Class 8 NCERT bridge course Answers Activity W6.8 The Idli-Vada Number Game!

 Activity W 6.8: The Idli-Vada Number Game!

A fun and educational game blending math with movement and memory!

Game! Students may be asked to sit in a circle and play a game of numbers. 

Game Rules Recap:

• Say numbers in order starting from 1.

• Say "idli" instead of numbers that are multiples of 3.

• Say "vada" instead of numbers that are multiples of 5.

• Say "idli-vada" if the number is a multiple of both 3 and 5.

• Mistakes = Out! The game continues until one student is left.

 One of the children starts by saying ‘1’. 

The second player says ‘2’, and so on. 

But when it is the turn of 3, 6,9, … (multiples of 3), the player should say ‘idli’ instead of the number.

 When it is the turn of 5, 10, … (multiples of 5), the player should say ‘vada’ instead of the number. 

When a number is both a multiple of 3 and a multiple of 5, the player should say ‘idli-vada’! 

If a player makes any mistake, they are out. 

The game continues in rounds till only one person remains. 

Teacher/Students may ask such questions for this game— 

1. For which numbers should players say “idli”instead of saying the number?

 All multiples of 3:
3, 6, 9, 12, 18, 21, 24, ..., etc.
 Exclude numbers also divisible by 5 (those are "idli-vada").

2. For which numbers should players say “vada”?

All multiples of 5:
5, 10, 20, 25, ..., etc.
Exclude numbers also divisible by 3.

3. What is the first number for which players say “idli-vada”?

15 (First common multiple of 3 and 5)
LCM(3, 5) = 15

 

4. At what number is “idli-vada” said for the 10th time?

 These occur at: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
 So, 150 is the 10th occurrence.

If the game is played for the numbers 1 to 90, 

Analysis for Numbers 1 to 90

• Multiples of 3 from 1 to 90:
  ⟶ 3, 6, ..., 90 → Total = 30 numbers

• Multiples of 5 from 1 to 90:
  ⟶ 5, 10, ..., 90 → Total = 18 numbers

• Multiples of 15 (i.e. both 3 and 5):
  ⟶ 15, 30, ..., 90 → Total = 6 numbers

 So:

find out: 

How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)? 

• "idli" is said: 30 times (includes 6 “idli-vada”)
  ⟶ Only “idli” = 30 - 6 = 24

How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)?

• "vada" is said: 18 times (includes 6 “idli-vada”)
  ⟶ Only “vada” = 18 - 6 = 12

How many times would the children say ‘idli-vada’? 

• "idli-vada" is said: 6 times

The teacher may ask students to play the game for the following pairs of numbers

— Idli Vada 

2 5 

3 7 

4 6 

Idli (A)	Vada (B)	First "idli-vada"	Next few
2	5	10	20, 30, 40...
3	7	21	42, 63, 84...
4	6	12	24, 36, 48...

Class 8 NCERT bridge course Answers Activity W6.7 Math Logic Puzzle Challenge

Students may be asked to solve the following puzzles. 

They may explain their logic of getting the solution

Supercell Swap Puzzle

 There is only one supercell (number greater than all its neighbours) in the following grid. If you exchange two digits from one of the numbers, there will be 4 supercells. Figure out which digits to swap.”

Answer:

Swap the digits 6 and 2 in 62,871 → it becomes 26,871.

Logic:

• Initially, only 62,871 is a supercell (greater than all 8 neighbors).

• After the swap, 62,871 becomes 26,871, which is no longer the greatest.

• Now, four different cells become local maxima (supercells), satisfying the condition.

2. Students may be asked ‘How many rounds does your birth year take to reach the kaprekar constant?

2. Kaprekar Constant Puzzle

“How many rounds does your birth year take to reach the Kaprekar constant?”

Instructions for students:

• Use your birth year (e.g., 1998).

• Rearrange digits to make the largest and smallest possible 4-digit numbers.

• Subtract the smaller from the larger.

• Repeat until you reach 6174 (Kaprekar's constant).

Example (for 1998):

1. 9981 − 1899 = 8082

2. 8820 − 0288 = 8532

3. 8532 − 2358 = 6174 
   Answer: 3 rounds

 

3. Students may be asked ‘Write one 5-digit number and two 3-digit numbers, such that their sum is 18,670.

3. Sum to 18,670

“Write one 5-digit number and two 3-digit numbers, such that their sum is 18,670.”

Answer Example:

• 5-digit number: 15,432

• 3-digit numbers: 1,765 and 1,473

Check:
15,432 + 1,765 + 1,473 = 18,670

Class 8 NCERT bridge course Answers Activity W6.6 Estimation Nation – Numbers All Around Us!

 Activity W 6.6 Estimation Nation – Numbers All Around Us!

 Students may be asked to do some simple estimates. 

It is a fun exercise, and they may find it amusing to know the various numbers around them.

 Remember, exact numbers are not required for the following questions. 

Students may share their methods of estimation with the class. 

 Steps you would take to walk— 

Steps Estimation

1. From desk to classroom door → ~20 steps

2. Across school ground → ~150 steps

3. Classroom to school gate → ~300 steps

4. School to home (walking) → ~3,000–5,000 steps (depends on distance)

 From the place you are sitting to the classroom door. 

