starts reading a story at 4:15 PM. She finishes reading it in 45 minutes. Show the time that she finished reading the story.Ans:
Start: 4:15 PM.
Add 45 minutes: 4:15 + 45 = 4:60 = 5:00 PM.
Ans: 5:00 PM.
(c) Akira leaves for school at 8:00 AM. She reaches school in 15 minutes. Ans:
(d) Who do you think is correct? Is there any relation between 1 hour and 60 minutes?
Ans: Both are right!
Akira says she spent 1 hour (from 8:00 to 9:00).
The other person says 60 minutes.
As, 1 hour = 60 minutes
Observe the shaded portions Ans:
Page No. 183
Q: Find out how much time you take to (a) boil milk Ans: Example: Boiling milk takes ~10 minutes.
(b) fill water from tap in a bucket Ans: Example: Filling a bucket takes ~10 minutes.
Q: What activities can you do in 5 minutes? Ans: Examples: Brush teeth, tie shoes, eat a snack, read a page.
Let Us Check
Three friends read time from a clock. Who is right? Discuss the error and explain how one reads the clock correctly.Ans:First Row: Big Hand at 12, Small Hand at 4
Correct Time: 04:00
Rani is correct.
Second Row: Big Hand at 7, Small Hand at between 5 and 6
Is it a symmetrical pattern? Where would you draw the line that divides this design into two equal halves? Isn’t this line called the line of symmetry? Ans: Yes, folding paper and pressing spreads ink evenly, creates mirror images. Yes, there is a line of symmetry along the fold (vertical center).
2. Making a paper airplane
Follow the steps.
(a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
Ans:
(b) How many lines of symmetry can you see in Fig. 8? Ans:
One line of symmetry.
(c) Where will you place a mirror to see the reflection of the right half side of Fig. 8? Will it look the same as the left half side? Ans: Place mirror: Along vertical line of symmetry (center).
Reflection: Yes, right half reflects to match left half (symmetrical).
Along center; yes, same.
(d) Fly the plane. Ans: Action: Follow folding steps and fly the plane.
(e) Will the plane fly if there is no line of symmetry? Ans: No symmetry: Plane may be unbalanced, affecting flight.
(f) Try to make an asymmetrical plane. Ans: Fold unevenly (e.g., one wing larger).
Create uneven folds.
(g) Fly both the planes and see which plane flies for a longer time. Ans: Symmetrical plane: Likely flies longer due to balance.
Asymmetrical plane: May wobble or crash sooner.
Symmetrical plane flies longer.
(h) Share your observations with your friends. Ans: Observation: Symmetrical plane flies better; asymmetrical plane is unstable.
3. Holes and Cuts
Mini has made this design by folding and cutting paper.
Now it’s your turn! Take a square sheet of paper. Do as instructed below.
Let us see what Rani is making. Rani takes a piece of paper and folds it twice.
She makes a straight cut at the corner and cuts out two squares on two sides as shown in the picture.
Challenge 1: Where would the hole and cut appear when you open the paper?Ans: When the paper will open, the hole and cut appear as follows:
Challenge 2: Fold a piece of paper once; put two cuts in the middle as shown. How many sides will this shape have when you open the folded paper?Ans: The shape have 4 sides.
Challenge 3: Fold a paper twice. Where would you cut to make a square hole in the center of the paper? How many cuts are required?Ans: Do it Yourself.
4. Complete the designs belowAns: Do it Yourself.
Page no. 167
Let Us Do
Symmetry in shapes
Q1: Look at the shapes given along the border. Draw these shapes on the dot grid. Which of the shapes are symmetrical? Draw the lines of symmetry.Ans:
All shapes are symmetrical as by drawing a line of symmetry, it divides the figures into equal parts.
Page 168
Q2: Games with a Mirror (a) Where should we place the mirror in shape A to get the shapes given below? Ans:
(b) Circle the numbers whose mirror image is the same number.Ans:
Which digits from 0 to 9 have the same mirror image?
Ans: 0, 1 & 8 will have same mirror images and 3 (in some digital fonts).
Make some 4-digit numbers such that the mirror image is the same number. Where would you keep the mirror in each case? How many such numbers can you make?
Ans: Some examples of the 4-digit numbers that have the same mirror images are: 1881, 8118, 1001, 8008, etc. We will keep the mirror to the left or right side of the number in each case.
(c) Make similar questions and ask your friends to guess the numbers. Ans: Do it Yourself!
Page 169
Q3. What do you notice about the letters written on the ambulance? Why are they written this way? Discuss.Ans: The word “AMBULANCE” is written backward (like in a mirror) on the front of the ambulance.
Why?
So drivers in cars ahead see it correctly in their rearview mirror and move out of the way quickly!
It is written CAT and the mirror has been kept horizontally below the word.
Can you identify these words? Where will you place the mirror to read the following words correctly?Ans:
Now, you try to write some words/names in this way and challenge your friends to guess them.
Ans: Do it Yourself!
Q4. Complete the following to make symmetrical shapes.
Ans:
Page 170
Q5: Observe the shapes. How many sides does each shape have?
How many lines of symmetry does each shape have? You may trace these shapes and check the lines of symmetry by folding the shapes.Ans: Do it Yourself!Tiling the Tiles
Here are some patterns with tiles. Identify the repeating unit (tile) and continue the patterns.Ans: Do it Yourself!
Page 171
Tiles at the Tile Shop
Bablu Chacha makes beautiful tiles of the kinds shown below. Design creative tiles of your own in the spaces given below. You may use a rangometry kit or shape cutouts.
Q1: Which shapes have you used to make the tiles?
Ans: Do it Yourself!
Q2: Which of the tiles are symmetrical? Draw the lines of symmetry (if any). Ans:
Q3: Make more tiles by joining two or more shapes. Trace them in your notebook to create paths with no gaps or overlaps. Ans: Do it Yourself!
Q4: Look at the following shapes. What do you notice? Discuss.Ans: Both are identical. The difference is of the colour pattern.
Page No. 172
Let Us Do
Q1: Make floor patterns with your tile. Mini has made a floor pattern as shown below.Ans: Do it Yourself!
Q2: Making a catty wall!
Create more of these tiles. Some ideas to make creative wall patterns are given below.
Ans: Do it Yourself!
Q3: Let us go on a nature walk (Project time)
Go for a nature walk to a nearby park or around your school with your teacher or your parents. Observe the patterns, designs, or symmetry around you carefully. Collect leaves, petals, and flowers that have fallen on the ground.
You have played a version of this game in the chapter ‘Vacation with my Nani Maa’ in Grade 3. We will add either 1 or 2 each time to reach the target number 10.
Can you win the game if(a) The other player has reached the total of 6 and it is your turn?
Ans: Yes, we can win the game. Add 1 bringing the total to 7. On other player’s tun n, the opponent can add either 1 or 2. T-f he/she adds 1, the total becomes 8 and or.i our turn, we can add 2 to reach 10 and win. If he/ she adds 2, the total becomes- 9 and on our turn, we can add 1 to reach 10 and win.
(b) The other player has reached the total of 7 and it is your turn?
Ans: No, we cannot win. We can add either 1 or 2. If we add 1, the total becomes 8 and the other player can a dd 2 to reach 10 and win. If we add 2, the; total becomes 9 and the other player can add 1 to reach 10 and win.
(c) The other player has reached the total of 8 and it is your turn?
Ans: Yes, we can win. Add 2, bringing the total to 10 and we will win. Play the game to reach other target numbers (like 10, 11 or 12) by adding 1 or 2 each time.
Q: Can you find a number in each case when you are sure that you can win?
Ans: Suppose, if other player has reached the total 9 and its our turn, we can add 1 to reach 10 and win. Similarly, we can find some numbers in each case when we are sure that we can win if the target number is 11 or 12. For example, if the target number is 11 and the other player has reached the total 7 and its our turn. Then we can add 1 to reach 8. The other player can either add 1 or 2. If they add 1 the total becomes 9 and in our turn we can add 2 to win.
If the player add 2, the total becomes 10 and in our turn we can add 1 to reach 11 and win. Similarly, if the target number is 12 and the other player has reached the total 8 and its our turn, then we can be sure to win.
Page No. 150
Addition Chart
Q1: Identify some patterns in the table.
Following are some patterns that can be observed in the table.
Any number plus 0 remains the same.
The sum increases by 2 when moving diagonally.
Each row and column increase by 1 as we move right or down, respectively.
The table mirrors itself across the main diagonal.
Q2: Observe the cells where the number 9 appears in the table. How many times do you see number 9? What about other numbers?
Ans: There are ten 9’s in the table.
Following are the patterns of appearance of the numbers.
Each number appears one more time than its value till the number 12 and then the appearances of numbers start decreasing symmetrically.
Q3: Are there any rows or columns that contain only even numbers or only odd numbers? Explain your observation.
Ans: Every row and column in the table has both odd and even numbers. This happens because adding two even numbers or two odd numbers gives an even number as resulf while adding one odd and one even number gives an odd number as result.
Q4: Look at the window frame highlighted in red colour in the table. (a) Find the sum of the two numbers in each row.
Ans: Sum of 10 and 11 = 10 +11 = 21 Sum of 11 and 12 = 11 + 12 = 23
(b) Find the sum of the two numbers in each column. What do you notice? Ans: Sum of 10 and 11 = 21 (in column) Sum of 11 and 12 = 23 Again we get numbers 21 and 23 as result.
(c) Now, find the sum of the numbers in each of the two diagonals marked by arrows. What do you notice? Ans: Sum of 10 and 12 = 22 Sum of 11 and 11 = 22 The sum of the numbers in two diagonals is same.
(d) Now, put the red window frame in other places and find the sums as above. What do you notice?
Ans: If we put the window frame in any two consecutive numbers in row and column, the sum of rows and columns will change but the difference between the sum of any two rows, columns and diagonals will remain the same.
Q5: Identify some patterns and relationships among the numbers in the blue window frame.
Ans: In the blue window frame, numbers in each row and in each column are same and the difference between the sum of numbers of each row and each column is 3.
Page No. 151
Reverse and Add
(a) Take a 2-digit number say, 27. Reverse its digits (72). Add them (99). Repeat for different 2-digit numbers.
27 + 72 = 99.
45 + 54 = 99.
19 + 91 = 110.
Ans: Sums like 99, 110, etc.
(b) What sums can we get when we add a 2-digit number with its reverse?
Ans: Let’s add some 2-digit numbers and their reverse to identify any pattern. 10 + 01 = 11 = 1 × 11 11 + 11 = 22 = 2 × 11 12 + 21 = 33 = 3 × 11 13 + 31 = 44 = 4 × 11 . . . . . 18 + 81 = 99 = 9 × 11 99 + 99 = 198 = 18 × 11 We can observe that, when we add a 2-digit number with its reverse, we get a number that can be obtained in the times-11 table.
(c) List down all numbers which when added to their reverse give (i) 55
Ans: 14 + 41 = 55, 32 + 23 = 55, 50 + 05 = 55 Thus, all the numbers that, when added to their reverse give 55 are 14, 23, 32, 41 and 50.
(ii) 88
Ans: 17 + 71 = 88, 26 + 62 = 88, 35 + 53 = 88 44 + 44 = 88, 80 + 08 = 88 Thus, all the numbers that, when added to their reverse give 88 are 17, 26, 35, 44, 53, 62, 71, and 80.
(d) Can we get a 3-digit sum? What is the smallest 3-digit sum that we can get?
Ans: Yes, we can get a 3-digit sum by adding a 2-digit number and its reverse. The smallest such 3-digit number is 110. As, 19 + 91 = 110.
