负数余额的绝对值：汉克买自行车的债务问题

几何画板及绘图内容加载中，请稍等……

2015-11-03 04:37

所属专题 CCSS Support Math II Unit 2

该范例通过一个实际生活情境——汉克向父母借钱买自行车，余额显示为–55美元，来演示如何求负数的绝对值（即债务的大小）。核心数学概念是绝对值与数轴上的距离，理解负号表示方向，而绝对值表示量的大小。作图要点：使用GeoGebra的线段、距离、正交线、向量等命令构建数轴和点，通过滑块和序列动态展示从负数到其绝对值的转换过程，并利用文本和按钮提供交互提示。适合初中数学阶段学习有理数、绝对值概念时使用，也可用于引入数轴上的距离概念。

GeoGebra 命令及参数

Segment(C_0, (x(C_0), 0)) → D_1
Distance(L2, D_1) → val1
OrthogonalLine(L2, xAxis) → c
OrthogonalLine(L2, xAxis) → k
Vector(B_0, C_0) → u
LaTeX("\text{Hank borrowed money from his parents to buy a new bike. His parents have determined his balance is}") → Question1
LaTeX("\text{Find the absolute value.}") → text1
LaTeX("\text{Find the magnitude of Hank’s debt.}") → text4
LaTeX("\text{The magnitude of his debt is represented by the absolute value of his debt; therefore the magnitude, }") → text5
LaTeX((("\text{\textcolor{#000099}{" * val2) * "}.}")) → text7
LaTeX("\text{What is the magnitude of his debt?}") → Question2
Sequence(Sequence[Segment[A_0 + ((0.5 * i) + j, 0), A_0 + ((0.5 * i) + j, -1)], j, 1, 1], i, 0, 99) → list3
Sequence(Segment[A_0 + (i, 0), A_0 + (i, (-2))], i, 0, 50) → list1
Sequence(Segment[A_0 + (i - 0.5, 0), A_0 + (i - 0.5, -1)], i, 1, 50) → list2
Segment((0.09275, 0), (0.09275, 4)) → i
LaTeX((("\text{\textcolor{#000099}{" * val2) * "}.}")) → text7_1
LaTeX((("\text{Absolute value=" * val2) * "}")) → text26
Point(xAxis) → B
Point(i) → A
Point(xAxis) → C
Point(i) → D
Point(xAxis) → E
Segment(D, E) → d
LaTeX((((((("\text{The absolute value of \textcolor{#000099}{-" * val2) * "} can be written as \textcolor{#000099}{|-") * val2) * "|}, which is equal to \textcolor{#000099}{") * val2) * "}.}")) → text2
LaTeX("\text{or size, of Hank’s debt is}") → text6
LaTeX("\text{absolute value}") → text8_1
LaTeX("\text{a number’s distance from \textcolor{#000099}{0} on a number line; the positive value }") → text8_3
LaTeX("\text{of a quantity}") → text8_4