Class 6 NCERT bridge course Answers Activity W1.6 Another Number Game

Activity W1.6   Another Number Game

 Another number game:

 Ask the children to write 3 numbers less than 10 in descending order and don’t show it to anyone.

Let them find the following: 

- Add the first and second numbers. 

 - Add the second and third numbers. 

- Add the third and first numbers. 

 Ask them to tell the three sums they got in order.

 The teacher can tell the three numbers the child thought of.

Activity W1.6: Another Number Game

Objective:

To practice addition and reasoning skills by finding three numbers less than 10, then using sums of pairs to identify those numbers.

Instructions for the Children:

1. Think of 3 numbers less than 10 and write them down in descending order (from largest to smallest).

2. Don’t show your numbers to anyone.

3. Calculate these three sums:

   • Add the first and second numbers.

   • Add the second and third numbers.

   • Add the third and first numbers.

4. Write down the three sums in order.

5. Share these sums with the teacher or a friend.

6. The teacher (or friend) will try to find the original three numbers from these sums.

How the Teacher Finds the Numbers:

Suppose the three numbers are $a$, $b$, and $c$ such that $a > b > c$.

The three sums given are:

• $S_1=a+b$

• $S_2=b+c$

• $S_3=c+a$

To find $a$, $b$, and $c$:

1. Add all three sums:

   $$S_1+S_2+S_3=(a+b)+(b+c)+(c+a)=2(a+b+c)$$

2. So,

   $$a+b+c=(\frac{S_1+S_2+S_{\mathrm{3)/}}}{2}$$

3. Then,

   $$a=(a+b+c)-(b+c)=(\frac{S_1+S_2+S_{\mathrm{3)/}}}{2}-S_2$$

4. Similarly,

   $$b=(a+b+c)-(c+a)=(\frac{S_1+S_2+S_{\mathrm{3)/}}}{2}-S_3$$

5. And,

   $$c=(a+b+c)-(a+b)=(\frac{S_1+S_2+S_{\mathrm{3)/}}}{2}-S_1$$

• Child’s numbers: 7, 5, 2 (in descending order)

• Sums:

  • $7+5=12$

  • $5+2=7$

  • $2+7=9$

• Sums given: 12, 7, 9

Teacher calculates:

$$a+b+c=(\frac{12+7+\mathrm{9)/}}{2}=\frac{\mathrm{28/}}{2}=14$$

$$a=14-7=7,$$

$$b=14-9=5,$$

$$c=14-12=2$$

So, the numbers are 7, 5, 2.

Example 2:

• Child’s numbers: 6, 4, 1

• Sums:

  • $6+4=10$

  • $4+1=5$

  • $1+6=7$

• Sums given: 10, 5, 7

Teacher calculates:

$$a+b+c=(\frac{10+5+\mathrm{7)/}}{2}=\frac{\mathrm{22/}}{2}=11$$

$$a=11-5=6,$$

$$b=11-7=4,$$

$$c=11-10=1$$

Numbers are 6, 4, 1.

Summary Table

Numbers (a,b,c)	Sum 1 (a+b)	Sum 2 (b+c)	Sum 3 (c+a)	Total Sum/2	Recovered Numbers
7, 5, 2	12	7	9	14	7, 5, 2
6, 4, 1	10	5	7	11	6, 4, 1
9, 8, 3	17	11	12	20	9, 8, 3

Class 6 NCERT bridge course Answers Activity W1.3 The Magic Number Trick!

 Activity W1.3 

The Magic Number Trick!

 Think of a number;

 multiply it by 2; 

add 6; 

take half of the number; 

 subtract 1; 

subtract the number thought of;

 I predict you now have 2. 

 Let the students play this game in pairs. 

Ask them to discuss and find out the trick behind it. 

 Encourage them to come up with similar such tricks

Activity W1.3 – The Magic Number Trick!

“No Matter What Number You Choose… I Predict the Answer!”

Objective:

To explore number patterns and reasoning by using arithmetic operations that lead to a surprising fixed result—the number 2—every time!

The Magic Trick Steps:

1. Think of any number → Let’s call it x

2. Multiply it by 2 → Result = 2x

3. Add 6 → Result = 2x + 6

4. Take half of it → Result = (2x + 6) ÷ 2 = x + 3

5. Subtract 1 → Result = x + 2

6. Subtract the number you started with (x)
   Result = (x + 2) – x =  2

Example:

Let's start with 7

1. Start with: 7

2. Multiply by 2 → 7 × 2 = 14

3. Add 6 → 14 + 6 = 20

4. Half of 20 = 10

5. Subtract 1 → 10 – 1 = 9

6. Subtract original number → 9 – 7 =  2

 It works!

Why This Trick Works (The Math Behind It):

Let the number be x

• Multiply by 2 → 2x

• Add 6 → 2x + 6

• Half → (2x + 6)/2 = x + 3

• Subtract 1 → x + 2

• Subtract x → Answer is always 2

It’s algebra magic!

Pair Activity:

• One student chooses a number and follows the steps.

• The partner predicts the answer (2), then checks it.

• Swap roles and repeat with different numbers.

Challenge Students:

• Can you create a new trick that always results in another fixed number (like 5 or 10)?

• Use operations like: add, subtract, double, triple, halve, etc.

• Try writing your own step-by-step magic pattern!

Illustrative Image: Magic Number Trick Flowchart

Shows the trick path where any number always leads to 2.

Class 6 NCERT bridge course Answers Activity W1.4 The “Guess My Number” Card Trick!

 Activity W1.4 

 Take two cards (paper or cardboard cutouts). 

Write some specific numbers from 1 to 4 on each of them. 

 Ask your friend to think of a number between 1 and 4; 

then, for each card, ask: "Is your number on this card?"; 

with their two yes/no answers, you should be able to tell them the number they thought of! 

