Mathematics for Class 5 ( Maths Mela ) Solutions

PageNo. 113

Match the map and Photo:Q1: Have you seen a map? Look at the Map. Match it with the photo and find out where India Gate is. Draw it on the map.
Sol: Yes, I have seen a map.

Q2: Name roads that you will cross on your way from Rashtrapati Bhawan to India Gate.
Sol: The roads that I will come across on my way from Rashtrapati Bhawan to India Gate are Rafi Marg, Janpath and Tilak Marg.

Q3: Look for the National Stadium in Map 1. Can you see it in the photo?
Sol: The National Stadium is seen in Map 1, but cannot be seen in the photo.

Page No. 114

The Central hexagon
If we zoom in to look more closely at one part of the map, it looks like this.

Find out from the map:
Q1: If you are walking on Rajpath then after India Gate on which side would Children’s Park be?
Sol: The Children’s Park would be on the right side, while walking on Rajpath.

Q2: Which of these roads make the biggest angle between them?
(a) Man Singh Road and Shahjahan Road
(b) Ashoka Road and Man Singh Road (the angle away from India Gate)
(c) Janpath and Rajpath
Sol: Ashoka Road and Man Singh Road

Q3: Which of the above pairs of roads cut at right angles?
Sol: Janpath and Rajpath cut at right angles.

Page No. 115

Waiting for the parade

While waiting for the parade, Kancha and some of his friends wonder where this parade ends. Vijay Chowk — Rajpath — India Gate — Tilak Marg — B.S. Zafar Marg — Subhash Marg — Red Fort. Kancha is carrying a newspaper in which the route of the parade is written —

Page No. 116

Mark the route:
Q1: Trace the route of the parade in Map 3 and mark India Gate and Rajpath
Sol: The route of the parade is traced below.

Q2: Look at the map carefully and find out:
(a) Which of these is the longest road?
(i) B S Zafar Marg 
(ii) Subhash Marg
(iii) Tilak Marg
Sol: Subhash Marg is the longest road among them.

(b) If Rubia is coming from Jama Masjid to join the parade, guess how far she has to walk.
Sol: We know that the route of the parade through Subhash Marg and the Jama Masjid is 1 cm away from the Subhash Marg on the map.
In given map the scale is 2 cm = 1 km so, 1 cm = 0.5 km
We know that, 1 km = 1000 m so, 0.5 km = 500 m
Thus, Rubia will have to walk about 500 m to join the parade

(c) The total route of the parade is about how long?
(i) 3km 
(ii) 16km 
(iii) 25 km 
(iv) 8km
Sol: The total distance of the parade on the map is 16 cm.
And we know that, 2 cm on map = 1 km Thus, 16 cm = 8 km
So, the total route of the parade will be about 8 km.

Page No. 117

Trip to Red Fort

Page No. 118

Find out from Map 4
Q1: Which of these is nearer to river Yamuna? — The Diwan-e-Aam or the Diwan-e-Khaas?
Sol: Diwan-e-Khaas is nearer to river Yamuna than Diwan-e-Aam.

Q2: Between which two buildings is Aaram Gah?
Sol: Aaram Gah is between Diwan-e-Khaas and Rang Mahal.

Q3: Which buildings do you pass while going from Rang Mahal to the Hammam?
Sol: We will pass through Aram Gah and Diwan-e-Khaas while going from Rang Mahal to the Hammam.

Q4: Which building on this map is farthest from Meena Bazar?
Sol: Hammam is farthest from Meena Bazar.

Q5: About how far is Lahori Gate from Diwan-e-Khaas?
Sol: The map distance of Lahori Gate from Diwan-e-Khaas is about 6 cm.
We know 1 cm = 100 m
So, the ground distance of Lahori Gate from Diwan-e-Khaas = 6 ×100 = 600 m

Page No. 119

Make it bigger, make it smaller

Here are some pictures drawn on a 1cm square grid. Try making the same pictures on a 2 cm grid and also on a ½ cm grid.

The side of the square was made two times bigger. Does its area also become two times bigger?
Sol: Suppose the original length of the side of the square is 1 cm. Now, area of square = side × side = 1 × 1 square cm = 1 square cm
When the side of the square is made two times bigger, then the new length of the side of the square will be 2 cm Area of square = side × side = 2 × 2 square cm = 4 square cm
So, when the side of the square is made 2 times bigger, then its area becomes 4 times bigger than the original area.

Page No. 120

Dancers from Different States

Page No. 121 

Look at the map of India below and find the states these children are talking about. Answer the questions.Q1: The Karnataka team starts from Bangalore and moves in the north direction. Which states does it cross to reach Delhi?
Sol: Maharashtra, Madhya Pradesh and Rajasthan.

Page No. 122

Q2: Jammu and Kashmir is to the north of Delhi so the team from there travels towards south to reach Delhi. Which states does it cross?
Sol: Himachal Pradesh, Punjab and Haryana.

Q3: Nonu lives in Gujarat. Nonu’s friend Javed lives in West Bengal. Nonu wants to visit his friend. In which direction will he travel?
(a) Towards west
(b) Towards east 
(c) Towards south 
(d) Towards north
Sol: Towards the east

Q4: Is there any state which is to the north of Jammu and Kashmir?
Sol: No, there is no state which is to the north of Jammu and Kashmir.

Q5: Is there any state which is to the west of Gujarat?
Sol: No, there is no state which is to the west of Gujarat.

Q6: If 1 cm on the map shows 200km on the ground, use this scale to find out:
(A) About how far is Delhi from Jaipur?
(i) 50 km 
(ii) 500 km 
(iii) 250 km
Sol: 250 km

(B) Estimate how far Jaipur is from Bhopal.
On the map = _______ cm.
On the ground = _______ km
Sol: On the map = 2cm.
On the ground = 400km

Q7: Look at the map and tell:
(a) Which state is surrounded by four other states?
Sol: Madhya Pradesh
(b) Which state has the largest area? If its name is not in the map, find it from your teacher or parents. Explain how you got your answer.
Sol: Rajasthan. This can be observed from the given map.
(c) Which state is about 8 times bigger in area than Sikkim?
(i) Uttar Pradesh
(ii) Tripura
(iii) Maharashtra
(iv) Himachal Pradesh
Sol: Himachal Pradesh
(d) About how many times of Punjab is the area of Rajasthan?
Sol: Rajasthan is about 7 times the area of Punjab.

