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Interactive Multiplication Table: From Natural Numbers to Functions and Geometry

Interactive Multiplication Table: From Natural Numbers to Functions and Geometry
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2020-07-27 18:45
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This GeoGebra example presents an interactive multiplication table (Tabliczka mnożenia) that visualizes the distribution of products of natural numbers in a grid. It integrates core mathematical concepts such as natural number multiplication, sequence generation, divisibility and modulo operations, while also incorporating step functions, angles, and the unit circle to bridge arithmetic with geometry and introductory calculus. The construction uses GeoGebra commands including Product, Sequence, Segment, Polygon, If, Unique, Join, Element, Div, Mod, Text, and button (klawisz) to create dynamic grids, conditional logic, and interactive controls. Suitable for upper elementary and middle school students to explore multiplication patterns, and for high school students to investigate connections between arithmetic, functions, and geometric representations. The example serves as a versatile teaching tool for both basic arithmetic practice and advanced mathematical exploration.

GeoGebra Commands & Parameters

  1. Product(lista4) → l
  2. If(Element[lista1, 5] ≠ Element[lista2, 5], 60 - Element[lista1, 2] + Element[lista2, 2], (3600 * (Element[lista2, 4] - Element[lista1, 4])) + (60 * (Element[lista2, 3] - Element[lista1, 3])) + Element[lista2, 2] - Element[lista1, 2]) → b
  3. If(b > 10, 0, 10 - b) → c
  4. Unique(Join[Sequence[Sequence[(i * j), j, 1, 10], i, 1, 10]]) → lista3
  5. Join(Sequence[Sequence[{i, j}, j, 1, 10], i, 1, 10]) → m1
  6. Segment(A, C) → d
  7. Segment(B, D) → e
  8. Sequence(Segment[((10 - i) / 10 * A) + (i / 10 * C), ((10 - i) / 10 * B) + (i / 10 * D)], i, 0, 10) → lista5
  9. Element(lista3, A1) → B1
  10. Element(lista3, A2) → B2
  11. Element(lista3, A3) → B3
  12. Element(lista3, A4) → B4
  13. Element(lista3, A5) → B5
  14. Element(lista3, A6) → B6
  15. Element(lista3, A7) → B7
  16. Element(lista3, A8) → B8
  17. Element(lista3, A9) → B9
  18. Element(lista3, A10) → B10
  19. Element(lista3, A11) → B11
  20. Element(lista3, A12) → B12
  21. Element(lista3, A13) → B13
  22. Element(lista3, A14) → B14
  23. Element(lista3, A15) → B15
  24. Element(lista3, A16) → B16
  25. Element(lista3, A17) → B17
  26. Element(lista3, A18) → B18
  27. Element(lista3, A19) → B19
  28. Element(lista3, A20) → B20
  29. Element(lista3, A21) → B21
  30. Element(lista3, A22) → B22
  31. Element(lista3, A23) → B23
  32. Element(lista3, A24) → B24
  33. Element(lista3, A25) → B25
  34. Element(lista3, A26) → B26
  35. Element(lista3, A27) → B27
  36. Element(lista3, A28) → B28
  37. Element(lista3, A29) → B29
  38. Element(lista3, A30) → B30
  39. Element(lista3, A31) → B31
  40. Element(lista3, A32) → B32
  41. Element(lista3, A33) → B33
  42. Element(lista3, A34) → B34
  43. Element(lista3, A35) → B35
  44. Element(lista3, A36) → B36
  45. Element(lista3, A37) → B37
  46. Element(lista3, A38) → B38
  47. Element(lista3, A39) → B39
  48. Element(lista3, A40) → B40
  49. Element(lista3, A41) → B41
  50. Element(lista3, A42) → B42
  51. Div(A1 - 1, 7) → C1
  52. Div(A2 - 1, 7) → C2
  53. Div(A3 - 1, 7) → C3
  54. Div(A4 - 1, 7) → C4
  55. Div(A5 - 1, 7) → C5
  56. Div(A6 - 1, 7) → C6
  57. Div(A7 - 1, 7) → C7
  58. Div(A8 - 1, 7) → C8
  59. Div(A9 - 1, 7) → C9
  60. Div(A10 - 1, 7) → C10
  61. Div(A11 - 1, 7) → C11
  62. Div(A12 - 1, 7) → C12
  63. Div(A13 - 1, 7) → C13
