MathPlotAI Logo MathPlotAI

Algebra Tiles by Duane Habecker

Algebra Tiles by Duane Habecker
Loading the math board and drawing, please wait…
2017-01-07 12:21
Coordinate GeometryGeometric Construction
In collections Expressions and equations Expressions and equations
Use algebra tiles to multiply binomials. Click on the tiles to switch between positive (blue) and negative (red). This example demonstrates the concept of binomial multiplication, involving algebra and polynomials. The construction uses commands like Random, Circle, Point, Polygon, Segment, OrthogonalLine, Intersect, Line, Ray. Suitable for middle school and above students learning algebra.

GeoGebra Commands & Parameters

  1. Random(-2, 2) → c
  2. Circle(A_1, tilewidth) → c_1
  3. Point(c_1) → B_1
  4. Polygon(B_1, A_1, 4) → Unit2, f_1, g_1, h_1, i_1, C_1, D_1
  5. Circle(A_2, tilewidth) → c_2
  6. Point(c_2) → B_2
  7. Polygon(B_2, A_2, 4) → Unit4, f_2, g_2, h_2, i_2, C_2, D_2
  8. Circle(A_3, tilewidth) → c_3
  9. Point(c_3) → B_3
  10. Polygon(B_3, A_3, 4) → Unit5, f_3, g_3, h_3, i_3, C_3, D_3
  11. Circle(A_4, tilewidth) → c_4
  12. Point(c_4) → B_4
  13. Polygon(B_4, A_4, 4) → Unit3, f_4, g_4, h_4, i_4, C_4, D_4
  14. Circle(A_5, tilewidth) → c_5
  15. Point(c_5) → B_5
  16. Polygon(B_5, A_5, 4) → Unit6, f_5, g_5, h_5, i_5, C_5, D_5
  17. Circle(A_6, tilewidth) → c_6
  18. Point(c_6) → B_6
  19. Polygon(B_6, A_6, 4) → Unit7, f_6, g_6, h_6, i_6, C_6, D_6
  20. Circle(A_7, tilewidth) → c_7
  21. Point(c_7) → B_7
  22. Polygon(B_7, A_7, 4) → Unit8, f_7, g_7, h_7, i_7, C_7, D_7
  23. Circle(A_8, tilewidth) → c_8
  24. Point(c_8) → B_8
  25. Polygon(B_8, A_8, 4) → Unit9, f_8, g_8, h_8, i_8, C_8, D_8
  26. Circle(A_9, tilewidth) → c_9
  27. Point(c_9) → B_9
  28. Polygon(B_9, A_9, 4) → Unit10, f_9, g_9, h_9, i_9, C_9, D_9
  29. Circle(A_{10}, tilewidth) → c_{10}
  30. Point(c_{10}) → B_{10}
  31. Polygon(B_{10}, A_{10}, 4) → Unit11, f_{10}, g_{10}, h_{10}, i_{10}, C_{10}, D_{10}
  32. Circle(A_{11}, tilewidth) → c_{11}
  33. Point(c_{11}) → B_{11}
  34. Polygon(B_{11}, A_{11}, 4) → Unit12, f_{11}, g_{11}, h_{11}, i_{11}, C_{11}, D_{11}
  35. Circle(A_{12}, tilewidth) → c_{12}
  36. Point(c_{12}) → B_{12}
  37. Polygon(B_{12}, A_{12}, 4) → Unit13, f_{12}, g_{12}, h_{12}, i_{12}, C_{12}, D_{12}
  38. Circle(A_{13}, tilewidth) → c_{13}
  39. Point(c_{13}) → B_{13}
