📚 Student’s Edition Grade 1 Lesson 16-1: Equal Shares | 学生版一年级第16-1课：均等分配
Welcome to Lesson 16-1. In this lesson, you will learn how to split a whole shape into equal shares. You will meet two important equal shares: halves and fourths. You will also learn to recognise whether parts are equal or unequal, and you will begin to use basic fraction words such as ‘half’, ‘fourth’, and ‘quarter’.
欢迎来到第16-1课。本课你将学习如何把一个完整图形分成均等份额。你将认识两种重要的均等份额：二等份和四等份。你还将学会判断部分是否相等，并开始使用 ‘half’、’fourth’ 和 ‘quarter’ 等基础分数词汇。
1. What Are Equal Shares? | 什么是均等分配？
Equal shares are parts that have exactly the same size. When a shape is cut into equal shares, the pieces cover the same amount of the original shape. For example, if you fold a square so that the two parts match perfectly, you have made two equal shares.
均等分配是指大小完全相同的部分。当一个图形被切成均等份额时，每一块覆盖原图形同样大小的面积。例如，如果你把一个正方形对折，使两个部分完全重合，你就得到了两个均等份额。
In Grade 1, we usually work with shapes divided into 2 equal shares or 4 equal shares. Equal shares do not always need to have exactly the same shape, but in simple circles, squares, and rectangles they usually do.
在一年级，我们通常处理被分成 2 等份或 4 等份的图形。均等份额并不一定总要形状完全相同，但在简单的圆形、正方形和长方形中，它们通常是相同的。
- Two equal shares are called halves.
- Four equal shares are called fourths or quarters.
- Unequal parts are not equal shares.
- 两个相等的部分叫做 halves。
- 四个相等的部分叫做 fourths 或 quarters。
- 不等的部分不是均等份额。
2. Two Equal Shares: Halves | 二等份：一半
When one whole shape is split into two equal shares, each share is called one half. The word ‘half’ means one of two equal parts. If you colour one half of a shape, you colour exactly one of the two equal pieces.
当一个完整图形被分成两个相等的份额时，每一份叫做一个 half（一半）。单词 half 表示两个相等部分之一。如果你给一个图形的一半涂色，你就正好涂了两个相等部分中的一份。
Two halves always make one whole. This can be written as:
两个一半总是组成一个整体。这可以写成：
½ + ½ = 1
A circle folded through its centre gives two half-circles. A square cut straight down the middle gives two equal rectangles. Each of these pieces is one half of the original shape.
一个圆沿中心对折会得到两个半圆。一个正方形从正中间直切会得到两个相等的长方形。这些块中的每一块都是原图形的 ½。
3. Four Equal Shares: Fourths and Quarters | 四等份：四分之一
When a whole is split into four equal shares, each share is called one fourth or one quarter. ‘Fourth’ comes from the number four, and ‘quarter’ is another common word for the same idea: one of four equal parts.
当一个整体被分成四个相等份额时，每一份叫做一个 fourth（四分之一）或一个 quarter（四分之一）。Fourth 来自数字四，quarter 是表示相同含义的另一个常用词：四个相等部分之一。
Four fourths together make one whole. This can be written as:
四个四分之一合在一起组成一个整体。这可以写成：
¼ + ¼ + ¼ + ¼ = 1
For example, if a rectangle is divided by one vertical line and one horizontal line through the centre, it makes four equal smaller rectangles. Each smaller rectangle is one fourth or one quarter of the whole rectangle.
例如，如果一个长方形通过中心的一条竖线和一条横线被分割，就会得到四个相等的小长方形。每个小长方形就是整个长方形的一个 fourth 或 quarter。
4. Equal or Not Equal? | 均等还是不均等？
A key skill in this lesson is to decide whether parts are equal or not equal. Equal shares must have the same size. If the pieces are different sizes, they are not equal shares, even if there are two or four pieces.
本课的一个关键技能是判断部分是否相等。均等份额必须大小相同。如果各块大小不同，它们就不是均等份额，即使有两块或四块也是一样。
Look carefully at the area of each piece, not just the number of pieces. Four pieces are not automatically fourths unless the four pieces cover the same amount of the original shape.
要仔细看每一块的面积，而不仅仅是块的数量。四块不一定是四分之一，除非四块覆盖原图形同样大小的面积。
- Equal: two pieces with the same size and area.
- Not equal: one large piece and one small piece.
- Equal: four identical smaller squares from one large square.
- Not equal: four pieces of different sizes.
- 相等：两块大小和面积相同。
- 不等：一块大和一块小。
- 相等：一个大正方形分出的四个相同小正方形。
- 不等：四块大小不同。
5. Halves in a Circle | 圆形的二等分
A circle can be divided into two equal shares by drawing one straight line through the centre. This line is called a diameter. Folding the circle so that the edges match is a hands-on way to check that the halves are equal.
通过圆心画一条直线，可以把圆分成两个相等份额。这条线叫做直径。把圆对折、让边缘重合，是动手检验两半是否相等的方法。
Each half-circle is one half of the circle. You can turn one half around and it will still fit exactly over the other half. This shows that the two halves have equal area.
每个半圆是圆的 ½。你可以把一个半圆翻转，它仍能与另一个半圆完全重合。这说明两个半圆面积相等。
1 circle = 2 half-circles
If you colour one half-circle, you colour ½ of the circle. If you colour both half-circles, you colour the whole circle.