Fill in the blanks with appropriate numbers. (a)
Ans:
(b) Ans:
(c)
Ans:
Page 154
How Many Animals? (Continued)
Q3: Maharashtra has 444 tigers. Madhya Pradesh has 341 more tigers than Maharashtra. Uttarakhand has 116 tigers more than Maharashtra. (a) How many tigers does Madhya Pradesh have? Ans:
So, Madhya Pradesh has 785 tigers.
(b) How many tigers does Uttarakhand have?
Ans:
Therefore, there are 560 tigers in Uttarakhand.
(c) How many tigers does Madhya Pradesh and Uttarakhand have?
Ans:
So, there are 1345 tigers in Uttarakhand and Madhya Pradesh.
(d) How many tigers are there in total across the three states? Ans:
So, there are 1789 tigers across the three states.
Page 156
More or Less?
1. Assam has 5719 elephants. It has 3965 more elephants than Meghalaya. How many elephants are there in Meghalaya? 1754 elephants are there in Meghalaya.
2. The population of leopards as per the 2022 census was 8820 in the Central India and the Eastern Ghats. It had increased by 749 in comparison to the number of leopards in 2018 in the same region. How many leopards were there in 2018? _________ leopards were there in 2018.
Write the number of animals on this map based on the data from the problems in the previous pages.
Ans:
Elephants: Karnataka (6049), Kerala (3054), Assam (5719), Meghalaya (1754).
Q1: The board in the ticket office in the Kaziranga National Park shows the following:(a) How many more visitors came in December than in November?
Ans: Number of visitors in December = 8591 Number of visitors in November = 6415 The difference between the number of visitors in these two months = 8591 – 6415 = 2176 Therefore, 2176 more visitors came in December than in November.
(b) The number of visitors in November is 1587 more than October. How many visitors were there in October?
Ans: Number of visitors in November = 6415 Since the number of visitors in November is 1587 more than October. Therefore, the number of visitors in October = 6415 – 1587 = 4828. Thus, there were 4828 visitors in October.
Q2: In a juice making factory, women make different types of juices as given below:(a) The number of bottles of guava juice is 759 more than the number of bottles of pineapple juice. Find the number of bottles of guava juice.
Ans: Number of bottles of pineapple juice = 1348. Number of bottles of guava juice is 759 more than number of bottles of pineapple juice. Number of bottles of guava juice = 1348 + 759 = 2107 Therefore, the number of bottles of guava juice is the number of bottles of guava juice.
(b) The number of bottles of orange juice is 1257 more than the number of bottles of guava juice and 1417 less than the number of bottles of passion fruit juice. How many bottles of orange juice are made in a month?
Ans: The number of bottles of guava juice = 2107. Number of bottles of orange juice is 1257 more than the number of bottles of guava juice. Number of bottles of orange juice = 2107 + 1257 = 3364 Therefore, 3364 bottles of orange juice is packed in a month.
(c) Is the total number of bottles of guava juice and orange juice more or less than the number of bottles of passion fruit juice? How much more or less?
Ans: Total number of bottles of guava juice and orange juice = 2107 + 3364 = 5471 Number of bottles of passion fruit juice = 4781 ∵ 5471 -4781 = 690 Thus, the number of bottles of guava juice and orange juice is 690 bottles more than passion fruit juice.
Page 158
Let Us Do (Continued)
Q3: In a small town, the following vehicles were registered in the year 2022. Find the number of vehicles as per the conditions given below. (a) The number of buses is 253 more than the number of jeeps. How many buses are there in the town? Ans: Number of jeeps = 6304 Number of buses = 253 more than 6304 = 253 + 6304 = 6557 Therefore, there are 6557 buses in the town.
(b) The number of tractors is 5247 less than the number of buses. How many tractors are in the town? Ans: Number of buses = 6557 Number of tractors = 5247 less than 6557 = 6557 – 5247 = 1310 Therefore, there are 1310 tractors.
(c) The number of taxis is 1579 more than the number of tractors? How many taxis are there? Ans: Number of tractors = 1310 Number of taxis = 1579 more than 1310 = 1579 + 1310 = 2889 Therefore, there are 2889 taxis.
(d) Arrange the numbers of each type of vehicle from lowest to highest. Ans: We have, Jeeps: 6304; Buses: 6557; Tractors: 1310; Taxis: 2889. The order of these numbers from the lowest to the highest is: 1310, 2889, 6304, 6557.
Answer: Tractors, Taxis, Jeeps, Buses
Q4: Solve (a) 1459 + 476 Ans: 1459 + 476 = 1935.
(b) 3863 + 4188 Ans: 3863 + 4188 = 8051.
(c) 5017 + 899 Ans: 5017 + 899 = 5916.
(d) 4285 + 2132 Ans: 4285 + 2132 = 6417.
(e) 3158 + 1052 Ans: 3158 + 1052 = 4210.
(f) 7293 − 2819 Ans: 7293 − 2819 = 4474.
(g) 3105 − 1223 Ans: 3105 − 1223 = 1882.
(h) 8006 − 5567 Ans: 8006 − 5567 = 2439.
(i) 5000 − 4124 Ans: 5000 − 4124 = 876.
(j) 9018 − 487 Ans: 9018 − 487 = 8531.
Page 159
Let Us Do (Continued)
Q5: The children in a school in Chittoor are planning to organise a Baal Mela in their school. Raju, Rani and Roja decided to raise some money to make arrangements for the mela. The money is available in notes of 500, 100, 50, 10 and coins of 5, 2 and 1. They decide to put the money in the School Panchayat Bank.
Help each of the children fill the deposit slip given below.
Different combinations of notes can give the same amount. Can you guess a possible combination of notes they might have? Fill in the amounts appropriately.
Total in words: Two thousand forty-five.
Ans: Raju’s slip completed as shown.
Page 160
Let Us Do (Continued)
1. Rani
2. Roja
Page 161
Let Us Solve
Q1: Solve Ans:
Q2: Arrange the following in columns and solve in your notebook.(a) 3683 − 971 Ans: 3683 − 971 = 2712.
(b) 8432 − 46 Ans: 8432 − 46 = 8386.
(c) 4011 − 3666 Ans: 4011 − 3666 = 345.
(d) 5203 − 2745 Ans: 5203 − 2745 = 2458.
(e) 1465 + 632 Ans: 1465 + 632 = 2097.
(f) 3567 + 77 Ans: 3567 + 77 = 3644.
(g) 8263 + 3737 Ans: 8263 + 3737 = 12000.
(h) 5429 + 3287 Ans: 5429 + 3287 = 8716.
Page 162
Let Us Solve
Q1: Find easy ways to solve the following problems.(a) 8787 − 99 Ans: 8787 − 100 + 1 = 8688.
(b) 4596 + 104 Ans: 4596 + 100 + 4 = 4700.
(c) 3459 + 21 Ans: 3459 + 20 + 1 = 3480.
(d) 5010 + 95 Ans: 5010 + 100 − 5 = 5105.
(e) 4990 + 310 Ans: 4990 + 300 + 10 = 5300.
(f) 7844 − 15 Ans: 7844 − 20 + 5 = 7829.
(g) 260 + 240 Ans: 260 + 240 = 500.
(h) 1575 − 125 Ans: 1575 − 100 − 25 = 1450.
(i) 3999 + 290 Ans: 3999 + 300 − 10 = 4289.
Q2: Use the signs <, =, > as appropriate to compare the following without actually calculating.Ans:
Q3: Use the given information to find the values. Ans:
Q3: Fill the squares with the numbers 1-9. The difference between any two neighbouring squares (connected by a line) must be odd.Ans:
Yes, we can fill the squares in many ways.
No, it is not possible to fill the squares such that the difference between any two neighbouring squares is even. This happens because the difference of either two odd numbers is even or two even numbers is even, means we cannot fill any even number that is connected to an odd number and vice versa, that is not possible in the given connected squares.
Fill in the blank spaces with the appropriate numbers. Find how many jumps the animal needs to take to reach its food. Q1: The frog jumps 3 steps at a time. Which numbers will the frog touch? Will it touch 67?
Ans:
The frog will only touch numbers that are multiples of 3.
Since 67 is not a multiple of 3, the frog will not touch 67.
Q2: The squirrel jumps 4 steps at a time. Which numbers will the squirrel touch? How many times should the squirrel jump to reach 60?
Ans:
Numbers: Multiples of 4 (4, 8, 12, …, 60, 64, …).
60 ÷ 4 = 15 jumps.
Ans: Squirrel touches multiples of 4; 15 jumps to reach 60.
Page 129
Animal JumpsQ3: The rabbit jumps 6 steps at a time.
Which numbers will the rabbit touch?
What is the smallest 3-digit number on which the rabbit will land?
How many times did the rabbit jump to reach this number?
Smallest 3-digit number: 102 (first multiple of 6 ≥ 100).
102 ÷ 6 = 17 jumps.
Ans: Multiples of 6; smallest 3-digit number is 102; 17 jumps.
Q4: The kangaroo jumps 8 steps at a time. Which numbers will the kangaroo touch? Are there numbers that both the rabbit and the kangaroo will touch?Are there numbers that both the rabbit and the kangaroo will touch? Ans:
Common numbers: Common multiples of 6 and 8 (LCM = 24). E.g., 24, 48, 72, …
Ans: Multiples of 8; yes, rabbit and kangaroo touch numbers like 24, 48, 72.
Q5: To reach 48, how many times did the rabbit jump? How many times did the kangaroo jump to reach the same number? What did you observe? Ans: Since the rabbit jumped 6 steps at a time, 6 steps × 8 = 48. So, the rabbit jumped 8 times to reach 48. And the kangaroo jumped 8 steps at a time, 8 steps × 6 = 48. So, the kangaroo jumped 6 times to reach the number 48. We observe that due to size, rabbit take shorter steps than kangaroo and so reach later than kangaroo.
Page 130
Animal Jumps
Q6: To reach 60, how many times did the frog jump? How many times did the rabbit jump to reach the same number? What do you observe?
Ans: Since a frog jumped 3 steps at a time and 3 steps × 20 = 60. So, the frog jumped 20 times to reach the number 60. And the rabbit jumped 6 steps at a time, 6 steps × 10 = 60. So, the rabbit jumped 10 times to reach the number 60. We observe that due to difference in jump size, frog has to take more steps to reach the number 60.
Common Multiples
Q1: Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are _________________. Ans:
Frog: Multiples of 3 (3, 6, 9, 12, …).
Squirrel: Multiples of 4 (4, 8, 12, …).
Common multiples (LCM = 12): 12, 24, 36, …
12, 24, 36, …
Q2: Which numbers do both the rabbit and the kangaroo touch? A few common multiples of 6 and 8 are ___________________. Ans:
Rabbit: Multiples of 6 (6, 12, 18, 24, …).
Kangaroo: Multiples of 8 (8, 16, 24, …).
Common multiples (LCM = 24): 24, 48, 72, …
24, 48, 72, …
Q7: If the cat and the rat land on the same number, the cat will catch the rat. The cat is now on 6 and the rat on 12. When the cat jumps 3 steps forward, the rat jumps 2 steps forward. Will the cat catch the rat? If yes, at which number?
Common number: 24 (cat reaches 24 in 6 jumps, rat in 6 jumps).
Yes, cat catches rat at 24.
Q8: Find multiplication and division sentences in the grid. Shade the sentences. How many can you find?Two examples are done for you. Ans:
We can make 15 such sentences.
Page 131
Gulabo’s Garden
Q1: Gulabo’s garden has lily flowers. Each lily flower has 3 petals. How many petals are there in 12 flowers? Show how you found your answer. Gulabo will have 12 × 3 petals. Petals in 10 lilies 10 × 3 petals = 30 petals Petals in 2 lilies __________________ Petals in 12 lilies _________________ Ans: There are 36 petals in 12 flowers. I found it by multiplying 12 flowers by 3 petals each: 12 × 3 = 36. First, 10 lilies have 10 × 3 = 30 petals. Then, 2 lilies have 2 × 3 = 6 petals.
