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Practice Proportions with Singapore Method and Multiple Solutions

Practice Proportions with Singapore Method and Multiple Solutions
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2012-07-25 22:07
PolygonGeometric ConstructionSlider Animation
In collections Primary School Mathematics Collection Ratios and Proportions Ratios and Proportions
This example demonstrates how to use the Singapore bar model to visualize proportional relationships and offers three different solving methods. Learners can interact with ratio boxes and dynamic polygons to explore changes in numerators, denominators, and totals, practicing percentages, ratios, and division. The construction employs GeoGebra commands such as Random, GCD, Circle, OrthogonalLine, Intersect, Polygon, CreateRatioBoxes, CircumcircleArc, TableMaker, and Segment, along with objects like setnumeratorunits, to generate random proportion problems, draw bar models, and check solutions automatically. It is suitable for elementary and middle school students as a teaching aid or practice material for ratio concepts.

GeoGebra Commands & Parameters

  1. Random(1, 10) → seednumerator
  2. Random(1, 11) → seeddenominator
  3. GCD(seednumerator, seeddenominator) → seedGCF
  4. Random(2, 50) → multiplier
  5. Circle(A, 2) → c
  6. Circle(A, 1) → d
  7. OrthogonalLine(A, yAxis) → a
  8. OrthogonalLine(A, a) → b
  9. Intersect(d, b, 1) → B
  10. Intersect(c, a, 1) → C
  11. OrthogonalLine(C, a) → e
  12. OrthogonalLine(B, b) → f
  13. Intersect(e, f) → D
  14. Polygon(A, C, D, B) → poly1, a_1, c_1, d_1, b_1
  15. Intersect(c_1, a_1) → E
  16. CreateRatioBoxes(E) → poly2
  17. CreateRatioBoxes(F) → poly3
  18. CreateRatioBoxes(G) → poly4
  19. CreateRatioBoxes(H) → poly5
  20. CreateRatioBoxes(I) → poly6
  21. CreateRatioBoxes(J) → poly7
  22. CreateRatioBoxes(K) → poly8
  23. CreateRatioBoxes(L) → poly9
  24. CreateRatioBoxes(M) → poly10
  25. CreateRatioBoxes(N) → poly11
  26. CreateRatioBoxes(O) → poly12
  27. CreateRatioBoxes(P) → poly13
  28. CreateRatioBoxes(Q) → poly14
  29. CreateRatioBoxes(R) → poly15
  30. CreateRatioBoxes(S) → poly16
  31. CreateRatioBoxes(T) → poly17
  32. CreateRatioBoxes(U) → poly18
  33. CreateRatioBoxes(V) → poly19
  34. CreateRatioBoxes(W) → poly20
  35. CreateRatioBoxes(Z) → poly21
  36. CreateRatioBoxes(A_1) → poly22
  37. CircumcircleArc(F_1, H_1, G_1) → k
  38. CircumcircleArc(I_1, J_1, K_1) → p
  39. CircumcircleArc(B_1, L_1, C_1) → g
  40. CircumcircleArc(D_1, M_1, E_1) → h
  41. Random(1, 8) → selector
  42. Polygon(N_1, O_1, P_1, Q_1) → poly23, n_1, o_1, p_1, q_1
  43. Polygon(R_1, S_1, T_1, U_1) → poly24, r_1, s_1, t_1, u_1
  44. Polygon(V_1, W_1, Z_1, A_2) → poly25, v_1, w_1, z_1, a_2
  45. Polygon(B_2, C_2, D_2, E_2) → poly26, b_2, c_2, d_2, e_2
  46. Polygon(H_2, I_2, J_2, K_2) → poly27, h_2, i_2, j_2, k_2
  47. TableMaker(L_2, tablewidth, tableheight, tablecolumns, tablerows) → list1, list2, list3, list4, list5, list6
  48. Polygon(M_2, N_2, O_2, P_2) → poly28, m_2, n_2, o_2, p_2
  49. Segment(Q_2, R_2) → e_1
  50. Segment(S_2, T_2) → f_1

AI Drawing Prompt Reference

Draw a dynamic geometric figure to demonstrate proportional relationships. Include two concentric circles and a square inside, divided into multiple ratio bars that can be adjusted with sliders to show different solutions. Connect a central point to the circles with orthogonal lines to form intersection points, linking them into a polygon. The entire figure dynamically adjusts ratio bars and polygons to illustrate various solutions to proportional problems.
The prompt above was compiled from the original drawing commands and is for reference only.