📚 Student's Edition: Grade K Lesson 15-4 - Counting and Comparing Numbers to 20 | 学生版：幼儿园第15课第4节——数到20并比较大小
In this lesson, young learners explore how to count objects up to 20 and compare two groups using the ideas of more, fewer, and equal. These early number skills build the foundation for later IGCSE topics such as inequalities, ordering integers, and reading number lines.
在本课中，低年级学生将练习数到20，并用“多、少、相等”来比较两组物体。这些早期数字技能将为后续 IGCSE 中的不等式、整数排序和数轴阅读等内容打下基础。
1. Learning Goals | 学习目标
, fewer, and the same. You will also learn to use the symbols >, <, and = correctly.
学完本课后，你应能正数1到20，将数字与数量对应，并用“更多”“更少”和“一样多”比较两组物体。你还将学会正确使用 >、< 和 = 符号。
The goals are designed to build number sense step by step. First you count, then you match, and finally you compare. This is the same process used in many IGCSE questions that ask you to order or compare integers.
这些目标旨在逐步培养数感。先数数，再对应数量，最后进行比较。这与许多 IGCSE 题目中要求排序或比较整数的过程相同。
2. Warm-Up Counting to 20 | 热身：数到20
Start by counting aloud from 1 to 20. Touch each object as you say the number so that every object is counted exactly once. This is called one-to-one correspondence, and it is the most important skill for accurate counting.
开始先大声从1数到20。边数边触摸每个物体，确保每个物体只数一次。这叫做一一对应，它是准确计数最重要的技能。
A common warm-up is to count steps, claps, or drawings. Use a number chart to point to each numeral while saying its name. You can also count backwards from 20 to 1 to strengthen your sense of order.
常见的热身活动是数步子、拍手或图画。使用数字表，边读数字名称边指出每个数字。你也可以从20倒数到1，以增强对顺序的感知。
| 1-10 | 11-20 |
|---|---|
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 |
Practice counting both rows until you can say the numbers without looking. This fluency makes comparison much easier.
练习数这两行数字，直到你能不看着说出来。这种流畅度会让比较变得容易得多。
3. Understanding More, Less, and Equal | 理解多、少和相等
When comparing two groups, we can line them up or count them. The group with the greater count has more; the group with the smaller count has fewer. If both counts are the same, we say they are equal.
比较两组物体时，可以排成一排或数一数。数量多的一组“更多”，数量少的一组“更少”。如果数量相同，我们说“相等”。
For example, if you have 7 red counters and 5 blue counters, the red group has more because 7 is greater than 5. The blue group has fewer because 5 is less than 7.
例如，如果你有7个红色计数片和5个蓝色计数片，红色组更多，因为7比5大。蓝色组更少，因为5比7小。
7 > 5
We read this as '7 is greater than 5'.
我们读作“7大于5”。
5 < 7
We read this as '5 is less than 7'.
我们读作“5小于7”。
6 = 6
We read this as '6 is equal to 6'.
我们读作“6等于6”。
4. Comparing with Objects | 用实物比较
Draw 8 red circles and 5 blue squares. Count each group carefully. Since 8 is more than 5, the red group has more. We can write this as:
画8个红色圆形和5个蓝色正方形。仔细数每组。因为8比5大，所以红色组更多。可以写作：
8 > 5
When the groups are small, pairing objects is a useful strategy. Remove one object from each group at a time; the group that still has objects left is the group with more. This visual method helps you see the difference without needing to count perfectly.
当数量较小时，配对法很有用。每次从两组中各拿走一个物体；最后还有剩余的那组就是更多的组。这种直观方法可以帮助你看出差别，而不必完全依赖数数。
You can also match one red object to one blue object. If every blue object has a red partner and there are red objects left over, then there are more red objects than blue objects.
你也可以把一个红色物体和一个蓝色物体配对。如果每个蓝色物体都有一个红色伙伴，还剩下红色物体，那么红色物体就比蓝色物体多。
5. Using Comparison Symbols | 使用比较符号
The symbol > means 'is greater than', < means 'is less than', and = means 'is equal to' gt; or < always faces the larger number. This visual trick prevents many common errors.
符号 > 表示“大于”，< 表示“小于”，= 表示“等于”。记住 > 和 < 的开口始终朝向较大的数。这个视觉技巧能避免许多常见错误。
- 8 > 5 means eight is greater than five.
- 4 < 6 means four is less than six.
- 7 = 7 means seven is equal to seven.
- 8 > 5 表示8大于5。
- 4 < 6 表示4小于6。
- 7 = 7 表示7等于7。
Practice reading each statement aloud. If you can say the whole sentence, you are less likely to confuse the symbols.
练习大声读出每个式子。如果你能说出完整的句子，就不太可能混淆符号。
6. Number Lines and Order | 数轴与顺序
A number line from 0 to 20 helps us see the order of numbers. Numbers to the right are greater; numbers to the left are smaller. This is why comparing numbers on a number line is a reliable strategy.
0到20的数轴帮助我们看清数字的顺序。右边的数更大，左边的数更小。这就是为什么在数轴上比较数字是一种可靠的方法。
0 → 1 → 2 → 3 → ... → 20
For example, on a number line, 14 is to the right of 9, so 14 > 9. In the same way, 3 is to the left of 11, so 3 < 11.
