📚 Animated Math Practice G-3-1: Introduction to Fractions | 数学练习动画G-3-1：分数的初步认识 知识点精讲
Welcome to the animated math adventure for Grade 3, Lesson 1! In this lesson, we explore one of the most exciting ideas in early mathematics: fractions. Through colourful animations and step-by-step examples, we’ll discover what fractions really are, how to read and write them, and why they matter in everyday life. Whether you are sharing a pizza or measuring ingredients, fractions help us describe parts of a whole. Let’s dive in and build a rock-solid foundation together.
欢迎来到三年级数学动画第一课！在本课中，我们将探索早期数学中最令人兴奋的概念之一：分数。通过生动的动画和循序渐进的示例，我们将真正理解什么是分数，如何读、写分数，以及它们为何在日常生活中如此重要。无论是分享一块比萨饼还是测量配料，分数都能帮助我们描述整体的一部分。让我们一起深入学习，建立扎实的基础。
1. What Is a Fraction? | 什么是分数？
A fraction is a number that represents a part of a whole. The whole could be a single object, like a cake, or a group of objects, like a dozen eggs. Fractions are written with two numbers separated by a line: one number above the line and one below. The top number tells how many parts we have, and the bottom number tells how many equal parts the whole is divided into.
分数是表示整体一部分的一个数。这个整体可以是一个物体，例如一个蛋糕，也可以是一组物体，例如一打鸡蛋。分数由一条线分开的两个数字书写：一个数字在线之上，一个在线之下。上面的数字表示我们有多少份，下面的数字表示整体被分成了多少等份。
For example, if you cut a pizza into 4 equal slices and eat 1 slice, you have eaten 1/4 (one‑fourth) of the pizza. The whole pizza has 4 equal parts, so the denominator is 4. The part you ate is 1 slice, so the numerator is 1.
例如，如果你将一个比萨饼切成 4 等份，并吃了 1 片，那么你吃了这个比萨饼的 1/4（四分之一）。整个比萨饼有 4 等份，因此分母是 4。你吃掉的部分是 1 片，因此分子是 1。
In the animated video, a friendly character named Slicey cuts different shapes into equal slices to show fractions like 1/2, 1/3, and 1/4. This helps you see the relationship between the parts and the whole.
在动画视频中，一个名叫 Slicey 的友好角色将不同的形状切成等份，以展示如 1/2、1/3 和 1/4 这样的分数。这有助于你理解部分与整体之间的关系。
2. Numerators and Denominators | 分子与分母
Every fraction has two key parts: the numerator and the denominator. Let’s use 3/8 as an example. The number on top, 3, is the numerator. It counts how many equal parts we are considering. The number on the bottom, 8, is the denominator. It tells us the total number of equal parts that make up the whole. Remember: Denominator = Down, it tells how many pieces the whole is divided into.
每个分数都有两个关键部分：分子和分母。我们以 3/8 为例。上面的数字 3 是分子。它表示我们所考虑的部分有多少份。下面的数字 8 是分母。它告诉我们构成整体的等份总数。请记住：分母在下，它表示整体被分成了多少块。
The animation highlights the numerator in red and the denominator in blue to make the distinction crystal clear. You’ll see that the denominator cannot be zero, because you cannot divide something into zero pieces. A fraction like 4/0 does not make sense.
动画将分子用红色高亮显示，分母用蓝色高亮显示，以使区别一目了然。你将看到分母不能为零，因为你不能将某物分成零块。像 4/0 这样的分数是毫无意义的。
When the numerator is smaller than the denominator, the fraction is less than 1 and is called a proper fraction. Examples: 2/5, 3/7, 1/9. When the numerator equals the denominator, the fraction equals exactly 1. Example: 5/5 = 1.
当分子小于分母时，分数小于 1，称为真分数。例如：2/5、3/7、1/9。当分子等于分母时，分数正好等于 1。例如：5/5 = 1。
3. Representing Fractions with Shapes | 用形状表示分数
One of the best ways to understand fractions is to look at shapes divided into equal parts. The animation shows circles, rectangles, and triangles cut into halves, thirds, quarters, and more. For instance, a circle with 3 equal coloured sections out of 4 shows 3/4. A rectangle split into 8 equal strips with 3 shaded shows 3/8.
