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A square arrangement of dots grows by adding an L-shaped border each time: 1, then 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. How many dots must the NEXT border add, and what is the new total?

Class 6Whole NumbersWhole Numbers
  • A8 dots ; 24 in all
  • B9 dots ; 25 in all
  • C16 dots ; 32 in all
  • D5 dots ; 21 in all

Step-by-Step Solution

The borders added are the odd numbers 3, 5, 7, so the next border is 9 dots. Adding it gives 16 + 9 = 25, which is and so is still a perfect square. Answering 32 comes from doubling 16 and ignoring the pattern altogether.
Answer: B) 9 dots ; 25 in all

Key idea: From counting to whole numbers

Natural numbers (1, 2, 3, …) answer 'how many?' when there is at least one of something. But what if there are none? You need a number for that — and that number is zero. Adding 0 to the natural numbers gives the whole numbers: 0, 1, 2, 3, …. Every whole number sits at a fixed point on the number line, and they never run out — for any whole number you pick, there is always a larger one.

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