Petals in 12 lilies = 12 × 3 = 36 petals Adding them together, 30 + 6 = 36 petals.
Q2: In a hibiscus flower there are 5 petals. Gulabo counted all the petals and found them to be 80. How many flowers did she have?Gulabo has 80 ÷ 5 flowers. 5 petals is 1 flower. 10 petals are 2 flowers. 50 petals are 10 flowers. Then, 80 petals are _______ flowers. Ans:
80 ÷ 5 = 16 flowers.
Method: 50 ÷ 5 = 10, 30 ÷ 5 = 6, 10 + 6 = 16.
16 flowers; 80 ÷ 5 = 16.
Page 132
Gulabo’s Garden
Q3: Gulabo plants some marigold saplings in a box as shown in the picture. There are ______ saplings in each row. There are ______ rows. How many saplings has she planted? How did you calculate it? Mathematical Statement _________________
Ans: There are 11 saplings in each row. There are 3 rows. Gulabo has planted a total of 33 saplings in the box. By using multiplication, we found the number of saplings. Mathematical statement: There are 3 rows in the box, where the saplings planted are 11 times the number of rows. Total saplings planted = 3 × 11 = 33
Q4: “Dailyfresh” supermarket has kept boxes of strawberries in a big tray. How many boxes of strawberries does the supermarket have? Show how you found them.There are _______ columns of strawberry boxes. There are _______ boxes in each column. There are _______ boxes in all. Mathematical Statement _________________ Ans: There are 16 columns of strawberry boxes.
There are 6 boxes in each column. There are 16 × 6 = 96 boxes in all. Mathematical statement: The number of boxes of strawberry = Number of columns of strawberry boxes × number of boxes in each column = 16 × 6 boxes = 96 boxes
Q5: Radha runs a bakery shop. She bakes 18 cupcakes in one tray of the size shown below. (a) Complete arranging the cupcakes in the two trays given below.
Ans: Radha has 18 cupcakes to arrange in two trays. The first tray already has 8 cupcakes.
First tray: 8 cupcakes are already there.
Cupcakes left = 18 – 8 = 10 cupcakes.
Put the remaining 10 cupcakes in the second tray.
So, the arrangement is:
First tray: 8 cupcakes.
Second tray: 10 cupcakes.
(b) She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt? _______ Ans: Number of cupcakes in a tray = 18 Number of cupcakes in two trays = 2 × 18 = 36 The number of cupcakes, she can make in one attempt = 36
(c) Today she has received a special order. She has made 108 cupcakes. How many trays has she baked? Ans: Number of cupcakes in two trays = 36 Number of cupcakes in 4 trays = 2 × 36 = 72 Number of cupcakes in 6 trays = 3 × 36 = 108 So, the required number of trays = 6
(d) She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below.Number of columns: _______ Number of cupcakes in each column: _______ Multiplication statement _______ Ans: Number of columns = 6 Number of cupcakes in each column = 6 Multiplication statement: 6 × 6 = 36.
Q: Find different ways of arranging the following numbers of cupcakes in rows and columns in your notebook. 36, 8, 12, and 24 Ans:
36 cupcakes can also be arranged in a tray having 9 rows, and each row has 4 cupcakes.
8 cupcakes can be arranged in 4 columns, with 2 cupcakes in each column.
12 cupcakes can be arranged in 2 rows, with each row having 6 cupcakes.
24 cupcakes can be arranged in 6 columns, and each column has 4 cupcakes.
Page 134
The Doubling Magic
Magician Anvi came one day, To Gulabo’s house, ready to play. From her coat, with a grand display,
(a) Double of 32 =_____ Ans: 32 × 2 = 64
(b) Double of 14 =_____ Ans: 14 × 2 = 28
(c) Double of 26 =_____ Ans: 26 × 2 = 52
(d) Double of 17 =_____ Ans: 17 × 2 = 34
(e) Double of 39 =_____ Ans: 39 × 2 = 78
(f) Double of 45 =_____ Ans: 45 × 2 = 90
1. Guess what will be the ones digit of the following numbers when doubled. Write the ones digit in the space provided. (a) 28 ______ Ans: 28 × 2 = 56; ones digit: 6
(b) 56 ______ Ans: 56 × 2 = 112; ones digit: 2
(c) 45 ______ Ans: 45 × 2 = 90; ones digit: 0
(d) 17 ______ Ans: 17 × 2 = 34; ones digit: 4
2. Give examples of numbers that when doubled give the following digits in the ones place. (a) 0 _______ Ans: 5, 10, 15 (e.g., 5 × 2 = 10)
What do we notice about the numbers that we get after doubling? Even or Odd? Observation: Doubled numbers are even.
Page 135 & 136
Multiplication Chart
Fill each square in the chart by multiplying the row number by the column number. What do you notice about the numbers shaded in green? Why is this happening?
Ans: We notice that the numbers shaded in green, show that when we multiply any two numbers, the order does not matter. For example, 1 × 2 = 2 = 2 × 1, 2 × 3 = 6 = 3 × 2, 5 × 2 = 10 = 2 × 5 and so on.
Q1: Share the patterns that you notice in the table. Ans: We notice that each row/column is a multiple of its row/column number. Also its diagonal cells are all perfect squares.
Q2: Are the numbers in row 7 the same as the numbers in column 7? In general, are the numbers in a given row the same as the numbers in the corresponding column? Why does this happen? Ans:
General: Row n = column n due to commutative property (a×b = b×a).
Q3: Is there a row where all answers (products) are even numbers? Which rows have this property Ans: Rows 2, 4, 6, 8 (multiples of 2, 4, 6, 8 are even).
Q4: Is there a row having only odd numbers as products? Ans: No; odd row (e.g., 7) has even products (e.g., 7×2 = 14).
Q5: Are there rows that have both even and odd numbers? What do you notice? Why is it so? Ans: Yes, the rows of 1, 3, 5, 7, and 9 have both even and odd numbers. It is because when an odd number is multiplied with an even number, we get an even number, but when an odd number is multiplied with another odd number, we get an odd number.
Q6: Are there more even numbers in the chart or odd numbers? How do you know? Ans: More even; even rows dominate, and odd rows have even products.
Q7: Colour the common multiples of the following numbers. Use different colours for each item. (a) 2 and 3 Ans: LCM = 6; multiples: 6, 12, 18, …
(b) 4 and 8 Ans: LCM = 8; multiples: 8, 16, 24, …
(c) 7 and 9 Ans: LCM = 63; multiples: 63, 126, 189, … Observation: Common multiples are less frequent for larger numbers.
Q8: Observe the pattern in the ones digits of the products in row 5? Observe the ones digit of the products in other rows also. What patterns do you notice? Ans:
Q9: Here is row 8 of the chart: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. The ones digit of the products are: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0. Do you see a repeating pattern here? Guess the ones digit of the following products. Verify your answer by multiplying. Write the digit in the space given. (a) 11 × 8 (b) 12 × 8 (c) 13 × 8 Ans: Yes, the pattern of ones digits is 8, 6, 4, 2, 0 and is repeating. Since 1 × 8 = 8, 2 × 8 = 16, 3 × 8 = 24. So, the ones digits of 11 × 8, 12 × 8, and 13 × 8 are 8, 6, and 4, respectively. 11 × 8 = 88 12 × 8 = 96 13 × 8 = 104
Q10: In row 8 of the chart, there is no number whose ones digit is 1. What other digits do not appear as the ones digit? Ans: Row 8: 8, 6, 4, 2, 0. Missing: 1, 3, 5, 7, 9.
Q11: Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property? Ans: Yes, rows 1, 3, 7, and 9 have this property.
Q12: It can be seen in row 8 that 0 appears as the ones digit two times. ____ × 8 gives 0 as the ones digit. What numbers can go in the box? Give 5 examples of such numbers. Ans: 5 × 8 = 40 or 10 × 8 = 80, gives 0 as the ones digit. 15 × 8 = 120, 20 × 8 = 160, 25 × 8 = 200, 30 × 8 = 240, 35 × 8 = 280.
Q13: Is there a row in which 0 appears as the ones digit only once? Which rows have this property? Ans: Yes, the rows of 1, 3, 7, and 9 have this property.
Q14: What do you notice about the answers for Questions 11 and 13? Share in the grade. Ans: Both have the same answers.
Page 137
Multiples of Tens
Q1: Let us count the number of wheels in tricycles.
(a) Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = ______ wheels. Ans: Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = 30 wheels.
(b) Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 wheels = _______ wheels. Ans: Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 = 30 wheels.
(c) Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = ______ + _____ = ______ wheels. Ans: Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = 30 + 30 = 60 wheels.
Q2: Let us count the number of wheels in cars. (a) Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = _______ wheels. Ans: Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = 40 wheels.
(b) Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = _____ + _____ + _____ = _____ wheels. Ans: Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = 40 + 40 + 40 = 120 wheels.
Q3: Solve the following in a similar way. Share how you found the answers. (a) 10 × 6 = ________ Ans:
Multiplication: 10 × 6 means 10 groups of 6.
I know that 10 × 6 = 60 (using basic multiplication facts).
Alternatively, think of it as adding 6 ten times: 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 60.
(b) 40 × 6 = ________ Ans:
Break it down: 40 = 4 × 10, so 40 × 6 = (4 × 10) × 6.
Q: What happens when the number of groups is a multiple of 10?
Ans: If a number of groups is a multiple of 10, then it always ends with 0 as ones digit.
Page 138
Multiplying Using 10s
Q1: Radha is packing cupcakes in boxes of 4. She has packed 18 boxes. How many cupcakes are there in the packed boxes?
Ans:
Q2: 8 bamboo rods are needed to make a bullock cart. How many bamboo rods are needed for 23 carts? One cart needs 8 bamboo rods. 23 carts need 23 × 8 rods. 20 carts with 8 rods in each need 20 × 8 rods = ________ rods. 3 carts with 8 rods in each need 3 × 8 rods = _________ rods. Ans: First, we calculate for 20 carts: 20 carts with 8 bamboo rods each = 20 × 8 = 160 rods. Next, we calculate for 3 carts: 3 carts with 8 bamboo rods each = 3 × 8 = 24 rods. Now, add the rods for all 23 carts: 160 + 24 = 184 rods. So, 184 bamboo rods are needed for 23 carts.
Page 139
Let Us Solve
Q1: A flock of 25 geese and 12 sheep have gathered around a pond. Chippi the lizard sees many legs. How many legs does it see? Ans: Each goose has 2 legs, and each sheep has 4 legs. 25 geese have, 25 × 2 legs = 50 legs 12 sheep have, 12 × 4 legs = 48 legs Total legs seen by Chippi = 25 geese’s legs + 12 sheep’s legs = 50 legs + 48 legs = 98 legs.
Q2: In an auditorium, 8 children are sitting in each row. There are 15 such rows in the school auditorium. How many children are in the auditorium? Ans: Children sitting in 1 row = 8 Children sitting in 15 rows = 15 × 8 = 120 So, 120 children are in the auditorium.
Q3: A book shop has kept 9 books in each pile. There are 14 such piles. How many books does the shop have? Ans: 1 pile has 9 books. 14 piles have, 14 × 9 books = 126 books So, the shop has a total of 126 books.
