Saturday, 22 August 2015

Explorations on a Hundreds Chart

Finding patterns on the Hundreds Board.

The Hundreds Chart is a wonderful piece of Maths Equipment that can be used for pattern discovery from the Early Years on. Ideally the use of a Flip Hundred’s Board is what I would encourage, but paper with coloured pencils will suffice.
With younger children the use of counters or Unifix type blocks can also help to model the patterns.

Please encourage the students to find the patterns, rather than tell them what the patterns are.  Mathematics should be student exploration, not practising what the teacher tells!

  • Our task is to be a guide on the side!
  • If we encourage lots of exploration students will not need too many directions,
  • they will find them for themselves, and be prepared to be blown away
  • by their discoveries, often they will find patterns that we least expect
  • or have never seen before!

  • The usual patterns of Odds and Evens, Adding 2, 3, 4 (multiples/Times Tables) are obvious starters
  •  Later, when Times Tables are known, an exploration of the Sieve of Eratosthenes to produce the Primes 
  •  Figurate Numbers (square, cubic.. numbers) can also be found on the board 
  • Niven Numbers; Any whole number that is divisible by the sum of its digits:  e.g. 4 + 5 = 9; 45 ÷ 0 = 5
  • Create Codes (Find the end point): ↑→↓←  (Each arrow means move one square in direction of arrow)                                                                                                              So 46 ↑→↓← means you move up one, right one, down one, left one so end at 46
  • Put a grid around any nine adjacent number. 
    • What Patterns can you find within the grid? e.g. what do the diagonals sum to?    
    • What do the mid number of each side sum to? What is the Mean of each row or column?….  
    • Do similar patterns occur in any group of 9? What patterns are there in a group of 4x4
              numbers? 5x 5? etc.

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