例如，在数轴上，14在9的右边，所以14 > 9。同样，3在11的左边，所以3 < 11。
You can draw your own number line and mark two numbers. The number that comes later in the counting sequence is always the greater number.
你可以画一条自己的数轴并标出两个数。在数数顺序中后出现的数总是更大的数。
7. Comparing Tens and Ones | 比较十位和个位
For numbers from 10 to 20, look at the tens digit first. A number with 1 ten is always greater than a number with 0 tens. For example, 12 > 9 because 12 has one ten and 9 has zero tens.
对于10到20的数，先看十位数字。有1个十的数总比没有十的数大。例如12 > 9，因为12有1个十，而9没有十。
When both numbers have 1 ten, compare the ones digit. For example, 17 > 14 because 7 ones are more than 4 ones. This method works even when the numbers are written as words.
当两个数都有1个十时，再比较个位数字。例如17 > 14，因为7个一比4个一更多。即使数字是用文字写出来，这个方法仍然有效。
| First number | Second number | Comparison |
|---|---|---|
| 13 | 15 | 13 < 15 |
| 19 | 11 | 19 > 11 |
| 10 | 10 | 10 = 10 |
Use this table to see how tens and ones decide the comparison. The structure stays the same for larger numbers later in IGCSE.
用这个表格看看十位和个位如何决定比较结果。这个结构在以后 IGCSE 中更大的数字上仍然适用。
8. Sorting Numbers | 给数字排序
Sorting numbers means putting them in order from smallest to greatest or from greatest to smallest. Start by finding the smallest number and placing it first, then find the next smallest, and continue.
给数字排序就是把它们从小到大或从大到小排列。先找出最小的数放在第一位，再找出下一个最小的数，依此类推。
For example, sort 14, 6, 19, and 11 from smallest to greatest. The smallest is 6, then 11, then 14, and the greatest is 19. We write: 6 < 11 < 14 < 19.
例如，将14、6、19和11从小到大排序。最小的是6，然后是11、14，最大的是19。我们写作：6 < 11 < 14 < 19。
Sorting is used when reading data in charts or when comparing measurements. Practising with small numbers makes the skill automatic.
排序在阅读图表数据或比较大小时都会用到。练习小数字可以让这项技能变得熟练。
9. Common Mistakes | 常见错误
A common mistake is counting too quickly and skipping an object. Always touch or mark each item as you count. Another mistake is reading the symbol backwards; remember the wide part faces the bigger number.
常见错误是数得太快而漏掉物体。数数时一定要触摸或标记每个物品。另一个错误是把符号读反；记住开口朝向较大的数。
Some learners think a larger-looking group always has more. If objects are spread out, the group can look bigger but actually have fewer items. Always count rather than guess based on appearance.
有些学生认为看起来占地方大的组一定更多。如果物体摆得分散，一组可能看起来更大，但实际数量更少。一定要数一数，而不是根据外观猜测。
Also, when comparing two numbers such as 12 and 8, do not compare only the ones digit. Look at the tens digit first. This prevents errors like saying 8 is greater than 12.
此外，比较12和8这样的两个数时，不要只比较个位数字。先看十位数字。这样可以避免出现“8大于12”这样的错误。
10. Practice Questions | 练习题
tions. Count first, then compare using >, <, or =. Write your answers in a notebook.
试试下面的练习题。先数一数，再用 >、< 或 = 比较。把答案写在笔记本上。
- 9 and 7
- 12 and 15
- 6 and 6
- 18 and 11
- 5 and 9
- 13 and 13
- 10 and 20
- 4 and 2
are: 9 > 7, 12 < 15, 6 = 6, 18 > 11, 5 < 9, 13 = 13, 10 < 20, and 4 > 2.
答案是：9 > 7、12 < 15、6 = 6、18 > 11、5 < 9、13 = 13、10 < 20、4 > 2。
After you finish, check each answer by drawing objects or using a number line. If you made a mistake, find the step where the counting or symbol use went wrong.
完成后，通过画物体或使用数轴检查每个答案。如果做错了，找出是哪一步数数或符号使用出了问题。
11. Challenge: Missing Number Comparisons | 挑战：缺失数字比较
Now try a harder challenge. Fill in a missing number so that the comparison is true. There may be more than one correct answer.
现在尝试更有难度的挑战。填入一个缺失的数字，使比较成立。可能有多个正确答案。
? < 12
Any whole number less than 12 can be placed in the blank, such as 5, 8, or 11. Also try this one:
任何小于12的整数都可以填入空白处，例如5、8或11。再试试这个：
15 > ?
Here the missing number must be less than 15, such as 10 or 0. Finally, make this true with an equal number:
这里缺失的数字必须小于15，例如10或0。最后，填入相等的数字使这个式子成立：
? = 16
The only correct answer is 16. These challenges prepare you for solving simple inequalities later.
唯一正确的答案是16。这些挑战为你以后解决简单不等式做好准备。
12. Key Takeaways | 要点总结
Counting to 20 and comparing numbers build number sense. Use one-to-one counting, look at tens and ones, and remember that the open side of a comparison symbol faces the larger number.
数到20并比较数字能培养数感。使用一一对应数数，先看十位和个位，并记住比较符号的开口朝向较大的数。
These skills are not just for early years. They help you order integers, read inequalities, and solve problems in IGCSE mathematics with confidence.
这些技能不仅适用于低年级。它们将帮助你在 IGCSE 数学中自信地排序整数、阅读不等式和解决问题。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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