  64. Div(A14 - 1, 7) → C14
  65. Div(A15 - 1, 7) → C15
  66. Div(A16 - 1, 7) → C16
  67. Div(A17 - 1, 7) → C17
  68. Div(A18 - 1, 7) → C18
  69. Div(A19 - 1, 7) → C19
  70. Div(A20 - 1, 7) → C20
  71. Div(A21 - 1, 7) → C21
  72. Div(A22 - 1, 7) → C22
  73. Div(A23 - 1, 7) → C23
  74. Div(A24 - 1, 7) → C24
  75. Div(A25 - 1, 7) → C25
  76. Div(A26 - 1, 7) → C26
  77. Div(A27 - 1, 7) → C27
  78. Div(A28 - 1, 7) → C28
  79. Div(A29 - 1, 7) → C29
  80. Div(A30 - 1, 7) → C30
  81. Div(A31 - 1, 7) → C31
  82. Div(A32 - 1, 7) → C32
  83. Div(A33 - 1, 7) → C33
  84. Div(A34 - 1, 7) → C34
  85. Div(A35 - 1, 7) → C35
  86. Div(A36 - 1, 7) → C36
  87. Div(A37 - 1, 7) → C37
  88. Div(A38 - 1, 7) → C38
  89. Div(A39 - 1, 7) → C39
  90. Div(A40 - 1, 7) → C40
  91. Div(A41 - 1, 7) → C41
  92. Div(A42 - 1, 7) → C42
  93. Mod(A1 - 1, 7) → D1
  94. Mod(A2 - 1, 7) → D2
  95. Mod(A3 - 1, 7) → D3
  96. Mod(A4 - 1, 7) → D4
  97. Mod(A5 - 1, 7) → D5
  98. Mod(A6 - 1, 7) → D6
  99. Mod(A7 - 1, 7) → D7
  100. Mod(A8 - 1, 7) → D8
  101. Mod(A9 - 1, 7) → D9
  102. Mod(A10 - 1, 7) → D10
  103. Mod(A11 - 1, 7) → D11
  104. Mod(A12 - 1, 7) → D12
  105. Mod(A13 - 1, 7) → D13
  106. Mod(A14 - 1, 7) → D14
  107. Mod(A15 - 1, 7) → D15
  108. Mod(A16 - 1, 7) → D16
  109. Mod(A17 - 1, 7) → D17
  110. Mod(A18 - 1, 7) → D18
  111. Mod(A19 - 1, 7) → D19
  112. Mod(A20 - 1, 7) → D20
  113. Mod(A21 - 1, 7) → D21
  114. Mod(A22 - 1, 7) → D22
  115. Mod(A23 - 1, 7) → D23
  116. Mod(A24 - 1, 7) → D24
  117. Mod(A25 - 1, 7) → D25
  118. Mod(A26 - 1, 7) → D26
  119. Mod(A27 - 1, 7) → D27
  120. Mod(A28 - 1, 7) → D28
  121. Mod(A29 - 1, 7) → D29
  122. Mod(A30 - 1, 7) → D30
  123. Mod(A31 - 1, 7) → D31
  124. Mod(A32 - 1, 7) → D32
  125. Mod(A33 - 1, 7) → D33
  126. Mod(A34 - 1, 7) → D34
  127. Mod(A35 - 1, 7) → D35
  128. Mod(A36 - 1, 7) → D36
  129. Mod(A37 - 1, 7) → D37
  130. Mod(A38 - 1, 7) → D38
  131. Mod(A39 - 1, 7) → D39
  132. Mod(A40 - 1, 7) → D40
  133. Mod(A41 - 1, 7) → D41
  134. Mod(A42 - 1, 7) → D42
  135. Text(B1, E1, true, true) → F1
  136. Text(B2, E2, true, true) → F2
  137. Text(B3, E3, true, true) → F3
  138. Text(B4, E4, true, true) → F4
  139. Text(B5, E5, true, true) → F5
  140. Text(B6, E6, true, true) → F6
  141. Text(B7, E7, true, true) → F7
  142. Text(B8, E8, true, true) → F8
  143. Text(B9, E9, true, true) → F9
  144. Text(B10, E10, true, true) → F10
  145. Text(B11, E11, true, true) → F11
  146. Text(B12, E12, true, true) → F12
  147. Text(B13, E13, true, true) → F13
  148. Text(B14, E14, true, true) → F14
  149. Text(B15, E15, true, true) → F15
  150. Text(B16, E16, true, true) → F16
  151. Text(B17, E17, true, true) → F17
  152. Text(B18, E18, true, true) → F18
  153. Text(B19, E19, true, true) → F19
  154. Text(B20, E20, true, true) → F20
  155. Text(B21, E21, true, true) → F21
  156. Text(B22, E22, true, true) → F22
  157. Text(B23, E23, true, true) → F23
  158. Text(B24, E24, true, true) → F24
  159. Text(B25, E25, true, true) → F25
  160. Text(B26, E26, true, true) → F26
  161. Text(B27, E27, true, true) → F27
  162. Text(B28, E28, true, true) → F28
  163. Text(B29, E29, true, true) → F29
  164. Text(B30, E30, true, true) → F30
  165. Text(B31, E31, true, true) → F31
  166. Text(B32, E32, true, true) → F32
  167. Text(B33, E33, true, true) → F33
  168. Text(B34, E34, true, true) → F34
  169. Text(B35, E35, true, true) → F35
  170. Text(B36, E36, true, true) → F36
  171. Text(B37, E37, true, true) → F37
  172. Text(B38, E38, true, true) → F38
  173. Text(B39, E39, true, true) → F39
  174. Text(B40, E40, true, true) → F40
  175. Text(B41, E41, true, true) → F41
  176. Text(B42, E42, true, true) → F42