Page No. 123

The sea

Bala is standing on the sea-coast and looking at the vast sea. The sea looks endless.

Q1: Have you seen the sea? In the picture where is the sea? Now look for the sea in the map of India. What colour is used to show the sea?
Sol: Yes, I have seen the sea. The blue colour represents the sea in the given picture. The blue colour is used to show the sea on the map of India.

Q2: Mark those states which have the sea on one side.
Sol: The red colour dot shows states which have the sea on one side in below-given map.

Q3: Name one state which does not have the sea on any side.
Sol: Madhya Pradesh

Page No.124

Distance between towns

These are five towns. Find out:
Q1: How many cm away is Idlipur from Barfinagar on the map?
Sol: The distance between Idlipur and Barfinagar is 5 cm on the map.

Q2: How many kilometers will you have to travel if you travel from Idlipur to Barfinagar?
Sol: Given, the scale is 1 cm = 10 km
Distance between Idlipur and Barfinagar on the map = 5 cm
Now, actual distance between Idlipur and Barfinagar = 5 × 10 = 50 km
Thus, we have to travel 50 km to go from Idlipur to Barfinagar.

Q3: There is a place called Thukpagram midway between Idlipur and Barfinagar. Mark it with a ‘T’.
Sol:

Q4: A town called Jalebipur is 35 km away from both Chholaghat and Dhoklabad. Where do you think it can be? Mark ‘J’ for it.
Sol:

Ashi’s School

Ashi’s school looks like this from the top.
Use the squares to find out:

Q1: How many times bigger is the area of the Assembly ground than that of the office?
Sol: The area of the assembly ground is five times bigger than that of the office.

Q2: How much is the length and width of each classroom?
(a) Length 5 m, width 4 m
(b) Length 2 m, width 1 m
(c) Length 12 m, width 10 m
(d) Length 5 m, width 5 m
Sol: Length 5 m, width 4 m

Q3: All the classrooms in Ashi’s school look like this.

Look carefully and answer.
(a) Which of these is exactly opposite to the blackboard?
 Almirah, windows, notice board, display board
Sol: The display board is exactly opposite to the blackboard.

(b) Can a child sitting in III A see the playground?
Sol: No, a child sitting in III A cannot see the playground

Page 57

Let Us Find

Identify the appropriate units for measuring each of the following.

Answer: 

Different Units but Same Measure

Shikha and Sonu are measuring the lengths of saris and stoles in the village weaving centre. Find which measures represent the same sari or stole. You can take help of the double number line below.

Answer:
Based on the conversion 

100 cm & 1 m

200 cm & 2 m
400 cm & 4 m
500 cm & 5 m
700 cm & 7 m

Therefore, the measures that represent the same sari or stole are:

• 204 cm and 2 metre 4 cm

• 540 cm and 5 metre 40 cm

• 750 cm and 6 metre 150 cm

• 240 cm and 2 metre 40 cm

• 404 cm and 2 metre 204 cmPage 58

Let Us Compare

1.Ritika is comparing the lengths of different rods. Compare them using <, =, > signs.

(a) 456 cm ____ 5 m
Answer: 456 cm < 5 m (since 5 m = 500 cm)

(b) 55 cm + 200 cm ____ 200 cm + 54 cm
Answer: 55 cm + 200 cm > 200 cm + 54 cm (since 255 cm > 254 cm)

(c) 6 m 5 cm ___ 6 m 50 cm
Answer: 6 m 5 cm < 6 m 50 cm (since 605 cm < 650 cm)

(d) 2 m 150 cm ___ 3 m 50 cm
Answer: 2 m 150 cm < 3 m 50 cm (since 350 cm < 350 cm is false, 2m 150cm = 350cm, 3m 50cm = 350cm, so 2 m 150 cm = 3 m 50 cm)

(e) 238 cm ____ 138 cm + 1 m
Answer: 238 cm = 138 cm + 1 m (since 138 cm + 100 cm = 238 cm)

2. World’s tallest statue

​

(a) What is the difference between the height of the tallest statue in the world and the Statue of Liberty?
Answer: Tallest statue in the world (from the given list) is Unity, India (182 m). 
Height of Statue of Liberty is 93 m. 
Difference = 182 m – 93 m = 89 m.

(b) Identify the statues whose heights have the least difference.
Answer: Let’s list the heights: Unity, India: 182 m 
Spring Temple Buddha, China: 128 m 
Guanyin of Nanshan, China: 108 m 
Christ the Redeemer, Brazil: 38 m 
The Motherland Calls, Russia: 91 m Statue of Liberty, USA: 93 m

Differences: Statue of Liberty (93m) and The Motherland Calls (91m): 93 – 91 = 2 m (Least difference)

(c) Identify the statues whose heights have the largest difference.
Answer: Largest difference would be between the tallest and the shortest. 
Tallest: Unity, India (182 m) Shortest: Christ the Redeemer, Brazil (38 m) 
Difference = 182 m – 38 m = 144 m (Largest difference)

(d) The height of which Statue will be equal to the height of the Statue of Unity, if it is doubled?
Answer:
Height of Statue of Unity = 182 m. We need to find a statue whose height, when doubled, equals 182 m. 182 m / 2 = 91 m. 
The Statue of The Motherland Calls, Russia has a height of 91 m. 
So, if its height is doubled, it will be equal to the height of the Statue of Unity.Page 59

Let Us Do

Measure 100 m and 200 m on your school playground, or any other place in and around your school, using a Long Tape. Mark these points and draw a straight line. Walk on the lines and count the number of steps. Use this relationship between the number of steps taken and distance walked to find distances around you for at least 3 locations. Wherever possible, walk and find the number of steps. Otherwise, find the distance and estimate the number of steps.