Q4: Surya is making a patch work with beads of two colours as shown in the picture. How many beads has he used? How many each of golden colour beads and white colour beads has he used in making this patch work? Ans: Number of columns in the patch = 8 Number of beads in 1 column = 4 × 5 = 20 Total number of beads used by Surya = 20 × 8 = 160 Number of white beads in each consecutive 2 columns = 20, so total number of white beads in the patch = 20 × 4 = 80 Also, Number of golden beads in each consecutive 2 columns = 20, so total number of golden beads in the patch = 20 × 4 = 80.
Q5: For each of the following multiplication problems, make your own stories as above. Then find out the product.
a) 34 × 3 = 102 Story: There are 34 chairs, and each chair has 3 legs. Answer: Total legs = 102
b) 75 × 5 = 375 Story: A classroom has 75 desks, and each desk has 5 books. Answer: Total books = 375
c) 46 × 6 = 276 Story: A bus has 46 rows of seats, and each row has 6 seats. Answer: Total seats = 276
d) 50 × 9 = 450 Story: A shopkeeper has 50 bags, and each bag contains 9 apples. Answer: Total apples = 450
Page 140 & 141
Division
Q1: A factory has ordered 58 wheels for the small tempos that they make. Each tempo has 3 wheels. In how many tempos can they fix the wheels? Discuss your thinking in each step. Number of tempos is 58 ÷ 3
30 wheels are needed for 10 tempos. _______wheels are left. 15 wheels are needed for _______ tempos. _______wheels are left. 9 wheels are needed for_______ tempos. _______ wheels are left. _______ wheels are needed for_______ tempos. _______ wheels are left. Can we make another tempo? How many total tempos can the factory make using the 58 wheels? ___ With 58 wheels, we can make 19 tempos. 1 wheel is left. Ans: 58 ÷ 3 = 19 tempos, 1 wheel left.
Method:
10 tempos: 30 wheels, 58 − 30 = 28 left.
5 tempos: 15 wheels, 28 − 15 = 13 left.
3 tempos: 9 wheels, 13 − 9 = 4 left.
1 tempo: 3 wheels, 4 − 3 = 1 left.
Total: 10 + 5 + 3 + 1 = 19 tempos.
Ans: 19 tempos, 1 wheel left.
Q2: A dairy farm has many cows. Chippi the lizard is surprised to see 88 legs. How many cows are there in the farm? Write appropriate sentences as above to show your thinking. Number of legs of a cow: ________ Number of cows is 88 ÷ ________ Show your work using the table below. Hint: Taking out groups of 10s is easy. Total number of cows = ______ Ans: 88 ÷ 4 = 22 cows. Method:
Total: 10 + 10 + 2 = 22 cows.
Ans: 22 cows.
Let Us Solve
Q1: In a big aquarium, Jolly fish sees 72 legs of octopuses. How many octopuses are there in the aquarium?
Q2: A sports store packs 4 shuttlecocks in a bigger box. They have 50 shuttlecocks. How many boxes will they need to pack all of them? Can they pack all the shuttlecocks in the boxes? How many are left? Ans: 50 ÷ 4 = 12 boxes, 2 left. Method: 10 × 4 = 40, 2 × 4 = 8, 40 + 8 = 48, 50 − 48 = 2. Ans: 12 boxes, 2 shuttlecocks left.
Q3: Rakul Chachi uses a part of her farm to grow flowering plants for the upcoming festive season. She has planted 75 saplings of roses. Each row has 5 saplings. How many rows of saplings has she planted? Ans: 75 ÷ 5 = 15 rows. Method: 10 × 5 = 50, 5 × 5 = 25, 50 + 25 = 75, 10 + 5 = 15. Ans: 15 rows.
Q4: Make stories for the following problems and solve them:
a) 70 ÷ 5
Story: Riya has 70 candies. She wants to share them equally among 5 friends. How many candies will each friend get?
Solution: 70 ÷ 5 = 14 Answer: Each friend will get 14 candies.
b) 84 ÷ 7
Story:A librarian has 84 books. She wants to place them equally on 7 shelves. How many books will go on each shelf?
Solution: 84 ÷ 7 = 12 Answer: Each shelf will have 12 books.
c) 69 ÷ 3
Story: There are 69 eggs packed in trays. Each tray holds 3 eggs. How many trays are needed?
Solution: 69 ÷ 3 = 23 Answer: She needs 23 trays.
d) 93 ÷ 6
Story: A teacher has 93 chairs to arrange around 6 tables. How many chairs will be around each table, and how many will be left?
Solution: 93 ÷ 6 = 15 remainder 3 Answer: Each table will get 15 chairs, and 3 chairs will be left.
Page 142
Multiples of 100 100 bikes with 2 people on each have 100 × 2 people = _____ people. 200 bikes with 2 people on each have ______people. How did you find it? 100 cars with 4 people in each have 100 × 4 people = _______ people. 500 cars with 4 people in each have ______people. How did you find it? Ans: 100 bikes with 2 people on each have = 100 × 2 people = 200 people.
200 bikes with 2 people on each have = 200 × 2 people = 100 × 2 people + 100 × 2 people = 200 people + 200 people = 400 people.
100 cars with 4 people in each have = 100 × 4 people = 400 people.
500 cars with 4 people in each have = 500 × 4 people = (100 × 4 + 100 × 4 + 100 × 4 + 100 × 4 + 100 × 4) = (400 + 400 + 400 + 400 + 400) people = 2000 people.
How did you find it? 500 × 4 = _____ 100 × 4 = _____ 5 × 4 = _____ 50 × 4 = _____ Ans: We multiplied the number of bikes by the number of people on each bike. 500 × 4 = 2000 5 × 4 = 20 100 × 4 = 400 50 × 4 = 200
What do you notice about multiplying by multiples of 100s?
Ignore the zeros, multiply the other numbers, then add two zeros at the end.
Examples:
6 × 100 = 600 (6 × 1 = 6, add two zeros)
4 × 300 = 1200 (4 × 3 = 12, add two zeros)
Rule: Multiply the main numbers, then add 00.
Page 143
Q: Observe the pattern and complete the answers.
Ans:
Page 143
More Multiplication
Q1: Big electric autorickshaws run in small towns of India and can carry 8 passengers. How many people can travel in 125 such autos in a single round? The total number of passengers 125 × 8. 100 autorickshaws with 8 passengers in each have 100 × 8 passengers = ______ passengers. 20 autorickshaws with 8 passengers in each have 20 × 8 passengers = _______ passengers. 5 autorickshaws with 8 passengers in each have 5 × 8 passengers = __________ passengers. 125 autorickshaws with 8 passengers in each have ____ + ____ + ______= _________ passengers. Ans: The total passengers are 125 100 autorickshaws with 8 passengers in each have = 100 × 8 passengers = 800 passengers 20 autorickshaws with 8 passengers in each have = 20 × 8 passengers = 160 passengers 5 autorickshaws with 8 passengers in each have = 5 × 8 passengers = 40 passengers 125 autorickshaws with 8 passengers in each have = 800 + 160 + 40 = 1000 passengers
Q2: Kahlu and Rabia are potters and make earthen pots (kulhad) for trains. They pack 6 kulhads in a box and have packed 174 boxes for delivery. How many kulhads have they made? The total number of kulhads is ________.
Ans: The total number of kulhads is 174 × 6 = 600 + 420 + 24 = 1044
Page 144 & 145
Let Us Solve
Q1: BP Girl’s school has decided to give all its students two pencils on the first day of school. It has 465 students. How many pencils does the school need to buy? Ans: Number of pencils given to each student = 2 Total number of students = 465 Total pencils school need to buy = 465 × 2 = 800 + 120 + 10 = 930
Q2: 234 children of a school have decided to organise a school mela. Each child contributes ₹5 for the organisation of the mela. How much money do they collect? Ans: Money contributed by each child = ₹ 5 Total children in school mela = 234 Money collected for school mela = 234 × ₹ 5
The total money collected from 234 children, with each contributing ₹ 5 = ₹ 1000 + ₹ 150 + ₹ 20 = ₹ 1170
Q3: Make stories for the following problems and solve them.
a) 439 × 4
Story: A school has 439 students in each house. There are 4 houses in the school. How many students are there in total?
Solution: 439 × 4 = 1,756
Answer: There are 1,756 students in total.
b) 514 × 8
Story: A library has 514 books on each shelf. There are 8 shelves. How many books are there in all?
Solution: 514 × 8 = 4,112
Answer: The library has 4,112 books.
c) 356 × 5
Story: A factory packs 356 toys in each box. There are 5 boxes. How many toys are packed?
Solution: 356 × 5 = 1,780
Answer: There are 1,780 toys packed.
d) 623 × 7
Story: There are 623 apples in each basket. A farmer has 7 baskets. How many apples does the farmer have?
Solution: 623 × 7 = 4,361
Answer: The farmer has 4,361 apples.
Page 146
Patterns in Division
How much money will each get? Draw arrows linking the money and the children to answer the questions. Ans:
1. ₹ 30 shared equally among 3 children ______________
We divide ₹30 by 3:
₹30 ÷ 3 = ₹10 Each child will get ₹10
2. ₹ 900 shared equally among 3 children ______________
We divide ₹900 by 3:
₹900 ÷ 3 = ₹300 Each child will get ₹300
Ans:
Q1: A load carrying truck has 6 tyres. Chippi the lizard sees 60 tyres. How many trucks are there? Ans: We know 1 truck has 6 tyres. If there are 60 tyres, we divide:
60 ÷ 6 = 10 trucks
(Each truck has 6 tyres. So 10 trucks × 6 tyres = 60 tyres)
Q2: Chippi sees 80 wheels in a car parking space. How many cars are standing in the parking space? Ans: We know 1 car has 4 wheels. If there are 80 wheels, we divide:
80 ÷ 4 = 20 cars
(Each car has 4 wheels. 20 × 4 = 80 wheels)
Q3: Chippi sees 600 legs of ants walking towards the anthill. How many ants are there? Ans: We know 1 ant has 6 legs. If there are 600 legs, we divide:
600 ÷ 6 = 100 ants
(Each ant has 6 legs. 100 × 6 = 600 legs)
Q4: A fancy shop has packed 800 rubber bands in several packets. Each packet has 4 rubber bands. How many packets of rubber bands does the shop have? Ans: We know 1 packet = 4 rubber bands If there are 800 rubber bands, we divide:
800 ÷ 4 = 200 packets
(Each packet holds 4 rubber bands. 200 × 4 = 800)
Page 147
Let Us Solve
Q1: A school bus hires 7 buses to take 245 children to the transport museum. Each bus carry the same number of children. How many children are traveling in each bus? Ans: 245 ÷ 7 = 35 children/bus. Method: 30 × 7 = 210, 5 × 7 = 35, 210 + 35 = 245, 30 + 5 = 35. 35 children/bus.
Q2: The Darjeeling Himalayan Railway is fondly called the “Toy Train”. This toy train ride is also a UNESCO World Heritage Site. This amazing train runs between New Jalpaiguri and Darjeeling and it also passes through one of the highest stations in the world, namely, Ghum. It runs 88 km daily. How much distance does it travel in a week? Ans: 88 × 7 = 616 km. Method: 80 × 7 = 560, 8 × 7 = 56, 560 + 56 = 616.
Q3: The 16 Km river rafting from Shivpuri to Rishikesh in the Ganga provides the most interesting rafting opportunity. In the summer months, Venture Out company took 259 people for rafting. Each raft can take 7 people. How many rafts did it take?
