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Exploring Integers on a Thermometer

Exploring Integers on a Thermometer
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2013-03-05 05:24
PolygonCoordinate GeometryGeometric Construction
This example uses a thermometer model to demonstrate reading, ordering, and adding/subtracting integers. It covers key concepts such as integers and thermometers. GeoGebra commands used include Line, Point, Dilate, Segment, Sequence, Circle, Mirror, CircleSector, Intersect, Polygon, Midpoint, Unique, Shuffle, OrthogonalLine, Rotate, Angle, Element, If, Textfield, Random, PolyLine, Text. Suitable for upper elementary to middle school students.

GeoGebra Commands & Parameters

  1. Line(A_2, A_1) → c
  2. Point(c) → P_0
  3. Dilate(B_1, 1 / brPodjela, A_1) → B_p
  4. Point(Circle[A, a]) → B
  5. Segment(A, B) → b
  6. Sequence(Segment[Translate[A_2, Vector[i * Vector[A_1, B_p]]], Translate[A_1, Vector[i * Vector[A_1, B_p]]]], i, 1, brPodjela - 1) → lista1
  7. Line(B_2, B_1) → d
  8. Point(c) → C_1
  9. Point(c) → C_2
  10. Point(d) → D_1
  11. Point(d) → D_2
  12. Dilate(D_1, 1 / brPodjela, C_1) → D_p
  13. Sequence(Segment[Translate[C_2, Vector[i * Vector[C_1, D_p]]], Translate[C_1, Vector[i * Vector[C_1, D_p]]]], i, 1, brPodjela - 1) → lista2
  14. Line(B_p, D_p) → e
  15. Point(e) → C
  16. Line(C, yAxis) → f
  17. Point(f) → D
  18. Circle(D, C) → g
  19. Mirror(C, D) → C'
  20. CircleSector(D, C, C') → h
  21. CircleSector(D, C', C) → k
  22. Segment(A_1, B_1) → i
  23. Point(i) → E
  24. Line(E, xAxis) → j
  25. Intersect(f, c) → F
  26. Intersect(f, j) → G
  27. Line(H, yAxis) → l
  28. Intersect(l, c) → I
  29. Intersect(l, j) → J
  30. Polygon(F, I, J, G) → mnogokut1, f_1, i_1, j_1, g_1
  31. Line(K, yAxis) → m
  32. Segment(C_2, D_2) → n
  33. Point(n) → L
  34. Line(L, xAxis) → p
  35. Intersect(p, f) → M
  36. Intersect(m, p) → N
  37. Intersect(m, c) → O
  38. Polygon(O, F, M, N) → mnogokut2, o, f_2, m_1, n_1
  39. Segment(A_1, C_2) → q
  40. Segment(B_1, D_2) → r
  41. Segment(E, G) → s
  42. Segment(L, M) → t
  43. Segment(A_2, P_0) → a_1
  44. Segment(R_1, P_1) → b_1
  45. Segment(R_2, P_2) → c_1
  46. Segment(R_3, P_3) → d_1
  47. Segment(R_4, P_4) → e_1
  48. Segment(R_5, P_5) → h_1
  49. Segment(R_6, P_6) → k_1
  50. Segment(R_7, P_7) → l_1
  51. Segment(B_2, P_8) → p_1
  52. Point(c) → Q_0
  53. Segment(Q_8, D_1) → q_1
  54. Segment(Q_7, T_7) → r_1
  55. Segment(Q_6, T_6) → s_1
  56. Segment(Q_5, T_5) → t_1
  57. Segment(Q_4, T_4) → a_2
  58. Segment(Q_3, T_3) → b_2
  59. Segment(Q_2, T_2) → c_2
  60. Segment(Q_1, T_1) → d_2