 What numbers will you write on the two cards?

 Extension: 

There are six cards (which can be printed on one sheet of paper and then cut into six pieces) - each has numbers between 1 and 50; 

ask your friend/family member to think of a number between 1 and 50; 

shuffle the cards;

 then, for each card, ask: "Is your number on this card?"; 

with their six yes/no answers, you can tell them the number they thought of!

 How does it work?

Activity W1.4 – The “Guess My Number” Card Trick!

A Number Magic Using Logic and Cards!

Objective:

Use simple YES/NO questions with specially designed number cards to guess your friend’s secret number between 1 and 4 — or even up to 50!

Part 1: Guess a Number Between 1 and 4

 Step-by-Step:

1. Prepare 2 cards with the following numbers:

   • Card A: 1, 2

   • Card B: 2, 3

2. Ask your friend to secretly think of a number between 1 and 4.

3. Show each card and ask:
    “Is your number on this card?”

4. Based on the yes/no answers, you can guess the number!

Example:

• Friend thinks of: 2

• Card A? →  YES

• Card B? →  YES

• Only number common to both cards = 2

Why It Works:

You are narrowing down possibilities using logical elimination based on presence/absence in each card!

Extension: Guess Numbers Between 1 and 50

You can create 6 cards like this:

Each card contains numbers where a specific binary digit is 1 at certain positions. For example:

Card 1 (Bit 1 = 1)	1, 3, 5, 7, ..., 49
Card 2 (Bit 2 = 1)	2, 3, 6, 7, ..., 50
Card 3 (Bit 3 = 1)	4, 5, 6, 7, ..., 47
Card 4 (Bit 4 = 1)	8, 9, 10, 11, ..., 47
Card 5 (Bit 5 = 1)	16–31, 48–50
Card 6 (Bit 6 = 1)	32–50

How to Guess the Number:

1. Ask: “Is your number on this card?” for all 6.

2. For each YES, add the number associated with that card:

   • Card 1 = 1

   • Card 2 = 2

   • Card 3 = 4

   • Card 4 = 8

   • Card 5 = 16

   • Card 6 = 32

3. The sum of YES answers = Your friend’s number!

Example:

• Friend thinks of: 37

• Card 1? YES → +1

• Card 2? NO

• Card 3? NO

• Card 4? YES → +8

• Card 5? NO

• Card 6? YES → +32

Total = 1 + 8 + 32 =  41

Why It Works:

Each number between 1 and 50 can be represented as a binary number using 6 digits. Each card corresponds to one binary digit (bit), and their presence tells you which bits are "on."

Illustrative Image: “Guess My Number Cards”

Class 6 NCERT bridge course Answers Activity W1.2 The Hailstone Number Game

 Activity W1.2   The Hailstone Number Game

 Step 1: Think of any number 

 Step 2: If the number is odd, triple it and add 1, if the number is even, halve it. 

 Step 3: Continue step 2, based on the resulting number in step 2 and continue the steps

Step 4: Write the pattern generated., 

e.g.,

 Step 1: 5 

 Step 2: 3x5+1= 16 

 Step 3: 16/2 = 8 

 Step 4: 8/2 = 4 

 Step 5: 4/2 =2 

 Step 6: 2/2 =1 

 Step 7: 3x1+1 = 4 

 Step 8: 4/2 = 2 

 Step 9: 2/2 =1 ……………………….

 Resulting pattern is 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, ………………….

 Ask the students to play it in pairs

 Let one child give the number, the other one develops the pattern and vice versa. 

 Discuss all the patterns they developed and ask them to find out the reason for the pattern which is named as hailstone numbers.

Explore a Magical Number Pattern!

Objective:

Students discover a repeating numerical pattern using simple rules and understand the concept of hailstone numbers (also called the Collatz sequence).

How to Play:

1. Step 1: Think of any positive number.

2. Step 2:

   • If the number is odd → multiply it by 3 and add 1.

   • If the number is even → divide it by 2.

3. Step 3: Repeat the process with the new number.

4. Step 4: Observe and record the pattern.

Example: Start with 7

Let's generate the pattern:

1. 7 (odd) → 3×7 + 1 = 22

2. 22 (even) → 22 ÷ 2 = 11

3. 11 (odd) → 3×11 + 1 = 34

4. 34 → 17

5. 17 → 52

6. 52 → 26

7. 26 → 13

8. 13 → 40

9. 40 → 20

10. 20 → 10

11. 10 → 5

12. 5 → 16

13. 16 → 8

14. 8 → 4

15. 4 → 2

16. 2 → 1

17. 1 → 4

18. 4 → 2

19. 2 → 1 → then continues as: 4, 2, 1...

Pattern:

7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1,...

What are Hailstone Numbers?

The numbers in this sequence are called hailstone numbers because they rise and fall unpredictably—like hailstones in a storm—before eventually settling into the loop 4 → 2 → 1.

This pattern is part of a famous mathematical problem called the Collatz Conjecture. No matter which number you start with, the pattern always falls to 1!

Classroom Pair Activity:

• Partner A: Chooses a number.

• Partner B: Applies the rules and writes down the sequence.

• Then switch roles!

• Compare patterns: Who reached 1 faster? Which number had more steps?

Questions for Discussion:

• Do all numbers eventually reach 1?

• Which numbers take longer?

• How do odd and even numbers affect the pattern?

Illustrative Image:

A fun and colorful visual representation of the pattern starting from 7:

hailstone number pattern image

(Image shows numbers rising and falling like hailstones, before looping into 4 → 2 → 1.)

Wrap-Up:

This activity builds logical thinking, pattern recognition, and number sense. It's exciting, unpredictable, and a great way to spark mathematical curiosity in your students!