Passage from One Square to a Succeeding Square

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  • Box of colored bead bars 1-1
  • One each of the squares of 1-10
  • Rubber bands



  1. The directress chooses a square.
  2. The child identifies the square chosen by the directress, i.e. the square of 4.
  3. Let's use this square to build a square of 5.
  4. Allow the child to suggest and discover ways of doing this.
  5. Guide the work, giving guidelines such as: 'The sides must be built upon.'
  6. Four bars are placed to the right and the bottom of the square.
  7. A one-bead fills in the hole left in the lower right hand corner.
  8. Superimpose the square of five to verify successful completion.
  9. Directress asks the child; "What was added to the square of 4 to make the square of 5? two bars of 4 and one unit".
  10. Square of 4 + what was added = square of 5
    4 x 4 = 16
    4 + 4 + 1 = 9
    5 x 5 = 25

Control Of Error

Points Of Interest


  • Iindirect preparation for the square of a binomial.