  61. Segment(Q_0, C_1) → e_2
  62. Segment(F, C') → g_2
  63. Point(i) → P
  64. Point(i) → Q
  65. Point(n) → R
  66. Point(n) → S
  67. Intersect(c, l) → T
  68. Intersect(c, m) → U
  69. Segment(U, T) → h_2
  70. Midpoint(h_2) → V
  71. Segment(V, T) → i_2
  72. Midpoint(i_2) → W
  73. Segment(V, U) → j_2
  74. Midpoint(j_2) → Z
  75. Line(R, xAxis) → k_2
  76. Line(Z, yAxis) → l_2
  77. Intersect(m, k_2) → E_1
  78. Intersect(l_2, k_2) → F_1
  79. Polygon(U, Z, F_1, E_1) → mnogokut3, u_1, z, f_3, e_3
  80. Segment(R, F_1) → m_2
  81. Line(Q, xAxis) → n_2
  82. Line(V, yAxis) → p_2
  83. Intersect(n_2, p_2) → G_1
  84. Intersect(n_2, l_2) → H_1
  85. Polygon(V, G_1, H_1, Z) → mnogokut4, v, g_3, h_3, z_1
  86. Segment(Q, H_1) → q_2
  87. Line(S, xAxis) → r_2
  88. Line(W, yAxis) → s_2
  89. Intersect(r_2, s_2) → I_1
  90. Intersect(r_2, p_2) → J_1
  91. Polygon(V, W, I_1, J_1) → mnogokut5, v_1, w, i_3, j_3
  92. Segment(S, I_1) → t_2
  93. Line(P, xAxis) → a_3
  94. Intersect(s_2, a_3) → K_1
  95. Intersect(a_3, l) → L_1
  96. Polygon(W, T, L_1, K_1) → mnogokut6, w_1, t_3, l_3, k_3
  97. Segment(P, K_1) → b_3
  98. Sequence(Random[-20, 20] + 0 * u, i, 1, 10) → Zad1SviBrojevi
  99. Unique(Zad1SviBrojevi) → Zad1Unique
  100. Shuffle(Zad1Unique) → Zad1Rnd
  101. Sequence(Element[Zad1Rnd, i], i, 1, 4) → Zad1Odabrani
  102. Point(xAxis) → M_1
  103. Point(xAxis) → N_1
  104. Point(xAxis) → O_1
  105. Point(xAxis) → S_1
  106. Line(M_1, yAxis) → c_3
  107. Line(N_1, yAxis) → d_3
  108. Line(O_1, yAxis) → m_3
  109. Line(S_1, yAxis) → n_3
  110. Point(yAxis) → U_1
  111. Line(U_1, xAxis) → p_3
  112. Intersect(p_3, c_3) → V_1
  113. Intersect(p_3, d_3) → W_1
  114. Intersect(p_3, m_3) → Z_1
  115. Intersect(p_3, n_3) → E_2
  116. Circle(V_1, 1) → q_3
  117. Circle(W_1, 1) → r_3
  118. Circle(Z_1, 1) → s_3
  119. Circle(E_2, 1) → c_4
  120. OrthogonalLine(V_1, p_3) → a_4
  121. Intersect(q_3, a_4) → F_2, G_2
  122. Intersect(q_3, p_3) → H_2, I_2
  123. Polygon(F_2, I_2, 4) → mnogokut7, b_4, d_4, e_4, f_4, J_2, K_2
  124. Point(r_3) → L_2
  125. Rotate(L_2, 60*°, W_1) → M_2
  126. Angle(L_2, W_1, M_2) → α
  127. Rotate(L_2, 300*°, W_1) → N_2
  128. Angle(N_2, W_1, L_2) → β
  129. Polygon(N_2, M_2, 3) → mnogokut8, g_4, h_4, i_4, O_2
  130. Point(s_3) → S_2
  131. Rotate(S_2, 30*°, Z_1) → U_2
  132. Angle(S_2, Z_1, U_2) → γ
  133. Rotate(S_2, 330*°, Z_1) → V_2
  134. Angle(V_2, Z_1, S_2) → δ
  135. Polygon(V_2, U_2, 6) → mnogokut9, j_4, B_3, k_4, l_4, m_4, n_4, p_4, W_2, Z_2, A_3
  136. Point(c_4) → C_3
  137. Rotate(C_3, 60*°, E_2) → D_3
  138. Rotate(C_3, 300*°, E_2) → E_3
  139. Angle(E_3, E_2, C_3) → ε