  40. Polygon(B_{13}, A_{13}, 4) → Unit14, f_{13}, g_{13}, h_{13}, i_{13}, C_{13}, D_{13}
  41. Circle(A_{14}, tilewidth) → c_{14}
  42. Point(c_{14}) → B_{14}
  43. Polygon(B_{14}, A_{14}, 4) → Unit15, f_{14}, g_{14}, h_{14}, i_{14}, C_{14}, D_{14}
  44. Circle(A_{15}, tilewidth) → c_{15}
  45. Point(c_{15}) → B_{15}
  46. Polygon(B_{15}, A_{15}, 4) → Unit16, f_{15}, g_{15}, h_{15}, i_{15}, C_{15}, D_{15}
  47. Circle(A_{16}, tilewidth) → c_{16}
  48. Point(c_{16}) → B_{16}
  49. Polygon(B_{16}, A_{16}, 4) → Unit17, f_{16}, g_{16}, h_{16}, i_{16}, C_{16}, D_{16}
  50. Circle(A_{17}, tilewidth) → c_{17}
  51. Point(c_{17}) → B_{17}
  52. Polygon(B_{17}, A_{17}, 4) → Unit18, f_{17}, g_{17}, h_{17}, i_{17}, C_{17}, D_{17}
  53. Random(1, 4) → d
  54. Segment(E, F) → j
  55. Random(1, 3) → e
  56. OrthogonalLine(F, j) → k
  57. Intersect(e, k, 2) → G
  58. Line(E, k) → l
  59. OrthogonalLine(G, l) → m
  60. Intersect(l, m) → H
  61. Polygon(E, F, G, H) → Xrod01, e_1, f_{18}, g_{18}, h_{18}
  62. Circle(E_1, tilewidth) → d_1
  63. Point(d_1) → F_1
  64. Segment(E_1, F_1) → j_1
  65. OrthogonalLine(F_1, j_1) → k_1
  66. Circle(F_1, (2.5 * tilewidth)) → e_2
  67. Intersect(e_2, k_1, 2) → G_1
  68. Line(E_1, k_1) → l_1
  69. OrthogonalLine(G_1, l_1) → m_1
  70. Intersect(l_1, m_1) → H_1
  71. Polygon(E_1, F_1, G_1, H_1) → Xrod02, e_3, f_{19}, g_{19}, h_{19}
  72. Circle(E_2, tilewidth) → d_2
  73. Point(d_2) → F_2
  74. Segment(E_2, F_2) → j_2
  75. OrthogonalLine(F_2, j_2) → k_2
  76. Circle(F_2, (2.5 * tilewidth)) → e_5
  77. Intersect(e_5, k_2, 2) → G_2
  78. Line(E_2, k_2) → l_2
  79. OrthogonalLine(G_2, l_2) → m_2
  80. Intersect(l_2, m_2) → H_2
  81. Polygon(E_2, F_2, G_2, H_2) → Xrod03, e_4, f_{20}, g_{20}, h_{20}
  82. Circle(E_4, tilewidth) → d_4
  83. Point(d_4) → F_3
  84. Segment(E_4, F_3) → j_3
  85. OrthogonalLine(F_3, j_3) → k_3
  86. Circle(F_3, (2.5 * tilewidth)) → e_7
  87. Intersect(e_7, k_3, 2) → G_3
  88. Line(E_4, k_3) → l_3
  89. OrthogonalLine(G_3, l_3) → m_3
  90. Intersect(l_3, m_3) → H_3
  91. Polygon(E_4, F_3, G_3, H_3) → Xrod04, e_6, f_{21}, g_{21}, h_{21}
  92. Circle(E_5, tilewidth) → d_5
  93. Point(d_5) → F_4
  94. Segment(E_5, F_4) → j_4
  95. OrthogonalLine(F_4, j_4) → k_4
  96. Circle(F_4, (2.5 * tilewidth)) → e_{10}
  97. Intersect(e_{10}, k_4, 2) → G_5
  98. Line(E_5, k_4) → l_4