(a) Identify and write the locations that are the nearest and the farthest from your home. 
Nearest location _______________________________________________________ 
Farthest location _______________________________________________________

Answer: Nearest location: Local grocery store 500 m
Farthest location: Grandparent’s house 5 km

(b) Write the distances obtained above in increasing order.
 _______________, _________________, _________________, __________________.

Answer: 500 m, 1 km, 2 km, 5 km

(c) Name a location that is equal to or more than 1,000 m from your home.

Answer: Local park 1500 m

Let Us Explore

When we walk 1,000 m, we say we have walked 1 km. 1,000 m = 1 km 
Kilo stands for thousand. This unit is used to measure long distances.

Question: Number of ropes needed to make 1 km

Page 60

Kilometre Race

Sheena and Jennifer are helping to organise a 3-km race. Help them with the arrangements for the race.

1.Water stations are to be arranged after every 500 m. How many water stations must be set up? At what positions from the starting point will these water stations be placed?

Answer: Total race distance = 3 km = 3000 m. Water stations every 500 m. 
Number of water stations = Total distance / Interval = 3000 m / 500 m = 6. 
Positions: 500 m, 1000 m (1 km), 1500 m (1.5 km), 2000 m (2 km), 2500 m (2.5 km), 3000 m (3 km – finish line). 
So, 6 water stations will be set up at 500 m, 1 km, 1.5 km, 2 km, 2.5 km, and 3 km from the starting point.

2. Children need to stand at an interval of 300 m to direct the runners. How many children are needed? At what positions from the starting point will the children be standing?

Answer: Total race distance = 3 km = 3000 m. Children every 300 m. 
Number of children = Total distance / Interval = 3000 m / 300 m = 10. 
Positions: 300 m, 600 m, 900 m, 1200 m (1.2 km), 1500 m (1.5 km), 1800 m (1.8 km), 2100 m (2.1 km), 2400 m (2.4 km), 2700 m (2.7 km), 3000 m (3 km – finish line). 
So, 10 children are needed at 300 m, 600 m, 900 m, 1.2 km, 1.5 km, 1.8 km, 2.1 km, 2.4 km, 2.7 km, and 3 km from the starting point.

3. Red and blue flags are to be placed alternately at every 50 m. How many red and blue flags are needed till the finish line?

Answer:
Total race distance = 3 km = 3000 m. Flags every 50 m. 
Number of flag positions = Total distance / Interval = 3000 m / 50 m = 60. 
Since flags are placed alternately, there will be 30 red flags and 30 blue flags.

Let Us Do: Longest Train Journey

The longest train journey in India is by The Vivek Express which runs from Dibrugarh in Assam to Kanniyakumari in Tamil Nadu. Look at the stations on the route shown in the table below and answer the questions.

1. The total length of the route from Dibrugarh to Kanniyakumari is _______________ km.

Answer: The total length of the route from Dibrugarh to Kanniyakumari is 4,187 km (distance of Kanniyakumari from Dibrugarh).

2. The distance between Vijayawada and Jalpaiguri road is _______________.

Answer: Distance of Vijayawada JN from Dibrugarh = 2,800 km
Distance of Jalpaiguri Road from Dibrugarh = 983 km 
Distance between Vijayawada and Jalpaiguri Road = 2,800 km – 983 km = 1,817 km.

3. Distance between Vijayawada and Visakhapatnam is _______________.

Answer: Distance of Vijayawada JN from Dibrugarh = 2,800 km 
Distance of Visakhapatnam from Dibrugarh = 2,450 km 
Distance between Vijayawada and Visakhapatnam = 2,800 km – 2,450 km = 350 km.

4. Which two stations are farther apart — Guwahati and Dimapur or Bhubaneswar and Jalpaiguri Road?

Answer: Distance between Guwahati and Dimapur: Guwahati = 556 km, Dimapur = 306 km 
Difference = 556 km – 306 km = 250 km.

Distance between Bhubaneswar and Jalpaiguri Road: Bhubaneswar = 2,007 km, Jalpaiguri Road = 983 km 
Difference = 2,007 km – 983 km = 1,024 km.

Comparing 250 km and 1,024 km, Bhubaneswar and Jalpaiguri Road are farther apart.

5. What is the distance between Guwahati and Coimbatore JN?

Answer: Distance of Coimbatore JN from Dibrugarh = 3,675 km 
Distance of Guwahati from Dibrugarh = 556 km 
Distance between Guwahati and Coimbatore JN = 3,675 km – 556 km = 3,119 km.Page 62

Let Us Do

Soak some seeds of whole moong or black or white chana overnight. Next morning, take them out and wrap them in a moist cloth to sprout them. Over the next 4 days, take out one seed each day and measure the length of sprout. For ease of measurement, you can either place the seed on a paper and mark the length of the sprout, or use a thread to find its length.

Answer: 

​

Let Us Draw

Draw lines of the following lengths in your notebook using a scale.

1.5 cm 5 mm

2.3 cm 6 mm

3.8 cm 3 mm

4.36 mm

5.67 mm

How did you draw lines of lengths 36 mm and 67 mm? Share your thoughts in class.

Answer: 

To draw lines of lengths 36 mm and 67 mm:

• For 36 mm: Since 10 mm = 1 cm, 36 mm is equal to 3 cm and 6 mm. So, place the scale on the notebook, mark a starting point, and then draw a line up to the 3 cm mark and then 6 small divisions (mm) further.

• For 67 mm: Similarly, 67 mm is equal to 6 cm and 7 mm. Place the scale, mark a starting point, and draw a line up to the 6 cm mark and then 7 small divisions (mm) further.Page 63

Let Us Do

1.Fill in the blanks appropriately in the double number lines given below.