Q4: Anu saves ₹45 every month by putting it in her piggy bank. (a) How much money will Anu save in 6 months? Ans: Money saved by Anu in 6 months = ₹ 45 × 6 = ₹ 40 × 6 + ₹ 5 × 6 = ₹ 240 + ₹ 30 = ₹ 270
(b) She distributes the total money saved after 6 months among 6 of her friends. How much does each friend get? Ans: Total money distributed equally 210 among 6 friends. So, money got by each 90- friend = ₹ 270 ÷ 3 = ₹(10 + 10 + 10 + 10 + 5) = ₹ 45
(c) If she decides to distribute the saved money among 3 friends after 6 months, how much money will each get? Ans: Money saved by Anu in 6 months = ₹ 270 Money got by each of 3 friends = ₹ 270 – 3 = ₹ (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = ₹ 90
Q5: Raju drives an auto in his village and takes people to the bus stand. He makes 8 trips in a day. Which of the following questions can be exactly calculated with the above statement? (a) How much money does he make in a day? Ans: We cannot say how much money he makes in a day as the price of each trip is not given.
(b) How many trips does he make in 7 days? Ans: Number of trips made in 7 days = 8 trips × 7 = 56 trips.
(c) How much time does one trip take? Ans: We cannot say how much time he takes for a trip, as time is not mentioned.
(d) How many trips does he make in 4 weeks? Ans: Number of trips in a week (7 days) = 8 × 7 = 56 Number of trips in 4 weeks = 56 × 4 = 50 × 4 + 6 × 4 = 200 + 24 = 224.
Q1: Look at the pictures given and write the names of the animals from heaviest to lightest.
Ans: Elephant > Giraffe > Dog > Squirrel > Ant
Q2: Write the name of the heaviest object in your home. How did you know?
Ans: Example: Fridge. Known by estimating or lifting, it feels much heavier than other objects like chairs or tables.
Q3: Do you carry your school bag with ease or with some effort?
Ans: With some effort (depends on bag weight, typically 2–5 kg for Class 4 students).
Q4: Write the name of the heaviest book in your bag. How did you know?
Ans: Example: Maths textbook. Known by comparing books; it feels heavier or looks thicker.
Q5: What is your weight? How did you know?
Ans: Example: 25 kg. Known by using a weighing scale at home or school.
Fun at Vegetable Market!
Rita and Shabnam went to the market to buy some fruits and vegetables. They saw the vegetable seller weighing vegetables.
Q: What do you think will be the weight of the half pumpkin?
Ans: A whole pumpkin is typically 2–5 kg. Half a pumpkin: ~1–2.5 kg (e.g., half of 4 kg = 2 kg). Verify with a scale.
Page 116
Let Us Do
Q: Estimate the weight of the following and put a tick mark (✓) in the appropriate cell. Verify with a weighing balance.
Ans:
Page 117
Let Us Find
Q1: How many 250 g daal packets will balance one 500 g daal packet? Draw as many packets of 250 g on the empty pan to balance the 500 g packet. What did you find? 250 g = ___ of 500 g (½, 2).
Ans:
500 g ÷ 250 g = 2 packets of 250 g.
Draw 2 packets of 250 g on the empty pan to balance.
Ans: 250 g = ½ of 500 g.
Page 118
Let Us Find
Q2: Draw arrows to indicate which side the pan balance will tilt?
Ans:
Q3: Match the unit convenient for measuring each of the following objects?
Ans:
Page 119
Let Us Do
Q1: How many erasers will weigh the same as a 50 g Haldi packet?
Ans: Assume an eraser weighs ~10 g. 50 g ÷ 10 g = 5 erasers.
So, 5 erasers will weigh equal to a 50 g Haldi packet.
Q2: A 100 g soap bar will weigh the same as ___ erasers.
Ans: 10 g = 1 eraser ⇒ 100 g = 10 × 10 g = 10 × 1 eraser = 10 erasers So, 100 g soap bar will weigh the same as 10 erasers.
Q3: ___ erasers will weigh the same as 250 g sugar.
Ans: 10 g =1 eraser ⇒ 250 g = 25 × 10 g = 25 × 1 eraser = 25 erasers So, 25 erasers will weigh the same as 250 g of sugar.
Page 119
Let Us Think (Boxes of Sweet)
Mr Shrinathan, a sweet shop owner, has several orders for 1 kg Kaju-katli but he has to pack them in different sized boxes.
Write the number of boxes needed to pack 1 kg Kaju-katli in the blank space:
1. Mr Das wants the sweets in boxes weighing 500 g each. Ans: Since 1 kg = 1000 g = 500 g + 500 g = 2 × 500 g So, Mr Shrinathan needs 2 boxes of500 g each to pack 1 kg Kaju-Katli.
2. Mrs Fernandes wants the sweets in boxes weighing 250 g each. Ans: Since 1 kg = 1000 g = 250 g + 250 g + 250 g + 250 g = 4 × 250 g So, Mr Shrinathan needs 4 boxes of250 g each to pack 1 kg Kaju-Katli.
3. Mrs Khan wants the sweets in boxes weighing 100 g each. Ans: Since 1 kg = 1000 g = 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g + 100 g = 10 × 100 g So, Mr Shrinathan needs 10 boxes of 100 g each to pack 1 kg Kaju-Katli.
4. Mr Patel wants the sweets in boxes weighing 50 g each. Ans: Since 1 kg = 1000 g = 10 × 100 g = 10 × (2 × 50 g) = 20 × 50 g So, Mr Shrinathan needs 20 boxes of 50 g each to pack 1 kg Kaju-Katli.
Page 120
Weighing Machines
Do you know the different types of weighing machines used to weigh different objects?
Ans: Do it Yourself!
Q: Ask your parents and find the amount of consumption of the following items at your home in a month.
Ans: Example (varies by household):
Taran and his sister are lifting packets of flour, rice, and salt.
What do you think they are experiencing while lifting these packets? Have you ever lifted such packets at your home? What do you experience? Discuss.
Ans: They feel effort while lifting heavy packets (e.g., 5 kg flour is harder than 1 kg salt).
Personal experience: Lifting 5 kg rice feels heavy, requires both hands; 1 kg salt is easier.
Discuss: Heavier packets strain arms, lighter ones are manageable.
Page 121
Let Us Do
Q1: Try to lift some objects around you and write the names of three objects that you can lift easily. Estimate and write their weights.
Ans:
Pencil: ~10 g
Notebook: ~200 g
Water bottle: ~500 g
Q2: Now write the names of things that you can lift with a lot of effort. Estimate and write their weights.
Ans:
School bag: ~3 kg
Chair: ~5 kg
Bucket of water: ~10 kg
Q3: How many 1 kg packets are in: a. 10 kg Ans: 10 kg = 10 × 1 kg There are 10 packets of 1 kg each in 10 kg. b. 20 kg Ans: 20 kg = 20 × 1 kg There are 20 packets of 1 kg each in 20 kg. c. 50 kg Ans: 50 kg = 50 × 1 kg There are 50 packets of 1 kg each in 50 kg. d. 25 kg Ans: 25 kg = 25 × 1 kg There are 25 packets of 1 kg each in 25 kg.
Q4: Match the objects in the left column with their estimated weights in the right column.
Ans:
Page 122
Measuring Capacity
Q: Do you remember the 1 litre bottle? How much water does your water bottle hold?
Find bottles and containers that can hold the following quantities of water.
Ans: Example: My water bottle holds 1 litre.
Page 123
Let Us Find
a) How many 500 ml bottles will fill a 1 l bottle?
Ans: Since 11 = 1000 ml = 500 ml + 500 ml = 2 × 500 ml Thus, two 500 ml bottles will fill a 1 l bottle.
b) How many 250 ml bottles will fill a 1 l bottle?
Ans: Since 1 l = 1000 ml = 250 ml + 250 ml + 250 ml + 250 ml = 4 × 250 ml Thus, four 250 ml bottles will fill a 1 litre bottle.
c) How many 100 ml bottles will fill a 1 l bottle?
Ans: Since 11= 1000 ml = 100 ml + 100 mlm + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml = 10 × 100 ml Thus, ten 100 ml bottles will fill a 1 l bottle.
d) How many
Ans:
1/2 l = 1/2 × 1000 ml = 500 ml = 250 ml + 250 ml = 2 × 250 ml So, there are two 250 ml in 12 l.
750 ml = 250 ml + 250 ml + 250 ml = 3 × 250 ml So, there are three 250 ml in 750 ml.
1/2 l = 1/2 × 1000 ml = 500 ml = 100 ml + 100 ml + 100 ml + 100 ml + 100 ml = 5 × 100 ml
So, there are five 100 ml in 12 l. 800 ml = 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml + 100 ml = 8 × 100 ml So, there are eight 100 ml in 800 ml.
Page 124
Let Us Do
Q1: Find a dosing cup or a bottle of 10 ml and try to find how many 10 ml will fill a 100 ml bottle __________________
Ans: 100 ml = 10 × 10 ml So, ten 10 ml cups will fill a 100 ml bottle.
Find how many 10 ml dosing cups will fill: a) 250 ml glass Ans: 250 ml = 25 × 10 ml So, 25 dosing cups of 10 ml will fill a 250 ml glass. b) 500 ml vessel Ans: 500 ml = 50 × 10 ml So, 50 dosing cups of 10 ml will fill a 500 ml vessel. c) 1 l bottle Ans: 1 l = 1000 ml = 100 × 10 ml So, 100 dosing cups of 10 ml will fill a 1 l bottle.
Q2: Take a 1 ml dropper and find out: a) How many 1 ml droppers will fill a 10 ml dosing cup? Ans: 10 ml ÷ 1 ml = 10 droppers b) How many droppers will fill a teaspoon? Ans: A teaspoon is ~5 ml. 5 ml ÷ 1 ml = 5 droppers
Q3: Find out how much of these liquids are used at a time: a) Eye drops Ans: Less than 1 ml (e.g., 0.05 ml per drop) b) Honey Ans: ~5–15 ml (1–3 teaspoons) c) Cough Syrup Ans: ~5–10 ml (per dose, check label) d) Cooking Oil Ans: ~15–30 ml (1–2 tablespoons per dish)
Page 125
Let Us Do
Q4: Mr Krishna packages perfumed oils in different sized bottles. During a festival, the following customers asked for 1 l perfumed oils but in different sized bottles. Write the number of bottles each of them will get. a) Ms Shetty wants bottles of 500 ml each Ans: 1 l = 1000 ml = 500 ml + 500 ml So Mr Krishna needs two 500 ml sized bottles. b) Mr Muthukumar wants bottles of 200 ml each Ans: 1 l = 1000 ml = 200 ml + 200 ml + 200 ml + 200 ml + 200 ml So, Mr Krishna needs five 200 ml sized bottles. c) Ms Naini wants bottles of 100 ml each Ans: 1 l = 1000 ml = 10 × 100 ml So, Mr Krishna needs ten 100 ml sized bottles. d) Ms Kannan wants bottles of 50 ml each Ans: 1 l = 1000 ml = 20 × 50 ml So, Mr Krishna needs twenty 50 ml sized bottles.
Q5: Estimate and verify by measuring. Use the bottles you have collected for this purpose (for example, 500 ml, 250 ml, 100 ml, 50 ml, and 10 ml).
Ans:
Page 125
Let Us Explore
Q: Visit nearby shops and make a list of different items that are sold in the following quantities.
Ans:
Page 126
Let Us Find
a) How many litres of water do you drink in a day? How did you find out?
Ans: ~1–2 litres. Found by counting glasses (e.g., 4 glasses × 250 ml = 1 litre).
b) How much water can a crow drink at a time?
Ans: ~10–20 ml (based on small beak capacity).
c) How much milk do you drink in one day?
Ans: ~200–500 ml (e.g., 1–2 glasses of 200 ml).
d) How much water does an elephant drink in a day?
Ans: ~100–200 litres (based on known elephant consumption).
Q: What do you use the most water for? What do you use the least water for? Compare this with a few others in your grade . In which activities is your water usage the same?