  99. OrthogonalLine(G_5, l_4) → m_4
  100. Intersect(l_4, m_4) → H_5
  101. Polygon(E_5, F_4, G_5, H_5) → Xrod05, e_8, f_{22}, g_{22}, h_{22}
  102. Circle(E_6, tilewidth) → d_6
  103. Point(d_6) → F_5
  104. Segment(E_6, F_5) → j_5
  105. OrthogonalLine(F_5, j_5) → k_5
  106. Circle(F_5, (2.5 * tilewidth)) → e_{11}
  107. Intersect(e_{11}, k_5, 2) → G_4
  108. Line(E_6, k_5) → l_5
  109. OrthogonalLine(G_4, l_5) → m_5
  110. Intersect(l_5, m_5) → H_4
  111. Polygon(E_6, F_5, G_4, H_4) → Xrod06, e_9, f_{23}, g_{23}, h_{23}
  112. Circle(E_7, tilewidth) → d_7
  113. Point(d_7) → F_6
  114. Segment(E_7, F_6) → j_6
  115. OrthogonalLine(F_6, j_6) → k_6
  116. Circle(F_6, (2.5 * tilewidth)) → e_{16}
  117. Intersect(e_{16}, k_6, 2) → G_9
  118. Line(E_7, k_6) → l_6
  119. OrthogonalLine(G_9, l_6) → m_6
  120. Intersect(l_6, m_6) → H_9
  121. Polygon(E_7, F_6, G_9, H_9) → Xrod07, e_{12}, f_{24}, g_{24}, h_{24}
  122. Circle(E_8, tilewidth) → d_8
  123. Point(d_8) → F_7
  124. Segment(E_8, F_7) → j_7
  125. OrthogonalLine(F_7, j_7) → k_7
  126. Circle(F_7, (2.5 * tilewidth)) → e_{17}
  127. Intersect(e_{17}, k_7, 2) → G_8
  128. Line(E_8, k_7) → l_7
  129. OrthogonalLine(G_8, l_7) → m_7
  130. Intersect(l_7, m_7) → H_8
  131. Polygon(E_8, F_7, G_8, H_8) → Xrod08, e_{13}, f_{25}, g_{25}, h_{25}
  132. Circle(E_9, tilewidth) → d_9
  133. Point(d_9) → F_8
  134. Segment(E_9, F_8) → j_8
  135. OrthogonalLine(F_8, j_8) → k_8
  136. Circle(F_8, (2.5 * tilewidth)) → e_{18}
  137. Intersect(e_{18}, k_8, 2) → G_7
  138. Line(E_9, k_8) → l_8
  139. OrthogonalLine(G_7, l_8) → m_8
  140. Intersect(l_8, m_8) → H_7
  141. Polygon(E_9, F_8, G_7, H_7) → Xrod09, e_{14}, f_{26}, g_{26}, h_{26}
  142. Circle(E_{10}, tilewidth) → d_{10}
  143. Point(d_{10}) → F_9
  144. Segment(E_{10}, F_9) → j_9
  145. OrthogonalLine(F_9, j_9) → k_9
  146. Circle(F_9, (2.5 * tilewidth)) → e_{19}
  147. Intersect(e_{19}, k_9, 2) → G_6
  148. Line(E_{10}, k_9) → l_9
  149. OrthogonalLine(G_6, l_9) → m_9
  150. Intersect(l_9, m_9) → H_6
  151. Polygon(E_{10}, F_9, G_6, H_6) → Xrod10, e_{15}, f_{27}, g_{27}, h_{27}
  152. Circle(E_{11}, tilewidth) → d_{11}
  153. Point(d_{11}) → F_{10}
  154. Segment(E_{11}, F_{10}) → j_{10}
  155. OrthogonalLine(F_{10}, j_{10}) → k_{10}
  156. Circle(F_{10}, (2.5 * tilewidth)) → e_{28}
  157. Intersect(e_{28}, k_{10}, 2) → G_{17}