Answer:

Answer:

Answer:

2. Use your understanding from above to fill in the blanks appropriately.

(a) 4 cm 5 mm = ______ mm
Answer: 4 cm 5 mm = 40 mm + 5 mm = 45 mm

(b) 89 mm = ____ cm ____ mm
Answer: 89 mm = 80 mm + 9 mm = 8 cm 9 mm

(c) 234 cm = ____ mm
Answer: 234 cm = 234 × 10 mm = 2340 mm

(d) 514 mm = ____ cm ____ mm
Answer: 514 mm = 510 mm + 4 mm = 51 cm 4 mm

(e) 6 m 34 cm = ____ cm
Answer: 6 m 34 cm = 600 cm + 34 cm = 634 cm

(f) 20 m 12 cm = ____ cm
Answer: 20 m 12 cm = 2000 cm + 12 cm = 2012 cm

(g) 397 m = ______ cm
Answer: 397 m = 397 × 100 cm = 39700 cm

(h) 5,792 cm = ______m ______ cm
Answer: 5,792 cm = 5700 cm + 92 cm = 57 m 92 cm

(i) 9,108 cm = ______ m ______ cm
Answer: 9,108 cm = 9100 cm + 8 cm = 91 m 8 cm

(j) 34 km = _______ m
Answer: 34 km = 34 × 1000 m = 34000 m

(k) 6,870 m = ____ km ____ m
Answer: 6,870 m = 6000 m + 870 m = 6 km 870 m

(l) 10,552 m = ____ km ___ m
Answer: 10,552 m = 10000 m + 552 m = 10 km 552 m

(m) 29 km 30 m = ____ m
Answer: 29 km 30 m = 29 × 1000 m + 30 m = 29000 m + 30 m = 29030 m

(n) 32 km 359 m = ____ m
Answer: 32 km 359 m = 32 × 1000 m + 359 m = 32000 m + 359 m = 32359 mPage 66

Let Us Do

1.Rani has two red-coloured ribbon rolls, one of length 3 m 75 cm and another 2 m 25 cm long. How much ribbon does she have?

Answer:
Length of first ribbon =        3 m 75 cm 
Length of second ribbon = 2 m 25 cm

Total ribbon = (3 m + 2 m) + (75 cm + 25 cm) 
Total ribbon = 5 m + 100 cm 
Since 100 cm = 1 m, Total ribbon = 5 m + 1 m = 6 m.

2. The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on the way, and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?

Answer: Total distance from Bhopal to Sanchi =              48 km 700 m 
Distance from Bhopal to Bhadbhada Ghat waterfall = 17 km 900 m

Distance from Sanchi to the waterfall = Total distance – Distance to waterfall

    km   m 
   48   700

 -17   900

We cannot subtract 900 m from 700 m. So, we borrow 1 km (1000 m) from 48 km.

    km   m 
   47  1700 (borrowed 1km = 1000m from 48km)

– 17   900

————-

30   800

So, Sanchi is 30 km 800 m from the waterfall.

3. Gulmarg Gondola in Gulmarg, Kashmir is the second longest and second highest cable car in the world. It is divided into two sections. The first section covers 2 km 300 m and the second section covers 2 km 650 m. What is the total distance covered by the cable car?

Answer:
Length of first section =        2 km 300 m 
Length of second section = 2 km 650 m

Total distance = (2 km + 2 km) + (300 m + 650 m) 
Total distance = 4 km + 950 m Total distance = 4 km 950 m.

4. Circle the bigger length and find the difference.

(a) 11 mm and 1 cm Difference — ________________
Answer: 1 cm = 10 mm. So, 11 mm is bigger. Difference = 11 mm – 10 mm = 1 mm.

(b) 26 mm and 2 cm Difference — ________________
Answer: 2 cm = 20 mm. So, 26 mm is bigger. Difference = 26 mm – 20 mm = 6 mm.

(c) 20 cm and 201 mm Difference — ________________
Answer: 20 cm = 200 mm. So, 201 mm is bigger. Difference = 201 mm – 200 mm = 1 mm.

(d) 1,020 mm and 1m Difference — ________________
Answer: 1 m = 1000 mm. So, 1,020 mm is bigger. Difference = 1020 mm – 1000 mm = 20 mm.

(e) 2 m and 245 cm Difference — ________________
Answer: 2 m = 200 cm. So, 245 cm is bigger. Difference = 245 cm – 200 cm = 45 cm.

(f) 5,678 m and 6 km Difference — ________________
Answer: 6 km = 6000 m. So, 6 km is bigger. Difference = 6000 m – 5678 m = 322 m.

(g) 6 km 1,480m and 7 km 479m Difference — ________________
Answer:6 km 1,480 m = 6 km + 1 km 480 m = 7 km 480 m. Comparing 7 km 480 m and 7 km 479 m, 6 km 1,480 m is bigger. Difference = 7 km 480 m – 7 km 479 m = 1 m.Page 67

Multiplying and Dividing Lengths 

1.A shop sells cloth for making bags at ₹100 for 5 m. How much money is needed to buy a 1 m cloth?

Answer: Cost of 5 m cloth = ₹100 Cost of 1 m cloth = ₹100 ÷ 5 = ₹20.

Now, use the double number line to find the cost of the cloth or the length of cloth that we can buy at a particular cost.

3. Anita is making an embroidery on the border of a sari. She needs a 1 m long thread to embroider a 50 cm sari. How much thread would she need for a 5 m sari border?

A 1 m long thread costs ₹50. How much money will be needed to buy the thread?

Answer: 
Thread needed for 50 cm sari = 1 m

First, convert 5 m sari border to cm: 5 m = 500 cm.

If 50 cm sari needs 1 m thread, then 500 cm sari (which is 10 times 50 cm) will need 10 times the thread. Thread needed for 5 m (500 cm) sari = 10 × 1 m = 10 m.