理解分数最好的方法之一是观察被分成等份的形状。动画展示了被切成二分之一、三分之一、四分之一等的圆形、矩形和三角形。例如，一个圆形有 4 等份中的 3 份被涂色，就表示 3/4。一个矩形被分成 8 等份的条带，其中 3 份涂色，就表示 3/8。
It is crucial that the parts are equal in size. If a shape is divided into parts that are not equal, we cannot use a fraction to describe a part of it. The animation includes a ‘tricky challenge’ where you must spot the shape divided into truly equal parts – a great way to sharpen your fraction eye!
至关重要的是，这些部分必须大小相等。如果一个形状被分成了大小不等的部分，我们就不能用分数来描述它的其中一部分。动画中包含了一个“狡猾的挑战”，你必须找出哪些形状被分成了真正相等的部分——这能很好地锻炼你的分数眼力！
You can also represent fractions on a number line. The number line from 0 to 1 is divided into equal segments according to the denominator. The animation places a hopping frog at each fraction to show positions like 1/2, 2/3, and 3/4.
你也可以在数轴上表示分数。从 0 到 1 的数轴根据分母被分成相等的线段。动画在每个分数处放置一只跳跃的青蛙，以显示像 1/2、2/3 和 3/4 这样的位置。
4. Unit Fractions and Non‑Unit Fractions | 单位分数与非单位分数
A unit fraction is a fraction where the numerator is 1. It represents one part of a whole that has been divided into equal parts. Examples: 1/2, 1/5, 1/10. These are the building blocks of all other fractions. A non‑unit fraction has a numerator greater than 1, like 2/3 or 4/7, and can be thought of as multiples of a unit fraction. For example, 3/4 is three copies of the unit fraction 1/4.
单位分数是分子为 1 的分数。它表示被分成等份的整体中的一份。例如：1/2、1/5、1/10。它们是构建所有其他分数的基础。非单位分数的分子大于 1，例如 2/3 或 4/7，可以看作单位分数的倍数。例如，3/4 就是单位分数 1/4 的三份。
The animation uses a ‘fraction factory’ where unit fractions are repeated to build non‑unit fractions. A wheel cuts a whole into 6 equal slices, and picking 1 slice gives 1/6; picking 4 slices gives 4/6. This visual repetition reinforces the idea of fractions as numbers made up of smaller equal parts.
动画中有一个“分数工厂”，通过重复单位分数来构建非单位分数。一个轮子将整体切成 6 等份，取 1 份得到 1/6；取 4 份得到 4/6。这种视觉上的重复强化了分数是由较小的等份构成的数这一观念。
5. Comparing Fractions with the Same Denominator | 比较同分母分数
When two fractions have the same denominator, comparing them is easy. The fraction with the larger numerator is the larger fraction, because you have more pieces of the same size. For example, 5/8 > 3/8, because 5 slices of a pizza cut into 8 equal pieces is more pizza than 3 slices.
当两个分数分母相同时，比较它们就很容易。分子较大的分数更大，因为你拥有更多相同大小的份。例如，5/8 > 3/8，因为将比萨饼切成 8 等份后，5 片比萨比 3 片更多。
The animation sets up a scenario where two characters, Tilly and Milo, each have a chocolate bar cut into 10 equal pieces. Tilly eats 3/10, Milo eats 7/10. By overlapping the coloured bars, students instantly see that 7/10 is larger. This builds confidence before moving on to fractions with different denominators.
动画设置了一个场景：两个角色 Tilly 和 Milo 各有一块被切成 10 等份的巧克力。Tilly 吃了 3/10，Milo 吃了 7/10。通过叠加彩色条块，学生们一眼就能看出 7/10 更大。在进入比较不同分母的分数之前，这可以建立信心。
We can use the symbols >, <, and = to write comparison statements. For instance:
4/9 < 7/9
This reads ‘four‑ninths is less than seven‑ninths’.