  158. Line(E_{11}, k_{10}) → l_{10}
  159. OrthogonalLine(G_{17}, l_{10}) → m_{10}
  160. Intersect(l_{10}, m_{10}) → H_{17}
  161. Polygon(E_{11}, F_{10}, G_{17}, H_{17}) → Xrod11, e_{20}, f_{28}, g_{28}, h_{28}
  162. Circle(E_{12}, tilewidth) → d_{12}
  163. Point(d_{12}) → F_{11}
  164. Segment(E_{12}, F_{11}) → j_{11}
  165. OrthogonalLine(F_{11}, j_{11}) → k_{11}
  166. Circle(F_{11}, (2.5 * tilewidth)) → e_{29}
  167. Intersect(e_{29}, k_{11}, 2) → G_{16}
  168. Line(E_{12}, k_{11}) → l_{11}
  169. OrthogonalLine(G_{16}, l_{11}) → m_{11}
  170. Intersect(l_{11}, m_{11}) → H_{16}
  171. Polygon(E_{12}, F_{11}, G_{16}, H_{16}) → Xrod12, e_{21}, f_{29}, g_{29}, h_{29}
  172. Circle(E_{13}, tilewidth) → d_{13}
  173. Point(d_{13}) → F_{12}
  174. Segment(E_{13}, F_{12}) → j_{12}
  175. OrthogonalLine(F_{12}, j_{12}) → k_{12}
  176. Circle(F_{12}, (2.5 * tilewidth)) → e_{30}
  177. Intersect(e_{30}, k_{12}, 2) → G_{15}
  178. Line(E_{13}, k_{12}) → l_{12}
  179. OrthogonalLine(G_{15}, l_{12}) → m_{12}
  180. Intersect(l_{12}, m_{12}) → H_{15}
  181. Polygon(E_{13}, F_{12}, G_{15}, H_{15}) → Xrod13, e_{22}, f_{30}, g_{30}, h_{30}
  182. Circle(E_{14}, tilewidth) → d_{14}
  183. Point(d_{14}) → F_{13}
  184. Segment(E_{14}, F_{13}) → j_{13}
  185. OrthogonalLine(F_{13}, j_{13}) → k_{13}
  186. Circle(F_{13}, (2.5 * tilewidth)) → e_{31}
  187. Intersect(e_{31}, k_{13}, 2) → G_{14}
  188. Line(E_{14}, k_{13}) → l_{13}
  189. OrthogonalLine(G_{14}, l_{13}) → m_{13}
  190. Intersect(l_{13}, m_{13}) → H_{14}
  191. Polygon(E_{14}, F_{13}, G_{14}, H_{14}) → Xrod14, e_{23}, f_{31}, g_{31}, h_{31}
  192. Circle(E_{15}, tilewidth) → d_{15}
  193. Point(d_{15}) → F_{14}
  194. Segment(E_{15}, F_{14}) → j_{14}
  195. OrthogonalLine(F_{14}, j_{14}) → k_{14}
  196. Circle(F_{14}, (2.5 * tilewidth)) → e_{32}
  197. Intersect(e_{32}, k_{14}, 2) → G_{13}
  198. Line(E_{15}, k_{14}) → l_{14}
  199. OrthogonalLine(G_{13}, l_{14}) → m_{14}
  200. Intersect(l_{14}, m_{14}) → H_{13}
  201. Polygon(E_{15}, F_{14}, G_{13}, H_{13}) → Xrod15, e_{24}, f_{32}, g_{32}, h_{32}
  202. Circle(E_{16}, tilewidth) → d_{16}
  203. Point(d_{16}) → F_{15}
  204. Segment(E_{16}, F_{15}) → j_{15}
  205. OrthogonalLine(F_{15}, j_{15}) → k_{15}
  206. Circle(F_{15}, (2.5 * tilewidth)) → e_{33}
  207. Intersect(e_{33}, k_{15}, 2) → G_{12}