Cost of 1 m thread = ₹50 Cost of 10 m thread = 10 × ₹50 = ₹500.

4. A road 12 km 600 m long is being laid in a town. The workers lay an equal length of road each day, and complete the work in 6 days. How much road-laying work is done on each day?

Answer:
Total length of road = 12 km 600 m 
Number of days to complete work = 6 days

Convert total length to meters: 12 km 600 m = 12 × 1000 m + 600 m = 12000 m + 600 m = 12600 m.

Length of road laid each day = Total length / Number of days = 12600 m / 6 = 2100 m

Convert back to km and m: 2100 m = 2000 m + 100 m = 2 km 100 m.

So, 2 km 100 m of road-laying work is done each day.

Page 33

A giant wheel makes a full turn when it comes back to the starting position E. Reema takes two half turns in the same direction. It is like a full turn.

What happens if she takes 2 quarter turns in the same direction? It is like a half turn.

What happens if she takes 4 quarter turns in the same direction? It is like a full turn.

Write some of the everyday objects that involve turns. For example, taps, door knobs, screwdrivers, wheels, keys, and jar lids.

What is the maximum possible turn in each of these cases? Check and tick.

Let Us Do (Page 35)

Question (b): You might have built houses using the hard covers of notebooks or cardboard pieces. Look at the angles marked in the house. What angles are you able to see in this house? Write your answers as right, acute or obtuse angle.

Answer: A: Obtuse angle B: Right angle C: Acute angle D: Acute angle E: Acute angle F: Right angle G: Right angle H: Obtuse angle

Question (c): Make a 5-sided shape with 2 right angles, 2 obtuse angles, and 1 acute angle in your notebook.

Answer: 

Look at the angle formation between the legs of these gymnasts. Identify whether the angles are acute, obtuse, right or straight.

Answer:

Let Us Think

In the following circles, the end points of  turns are shown. Draw arrows to show the starting points.

Answer:

Let Us Do (Page 38)

Question 1: Guess the measures of each of the angles shown below. Then, check using your angle measuring tools. You may need to use a combination of measures. Also, state whether each of the angles is acute, right, or obtuse.

Answer: 

2. Guess the measure of the turns made by the arrow in each of the following cases. Verify with a combination of angle measuring tools.

Answer:

​

Let Us Do (Page 39)

4: Draw angles for the given measures of turns using the given lines. 

Answer:

6: Guess the measure of turns the minute hand of a clock makes in each of the following cases. The initial position of the minute hand is given. Draw the final position of the minute hand on the clock face. Discuss your reasoning in class.

(a) When the minute hand moves by 15 minutes, it has made a _______ turn of the circle. 
(b) When the minute hand moves by 30 minutes, it has made a _______ turn of the circle. 
(c) When the minute hand moves by 45 minutes, it has made a _______ turn of the circle. 
(d) When the minute hand has turned by 1/12 of a full turn, it has moved by ______ minutes. 
(e) When the minute hand has turned a full-circle, it has moved by ______ minutes.

Answer:

Let Us Do (Page 40)

(f) When the minute hand has turned by 1/6 of a full turn, it has moved by _____ minutes. 
(g) When the minute hand has turned by 4/12 of a full turn, it has moved by _____ minutes.

Answer:

Which direction? (Page 40)

The creatures below have made a quarter turn once. Tick the direction in which they have moved.

​Answer:

​

Try these (Page 40)

Question: Observe the direction of movement while opening a tap, unscrewing a lid or loosening a nut. Do they move clockwise or anti-clockwise?

Answer:

• Opening a tap: Usually anti-clockwise (lefty loosey, righty tighty).

• Unscrewing a lid: Anti-clockwise.

• Loosening a nut: Anti-clockwise.

Fun with Turns (Page 9)

1. The children in a class are playing a game in which the teacher tells them the direction in which they should rotate. Complete the table by filling the direction the children will face on completing the given turns. The starting direction is given in the table.

Answer:

2. Padma is facing the toy shop. What place will she face if she takes a half turn clockwise?

Answer: She will face the ice cream side

What other way can she turn to face the same place?

Answer: She can turn a half turn anti clockwise to face the same side.

usually not a full turn without special hinges or breaking.)

Page 19Let Us Do

Question 1: In groups of 3 or 4, find different ways of making a whole with different fraction pieces from your kit. Write the equivalent fractions for the following that you may find in the process.

Answer:  
Examples of equivalent fractions are: 

Question 2: Find the following using your kit. You can also shade and check by shading the following. The first one is partially done for you.

A. How many 16
s make 1
3?

Answer: The shaded part is 1
3. Identify16 in the same whole and find how many 16s fit into1
3? (Answer: Two 16s make 13
).

B. How many 1/8s make (a) 1/4? (b) 1/2?

a) 

b)

Answer: (a) Two 1/8s make 1/4. (b) Four 1/8s make 1/2.

C. How many 1/12s make (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6?

Answer: (a) Six 1/12s make 1/2. (b) Four 1/12s make 1/3. (c) Three 1/12s make 1/4. (d) Two 1/12s make 1/6.

Page 21Let Us Do

Question 1: Fill in the blanks with equivalent fractions. There may be more than one answer.

(a) 1/7 = _____ (b) 2/3 = _____ (c) 3/4 = _____ (d) 3/5 = _____

Answer: 
(a) 1/7 = 2/14 (or 3/21, 4/28, etc.) 
(b) 2/3 = 4/6 (or 6/9, 8/12, etc.) 
(c) 3/4 = 6/8 (or 9/12, 12/16, etc.) 
(d) 3/5 = 6/10 (or 9/15, 12/20, etc.)

Question 2: Put a tick against the fractions that are equivalent.