Ans:
Most: Bathing (~20–50 litres)
Least: Drinking (~1–2 litres) Compare: Most classmates use similar amounts for bathing; drinking varies slightly.
Q: How much water may be used in the following activities? a. Water for taking a shower Ans: ~20–50 litres (bucket bath or 5–10 min shower) b. Watering crops in a field Ans: ~1000–5000 litres (depends on field size) c. Watering flowering plants Ans: ~1–5 litres per plantd. Washing clothes Ans: ~20–100 litres (manual or machine wash)
Page 127
Water Conservation in Everyday Life
Take a container and put it under a leaking tap for an hour. How much water is lost in an hour? Did it surprise you?
Ans: ~100–500 ml (slow drip, e.g., 1–5 ml per minute). Surprising as small drips add up significantly.
Q: How much water is lost in a day?
Ans: If water drips slowly and fills about 1 glass (250 ml) in an hour, then: In a day (24 hours) → 250 ml × 24 = 6,000 ml = 6 liters
About 6 liters of water can be lost in one day from a slow drip.
Q: How much water is lost in a week?
Ans: If 6 liters are lost in a day, then in 7 days: 6 liters × 7 = 42 liters
Around 42 liters of water can be wasted in one week.
Q: How would this wastage of water affect us?
Ans: Wasting water means we will have less clean water to use for drinking, bathing, cooking, and growing food. It can also lead to water shortages in the future. We should save water because it is very precious.
Q: Daisy and Lou are very excited about their trip. They join their mother in the weekly shopping as they need to buy things for their trip. The family makes a list of things to buy:
Fruits and vegetables
Field Trip Items-Biscuits, Water Bottles, and Dry Fruits.
Sapan Dada has a cart for selling vegetables and fruits. The prices of the vegetables and fruits are given below.
Sapan Dada asks Daisy and Lou to find the costs of different quantities of fruits and vegetables. Help them to complete the tasks. You may use a number line, play money or any other method to calculate.
Ans: The amount is double.
Q: Their mother buys things for ₹163. What might she have bought? There is more than one possibility.
Ans: Since, ₹ 163 = ₹ 45 + ₹ 95 + ₹ 23 = ₹ 70 + ₹ 70 + ₹ 23 So, the mother might have bought 1 kg custard apple, 1 kg beans, and 1 kg radish or 2 kg sapota and 1 kg radish or 1 kg beans, 1 kg yam and 1 kg radish.
Q: Daisy and Lou help Udaya Didi return the balance to customers. Calculate the balance for the given transactions.
Ans:
Q: Lou and Daisy buy 3 kg bananas to eat on the way with their friends. Which of the following options can they use to buy the bananas?
Ans: Cost of 1 kg banana = ₹ 55 Cost of 3 kg banana = ₹ 55 + ₹ 55 + ₹ 55 = ₹ 165 Therefore, Lou and Daisy will choose the option (b) to by the bananas.
Page 99
A Strange Puzzle!
Q: Four kids buy two oranges each at ₹21 per orange. They pay different notes: Krishna (₹50), Sudama (₹100), Mala (₹200), Neela (₹500). What is the balance each got?
Ans: Cost for 2 oranges = 2 × ₹21 = ₹42
Krishna: Paid ₹50, Balance: ₹50 − ₹42 = ₹8
Sudama: Paid ₹100, Balance: ₹100 − ₹42 = ₹58
Mala: Paid ₹200, Balance: ₹200 − ₹42 = ₹158
Neela: Paid ₹500, Balance: ₹500 − ₹42 = ₹458
Page 100
Let Us Play
Q1: Place the numbers 1–6 in the blanks so the sum on each side of the triangle is 9. No numbers should be repeated.
Ans: Place numbers such that each side (3 numbers) sums to 9:
Vertices: 1, 2, 3; Sides: 4, 5, 6
1 + 6 + 2 = 2 + 4+ 3 = 3 + 5 + 1 = 9
Q2: Use the same numbers 1–6 and make the sum 10 on each side of the triangle.
Ans: Example: 1, 3, 5 at corners; 2, 4, 6 on sides, arranged so each side sums to 10 (e.g., 1 + 4 + 5 = 10).
1 + 4 + 5 = 5 + 2 + 3 = 3 + 6 + 1 = 10
Q3: What other sums can you make with these 6 numbers? Can you make 12 on each side? Can you make 13?
Ans:
4 + 5 + 2 = 2 + 3 + 6 = 4 + 1 + 6 = 11 Thus the other sum can we make using these numbers is 11.
4 + 3 + 5 = 5 + 1 + 6 = 6 + 2 + 4 = 12 But we cannot make 13 using numbers 1-6 on each side of the triangle without repetition of the numbers. In a magic triangle, the numbers on each side must add to the same total. To get the highest possible side sum, we place the highest numbers (6, 5, 4) at the corners. Their sum, 6 + 5 + 4 = 15. Since corner numbers are counted twice, total corner sum = 15 × 2 = 30. Now, the sum of the remaining middle numbers = 1 + 2 + 3 = 6. So, maximum total side of sum 30 + 6 = 36. Therefore, maximum possible side sum = 36 + 3 = 12. Therefore, it is impossible to create a magic triangle with a sum of 13 using numbers 1-6 on each side of the triangle without repeating the numbers.
Q: What strategy did you use to place the numbers? Ans: Start with the smallest or largest numbers at corners, then adjust side numbers to balance the sum. Check each side’s sum and swap numbers if needed to ensure equality.
Page 101Add UpQ1: Estimate the number of teachers going. How many teachers are accompanying the children? Ans:
Estimate: 24 + 28 ≈ 20 + 30 = 50 teachers.
Exact: 24 + 28 = 52 teachers.
Q2: How many children are going on the trip? Estimate the number of children.
Q: Daisy and Lou ate one large piece of pusaw for ₹38. They liked it a lot and bought another small piece for ₹ 16. How much did they spend on pusaw?
Ans: ₹38 + ₹16 = ₹54
Page 104Daisy and Lou’s Piggy BankQ: Daisy and Lou had collected ₹ 185 in their piggy bank. Their mother gave them ₹ 125 more for the trip. How much money did they take for the trip?
Ans:
Daisy and Lou took ₹ 310 for the trip.
Page 105
Let Us Do
Q1: In Kalakshitij, a school of performing arts, the following number of students are learning to sing and play the tabla. Estimate and then find the total number of students.
15 more girls join the music school and they want to learn to play the tabla. How many girls play the tabla now?
Q3: Preeti’s school has 423 children. Her school has 178 less than her cousin’s school. How many children in Preeti’s cousin’s school?
Ans: Preeti’s cousin’s school has 178 children more than Preeti’s school. So, number of children in Preeti’s cousin’s school = 423 + 178 = 601 children
Page 108 & 110
Let Us Solve
Q1: Ram Chacha got 264 mangoes from his mango tree last year. This year he got 527 mangoes. How many more mangoes did he get this year?
Ans:
Thus, this year Ram Chacha got 263 more mangoes than previous year.
Q2: During the festival of dolls (Gombe Habba in Dussehra), Ranganna made 639 dolls. He was able to sell 531 dolls. How many dolls are left with him? Ans:
No. of dolls left = 639 – 531 = 108.
Q3: Subtract by aligning the numbers in columns. a) 83 − 29 Ans:b) 345 − 123 Ans:
c) 763 − 437 Ans:
d) 803 − 350 Ans:
e) 900 − 328 Ans:
Page 109
Let Us Solve
Q1. These books are in the community library of Wakanda village. Children borrow these books to read during their vacation.
a) Rami read Panchatantra Tales during the summer vacation. Kesu read Akbar Birbal, Karadi Tales and Blue Umbrella. Who do you think read more? How many more pages?
Ans: Rami read:Panchatantra Tales = 236 pages
Kesu read:
Akbar Birbal = 96 pages
Karadi Tales = 30 pages
Blue Umbrella = 90 pages
Total = 96 + 30 + 90 = 216 pages
Rami read more pages.
Rami read more. She read 20 pages more than Kesu.
b) Sumi read 23 pages of Adventures of Feluda. How many more pages to complete?
Ans: Total pages in Adventures of Feluda = 128
Pages read = 23
Pages left = 128 – 23 = 105
c) Jaggu finished Swami and Friends, Akbar Birbal, and 50 pages of Feluda. How many more pages to finish all books?
Q2: A daily train between Delhi and Aligarh travels a distance of 131 km. Look at the picture below and answer the questions that follow.
a) How many passengers are there on the train when it leaves Dadri? Passengers boarded at New Delhi = 894 Passengers boarded at Ghaziabad = 158 Passengers alighted at Ghaziabad = 23 Passengers boarded at Dadri = 67 Passengers alighted at Dadri = 75
Total passengers after Dadri = 894 + 158 – 23 + 67 – 75 = 1021
Answer: 1021 passengers
b) Find the number of people who got off the train at Aligarh. The train had 1021 passengers after leaving Dadri. If all the remaining passengers got off at Aligarh, then: Answer: 1021 people
c) Were there more people on the train in New Delhi or in Aligarh? How much more/less? Passengers in New Delhi = 894 Passengers in Aligarh = 1021
1021 – 894 = 127 more passengers in New Delhi
Answer: There were 127 more people on the train in New Delhi than in Aligarh.
d) How many people travelled altogether by the train? Total passengers who boarded: New Delhi = 894 Ghaziabad = 158 Dadri = 67
Total = 894 + 158 + 67 = 1119
Answer: 1119 people travelled altogether by the train.
Page 111
Let Us Solve
Solve: Ans:
c) Find quick ways of solving. Think about some of the strategies you learnt in Grade 3.
Ans:
d)Solve by aligning the numbers in columns in your notebook. 1. 38 + 943 Ans:
2. 465 + 305 Ans:
3. 435 + 462 Ans:
4. 764 – 657 Ans:
5. 518 – 209 Ans:
6. 879 – 53 Ans:
e) Find two numbers such that their sum is 856. Find another two numbers such that their difference is 563. Make your own word problems with these numbers.
Ans:
Page 112
Number Pair Hunt
Here is a grid of numbers. There are many number pairs in this grid. A number pair has 2 numbers which are next to each other, vertically or horizontally. For example, the numbers 111 and 185 are number pairs 48 and 185 are number pairs in this grid.
1. Find the number pair whose sum is the greatest.
2. Find the number pair whose sum is the smallest.
3. Find the number pair whose difference is the greatest.
4. Find the number pair whose difference is the smallest.
Q1: Look at the picture. What are the students measuring? Put a tick mark (✓) if you find it being measured.
Ans: Length, Weight, and Temperature are measured by the students in the above picture.
Q2: What is being used to measure the height? What other tools can be used to measure height? Ans: A measuring scale is used to measure height. Other tools include a ruler, height chart, or a meter stick.
Q3: Recall in Grade 3 you studied that lengths are measured in metres. Check and fill in the blanks whether the following are correct/incorrect for your classroom. (a) The height of most of the students in my grade is more than a metre. Ans: Correct (Most Class 4 students are taller than 1 meter.)
(b) The length of my arm is less than a metre. Ans: Correct (An arm is usually less than 1 meter.)
(c) The height of the door of the grade is less than a metre. Ans: Incorrect (A classroom door is usually more than 1 meter tall.)
(d) The breadth of the blackboard is more than a metre. Ans: Correct (A blackboard is typically wider than 1 meter.)
Page 81: Let Us Do
1. Walk, Jump, and Crawl on 1, 5 and 10 m line
Draw lines of 1 m, 5 m, and 10 m on the floor of the classroom or outside in the playground. How will you make these lines? Think and share with your friends. Walk, jump, and crawl on the lines. Ans: Do it Yourself!