  208. Line(E_{16}, k_{15}) → l_{15}
  209. OrthogonalLine(G_{12}, l_{15}) → m_{15}
  210. Intersect(l_{15}, m_{15}) → H_{12}
  211. Polygon(E_{16}, F_{15}, G_{12}, H_{12}) → Xrod16, e_{25}, f_{33}, g_{33}, h_{33}
  212. Circle(E_{18}, tilewidth) → d_{18}
  213. Point(d_{18}) → F_{17}
  214. Segment(E_{18}, F_{17}) → j_{17}
  215. OrthogonalLine(F_{17}, j_{17}) → k_{17}
  216. Circle(F_{17}, (2.5 * tilewidth)) → e_{35}
  217. Intersect(e_{35}, k_{17}, 2) → G_{10}
  218. Line(E_{18}, k_{17}) → l_{17}
  219. OrthogonalLine(G_{10}, l_{17}) → m_{17}
  220. Intersect(l_{17}, m_{17}) → H_{10}
  221. Polygon(E_{18}, F_{17}, G_{10}, H_{10}) → Xrod17, e_{27}, f_{35}, g_{35}, h_{35}
  222. Circle(E_{19}, tilewidth) → d_{19}
  223. Point(d_{19}) → F_{18}
  224. Segment(E_{19}, F_{18}) → j_{18}
  225. OrthogonalLine(F_{18}, j_{18}) → k_{18}
  226. Circle(F_{18}, (2.5 * tilewidth)) → e_{37}
  227. Intersect(e_{37}, k_{18}, 2) → G_{18}
  228. Line(E_{19}, k_{18}) → l_{18}
  229. OrthogonalLine(G_{18}, l_{18}) → m_{18}
  230. Intersect(l_{18}, m_{18}) → H_{18}
  231. Polygon(E_{19}, F_{18}, G_{18}, H_{18}) → Xrod18, e_{36}, f_{36}, g_{36}, h_{36}
  232. Circle(I, (2.5 * tilewidth)) → p
  233. Point(p) → J
  234. Polygon(I, J, 4) → Xsquare01, n, q, r, s, K, L
  235. Circle(I_1, (2.5 * tilewidth)) → p_1
  236. Point(p_1) → J_1
  237. Polygon(I_1, J_1, 4) → Xsquare02, n_1, q_1, r_1, s_1, K_1, L_1
  238. Circle(I_2, (2.5 * tilewidth)) → p_2
  239. Point(p_2) → J_2
  240. Polygon(I_2, J_2, 4) → Xsquare03, n_2, q_2, r_2, s_2, K_2, L_2
  241. Circle(I_3, (2.5 * tilewidth)) → p_3
  242. Point(p_3) → J_3
  243. Polygon(I_3, J_3, 4) → Xsquare04, n_3, q_3, r_3, s_3, K_5, L_5
  244. Circle(I_4, (2.5 * tilewidth)) → p_4
  245. Point(p_4) → J_4
  246. Polygon(I_4, J_4, 4) → Xsquare05, n_4, q_4, r_4, s_4, K_4, L_4
  247. Circle(I_5, (2.5 * tilewidth)) → p_5
  248. Point(p_5) → J_5
  249. Polygon(I_5, J_5, 4) → Xsquare06, n_5, q_5, r_5, s_5, K_3, L_3
  250. Circle(I_6, (2.5 * tilewidth)) → p_6
  251. Point(p_6) → J_6
  252. Polygon(I_6, J_6, 4) → Xsquare07, n_6, q_6, r_6, s_6, K_{11}, L_{11}
  253. Circle(I_7, (2.5 * tilewidth)) → p_7
  254. Point(p_7) → J_7
  255. Polygon(I_7, J_7, 4) → Xsquare08, n_7, q_7, r_7, s_7, K_{10}, L_{10}
  256. Circle(I_8, (2.5 * tilewidth)) → p_8
  257. Point(p_8) → J_8
  258. Polygon(I_8, J_8, 4) → Xsquare09, n_8, q_8, r_8, s_8, K_9, L_9