(a) 2/3 and 3/4 (b) 3/5 and 6/10 (c) 4/12 and 2/6 (d) 6/9 and 1/3

Answer:
(a) 2/3 and 3/4 (Not equivalent) 
(b) 3/5 and 6/10 Equivalent, because 3 x 2=6 and 5 x 2=10) 
(c) 4/12 and 2/6 Equivalent, because 2 x 2=4 and 6 x 2=12 
(d) 6/9 and 1/3 (Not equivalent) 

Question 3: Fill in the boxes such that the fractions become equivalent.

(a) 2/5 = /10 (b) 3/4 = /16 (c) 4/7 = 8/(d) 5/9 = 25/

Answer:
(a) 2/5 = 4/10 (because 5 x 2=10, so 2×2=4) 
(b) 3/4 = 12/16 (because 4×4=16, so 3×4=12) 
(c) 4/7 = 8/14 (because 4×2=8, so 7×2=14) 
(d) 5/9 = 25/45 (because 5×5=25, so 9×5=45)

Page 22Let Us Do

Question 1: Compare the fractions given below using < and > signs.

Answer:

Page 23Let Us Do

Question 1: Compare the following fractions using < and > signs.

Answer:

Let Us DoPage 28

Question 2: Circle the fractions that are greater than one (whole). How do you know? Discuss your reasoning in the class.

Answer: Fractions greater than one are those where the numerator is greater than the denominator.

Page 29Let Us Do

1. Compare the following fractions using 1 as a reference. Share your reasoning in the class.

​Answer:

Let Us Do Page 30

Question 1: Circle the fractions below that are equal to 1/2.

Answer: Fractions equal to 1/2 are those where the numerator is exactly half of the denominator.

Question 2: Some fractions are written in the box below. Circle the fractions that are less than half. How do you know? Discuss your reasoning in the class.

Answer: Fractions less than half are those where the numerator is less than half of the denominator.

Page 14Let Us Do

Question 1: Compare the following fractions. Where possible, compare the fractions with 1/2.

Answer:

• 2/9 and 4/7:

​2/9: Half of 9 is 4.5. Since 2 < 4.5, 2/9 < 1/2.

4/7: Half of 7 is 3.5. Since 4 > 3.5, 4/7 > 1/2.

​Therefore, 2/9 < 4/7.

•11/14 and 7/20:

​11/14: Half of 14 is 7. Since 11 > 7, 11/14 > 1/2.

7/20: Half of 20 is 10. Since 7 < 10, 7/20 < 1/2.

Therefore, 11/14 > 7/20.

•5/7 and 3/9:

5/7: Half of 7 is 3.5. Since 5 > 3.5, 5/7 > 1/2.

3/9: Half of 9 is 4.5. Since 3 < 4.5, 3/9 < 1/2.

Therefore, 5/7 > 3/9.

•6/7 and 4/10:

6/7: Half of 7 is 3.5. Since 6 > 3.5, 6/7 > 1/2.

4/10: Half of 10 is 5. Since 4 < 5, 4/10 < 1/2.

Therefore, 6/7 > 4/10.

•9/17 and 3/15:

​9/17: Half of 17 is 8.5. Since 9 > 8.5, 9/17 > 1/2.

3/15: Half of 15 is 7.5. Since 3 < 7.5, 3/15 < 1/2.

Therefore, 9/17 > 3/15.

•7/12 and 3/11:

7/12: Half of 12 is 6. Since 7 > 6, 7/12 > 1/2.

3/11: Half of 11 is 5.5. Since 3 < 5.5, 3/11 < 1/2.

Therefore, 7/12 > 3/11.

•1/3 and 5/9:

1/3: Half of 3 is 1.5. Since 1 < 1.5, 1/3 < 1/2.

5/9: Half of 9 is 4.5. Since 5 > 4.5, 5/9 > 1/2.

Therefore, 1/3 < 5/9.

•3/9 and 4/7: (This is a repeat of the first comparison, so the answer is the same)

3/9: Half of 9 is 4.5. Since 3 < 4.5, 3/9 < 1/2.

4/7: Half of 7 is 3.5. Since 4 > 3.5, 4/7 > 1/2.

Therefore, 3/9 < 4/7.

Reading and writing large numbers 

Page 1, 3, 4

Imagine you have a lot of things, like thousands of candies! How do we write such big numbers? 
Let’s start with 1,000. 
What numbers do we get when we keep adding a thousand?
If we keep adding 1,000, we get these numbers

Let us see how we write numbers beyond 10,000 and how we name them. We write them in the same way as numbers below 9,999.

Let Us Do

Page 5, 6

1. Fill in the blanks by continuing the pattern in each of the following sequences. Discuss the patterns in class. 
   • (a) 456 567 678
   • (b) 1,050 3,150 4,200
   • (c) 5,501 6,401 7,301
   • (d) 10,100 10,200 10,300
   • (e) 10,105 10,125
   • (f) 10,992 10,993
   • (g) 10,794 10,796 10,798
   • (h) 73,005 72,004
   • (i) 82,350 83,350
2. Fill in the blanks appropriately. Use commas as required. 

Answer:

2. Arrange the numbers below in increasing order. You can use the number line below if required. 

Answer:

4. A student said 9,990 is greater than 49,014 because 9 is greater than 4. Is the student correct? Why or why not?

Answer:

The student is not correct.

Here’s why:

When comparing two numbers, you must compare their place values starting from the left (the highest place value). Let’s break it down:

• 9,990 has 4 digits.
• 49,014 has 5 digits.

Any 5-digit number is always greater than any 4-digit number, regardless of what digits they start with.

Use the number line below to find the position of the numbers. Fill in the blanks.

Answer:

5. Digit swap 

(a) In the number 1,478, interchanging the digits 7 and 4 gives 1,748. Now, interchange any two digits in the number 1,478 to make a number that is larger than 5,500 

Answer: 

The original number is 1,478.

To make the largest possible number, swap the digits so the biggest digit is in the thousands place. The digits are 1, 4, 7, 8. The largest arrangement is 8,741 (swap 1 and 8).