  140. Polygon(E_3, D_3, 3) → mnogokut10, q_4, r_4, s_4, F_3
  141. Element(Zad1Odabrani, 1) → Zad1br1
  142. Element(Zad1Odabrani, 2) → Zad1br2
  143. Element(Zad1Odabrani, 3) → Zad1br3
  144. Element(Zad1Odabrani, 4) → Zad1br4
  145. If(Zad1br1 > Zad1br2, 1, 0) → Gscore_1
  146. If(Zad1br1 > Zad1br4, 1, 0) → Gscore_3
  147. If(Zad1br1 > Zad1br3, 1, 0) → Gscore_2
  148. If(Zad1br2 > Zad1br1, 1, 0) → Hscore_1
  149. If(Zad1br2 > Zad1br3, 1, 0) → Hscore_2
  150. If(Zad1br2 > Zad1br4, 1, 0) → Hscore_3
  151. If(Zad1br3 > Zad1br1, 1, 0) → Iscore_1
  152. If(Zad1br3 > Zad1br2, 1, 0) → Iscore_2
  153. If(Zad1br3 > Zad1br4, 1, 0) → Iscore_3
  154. If(Zad1br4 > Zad1br1, 1, 0) → Jscore_1
  155. If(Zad1br4 > Zad1br2, 1, 0) → Jscore_2
  156. If(Zad1br4 > Zad1br3, 1, 0) → Jscore_3
  157. If(((abs(x(G_3) - x(V_1)) ≤ 0.1) ∨ (abs(x(G_3) - x(W_1)) ≤ 0.1) ∨ (abs(x(G_3) - x(Z_1)) ≤ 0.1) ∨ (abs(x(G_3) - x(E_2)) ≤ 0.1)) ∧ (abs(y(G_3) - y(U_1)) ≤ 0.1), 1, 0) → GMoved
  158. If(((abs(x(H_3) - x(V_1)) ≤ 0.1) ∨ (abs(x(H_3) - x(W_1)) ≤ 0.1) ∨ (abs(x(H_3) - x(Z_1)) ≤ 0.1) ∨ (abs(x(H_3) - x(E_2)) ≤ 0.1)) ∧ (abs(y(H_3) - y(U_1)) ≤ 0.1), 1, 0) → HMoved
  159. If(((abs(x(I_3) - x(V_1)) ≤ 0.1) ∨ (abs(x(I_3) - x(W_1)) ≤ 0.1) ∨ (abs(x(I_3) - x(Z_1)) ≤ 0.1) ∨ (abs(x(I_3) - x(E_2)) ≤ 0.1)) ∧ (abs(y(I_3) - y(U_1)) ≤ 0.1), 1, 0) → IMoved
  160. If(((abs(x(J_3) - x(V_1)) ≤ 0.1) ∨ (abs(x(J_3) - x(W_1)) ≤ 0.1) ∨ (abs(x(J_3) - x(Z_1)) ≤ 0.1) ∨ (abs(x(J_3) - x(E_2)) ≤ 0.1)) ∧ (abs(y(J_3) - y(U_1)) ≤ 0.1), 1, 0) → JMoved
  161. If((abs(x(G_3) - GscoreTOT) ≤ 0.1) ∧ (abs(y(G_3) - y(U_1)) ≤ 0.1), 1, 0) → GTrue
  162. If((abs(x(H_3) - HscoreTOT) ≤ 0.1) ∧ (abs(y(H_3) - y(U_1)) ≤ 0.1), 1, 0) → HTrue
  163. If((abs(x(I_3) - IscoreTOT) ≤ 0.1) ∧ (abs(y(I_3) - y(U_1)) ≤ 0.1), 1, 0) → ITrue
  164. If((abs(x(J_3) - JscoreTOT) ≤ 0.1) ∧ (abs(y(J_3) - y(U_1)) ≤ 0.1), 1, 0) → JTrue
  165. If(GTrue ≟ 1 ∧ HTrue ≟ 1 ∧ ITrue ≟ 1 ∧ JTrue ≟ 1, "Excellent! The correct order!", "This is not the correct solution. Use the thermometer on the left for help.") → Zad1Provjera
  166. Element(Zad1Odabrani, 1) → Zad2br1
  167. Element(Zad1Odabrani, 2) → Zad2br2
  168. If(Zad2br1 > Zad2br2, 1, 0) → GreaterTrue
  169. If(Zad2br1 < Zad2br2, 1, 0) → LessTrue
  170. If(GreaterTrue ≟ 1 ∧ ClickedGreater ≟ 1 ∨ LessTrue ≟ 1 ∧ ClickedLess ≟ 1, "Excellent! You have compared numbers correctly.", "You didn't compare numbers correctly. Next time use the thermometer on the left for help.") → Zad2Provjera
  171. Textfield(Zad3Upisano) → txtPolje1
  172. Textfield(Zad4Upisano) → txtPolje2
  173. Textfield(Zad5Upisano) → txtPolje3
  174. Textfield(Zad6Upisano) → txtPolje4
