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Tiling with Cuisenaire Rods

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Applications of Fibonacci Numbers
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Abstract

Cuisenaire1 rods (“C-rods”) are color-coded rods used in kindergarten through eighth grade to help students develop an intuitive understanding of concepts such as whole numbers, fractions, measurement, ratio, area, perimeter, symmetry, congruence, three-dimensional geometry, patterns, and functions. All rods have square cross-section 1 cm. by 1 cm. and integer lengths from 1 cm. to 10 cm. The rods are white (1 cm.), red (2 cm.), green (3 cm.), purple (4 cm.), yellow (5 cm.), dark green (6 cm.), black (7 cm.), brown (8 cm.), blue (9 cm.), and orange (10 cm.).

C-rods were invented by the Belgian schoolmaster Georges Cuisenaire (1891–1976) and are available through the Cuisenaire Company of America [4].

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References

  1. Brigham, R.C., Caron, R.M., Chinn, P.Z. and Grimaldi, R. “A Tiling Scheme for the Fibonacci Numbers”. To appear in Journal of Recreational Mathematics.

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  2. Brigham, R.C., Chinn, P.Z., Holt, L., and Wilson, S. “Finding the Recurrence Relation for Tiling 2 x n Rectangles”. To appear in Cong. Num.

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  3. Chinn, P.Z., Colyer, G., Flashman, M., and Migliore, E. “Cuisenaire rods go to college”. PRIMUS, Vol. 2 (1992): pp. 118–130.

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  4. Davidson, P.S. Idea Book for Cuisenaire Rods at the Primary Level. Cuisenaire Company of America, Inc., White Plains, NY, 1977.

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  5. Graham, R.L., Knuth, D.E. and Patashnik, O. Concrete Mathematics. Addison-Wesley, Reading, Massachusetts, 1989.

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  6. Hare, E.O. “Tiling a 2 x n Area with Cuisenaire Rods of Length Less Than or Equal to k”. Submitted.

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  7. Hare, E.O. “Tiling a 3 x n Area with Cuisenaire Rods of Length Less Than or Equal to k”. Cong. Num., Vol. 105 (1994): pp. 33–45.

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  8. Larson, J.A. and Mitchell, W.J. Transition Matrices and Some Recursions Based on Tilings, prepublication manuscript.

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  9. Stanton, R.G., Bate, J.A. and Mullin, R.C. “Some Tables for the Postage Stamp Problem”. Proc. Fourth Manitoba Conference on Numerical Math., 1974, 351–356.

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© 1996 Kluwer Academic Publishers

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Hare, E.O., Chinn, P.Z. (1996). Tiling with Cuisenaire Rods. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_15

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  • DOI: https://doi.org/10.1007/978-94-009-0223-7_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6583-2

  • Online ISBN: 978-94-009-0223-7

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