• 8,741 is much greater than 5,500.
• So, you can swap the digits 1 and 8.

Any swap putting 7 or 8 in the leftmost place will create a number larger than 5,500 (such as 7,418, 8,471, etc.).

(b) Interchange two digits of 10,593 to make a number i) Between 11,000 and 15,000. ii) More than 35,000. 

Answer: 

i) Between 11,000 and 15,000

You need a five-digit number that starts with 11, 12, 13, or 14.

Try swapping 0 and 1: 01,593 (still 1,593 — not enough digits).
Try swapping 1 and 5: 50,193 (too large).
Swap 0 and 5: 15,093 (matches the condition).

• Swapping 0 and 5 gives: 15,093 (which is between 11,000 and 15,000).

ii) More than 35,000

You’d need 3 or higher in the ten-thousand place.

Try swapping 1 and 3: 30,591 (less than 35,000).
Swap 1 and 5: 50,193 (greater than 35,000).

• Swapping 1 and 5 gives: 50,193.

(c) Interchange two digits of 48,247 to make a number i) As small as possible. ii) As big as possible

Answer: 

i) As small as possible

You want the smallest possible digit (other than 0, which is not present) in the highest place.

Swapping 4 and 2: 28,447 (2 in the ten-thousands place).

• 28,447 is the smallest possible by swapping 4 and 2.

ii) As big as possible

Largest digit in leftmost place. The digits are 4, 8, 2, 4, 7; largest is 8.

Swap 4 and 8: 84,247.

• 84,247 is the biggest possible by swapping 4 and 8.

Nearest Tens (10s), Hundreds (100s), and Thousands (1,000s) 

Page 8

Fill in the boxes appropriately.

Let Us Think

Page 8

1. Vijay rounded off a number to the nearest hundred. Suma rounded off the same number to the nearest thousand. Both got the same result. Circle the numbers they might have used. 

Answer:

This is because all these three numbers are closest to 7,000.

2. Think and write two numbers that have the same 

• (a) Nearest ten.
• (b) Nearest hundred.
• (c) Nearest thousand.

Answer: ​​​​

(a) Nearest ten:
Any two numbers between the same pair of tens will round to the same ten.
Example: 42 and 47

• Both rounded to nearest ten = 40 (since digits in ones place <5 for 42 and ≥5 for 47, so 47 rounds to 50. For SAME value: use 42 and 44, both round to 40).

So, 42 and 44 → Nearest ten = 40.

(b) Nearest hundred:
Any two numbers within the interval of 100 that round to the same hundred.
Example: 163 and 187

• Both round to nearest hundred = 200 (163 rounds to 200 because tens digit is 6 (≥5); 187 rounds to 200). To get SAME, you want both under 150, say 121 and 149 → Both round to 100.

So, 121 and 149 → Nearest hundred = 100.

(c) Nearest thousand:
Any two numbers from 3,000 up to 3,499 will round to 3,000.
Example: 3,254 and 3,492

• 3,254 → 3,000
• 3,492 → 3,000

3. Think and write the numbers that have the same 

• (a) Nearest ten and nearest hundred.
• (b) Nearest hundred and nearest thousand.
• (c) Nearest ten, hundred and thousand.

Answer:

(a) Nearest ten and nearest hundred:
Pick numbers whose tens and hundreds digits are the same after rounding.
Example: 145 and 149

• 145 rounds to 150 (ten) and 100 (hundred);
• 146 rounds to 150 (ten) and 100 (hundred);
  But not matching. Instead, try numbers like 200 and 202 →
• 200 (ten: 200, hundred: 200)
• 202 (ten: 200, hundred: 200)
  So, 200 and 202.

(b) Nearest hundred and nearest thousand:
Pick numbers that, after rounding to hundred, also round to the same thousand.
Example: 3,040 and 3,080

• 3,040 to nearest hundred = 3,000; nearest thousand = 3,000
• 3,080 to nearest hundred = 3,100; nearest thousand = 3,000
  But for SAME: 3,010 and 3,020, both round to 3,000 (hundred: 3,000; thousand: 3,000).
  So, 3,010 and 3,020.

(c) Nearest ten, hundred, and thousand:
Pick numbers at the lower end so all three round the same.
Example: 1,001 and 1,004

• Rounds to 1,000 (ten, hundred, thousand).

So, 1,001 and 1,004.

Let Us Do

Page 10

1. A cyclist can cover 15 km in one hour. How much distance will she cover in 4 hours, if she maintains the same speed?

Answer: 

If a cyclist can cover 15 km in one hour and maintains the same speed, in 4 hours she will cover:

Distance = Speed × Time
= 15 km/hour × 4 hours
= 60 km

So, she will cover 60 km in 4 hours.

2. A school has 461 girls and 439 boys. How many vehicles are needed for all of them to go on a trip using the following modes of travel? The numbers in the bracket indicate the number of people that can travel in one vehicle. 

• (a) Bicycle (2)
• (b) Autorickshaw (3)
• (c) Car (4)
• (d) Big car (6)
• (e) Tempo traveller (10)
• (f) Boat (20)
• (g) Minibus (25)
• (h) Aeroplane (180)

Answer:

The total number of students = 461 (girls) + 439 (boys) = 900 students.

To find the number of vehicles needed for each mode, use the formula:
Number of vehicles = Total persons / Capacity per vehicle (and round up to the next whole number when necessary).

(a) Bicycle (2 per bicycle):
Number of vehicles = 900 / 2 = 450

(b) Autorickshaw (3 per rickshaw):
Number of vehicles = 900 / 3 = 300

(c) Car (4 per car):
Number of vehicles = 900 / 4 = 225

(d) Big car (6 per big car):
Number of vehicles = 900 / 6 = 150

(e) Tempo traveller (10 per traveller):
Number of vehicles = 900 / 10 = 90

(f) Boat (20 per boat):
Number of vehicles = 900 / 20 = 45

(g) Minibus (25 per minibus):
Number of vehicles = 900 / 25 = 36

(h) Aeroplane (180 per plane):
Number of vehicles = 900 / 180 = 5

Finding Large Numbers Around Us 

Page 10

1. Find something in the classroom whose count is a— (i) 4-digit number. (ii) 5-digit number.

Answer:

(i) 4-digit number:

• Number of pages in all the textbooks combined in a classroom can easily be a 4-digit number (for example, if there are 5 books of about 250 pages each, that’s 1,250 pages).
• Number of chalk pieces used in a year can also be in the thousands.

