📚 Graphing Number Patterns on the Coordinate Plane | 在坐标平面上绘制数字规律
In this lesson we will learn how to use the coordinate plane to show number patterns as graphs. We will review ordered pairs, build tables of values, and turn simple number rules into straight-line graphs that help us see how numbers change.
在本节课中，我们将学习如何利用坐标平面，把数字规律画成图像。我们会复习有序数对、列出数值表，并把简单的数字规则转化为直线图像，从而更直观地看出数字是如何变化的。
1. What Is the Coordinate Plane? | 什么是坐标平面？
A coordinate plane is a flat surface made by two number lines that cross each other at a right angle. One number line is horizontal and the other is vertical.
坐标平面是由两条互相垂直的数轴构成的平面。一条数轴水平放置，另一条数轴竖直放置。
- X-axis (x 轴): the horizontal number line. 水平的数轴叫做 x 轴。
- Y-axis (y 轴): the vertical number line. 竖直的数轴叫做 y 轴。
- Origin (原点): the point where the two axes cross, marked as (0, 0). 两条数轴相交的点叫做原点，记作 (0, 0)。
- Quadrants (象限): the four regions made by the two axes. 两条数轴把平面分成四个区域，叫做象限。
In Grade 5, most of our graphs stay in Quadrant I, where both the x-value and the y-value are positive numbers.
在五年级，我们绘制的图像大多位于第一象限，也就是 x 值和 y 值都是正数的区域。
2. Ordered Pairs | 有序数对
An ordered pair is a pair of numbers that tells the exact location of a point on the coordinate plane. We write it in the form (x, y).
有序数对是一对用于表示坐标平面上某个点位置的数，我们把它写成 (x, y) 的形式。
The first number is the x-coordinate. It tells how far to move right from the origin along the x-axis. The second number is the y-coordinate. It tells how far to move up along the y-axis.
第一个数是 x 坐标，表示从原点出发沿 x 轴向右移动的距离；第二个数是 y 坐标，表示再沿 y 轴向上移动的距离。
Always write (x, y) — across first, then up.
始终先写 (x, y) —— 先横着走，再竖着走。
For example, the point (3, 5) means move 3 units right and then 5 units up. The point (5, 3) means move 5 units right and then 3 units up. These are two different locations, so the order of the numbers matters.
例如，点 (3, 5) 表示向右移动 3 个单位，再向上移动 5 个单位；而点 (5, 3) 表示向右移动 5 个单位，再向上移动 3 个单位。这两个位置完全不同，所以数字的顺序非常重要。
| Point | x-coordinate | y-coordinate |
| A | 2 | 4 |
| B | 4 | 2 |
Point A is at (2, 4) and point B is at (4, 2). They are not the same point even though they use the same two numbers.
点 A 在 (2, 4)，点 B 在 (4, 2)。虽然它们用了相同的两个数字，但它们并不是同一个点。
3. How to Plot a Point | 如何描点
Plotting a point means marking its location on the coordinate plane. Follow these steps.
描点就是在坐标平面上标出一个点的位置。请按照下面的步骤来做。
- Step 1 (第一步): Start at the origin (0, 0). 从原点 (0, 0) 出发。
- Step 2 (第二步): Move right along the x-axis by the x-coordinate. 沿着 x 轴向右移动 x 坐标所表示的距离。
- Step 3 (第三步): Move up along the y-axis by the y-coordinate. 再沿着 y 轴向上移动 y 坐标所表示的距离。
- Step 4 (第四步): Draw a dot and label it with a capital letter. 画一个点，并用大写字母给它命名。
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