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Sums to 100 Pairs

Sums to 100 Pairs
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2017-12-01 01:09
FunctionSequenceGraphing
This example demonstrates pairs of numbers that sum to 100. It involves concepts of sequences and functions. Using GeoGebra commands such as Polygon, If, Mod, Div, and Sequence, the pairs are graphically represented. Suitable for high-grade elementary or junior high school students to learn about sequences and functions.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0.9, 0), 4) → poly1
  2. Polygon((2, 0), (2.9, 0), 4) → poly3
  3. Polygon((1, 0), (1.9, 0), 4) → poly2
  4. Polygon((-2, 0), (-1.1, 0), 4) → poly5
  5. Polygon((-1, 0), (-0.1, 0), 4) → poly6
  6. Polygon((0, 1), (0.9, 1), 4) → poly4
  7. Polygon((-5, 0), (-4.1, 0), 4) → poly8
  8. Polygon((-4, 0), (-3.1, 0), 4) → poly9
  9. Polygon((0, 2), (0.9, 2), 4) → poly7
  10. If(IsInRegion[A, poly9], 1, If[IsInRegion[B, poly9], 2, If[IsInRegion[C, poly9], 3, If[IsInRegion[D, poly9], 4, If[IsInRegion[E, poly9], 5, If[IsInRegion[F, poly9], 6, If[IsInRegion[G, poly9], 7, If[IsInRegion[H, poly9], 8, If[IsInRegion[I, poly9], 9, 0]]]]]]]]) → nineSum
  11. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → eightSum
  12. If(IsInRegion[A, poly6], 1, If[IsInRegion[B, poly6], 2, If[IsInRegion[C, poly6], 3, If[IsInRegion[D, poly6], 4, If[IsInRegion[E, poly6], 5, If[IsInRegion[F, poly6], 6, If[IsInRegion[G, poly6], 7, If[IsInRegion[H, poly6], 8, If[IsInRegion[I, poly6], 9, 0]]]]]]]]) → sixSum
  13. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → fiveSum
  14. If(IsInRegion[A, poly3], 1, If[IsInRegion[B, poly3], 2, If[IsInRegion[C, poly3], 3, If[IsInRegion[D, poly3], 4, If[IsInRegion[E, poly3], 5, If[IsInRegion[F, poly3], 6, If[IsInRegion[G, poly3], 7, If[IsInRegion[H, poly3], 8, If[IsInRegion[I, poly3], 9, 0]]]]]]]]) → threeSum
  15. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → twoSum
  16. Mod(onesPlace, 10) → SAone
  17. Mod(tensPlace + Div[onesPlace, 10], 10) → SAten
  18. Div(onesPlace, 10) → SAtensCarry
  19. Div(tensPlace + Div[onesPlace, 10], 10) → SAhundredsCarry
  20. Sequence(Point[{i, 2.5}], i, -5, 3) → anchors
  21. Polygon(L, M, N, O) → q1, l, m, n, o