我们可以使用 >、< 和 = 符号来书写比较语句。例如：
4/9 < 7/9
读作“九分之四小于九分之七”。
6. Comparing Fractions with the Same Numerator | 比较同分子分数
What if the numerators are the same, but the denominators are different? This is tackled next in the animated lesson. When you have the same number of pieces, the size of each piece depends on the denominator. A larger denominator means the whole is divided into more pieces, so each piece is smaller. Therefore, the fraction with the smaller denominator is larger. Example: 1/3 > 1/5, because a third of a cake is bigger than a fifth.
如果分子相同但分母不同呢？这是动画课程中要解决的下一个问题。当你拥有相同数量的份数时，每份的大小取决于分母。分母越大，意味着整体被分成的份数越多，因此每份越小。因此，分母较小的分数更大。例如：1/3 > 1/5，因为蛋糕的三分之一大于五分之一。
Using the same chocolate bar idea, the animation compares 2/4 and 2/6 by showing two identical bars, one divided into 4 equal pieces and the other into 6. Two pieces from the bar divided into 4 are visibly larger than two pieces from the bar divided into 6. The visual proof makes the abstract rule stick: when numerators are equal, the fraction with the smaller denominator is larger.
动画使用了同样的巧克力块概念，通过展示两个完全相同的长方形巧克力块来比较 2/4 和 2/6，其中一块被分成 4 等份，另一块被分成 6 等份。从分成 4 份的巧克力中取 2 块，显然比从分成 6 份的巧克力中取 2 块要大。这种视觉证明让这个抽象规则牢记于心：分子相等时，分母较小的分数更大。
7. Equivalent Fractions | 等值分数
Equivalent fractions are fractions that look different but name the same amount. For example, 1/2, 2/4, and 4/8 all represent exactly half of a whole. The animation draws a fascinating connection by shading identical‑sized portions of identical shapes that are divided into different numbers of parts. The shaded area is the same, so the fractions are equal.
等值分数是看起来不同但表示相同大小的分数。例如，1/2、2/4 和 4/8 都正好表示整体的一半。动画通过对被分成不同份数的相同形状涂上相同大小的阴影，展示了一种奇妙的联系。阴影区域相同，因此这些分数是相等的。
You can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number. This is called scaling. For instance, to get from 1/2 to 2/4, multiply both the top and bottom by 2:
1/2 = (1×2)/(2×2) = 2/4
你可以通过将分子和分母同时乘以或除以同一个数来找到等值分数。这叫做缩放。例如，要从 1/2 得到 2/4，将分子和分母都乘以 2：
1/2 = (1×2)/(2×2) = 2/4
The animated character ‘Fracto’ uses a magic fraction wand that scales fractions up and down, showing that equivalent fractions are simply the same proportion of the whole. A fraction wall display also appears, where strips are lined up to show equivalences: 1/2 lines up with 2/4 and 3/6, making the concept visible at a glance.
动画角色“Fracto”使用一根魔法分数棒，将分数放大和缩小，显示等值分数只是整体的相同比例。还出现了一面分数墙，其中将条块排列起来展示等值性：1/2 与 2/4 和 3/6 对齐，使这一概念一目了然。
8. Fractions on a Number Line | 数轴上的分数
A number line helps us see fractions as numbers with a specific position. To represent fractions on a number line, first mark 0 and 1. Then divide the space between them into equal parts based on the denominator. Each mark represents a fraction. For halves, divide into 2 equal parts; the first mark is 1/2. For thirds, divide into 3 equal parts; the marks are 1/3 and 2/3.
数轴帮助我们将分数看作有特定位置的数字。要在数轴上表示分数，首先标记 0 和 1。然后根据分母将它们之间的空间分成相等的部分。每个刻度代表一个分数。对于二分之一的分数，分成 2 等份；第一个刻度是 1/2。对于三分之一的分数，分成 3 等份；刻度分别是 1/3 和 2/3。
The animation features a digital number line where students can drag a pointer to different fractions. A bunny hops along, landing on 1/4, 2/4, 3/4, and finally 4/4 (which is 1). This activity builds understanding that fractions occupy precise locations, just like whole numbers. It also visually demonstrates that 2/4 is exactly halfway between 0 and 1, which lines up with 1/2 – reinforcing equivalent fractions.