Across the school ground from start to the end. 

 From your classroom door to the school gate. 

 From your school to your home.

Some other places may be also thought of. 

 Number of times you blink your eyes or the number of breaths you take— 

In a minute 

In an hour

 In a day 

Blinks and Breaths Estimation

1. Blinks per minute → ~15–20

2. Blinks per hour → ~900–1,200

3. Blinks per day → ~15,000–20,000

4. Breaths per minute → ~12–16

5. Breaths per hour → ~720–960

6. Breaths per day → ~17,000–24,000

 Name some objects around you that are— 

 A few thousand in number 

 More than ten thousand in number 

Object Estimation

• A few thousand: grains of rice in a lunchbox, sand particles in a small cup, strands of hair on your head

• More than 10,000: bricks in a school building, ants in an anthill, pages in a library

Try to guess within 30 seconds. Check your guess with your friends. 

 Number of words in your Maths textbook— 

a. More than 5000 

b. Less than 5000 

• Words in your math textbook: More than 5,000 ✅

• Students traveling by bus: More than 200 (depends on school size) ✅

Number of students in your school who travel to school by bus— 

a. More than 200

 b. Less than 200 

Travel Time Estimations (Walking)

• To a nearby favorite place → 15–30 minutes

• To a neighboring state’s capital → ~10–20 days (walking 30 km/day)

• From Kanyakumari to Kashmir → ~2,500 km = ~80–90 days walking

Earlier, people used to walk long distances as they had no other means of transport. 

Suppose you walk at your normal pace. 

Approximately, how long would it take you to go from:

a. Your current location to one of your favourite places nearby. 

b. Your current location to any neighbouring state’s capital city. 

c. The southernmost point in India to the northernmost point in India. 

 Make some estimation questions and challenge your classmates.

Estimation Questions You Can Create

• How many pencils in your classroom?

• How many tiles on the floor?

• How many liters of water used in your school each day?

Class 8 NCERT bridge course Answers Activity W6.5 Patterns in Time, Dates, and Numbers

 Activity W 6.5 Patterns in Time, Dates, and Numbers

Students may be engaged in discussing these puzzles. 

This will make them observe how mathematics is spread all around them.

Procedure 

1. Students may try and find out all possible times on a 12-hour clock of each of the type 4:44, 10:10, etc.

 Part 1: Clock Patterns (e.g., 4:44, 10:10)

Find all times where hour and minutes form a pattern:

Examples:

• 1:11

• 2:22

• 3:33

• 4:44

• 5:55

• 10:10

• 12:21 (palindromic)

✅ These are fun to spot on digital clocks—repetition or mirror-like symmetry.

2. They may try to find some dates from the past that obey a certain pattern. 

Part 2: Patterned Dates

Manish has his birthday on 20/12/2012, where the digits ‘2’, ‘0’, ‘1’and ‘2’ repeat in that order. 3. 

It could also be, Meghana, has her birthday on 11/02/2011, where the digits read the same from left to right and from right to left. 

Examples of cool dates:

• 20/12/2012 → digits: 2, 0, 1, 2 repeat

• 11/02/2011 → palindromic date

• 02/02/2020 → perfect palindrome

• 22/11/2022 → repeating pairs

• 01/01/1010 → alternating 0s and 1s

✅ Activity: Students can find birthdays or historical events with date patterns.

4. Some numbers may be given to the students. 

Part 3: Number Construction Puzzle

Given numbers:
40,000, 7,000, 300, 1,500, 12,000, 800

Example Target: 39,800

✅ Solution: 40,000 – 800 + 300 + 300

Try more:

• 45,000 = 40,000 + 7,000 – 1,500 + 1,500

• 5,900 = 7,000 – 1,500 + 300 + 100

• 17,500 = 12,000 + 7,000 – 1,500

• 21,400 = 12,000 + 7,000 + 1,500 + 900

✅ This encourages flexible arithmetic reasoning—use of both + and – with estimation.

They may be allowed to use both addition and subtraction to get the required number. 

For example, 40,000 7,000 300 1,500 12,000 800 

 Suppose the given numbers are— 

 To form a number 39800. 

We can write 39,800 = 40,000 – 800 + 300 + 300. 

Try for other numbers, such as 45000, 5900, 17500, 21400… 

 Teacher may change the set of given numbers and the required numbers. 

Students may try to do that.

Change the Number Set

Use different sets like:

• [5000, 1200, 150, 8500, 30000]

• [100, 200, 500, 1000, 2500]

• [750, 1250, 2750, 3200, 4100]

This introduces new challenges and encourages deeper number sense.

Change the Target Numbers

Ask students to create or solve for:

• Specific Targets: e.g., “Make 15,000 using 3 of these numbers.”

• Mystery Challenges: e.g., “I used three numbers to get 29,250. Can you guess which?”

Student-Generated Challenges

Let students:

• Choose a new number set.

• Create their own target numbers.

• Swap puzzles with classmates.

This boosts ownership and creative thinking.

Extension Ideas

• Use a different set of numbers each time (e.g., multiples of 100 or 1,000).

• Allow multiplication or division for advanced students.

• Have students make "mystery numbers" that others must recreate.