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