动画展示了一根数字数轴，学生可以在上面将指针拖到不同的分数位置。一只小兔子沿着数轴跳动，落在 1/4、2/4、3/4，最后是 4/4（即 1）。这个活动让学生理解分数和整数一样占据精确的位置。它还直观地展示了 2/4 正好位于 0 和 1 的中间，与 1/2 对齐——强化了等值分数的概念。
Remember: the distance from 0 to 1 on the number line represents one whole. Fractions between 0 and 1 are proper fractions. Fractions greater than 1 can also be shown, but that is explored in later lessons.
请记住：数轴上从 0 到 1 的距离代表一个整体。介于 0 和 1 之间的分数是真分数。也可以表示大于 1 的分数，但这将在后续课程中探讨。
9. Simple Fraction Addition and Subtraction | 简单的分数加减法
Once you understand that fractions with the same denominator are made of the same‑sized pieces, adding and subtracting them becomes as simple as working with whole numbers – you just add or subtract the numerators and keep the denominator the same. For example:
2/7 + 3/7 = 5/7
一旦你理解了同分母的分数是由相同大小的块组成的，它们的加减就变得像整数运算一样简单——你只需将分子相加或相减，分母保持不变。例如：
2/7 + 3/7 = 5/7
Why does this work? The denominator ‘7’ tells us the pieces are sevenths. Two sevenths plus three sevenths gives a total of five sevenths, just as 2 apples + 3 apples = 5 apples. The animation shows a jug that collects fraction pieces: pouring 2/8 of a litre and then another 3/8 makes 5/8 of a litre. The visual makes it crystal clear.
为什么这个运算成立？分母“7”告诉我们这些块是七分之一。两个七分之一加三个七分之一总共是五个七分之一，就像 2 个苹果 + 3 个苹果 = 5 个苹果一样。动画展示了一个收集分数块的量杯：倒入 2/8 升，再倒入 3/8 升，总共是 5/8 升。视觉效果使其一清二楚。
Subtraction works the same way: 7/10 − 4/10 = 3/10. A character eats 4 slices of a pizza cut into 10 slices, starting with 7 slices. The remaining amount is 3 slices out of 10, so 3/10.
减法同样：7/10 − 4/10 = 3/10。一个角色从 7 片开始，吃掉了比萨饼切成 10 片中的 4 片。剩下的量是 10 片中的 3 片，也就是 3/10。
Always check that the denominators are the same before adding or subtracting. If they are different, you need to find a common denominator first – a skill introduced later, but the animation gives a sneak peek using fraction strips to show how 1/2 + 1/4 can be turned into 2/4 + 1/4 = 3/4.
在加减之前，务必检查分母是否相同。如果不同，你需要先找到一个公分母——这是一项将在稍后引入的技能，但动画通过使用分数条展示了如何将 1/2 + 1/4 转化为 2/4 + 1/4 = 3/4，以此进行预告。
10. Fractions in Real Life | 生活中的分数
Fractions are everywhere! In the kitchen, recipes use 1/2 cup of flour or 3/4 teaspoon of salt. When telling time, a quarter past the hour is 1/4 of an hour. In sports, a basketball player might make 3/4 of their free throws. The animation connects fractions to real situations by following a family through their day: sharing a watermelon (each person gets 1/6), measuring ribbon (cutting 2/5 of a metre), and baking cookies.
分数无处不在！在厨房里，食谱会用到 1/2 杯面粉或 3/4 茶匙盐。在报时中，过一刻钟就是 1/4 小时。在体育运动中，篮球运动员可能罚球命中率为 3/4。动画通过讲述一个家庭的一天，将分数与现实情境联系起来：分享西瓜（每人得到 1/6）、测量丝带（剪下 2/5 米）以及烤饼干。
This real‑world connection helps students see why learning fractions matters. The animation ends with a challenge: ‘Find three fractions around your home and write them down!’ This encourages children to look for fractions in food packaging, rulers, and even LEGO blocks, turning everyday life into a math adventure.
这种与现实的联系有助于学生理解为什么学习分数如此重要。动画结尾提出了一个挑战：“在你的家里找出三个分数并写下来！”这鼓励孩子们在食品包装、尺子上，甚至乐高积木中寻找分数，将日常生活变成一场数学探险。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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