Class 8 NCERT bridge course Answers Activity W6.9 Number Puzzles and Pattern Talk

 Activity W 6.9  Number Puzzles and Pattern Talk

This activity develops number sense, understanding of multiples, special numbers, and pattern recognition.

Teacher may give these situations to students and ask them to discuss about them. 

1. Common Multiples Puzzle

1. In the diagram below, 

"Anant has erased all the numbers except the common multiples."

Find out what those numbers could be and fill in the missing numbers in the empty regions. 

Given common multiples: 72, 48, 24
We need to find two numbers whose common multiples include 72, 48, and 24.

Step 1: Find the LCM of 24, 48, and 72.
Since 72 is a multiple of 24 and 48, we know:

• Possible pair: Multiples of 6 and Multiples of 8 

  
  

Answer:

• Multiple of 6

• Multiple of 8

• Common Multiples: 24, 48, 72

•  Students can verify this:

• LCM(6,8) = 24

• 48 and 72 are higher common multiples

 

2. Special Numbers in Each Box

There are some boxes with four numbers in each box given below. 

"Within each box, say how each number is special compared to the rest."

Let’s look at each set:

Box 1:

5, 7, 12, 35

• 5 and 7 are primes

• 12 is sum of 5 and 7

• 35 is product of 5 and 7

Special: 12 (sum), 35 (product)

Box 2:

3, 8, 11, 24

• 3 + 8 = 11

• 3 × 8 = 24

Special: 11 (sum), 24 (product)

Box 3:

27, 3, 123, 31

• 27 ÷ 3 = 9

• 123 − 31 = 92

• 41 x 3 = 123

Box 4:

17, 27, 44, 65

• 17 + 27 = 44

• 17 × 27 = 459

• 44 + 21 = 65

 3.  The figure on the left shows the puzzle. 

The figure on the right shows the solution of the puzzle. 

Think what the rules can be to solve the puzzle.

Rules

Fill the grid with prime numbers only, so that the product of each row is the number to the right of the row and the product of each column is the number below the column—

(a) Prime Factorization Table

From the solution table (right side), these values are:

We already see the factorization of the numbers in the rightmost column (75, 42, 102):

• The 3 columns before 75/42/102 show the prime factors:

  • 75 → 5 × 5 × 3

  • 42 → 2 × 3 × 7

  • 102 → 17 × 2 × 3

  • 170 → 5 x 2 x 17

  • 30 → 5 x 3 x 2

  • 63 → 3 x 7 x 3

  • 

b)  

Solution

• Row products:

  • 7 x 5 x 3 = 105 

  • 2 x 5 x 2 = 20

  • 2 x 5 x 3 = 30

• Column products:

  • 7 x 2 x 2 = 28

  • 5 x 5 x 5 = 125

  • 3 x 2 x 3 = 18

Solution

Solution

Solution