(ii) 5-digit number:

• Number of pencil shavings collected over a year by all students in a classroom.
• Number of words written by students in their notebooks during a year can be over 10,000.

2. List some quantities whose count is a 4-digit or a 5-digit number in the context of— (i) A tree. (ii) Your village/town/city, or any other place of your choice.

Answer:

In the context of:

(i) A tree:

• 4-digit count: Number of leaves on a large tree (many trees have well over 1,000 leaves).
• 5-digit count: Number of flowers or fruits produced by a mature, flowering tree in a season (some large fruit trees or flowering trees can have 10,000+ flowers in full bloom).

(ii) Your village/town/city, or another place:

• 4-digit count:
  • Number of houses or families in a small town or village.
  • Number of streetlights in a medium city.
• 5-digit count:
  • Population of many towns or small cities (e.g., a town with 15,000 people).
  • Number of vehicles registered in a city.
  • Number of books in a large public library.
  • Number of school children in all schools combined in a mid-sized city.

Let Us Do

Page 13

1. Write 5 numbers between the numbers 23,568 and 24,234. ___________, ___________, ___________, ___________, and ___________

Answers: 23,600; 23,789; 23,920; 24,000; and 24,123.

2. Write 5 numbers that are more than 38,125 but less than 38,600. ___________, ___________, ___________, ___________, and ___________

Answers: 38,200; 38,300; 38,500; 38,450; and 38,555.

3. Ravi’s car has been driven for 56,987 km till now. Sheetal’s car has been driven 67,543 km. Whose car has been driven more? ________________.

Answer: Sheetal’s car.

4. The following are the prices of different electric bikes. Arrange the prices in ascending (increasing) order. ₹90,000 ₹89,999 ₹94,983 ₹49,900 ₹93,743 ₹39,999

Answer​:
₹39,999; ₹49,900; ₹89,999; ₹90,000; ₹93,743; ₹94,983.

5. The following table shows the population of some towns. Arrange them in a descending (decreasing) order.

Answer:

Town 6: 66,540
Town 1: 65,232
Town 3: 56,380
Town 2: 53,231
Town 4: 51,336
Town 5: 45,858

6. Find numbers between 42,750 and 53,500 such that the ones, tens, and hundreds digits are all 0?

Answer:

​These numbers would be the multiples of 1,000 in that range:
43,000; 44,000; 45,000; 46,000; 47,000; 48,000; 49,000; 50,000; 51,000; 52,000; 53,000

7. Write the following numbers in the expanded form. One has been done for you.

Answer:

​(a) 783 = 700 + 80 + 3
(b) 8,062 = 8,000 + 0 + 60 + 2
(c) 9,980 = 9,000 + 900 + 80 + 0 
(d) 10,304 = 10,000 + 300 + 0 + 4
(e) 23,004 = 20,000 + 3,000 + 0 + 0 + 4
(f) 70,405 = 70,000 + 0 + 400 + 0 + 5

8. Fill in the blanks with the correct answer. Share your thoughts in class. 

(a) 983 = 90 Tens + 83 Ones

(b) 68 = 5 Tens + 18 Ones
Explanation: 5 tens = 50, 18 ones = 18; 50 + 18 = 68. 

(c) 607 = 4 Hundreds + 207 Ones
Explanation: 4 hundreds = 400, 207 ones = 207; 400 + 207 = 607.

(d) 5,621 = 4 Thousand + 16 Hundreds + 2 Tens + 1 Ones
Explanation: 4 thousand = 4,000. 16 hundreds = 1,600. 2 tens = 20. 1 ones = 1. 

Total: 4,000 + 1,600 + 20 + 1 = 5,621.

(e) 7,069 = 0 Thousand + 70 Hundreds + 69 Ones
Explanation: 70 hundreds = 7,000. 69 ones = 69. 0 thousands = 0. 7,000 + 69 = 7,069.

(f) 37,608 = 2 Ten Thousand + 17 Thousand + 608 Ones
Explanation: 2 ten thousands = 20,000. 17 thousands = 17,000. 608 ones = 608. 20,000 + 17,000 + 608 = 37,608.

(g) 43,001 = 4 Ten Thousand + 3 Thousand + 0 Hundreds + 1 Ones.

9. Fill in the blanks with the correct answers.

Answer:

(a) How many notes of ₹10 are there in ₹7,934?
793 (since 7934 ÷ 10 = 793 full notes, remainder ₹4)

(b) How many notes of ₹100 are there in ₹7,934?
79 (since 7934 ÷ 100 = 79 full notes, remainder ₹34)

(c) How many thousands are there in 7,934?
7 (since 7934 ÷ 1000 = 7 full thousands, remainder ₹934)

(d) How many ₹500 notes are there in ₹7,934?
15 (since 7934 ÷ 500 = 15 full notes, remainder ₹434)

(e) How many notes of ₹10 are there in ₹65,342?
6,534 (since 65342 ÷ 10 = 6,534 full notes, remainder ₹2)

(f) How many notes of ₹100 are there in ₹65,342?
653 (since 65342 ÷ 100 = 653 full notes, remainder ₹42)

(g) How many thousands are there in 65,342?
65 (since 65342 ÷ 1000 = 65 full thousands, remainder ₹342)

(h) How many ₹500 notes are there in ₹65,342?
130 (since 65342 ÷ 500 = 130 full notes, remainder ₹342)