Page 82: Let Us Do
2. Long Jump
Each child can participate in a long jump competition. How far have your friends jumped? Measure as accurately as possible using a combination of ropes. Who jumped the longest distance? Who has jumped the shortest?
Fill the following table.
Ans:
Q3: Estimate how long and broad is your classroom. Measure and check.Ans: Estimate the classroom length and breadth (e.g., length ≈ 8 m, breadth ≈ 6 m). Use a measuring tape or meter rope to measure accurately. Compare your estimate with the actual measurement.
Page 83: Let Us Think: Guess the Length
Look at the pictures carefully and answer the questions.
Q1: What is the length of one bus in metres? What is the length of one cricket bat in metres? Ans: A bus is about 15 meters long. A cricket bat is about 1 meter long.
Q2: How many buses would be equal to the length of two blue whales? Ans: A blue whale is about 30 meters long. Two blue whales = 2 × 30 = 60 meters. A bus is about 15 meters. So, 60 ÷ 15 = 4 buses.
Q3: How many cricket bats will be needed to measure one whale? Ans: A blue whale is about 30 meters. A cricket bat is about 1 meter. So, 30 ÷ 1 = 30 cricket bats.
Q4: If two ostriches stand one above another, their height will be equal to the height of Ans: One ostrich’s height is 3 m. Therefore, the heights of two ostriches are 3m + 3m = 6m As we can see in the given picture, the crocodile’s length is also 6 metres. Therefore, the two ostriches’ height will be equal to the length of one crocodile.
Q5: How many crocodiles will be equal to the length of a blue whale? Ans: A crocodile is about 6 meters long. A blue whale is 30 meters. So, 30 ÷ 6 = 5 crocodiles.
Page 84: Let Us Observe
Chutki wants to keep track of the increase in height of her plant. Compare the metre rope with the measuring tape used by a tailor. Is the length of both the same or different?
Ans: The meter rope and tailor’s measuring tape are both 1 meter long, so their length is the same.
Observe the measuring tape carefully. What do you notice?
Ans: The measuring tape has marks for centimeters (cm) and millimeters (mm), with numbers every 1 cm or 10 cm. These marks help measure small lengths accurately.
Discuss how these marks help us measure clearly.
Ans: The red bar (10 cm) repeats 10 times to make 1 meter.
Q: 1 metre (m) = 100 centimetre (cm), ½ m = ___ cm, ¼ m = ___ cm Ans:
½ m = 50 cm (½ × 100 = 50)
¼ m = 25 cm (¼ × 100 = 25)
Page 85: Let Us Do
Q1: Measure each object using a scale.
Write the names of the objects in increasing order of length.
Ans:
Page 86: Let Us Do
Q2: Estimate the lengths of the following and compare your responses with your friends in the grade. Write some examples of things that can be lesser than or equal to 1 cm in length. Verify by measuring.Ans:
Q3: Take three toy cars and find out how far each one can go. You can use a small wooden ramp, or you might like to make a ramp using any material that you have. Measure the distance each of your cars travels using measuring tape and write the answers in cm. Ans:
Page 87: Let Us Do
Q4: Find the longest and the shortest route in this treasure hunt. You can go around the obstacles but cannot jump over them. You can only walk on the yellow tiles and not on the grass. Can you find the length of your route in centimetres? Look for the 1 cm clue in the map. Ans: Trace paths on yellow tiles, avoiding obstacles. Use the 1 cm clue to scale the map. Measure each route with a scale. Compare lengths to find the longest and shortest routes in cm.
Shortest Route: 16 cm.
Longest Route: 48 cm
Page 88: Let Us Do
Q5: Trace your hand on a piece of paper. Measure it using the scale. Length of my hand = ___ cm Ans: Trace your hand on paper. Measure the length from the wrist to the tip of the middle finger with a scale. Record in cm (e.g., 15 cm).
Q6: Use your hand to estimate the measurement of any object. Convert into centimetres. Verify using the scale.Ans:
Q7: Ashwin’s scale is broken. Can you help him to measure using this scale? Ans: If the scale is broken (e.g., missing the start), align the object with the first visible mark (e.g., 2 cm) and subtract the starting mark from the end mark to find the length. If an object starts at 8 cm and ends at 14 cm, length = 14 – 8 = 6 cm.
And if an object starts at 12 cm and ends at 16 cm, length = 16 – 12 = 4 cm.
Q8: Fill the blanks on the number line below appropriately.Ans:
Q9: The length of a board is 2 metres. Sonu has a decorative border sticker which is 20 cm long. How many such stickers are needed to cover the length of the board completely?
Ans: The board is 2 meters long. 1 meter = 100 cm, so 2 meters = 200 cm. Each sticker is 20 cm long. To find how many stickers are needed, divide the board’s length by the sticker’s length: 200 ÷ 20 = 10. So, 10 stickers are needed to cover the board.
Metre and Centimeters
Ramu and Shamu are using a measuring tape to measure their own height.
Ramu reads his height from the tape as 120 cm and Shamu reads it as 1 m 20 cm.
Who is correct?
Pinki says both are correct and draws this.
Ans: Ramu’s height = 120 cm Shamu’s height = 1 m 20 cm Since 1 metre = 100 cm, Now, convert 1 m 20 cm into cm: 1 m 20 cm = 1 × 100 cm + 20 cm = 120 cm Both measurements are the same. Pinki is correct because both Ramu and Shamu have given the same height in different units.
Page 90: Let Us Do
Q1: Fill in the blanks: A kilometre is 1000 metres.
i) 2 m = 200 cm
ii) ____ m = 400 cm Ans: 4m = 4 × 100 cm = 400 cm
iii) 6 m = _____ cm Ans: 6 m = 600cm
iv) _____ m = 800 m Ans: 8m = 800 cm (There is a mistake in the question)
b) Identify the wells with the same depth and match them. Ans:
Page 90: Let Us Explore
Activity: Students will measure their height using a measuring tape. Make a table in your notebook and complete it.
Answer the following questions.
1. Height of the tallest child is _____.
2. Height of the shortest child is _____.
3. Number of children who are more than 1 m tall _____.
4. Number of children who are shorter than 1 m _____.
Ans: Do it Yourself!
Page 91: Fencing and Lacing
How many bricks will Bhola need to make the boundary? Ans: 21 more bricks are needed to cover the boundary.
Page 92: Let Us Do
Q1: Bhola made the boundary of his gardens in the following ways. Circle the boundary that is longest. Ans: Compare the boundaries of each garden by counting the sides or measuring with a scale. Circle the garden with the most sides or longest total length.
Q2: Let us find the perimeter of some shapes using the dot grid. One is done for you. a) Colour the boundary with the longest length in blue. Ans: Count the dots along each shape’s boundary (1 dot = 1 cm). Colour the shape with the highest count in blue.
b) Colour the boundary with the shortest length in green. Ans: Colour the shape with the lowest count in green.
c) Tick the shapes with the same length. Ans: Tick shapes with the same number of dots along their boundaries.
Page 93: Let Us Do
Q3: Do any of the following shapes have the same perimeter? Tick them. Ans: Measure each shape’s perimeter using a scale or count sides on a grid. 1. Image A and C are Same: 12 cm 2. Image D, E and F are Same: 14 cm 3. Image B: 10 cm
Q4: Tick the garden with the minimum perimeter.Ans: Measure the perimeter of each garden. Tick the one with the smallest total length.
first fig. perimeter is 18 cm, second is 24 cm, third one is 20 cm.
Page 94: Let Us Do
Q5: Estimate and measure the perimeters of shapes around you using a scale and write them in the space given below.Ans:
Q6: Draw three different shapes with perimeter of 20 cm.Ans:
Ikra and her little sister, Samina, decide to make a drawing, but they are left with a single drawing sheet. Ikra wants to share the paper by dividing it in half, but Samina insists on having a bigger part of the paper. Ikra thought for a moment and proposed a solution.
Q1: Which part of the paper you would have chosen—one half or two quarters? Why? Ans: I would choose one half. One half is the same as two quarters because two quarters (2 × 1/4 = 2/4 = 1/2). Both are equal parts of the paper.
Q2: Do you think Ikra shared the paper equally? Why? Try with a paper. Ans: Yes, Ikra shared the paper equally. One half (1/2) is the same as two quarters (2/4). If you fold a paper in half or into four equal parts and take two parts, the size is the same.
Q3: How do you know that the paper has been divided equally? Ans: The paper is divided equally if each part is the same size. For one half, fold the paper into two equal parts. For two quarters, fold it into four equal parts and take two. Both cover the same area.
Q4: Why do you think Samina chose two quarters of the paper? Ans: Samina chose two quarters because she thought it sounded like a bigger part. She didn’t realize that two quarters (2/4) is the same as one half (1/2).
Page 63: Let Us Do
Q1: Samina has divided some figures into two parts. Colour the figures that are divided into halves correctly. How did you get the answer? Ans: To find halves, each part must be equal in size. Check if the figure is divided into two equal parts. Colour only those figures where both parts are the same size. I got the answer by looking at the shapes and comparing the size of the two parts.
Q2: Divide the shapes into halves by drawing a line. Ans: Draw a line through the middle of each shape so that both parts are equal in size. For example, for a rectangle, draw a vertical or horizontal line to split it into two equal parts.
Page 64: Let Us Do
Q3: Divide these shapes into 4 equal parts/quarters. Ans: Draw lines to split each shape into four equal parts. For a rectangle, draw one vertical and one horizontal line to make four equal rectangles. For a circle, draw two lines through the center to make four equal sections.
Page 64: Let Us Try
Q4: In how many different ways can you fold/cut a rectangular paper in two equal parts? Try it with a rectangular paper. Ans: You can fold or cut a rectangular paper in two equal parts in these ways:
Fold vertically to make two equal rectangles.
Fold horizontally to make two equal rectangles.
Fold diagonally from one corner to the opposite corner to make two equal triangles. There are at least three different ways.
Page 65: Let Us Do
Q2: Now try to draw and show five different ways in which we can fold/cut a rectangle into four equal parts (1/4 or quarter). Ans: Five ways to fold or cut a rectangle into four equal parts:
Draw three vertical lines to make four equal vertical strips.
Draw three horizontal lines to make four equal horizontal strips.
Draw one vertical and one horizontal line to make four equal rectangles.
Draw two diagonal lines from opposite corners to make four equal triangles.
Q3: Match the following parts with their corresponding wholes. Ans:
Page 68: Let Us Discuss
Q1: What is Sumedha observing about her share as each guest comes in? Ans: Sumedha observes that her share of dhokla gets smaller as more guests come. When shared with more people, each person gets a smaller piece.
Q2: In which situation will Sumedha get to eat more dhokla: when shared among 9 people or 11 people? Ans: Sumedha will get more dhokla when shared among 9 people. If the dhokla is divided into 9 parts, each piece is bigger than when divided into 11 parts.
Q3: How many pieces of 1/6 would make a complete dhokla? Ans: Six pieces of 1/6 make a complete dhokla because 6 × 1/6 = 6/6 = 1 whole.
Q4: What would be Sumedha’s share, if Idha and Vinayak both give their share of dhokla to her? Ans: Idha’s share = 1/5 Vinayak’s share = 1/5 Sumedha’s total share = 1/5 + 1/5 + 1/5 = 3/5 So, Sumedha will get 3/5 of the dhokla if both Idha and Vinayak give their share to her.
Page 68: Let Us Do
Q1: How much dhokla would each person get if it was shared equally among 6 people? Try also with 8 people. Who will get the bigger pieces of dhokla? Draw and explain. Ans:
For 6 people: Divide the dhokla into 6 equal parts. Each person gets 1/6 of the dhokla.