  177. Text(B1, G1, true, true) → H1
  178. Text(B2, G2, true, true) → H2
  179. Text(B3, G3, true, true) → H3
  180. Text(B4, G4, true, true) → H4
  181. Text(B5, G5, true, true) → H5
  182. Text(B6, G6, true, true) → H6
  183. Text(B7, G7, true, true) → H7
  184. Text(B8, G8, true, true) → H8
  185. Text(B9, G9, true, true) → H9
  186. Text(B10, G10, true, true) → H10
  187. Text(B11, G11, true, true) → H11
  188. Text(B12, G12, true, true) → H12
  189. Text(B13, G13, true, true) → H13
  190. Text(B14, G14, true, true) → H14
  191. Text(B15, G15, true, true) → H15
  192. Text(B16, G16, true, true) → H16
  193. Text(B17, G17, true, true) → H17
  194. Text(B18, G18, true, true) → H18
  195. Text(B19, G19, true, true) → H19
  196. Text(B20, G20, true, true) → H20
  197. Text(B21, G21, true, true) → H21
  198. Text(B22, G22, true, true) → H22
  199. Text(B23, G23, true, true) → H23
  200. Text(B24, G24, true, true) → H24
  201. Text(B25, G25, true, true) → H25
  202. Text(B26, G26, true, true) → H26
  203. Text(B27, G27, true, true) → H27
  204. Text(B28, G28, true, true) → H28
  205. Text(B29, G29, true, true) → H29
  206. Text(B30, G30, true, true) → H30
  207. Text(B31, G31, true, true) → H31
  208. Text(B32, G32, true, true) → H32
  209. Text(B33, G33, true, true) → H33
  210. Text(B34, G34, true, true) → H34
  211. Text(B35, G35, true, true) → H35
  212. Text(B36, G36, true, true) → H36
  213. Text(B37, G37, true, true) → H37
  214. Text(B38, G38, true, true) → H38
  215. Text(B39, G39, true, true) → H39
  216. Text(B40, G40, true, true) → H40
  217. Text(B41, G41, true, true) → H41
  218. Text(B42, G42, true, true) → H42
  219. klawisz(E1) → I1
  220. klawisz(E2) → I2
  221. klawisz(E3) → I3
  222. klawisz(E4) → I4
  223. klawisz(E5) → I5
  224. klawisz(E6) → I6
  225. klawisz(E7) → I7
  226. klawisz(E8) → I8
  227. klawisz(E9) → I9
  228. klawisz(E10) → I10
  229. klawisz(E11) → I11
  230. klawisz(E12) → I12
  231. klawisz(E13) → I13
  232. klawisz(E14) → I14
  233. klawisz(E15) → I15
  234. klawisz(E16) → I16
  235. klawisz(E17) → I17
  236. klawisz(E18) → I18
  237. klawisz(E19) → I19
  238. klawisz(E20) → I20
  239. klawisz(E21) → I21
  240. klawisz(E22) → I22
  241. klawisz(E23) → I23
  242. klawisz(E24) → I24
  243. klawisz(E25) → I25
  244. klawisz(E26) → I26
  245. klawisz(E27) → I27
  246. klawisz(E28) → I28
  247. klawisz(E29) → I29
  248. klawisz(E30) → I30
  249. klawisz(E31) → I31
  250. klawisz(E32) → I32
  251. klawisz(E33) → I33
  252. klawisz(E34) → I34
  253. klawisz(E35) → I35
  254. klawisz(E36) → I36
  255. klawisz(E37) → I37
  256. klawisz(E38) → I38
  257. klawisz(E39) → I39
  258. klawisz(E40) → I40
  259. klawisz(E41) → I41
  260. klawisz(E42) → I42
  261. Polygon(K1, L1, L2, K2) → M1, N1, O1, P1, Q1
  262. Polygon(K2, L2, L3, K3) → M2, N2, O2, P2, Q2
  263. Polygon(K3, L3, L4, K4) → M3, N3, O3, P3, Q3
  264. Polygon(K4, L4, L5, K5) → M4, N4, O4, P4, Q4
  265. Polygon(K5, L5, L6, K6) → M5, N5, O5, P5, Q5
  266. Polygon(K6, L6, L7, K7) → M6, N6, O6, P6, Q6
  267. Polygon(K7, L7, L8, K8) → M7, N7, O7, P7, Q7
  268. Polygon(K8, L8, L9, K9) → M8, N8, O8, P8, Q8
  269. Polygon(K9, L9, L10, K10) → M9, N9, O9, P9, Q9
  270. Polygon(K10, L10, L11, K11) → M10, N10, O10, P10, Q10

AI Drawing Prompt Reference

Create a 10x10 multiplication table where each cell shows the product of two numbers. Use angles and the unit circle to illustrate patterns in the multiplication table, and apply dynamic grids and conditional logic to change angles and colors based on different products.
The prompt above was compiled from the original drawing commands and is for reference only.