  259. Circle(I_9, (2.5 * tilewidth)) → p_9
  260. Point(p_9) → J_9
  261. Polygon(I_9, J_9, 4) → Xsquare10, n_9, q_9, r_9, s_9, K_8, L_8
  262. Circle(I_{10}, (2.5 * tilewidth)) → p_{10}
  263. Point(p_{10}) → J_{10}
  264. Polygon(I_{10}, J_{10}, 4) → Xsquare11, n_{10}, q_{10}, r_{10}, s_{10}, K_7, L_7
  265. Circle(I_{11}, (2.5 * tilewidth)) → p_{11}
  266. Point(p_{11}) → J_{11}
  267. Polygon(I_{11}, J_{11}, 4) → Xsquare12, n_{11}, q_{11}, r_{11}, s_{11}, K_6, L_6
  268. Circle(I_{12}, (2.5 * tilewidth)) → p_{12}
  269. Point(p_{12}) → J_{12}
  270. Polygon(I_{12}, J_{12}, 4) → Xsquare13, n_{12}, q_{12}, r_{12}, s_{12}, K_{15}, L_{15}
  271. Circle(I_{13}, (2.5 * tilewidth)) → p_{13}
  272. Point(p_{13}) → J_{13}
  273. Polygon(I_{13}, J_{13}, 4) → Xsquare14, n_{13}, q_{13}, r_{13}, s_{13}, K_{14}, L_{14}
  274. Circle(I_{14}, (2.5 * tilewidth)) → p_{14}
  275. Point(p_{14}) → J_{14}
  276. Polygon(I_{14}, J_{14}, 4) → Xsquare15, n_{14}, q_{14}, r_{14}, s_{14}, K_{13}, L_{13}
  277. Circle(I_{15}, (2.5 * tilewidth)) → p_{15}
  278. Point(p_{15}) → J_{15}
  279. Polygon(I_{15}, J_{15}, 4) → Xsquare16, n_{15}, q_{15}, r_{15}, s_{15}, K_{12}, L_{12}
  280. Circle(I_{16}, (2.5 * tilewidth)) → p_{16}
  281. Point(p_{16}) → J_{16}
  282. Polygon(I_{16}, J_{16}, 4) → Xsquare17, n_{16}, q_{16}, r_{16}, s_{16}, K_{19}, L_{19}
  283. Circle(I_{17}, (2.5 * tilewidth)) → p_{17}
  284. Point(p_{17}) → J_{17}
  285. Polygon(I_{17}, J_{17}, 4) → Xsquare18, n_{17}, q_{17}, r_{17}, s_{17}, K_{18}, L_{18}
  286. Circle(I_{18}, (2.5 * tilewidth)) → p_{18}
  287. Point(p_{18}) → J_{18}
  288. Polygon(I_{18}, J_{18}, 4) → Xsquare19, n_{18}, q_{18}, r_{18}, s_{18}, K_{17}, L_{17}
  289. Circle(I_{19}, (2.5 * tilewidth)) → p_{19}
  290. Point(p_{19}) → J_{19}
  291. Polygon(I_{19}, J_{19}, 4) → Xsquare20, n_{19}, q_{19}, r_{19}, s_{19}, K_{16}, L_{16}
  292. Random(-3, 3) → a
  293. Random(-2, 4) → b
  294. Circle(M, tilewidth) → t
  295. Point(t) → N
  296. Point(t) → O
  297. Ray(N, M) → t_1
  298. Ray(O, M) → a_1
  299. Random(2, 4) → f
  300. Random(1, 3) → g
  301. Random(1, 3) → h
  302. Random(-2, 2) → c_{18}
  303. Random(1, 4) → d_3
  304. Random(-3, 3) → a_2
  305. Random(-2, 4) → b_1
  306. Random(-2, 2) → c_{18}
  307. Random(1, 4) → d_{17}
  308. Random(-3, 3) → a_3
  309. Random(-2, 4) → b_2