如果你给一个半圆涂色，你就涂了圆的 ½。如果你给两个半圆都涂色，你就涂了整个圆。
6. Fourths in a Rectangle | 长方形的四等分
A rectangle can be divided into four equal shares by drawing one vertical line and one horizontal line through the centre. Each share is a smaller rectangle with one fourth of the area.
通过在中心画一条竖线和一条横线，可以把长方形分成四个相等份额。每一份是一个较小的长方形，占原长方形面积的四分之一。
If the original rectangle has area A, each fourth has area A ÷ 4. This is why the word ‘fourth’ is used: the whole area is divided by 4.
如果原长方形面积为 A，每个四分之一面积为 A ÷ 4。这就是为什么使用 ‘fourth’ 一词：整个面积被除以 4。
¼ + ¼ + ¼ + ¼ = 1
You can also make fourths by folding a rectangular piece of paper twice. First fold it into two equal halves, then fold it again so that the two halves match. When you open the paper, you will see four equal parts.
你也可以通过把一张长方形纸对折两次来得到四等份。先折成两个相等的半份，然后再对折使两个半份重合。打开纸后，你会看到四个相等的部分。
7. Describing Whole, Half, and Quarter | 描述整体、一半和四分之一
The word ‘whole’ describes the complete shape before cutting. ‘Half’ describes one of two equal parts. ‘Quarter’ or ‘fourth’ describes one of four equal parts. These words help you talk about fractions without needing formal fraction notation.
单词 whole 描述切割前的完整图形。Half 描述两个相等部分之一。Quarter 或 fourth 描述四个相等部分之一。这些词汇帮助你谈论分数，而不需要正式的分数写法。
If you colour 1 part out of 2 equal parts, you colour ½ of the shape. If you colour 1 part out of 4 equal parts, you colour ¼ of the shape.
如果你给 2 等份中的 1 份涂色，你就涂了图形的 ½。如果你给 4 等份中的 1 份涂色，你就涂了图形的 ¼。
| Word | Meaning | Example |
|---|---|---|
| whole | one complete shape | a full pizza |
| half | one of two equal parts | one slice of a pizza cut into 2 equal slices |
| fourth / quarter | one of four equal parts | one slice of a pizza cut into 4 equal slices |
8. Common Misconceptions | 常见误区
Misconception 1: any two pieces are halves. Correction: halves must be equal in area. If one piece is larger than the other, they are not halves.
误区一：任意两块都是 half。纠正：half 必须面积相等。如果一块比另一块大，它们就不是 half。
Misconception 2: a shape cut into four pieces always shows fourths. Correction: only equal-size pieces are fourths. Four unequal pieces do not show quarters.
误区二：图形切成四块就一定是 fourth。纠正：只有大小相同的四块才是 fourth。四块不等就不是 quarter。
Misconception 3: equal shares must have identical shape. Correction: area is what matters. In most Grade 1 examples the shapes are identical, but equal area is the key idea.
误区三：均等份额必须形状完全相同。纠正：面积才是关键。在大多数一年级例子中形状是相同的，但面积相等才是核心概念。
9. Quick Practice Questions | 快速练习
Try these questions to check your understanding. Answers are given below.
试试这些问题来检查你的理解。答案在下面。
- If a pizza is cut into 2 equal slices, what fraction of the pizza is one slice?
- A rectangle is divided into 4 equal parts. What is one part called?
- Draw a square and shade one quarter of it.
- True or false: two halves make one whole.
- 如果一个披萨被切成 2 块相等的片，一块是披萨的几分之几？
- 一个长方形被分成 4 等份，其中一份叫什么？
- 画一个正方形并涂色它的四分之一。
- 判断对错：两个一半组成一个整体。
Answers: ½, one fourth or one quarter, your shaded square should show 1 of 4 equal parts, true.
答案：½，一个 fourth 或 quarter，你涂色的正方形应显示 4 等份中的 1 份，正确。
10. Connection to IGCSE Fractions | 与 IGCSE 分数的衔接
IGCSE Mathematics builds on these early ideas by writing fractions in the form a/b. One half is written as 1/2, and one quarter is written as 1/4. The top number, called the numerator, shows how many equal parts are chosen. The bottom number, called the denominator, shows how many equal parts make one whole.
IGCSE 数学在这些早期概念的基础上，书写 a/b 形式的分数。一半写作 1/2，四分之一写作 1/4。上面的数叫分子，表示选取了多少个相等部分。下面的数叫分母，表示一个整体分成多少个相等部分。
Later, learners add, subtract, compare, and simplify fractions. They also meet equivalent fractions such as 2/4 = 1/2. Equal-share diagrams are the first step toward the area model used in many IGCSE fraction problems.
之后，学习者会进行分数的加减、比较和化简。他们还会学习等价分数，例如 2/4 = 1/2。均等分配图是许多 IGCSE 分数问题中面积模型的第一步。
2/4 = 1/2 and 4/4 = 1
Understanding that four quarters make one whole is the same as understanding that 4/4 = 1. This is a foundational idea for all later fraction work.
理解四个四分之一组成一个整体，就是理解 4/4 = 1。这是以后所有分数学习的基础概念。
11. Key Vocabulary Summary | 重要词汇总结
| Term | Meaning | Example |
|---|---|---|
| whole | one complete shape or object | one full circle |
| half | one of two equal parts | ½ of a square |
| fourth | one of four equal parts | ¼ of a rectangle |
| quarter | another word for fourth | ¼ of a pizza |
| equal shares | parts with the same size or area | 更多咨询请联系16621398022（同微信）
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