分数乘法几何演示 by Lee W Fisher
几何画板及绘图内容加载中,请稍等……
本范例通过几何面积模型直观演示分数乘法运算。①使用矩形或正方形面积表示分数,将两个分数分别作为长和宽绘制在坐标系中;②核心数学概念为分数乘法运算规则:分子乘分子作为结果的分子,分母乘分母作为结果的分母;③作图要点:利用Polygon命令绘制表示分数的矩形/正方形,用Point命令标记关键点,Segment命令绘制辅助线,Intersect命令找出交点以明确面积区域;④适合小学高年级或初中数学课堂演示,帮助学生建立分数乘法的几何直观理解,也可作为教师教学演示素材。
GeoGebra 命令及参数
Polygon(A, B, C, D) → q1, a, b, c, dPoint(d) → ESegment(E, F) → fPoint(d) → GSegment(G, H) → gPoint(b) → IPoint(d) → JSegment(I, J) → hSegment(K, L) → iPolygon(A_1, B_1, C_1, D_1) → q1_1, a_1, b_1, c_1, d_1Point(d_1) → E_1Segment(E_1, F_1) → f_1Point(d_1) → G_1Segment(G_1, H_1) → g_1Point(b_1) → I_1Point(d_1) → J_1Segment(I_1, J_1) → h_1Segment(K_1, L_1) → i_1Point(d_1) → MPoint(b_1) → NSegment(M, N) → jPoint(d_1) → OSegment(O, P) → kPoint(d_1) → QSegment(Q, R) → lPoint(d_1) → SPoint(b_1) → TSegment(S, T) → mPoint(d_1) → UPoint(b_1) → VSegment(U, V) → nPoint(d_1) → WPoint(b_1) → ZSegment(W, Z) → pPoint(d_1) → M_1Segment(M_1, N_1) → qPoint(d_1) → O_1Segment(O_1, P_1) → rPoint(d_1) → Q_1Point(b_1) → R_1Segment(Q_1, R_1) → sPoint(d_1) → S_1Point(b_1) → T_1Segment(S_1, T_1) → tPolygon(A, B, K, L) → q2, a_2, b_2, k_1, l_1Polygon(A_2, B_2, C_2, D_2) → q1_2, a_3, b_3, c_2, d_2Point(d_2) → E_2Segment(E_2, F_2) → f_2Point(d_2) → G_2Segment(G_2, H_2) → g_2Point(b_3) → I_2Point(d_2) → J_2Segment(I_2, J_2) → h_2Segment(K_2, L_2) → i_2Point(d_2) → M_3Point(b_3) → N_3Segment(M_3, N_3) → j_1Point(d_2) → O_3Segment(O_3, P_3) → k_2Point(d_2) → Q_3Segment(Q_3, R_3) → l_2Point(d_2) → S_3Point(b_3) → T_3Segment(S_3, T_3) → m_1Point(d_2) → U_1Point(b_3) → V_1Segment(U_1, V_1) → n_1Point(d_2) → W_1Point(b_3) → Z_1Segment(W_1, Z_1) → p_1Point(d_2) → M_2Segment(M_2, N_2) → q_1Point(d_2) → O_2Segment(O_2, P_2) → r_1Point(d_2) → Q_2Point(b_3) → R_2Segment(Q_2, R_2) → s_1Point(d_2) → S_2Point(b_3) → T_2Segment(S_2, T_2) → t_1Polygon(A_1, B_1, K_1, L_1) → q3, a_4, b_4, k_3, l_3Polygon(A_2, B_2, P_3, O_3) → q4, a_5, b_5, p_3, o_3Polygon(E_2, F_2, T_3, S_3) → q5, e_2, f_3, t_3, s_3Polygon(G_2, H_2, Z_1, W_1) → q6, g_3, h_3, z_1, w_1Polygon(J_2, O_2, P_2, I_2) → q7, j_2, o_2, p_2, i_3Polygon(A_2, B_2, K_2, L_2) → q8, a_6, b_6, k_4, l_4Polygon(A_3, B_3, C_3, D_3) → q1_3, a_7, b_7, c_3, d_3Point(d_3) → E_3Segment(E_3, F_3) → f_4Point(d_3) → G_3Segment(G_3, H_3) → g_4Point(b_7) → I_3Point(d_3) → J_3Segment(I_3, J_3) → h_4Segment(K_3, L_3) → i_4Point(d_3) → M_5Point(b_7) → N_5Segment(M_5, N_5) → j_3Point(d_3) → O_5Segment(O_5, P_5) → k_5Point(d_3) → Q_5Segment(Q_5, R_5) → l_5Point(d_3) → S_4Point(b_7) → T_4Segment(S_4, T_4) → m_2Point(d_3) → U_2Point(b_7) → V_2Segment(U_2, V_2) → n_2Point(d_3) → W_2Point(b_7) → Z_2Segment(W_2, Z_2) → p_4Point(d_3) → M_4Segment(M_4, N_4) → q_2Point(d_3) → O_4Segment(O_4, P_4) → r_2Point(d_3) → Q_4Point(b_7) → R_4Segment(Q_4, R_4) → s_2Point(d_3) → S_5Point(b_7) → T_5Segment(S_5, T_5) → t_2Polygon(A_3, B_3, K_3, L_3) → q8_1, a_8, b_8, k_6, l_6Polygon(A_3, D_3, C_3, B_3) → q9, a_{10}, d_4, c_4, b_{10}Intersect(a_8, l_6) → U_3Intersect(a_8, b_8) → V_3Intersect(p_4, b_8) → W_3Point(p_4) → Z_3Polygon(U_3, V_3, W_3, Z_3) → q10, u_3, v_3, w_3, z_3
AI 绘图提示语参考
在坐标系中绘制两个相邻的矩形,分别表示两个分数。第一个矩形由四个顶点构成,内部用线段划分出若干小格,以显示其长度和宽度分别对应分数的分子与分母。第二个矩形与第一个类似,但尺寸不同。在两个矩形之间,再绘制一个由两个矩形的边相交形成的重叠区域,该区域即为两个分数相乘的几何表示。用线段连接关键点,标出各部分的长度和宽度,并突出显示乘积对应的面积区域。整体图形用于直观展示分数乘法的面积模型。
以上提示语为根据原始绘图命令整理而来,仅供参考。