  175. Random(0, 40) → promjKoordK
  176. Line(K_3, xAxis) → t_4
  177. Intersect(t_4, l) → L_3
  178. Intersect(t_4, m) → M_3
  179. Polygon(O, I, L_3, M_3) → mnogokut11, o_3, i_5, l_5, m_5
  180. Segment(L_3, K_3) → a_5
  181. Circle(D, C) → c_5
  182. Textfield(Zad7Upisano) → txtPolje5
  183. Dilate(O_3, 1 / brPodjela, N_3) → S_3
  184. Sequence(Segment[Translate[U_3, Vector[i * Vector[N_3, S_3]]], Translate[N_3, Vector[i * Vector[N_3, S_3]]]], i, 0, brPodjela) → lista3
  185. Sequence(Random[-20, 20] + 0 * u, i, 1, 8) → Zad8Brojevi
  186. Element(Zad8Brojevi, 1) → C1
  187. Element(Zad8Brojevi, 2) → C2
  188. Element(Zad8Brojevi, 3) → C3
  189. Element(Zad8Brojevi, 4) → C4
  190. Element(Zad8Brojevi, 5) → C5
  191. Element(Zad8Brojevi, 6) → C6
  192. Element(Zad8Brojevi, 7) → C7
  193. Element(Zad8Brojevi, 8) → C8
  194. PolyLine({V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4}) → b_5
  195. Line(O_3, xAxis) → d_5
  196. Line(N_3, xAxis) → e_5
  197. Point(xAxis) → F_4
  198. Line(F_4, yAxis) → f_5
  199. Intersect(f_5, d_5) → G_4
  200. Intersect(f_5, e_5) → H_4
  201. Polygon(N_3, H_4, G_4, O_3) → mnogokut12, n_5, h_5, g_5, o_4
  202. Line(L_4, xAxis) → q_5
  203. Intersect(q_5, h_5) → Z_4
  204. Segment(L_4, Z_4) → j_5
  205. Point(h_5) → U_4
  206. Line(U_4, xAxis) → k_5
  207. Intersect(k_5, o_4) → V_4
  208. Segment(V_4, U_4) → p_5
  209. Line(I_4, xAxis) → r_5
  210. Line(J_4, xAxis) → s_5
  211. Line(K_4, xAxis) → t_5
  212. Line(M_4, xAxis) → a_6
  213. Line(N_4, xAxis) → b_6
  214. Line(O_4, xAxis) → c_6
  215. Intersect(r_5, h_5) → W_4
  216. Intersect(s_5, h_5) → A_5
  217. Intersect(t_5, h_5) → B_5
  218. Intersect(a_6, h_5) → C_5
  219. Intersect(b_6, h_5) → D_5
  220. Intersect(c_6, h_5) → E_5
  221. Segment(I_4, W_4) → d_6
  222. Segment(J_4, A_5) → e_6
  223. Segment(K_4, B_5) → f_6
  224. Segment(M_4, C_5) → g_6
  225. Segment(N_4, D_5) → h_6
  226. Segment(O_4, E_5) → i_6
  227. Random(1, 5) → Zad8RndNum
  228. Element(Zad8Odgovori, Zad8RndNum) → Zad8Answer
  229. Text(Element[Zad8Pitanja, Zad8RndNum]) → Zad8Question
  230. Textfield(Zad8Upisano) → txtPolje6

AI Drawing Prompt Reference

Draw a thermometer model to demonstrate reading, ordering, and adding/subtracting integers. Start by drawing a horizontal line as the thermometer, then mark 0 degrees and add equal spaced positive and negative integer marks on both sides. Use circles and mirroring to create the thermometer's scale, and finally use polygons to connect key points, forming the thermometer's scale and tick marks.
The prompt above was compiled from the original drawing commands and is for reference only.