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GeoGebra Drill: Divisibility by 9 with a “splat/ink blot” number task

GeoGebra Drill: Divisibility by 9 with a “splat/ink blot” number task
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2024-01-23 15:07
FunctionSequenceGeometric ConstructionGraphing
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This GeoGebra example demonstrates divisibility by 9 using an “ink blot/splat” style visualization that represents randomly assembled digits, helping students decide whether a number is divisible by 9. The key math ideas are divisibility, factors and multiples, and the rule that a number is divisible by 9 exactly when the sum of its digits is a multiple of 9 (equivalently, the appropriate congruence). Construction and interaction focus on generating digit combinations from randomized inputs, visualizing the corresponding graphical elements, and then validating the student’s reasoning against the correct result. It is built with commands such as Textfield, Shuffle, and Join for question setup and randomization; Polygon, Distance, Element, Append, Remove, and If for creating/adjusting geometric objects and applying conditional logic. Interactive objects like validate/solution display and counters (showanswer, showsolution, btnValidate, attemptCount, correctCount, btnTryAgain, btnNew, showhint) support hints, retry, and feedback. Suitable for primary students (grades 5–6) for practicing and explaining divisibility rules in an interactive way.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle(1…9) → Num1List, {7, 8, 4, 1, 9, 5, 2, 6, 3}
  4. Shuffle(0…9) → Num2List, {2, 5, 7, 9, 8, 0, 3, 4, 6, 1}
  5. Shuffle(0…9) → Num3List, {7, 5, 4, 2, 9, 3, 6, 0, 8, 1}
  6. Shuffle(0…9) → Num4List, {9, 3, 6, 1, 0, 8, 7, 2, 4, 5}
  7. Shuffle(Join[Sequence[{3, 4, 5}, i, 1, 10]]) → HelperList, {4, 4, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 4, 5, 3, 5, 4, 3, 5, 4, 4, 5, 4, 5, 5, 3, 4, 3, 4, 4}
  8. Join({{3}, HelperList}) → StellenAnzahlList
  9. Shuffle(1…stellenanzahl) → exList, {1, 2, 3}
  10. Shuffle(0…9) → Num5List, {0, 2, 5, 9, 8, 4, 1, 3, 7, 6}
  11. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  12. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 5, 10, 9, 4, 7, 3, 3, 1, 4, 3, 8, 7, 9, 8, 10, 3, 0, 4, 10, 4, 3, 0, 3, 3, 3, 6, 0, 10, 8, 8, 4, 2, 10, 8, 0, 10, 6, 8, 2, 10, 3, 4, 5, 1, 3, 9, 3, 6, 10, 10, 4, 8, 8, 7, 0, 7, 8, 10, 2, 7, 10, 9, 0, 1, 9, 1, 9, 3, 3, 1, 1, 9, 3, 8, 2, 0, 8, 1, 1, 9, 5, 3, 10, 3, 4, 4, 0, 6, 1, 9, 9, 5, 7, 3, 2, 2, 7, 5, 5}
  13. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  14. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {5, 6, 0, 4, 10, 1, 0, 8, 6, 4, 9, 0, 7, 2, 2, 1, 4, 9, 6, 4, 8, 10, 0, 9, 1, 0, 9, 3, 4, 8, 7, 3, 1, 1, 6, 9, 4, 3, 5, 6, 9, 3, 8, 6, 8, 1, 7, 8, 6, 3, 4, 3, 5, 6, 6, 1, 2, 8, 2, 5, 7, 1, 10, 2, 6, 7, 7, 7, 9, 5, 6, 10, 6, 8, 10, 4, 10, 5, 4, 9, 6, 6, 8, 0, 4, 0, 2, 3, 9, 3, 9, 8, 6, 9, 8, 3, 1, 2, 3, 6}
  15. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  16. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  17. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  18. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  19. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  20. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  21. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  22. Textfield(input3) → InputBox3
  23. Textfield(input4) → InputBox4
  24. If(multiplesol, 9, 9 - Mod[ziffernsummeohneinput, 9]) → sol
  25. Textfield(input5) → InputBox5
  26. Distance(G, H) → a

AI Drawing Prompt Reference

Draw a graph with randomly arranged numbers, containing a rectangle whose color depends on the divisibility of the numbers by 9. The numbers should be colored red if they are not divisible by 9 and blue if they are. The size of the numbers should be proportional to their values. The graph may also include some auxiliary lines and points to help users determine the divisibility of the numbers.
The prompt above was compiled from the original drawing commands and is for reference only.