For 8 people: Divide the dhokla into 8 equal parts. Each person gets 1/8 of the dhokla.
Explanation: The pieces are bigger when shared among 6 people because 1/6 is larger than 1/8. Draw a circle for the dhokla, divide it into 6 parts, and then into 8 parts to see that 1/6 is bigger.
Page 69: Let Us Do
Q2: Shade a portion of the dhokla to represent the fraction Sumedha would get when the dhokla is shared equally among the given number of people. Discuss why the fractions get smaller. Ans: Divide the dhokla into equal parts based on the number of people and shade one part to show Sumedha’s share. For example, if 4 people, shade 1/4; if 5 people, shade 1/5. The fractions get smaller because as more people share the same dhokla, each person’s share becomes a smaller part of the whole.
Page 69: Let Us Discuss
Q1: Share your observations about the different pieces and the whole. Ans: The whole is the complete object, like a dhokla or paper. When divided into equal pieces, each piece is a fraction of the whole. For example, 1/2 is one of two equal parts, and 1/4 is one of four equal parts. Smaller fractions mean more pieces and smaller sizes.
Q2: Take any two different pieces of the fraction kit and compare them. Discuss which one is smaller and why. Ans: Take two pieces, like 1/3 and 1/4. Compare their sizes. 1/4 is smaller than 1/3 because the whole is divided into more parts (4 parts) for 1/4, so each part is smaller than when divided into 3 parts for 1/3.
Q3: Sumedha noticed that when a whole is equally divided in a larger number of parts, each part gets smaller. Do you agree with Sumedha? Ans: Yes, I agree with Sumedha. When the whole is divided into more parts, each part is smaller. For example, 1/6 is smaller than 1/4 because 6 parts are smaller than 4 parts of the same whole.
Q4: Sumedha says, “When I join 5 pieces of 1/5, it makes a whole dhokla.” Try to do it yourself with your fraction kit.Ans: Yes, Sumedha is correct. Take 5 pieces of 1/5 from the fraction kit. When you join them, they make a whole dhokla because 5 × 1/5 = 5/5 = 1 whole.
Q5: Sumedha says that this part is one-third of the complete whole. Why is she saying so? Ans: Sumedha says it is one-third because the whole is divided into three equal parts, and one part is shaded or taken. One-third (1/3) means one out of three equal parts of the whole.
Page 70: Let Us Try
Q1: ______ is greater than _________. (1/5, 1/4). Ans: 1/4 is greater than 1/5. When the whole is divided into 4 parts, each part (1/4) is bigger than when divided into 5 parts (1/5).
Q2: ________ > __________. (1/9, 1/6). Ans: 1/6 is greater than 1/9. When the whole is divided into 6 parts, each part (1/6) is bigger than when divided into 9 parts (1/9).
Q3: 1/6 _______ 1/8. Ans: 1/6 is greater than 1/8. Same as above, 1/6 is larger because fewer parts mean bigger pieces.
Q4: ______ is smaller than _______ ( ______, _______). Ans: 1/7 is smaller than 1/5.
Page 70: My Flower Garden
Mogra in 1/5 or one-fifth part of the garden. Marigold in part of the garden. Jasmine in 1/5 or one-fifth part of the garden. Rose in 1/5 and 1/5 part or a total of 2/5 (two-fifths) part of the garden. 1/5 or one-fifth Ans: The garden is divided into 5 equal parts (1/5 each).
Mogra: 1/5
Lily: 1/5
Marigold: 1/5 (since 4 parts are used by Mogra, Rose, and Jasmine, 1 part remains)
Jasmine: 1/5 (one of the remaining parts)
Rose: 1/5
Page 70: Look at the garden and answer the questions.
Mogra in part…….. Marigold in part……… Rose in 1/5 + 1/5 + 1/5 part or a total of 3/5 (three-fifths) part……… Ans:
Mogra: 1/5 (one of the remaining parts)
Marigold: 1/5 (one of the remaining parts)
Rose: 3/5 (given as 1/5 + 1/5 + 1/5 = 3/5)
Look at the garden and answer the questions.
a) Marigold in ……….. Ans: The garden is divided into 5 equal parts (1/5 each).
Marigold: 1/5
b) Rose: 4/5 (given as 1/5 + 1/5 + 1/5 + 1/5 = 4/5): True
Page 71: Let Us Do
Make a flower garden with seven flowering seeds—Mogra, Marigold, Jasmine, Rose, Lily, Hibiscus, and Periwinkle?
Ans:
Page 73: Do It Yourself
Write the fractions for each of the toppings in the following dosas. Ans:
Make a dosa with 2/3 topping of Spicy onion, 1/3 of Classic potato. Ans: Divide the dosa into 3 equal parts. Shade 2 parts for Spicy onion (2/3) and 1 part for Classic potato (1/3).
Make a dosa with 2/3 of Classic potato, 1/8 of Chilly paneer and 4/5 of Tangy tomato mix. Ans: This seems incorrect as 2/3 + 1/8 + 4/5 exceeds 1. Assuming a typo, a possible correction is: Divide the dosa into 24 equal parts (LCM of 3, 8, 5). Shade 16/24 for Classic potato (2/3), 3/24 for Chilly paneer (1/8), and 19/24 for Tangy tomato (≈4/5, adjusted).
Page 73: Let Us Explore
Meena has 8 diyas. Colour 1/4 of her diyas red. To find 1/4, let us divide the number of diyas into 4 equal parts. Can you see how to divide the diyas into 4 equal parts? Now colour 2 diyas red. Ans: Divide 8 diyas into 4 equal parts: 8 ÷ 4 = 2 diyas per part. One-fourth (1/4) of 8 is 2 diyas. Colour 2 diyas red.
Page 74: Let Us Do
Now let us try to find fractions for the situations given below. Circle the appropriate parts in the pictures. Q1: There are 12 cookies. What fraction of cookies will each get if the number of children are as follows: a) 3 children Ans: 12 ÷ 3 = 4 cookies each. Fraction: 4/12 = 1/3.b) 6 children Ans: 12 ÷ 6 = 2 cookies each. Fraction: 2/12 = 1/6.c) 2 children Ans: 12 ÷ 2 = 6 cookies each. Fraction: 6/12 = 1/2.d) 4 children Ans: 12 ÷ 4 = 3 cookies each. Fraction: 3/12 = 1/4.
Q2: Simran calls her school friends for her birthday party. 1/3 of her friends receive a hairband as their return gift. Place hairbands on 1/3 of her friends. Ans: Count the number of friends. Divide by 3 to find 1/3. Place hairbands on that many friends. For example, if 9 friends, 1/3 = 3 friends get hairbands.
Q3: Draw flowers in 1/5 of the given number of pots. Ans: Count the number of pots. Divide by 5 to find 1/5. Draw flowers in that many pots. For example, if 15 pots, 1/5 = 3 pots with flowers.
Page 75: Let Us Find Fractions in Our Surroundings
Q1: Yesterday, Mummy asked to divide a box of barfis into four equal parts. There are 16 barfis in the box. Draw a picture of 16 barfis and find 1/4 of the whole. How many barfis are in each part? Ans: Draw 16 barfis in a 4×4 grid. Divide into 4 equal parts: 16 ÷ 4 = 4 barfis per part. One-fourth (1/4) is 4 barfis.
Q2: Rohan has a piece of ribbon to decorate his notebook. Mohan’s ribbon is one-fourth as long as Rohan’s ribbon. How long will Rohan’s ribbon be? Draw it.
Ans: If Mohan’s ribbon is 1/4 of Rohan’s, Rohan’s ribbon is 4 times Mohan’s. Draw Rohan’s ribbon 4 times longer than Mohan’s. For example, if Mohan’s is 1 cm, Rohan’s is 4 cm.
Page 75: Try Yourself
Observe your surroundings and think of situations where we use fractions, and write any two of them in the space provided below. Ans:
Dividing a pizza into 8 equal slices, each slice is 1/8.
Sharing 12 chocolates among 4 friends, each gets 3/12 = 1/4.
Page 76: Let Us Do
1. Take a rectangular piece of paper and fold the paper into three equal parts and then unfold it.
2. Colour one of the three equal parts as shown in the image.
3. Fold the paper back into three equal parts like before, and then fold it in half.
4. Observe the colored part. What is the fraction for the shaded part now? What does this mean?
5. Fold the paper again and check how the coloured part changes.
6. Write down what fraction you observe after each fold.
1/3 = 2/6 = ______ = ______ =______ Ans: Do it Yourself!
Page 77: Let Us Try
Take another piece of paper and try the same starting with two equal parts, and halving every time. Share the findings with your friends. Ans: Take a piece of paper. Fold it in half to make 2 equal parts. Fold it in half again to make 4 equal parts. Keep folding in half each time. You get 8 parts, then 16 parts, then 32 parts. Each fold makes twice as many parts as before.
1/2 = 2/4 = 4/8 = 8/16 = 16/32
Page 77: Let Us Discuss
Observe the fraction chart and discuss the following questions.
Q1: How many 1/4 s are equal to 1/2? Ans: Two 1/4s equal 1/2 because 1/4 + 1/4 = 2/4 = 1/2, then answer is 2.
Q2: Is 2/3 less than or greater than 1/2? Ans: 2/3 is greater than 1/2. Compare: 2/3 = 4/6, 1/2 = 3/6. Since 4/6 > 3/6, 2/3 is greater.
Q3: Ten pieces of 1/10 make a complete whole. Is this statement true? Ans: Yes, true. Ten pieces of 1/10 make 10/10 = 1 whole.
Q4: Three pieces of 1/6 are equal to two pieces of 1/8. Is this true? Ans: No, not true. Three pieces of 1/6 = 3/6 = 1/2. Two pieces of 1/8 = 2/8 = 1/4. Since 1/2 ≠ 1/4.
Q5: How many pieces of 1/8 make 1/4? Ans: Two pieces of 1/8 make 1/4 because 1/8 + 1/8 = 2/8 = 1/4.
Q6: Find the pieces that you can put together to make another bigger piece.
Ans: Do it Yourself!
Page 78: Let Us Do
Q1: Bablu is playing with square shapes. He wants to cut them in such a way that each piece is equal in size. Circle the squares that have been cut into equal parts. Write the fraction for the shaded part, whenever possible. Ans: Circle the squares where each piece is the same size. For example, if a square is divided into four equal parts and one is shaded, the fraction is 1/4. If it’s not equal, don’t circle it.
Q2: Check if the children’s claim below about the shaded parts of each of the pictures is correct. Circle the ones which you think are correct, cross out the ones which are not correct. You can draw additional lines to make the parts equal. Discuss your thinking. Ans: Do it Yourself!
Q3: Identify the fractions represented by the coloured parts in the given pictures.
Q4: Identify the fraction of the whole that the blue parts make in each of the pictures given below. Ans: Count the total parts and the blue parts. For example, if 3 out of 4 parts are blue, the fraction is 3/4.
Q5: Divide the following into equal parts and shade the appropriate parts in each. Ans:
Munna: ₹750 ÷ ₹50 = 15 notes
Chinnu: ₹750 ÷ ₹5 = 150 coins
Sansu: ₹750 ÷ ₹2 = 375 coins
Vertices: 1, 2, 3; Sides: 4, 5, 6
Fold vertically to make two equal rectangles.
Fold horizontally to make two equal rectangles.
Fold diagonally from one corner to the opposite corner to make two equal triangles.
Draw two diagonal lines from opposite corners to make four equal triangles.
Explanation: The pieces are bigger when shared among 6 people because 1/6 is larger than 1/8. Draw a circle for the dhokla, divide it into 6 parts, and then into 8 parts to see that 1/6 is bigger.
