Counting to 100: Building Blocks of Mathematics | 数到100：数学的基石

📚 Counting to 100: Building Blocks of Mathematics | 数到100：数学的基石

Welcome to Lesson 15-6 of our Grade K Mathematics series! In this lesson, we will explore the exciting world of numbers up to 100. Understanding how to count, read, and write numbers to 100 is one of the most important foundational skills in mathematics. This knowledge will accompany you all the way from kindergarten to IGCSE and beyond, because every advanced topic—from algebra to calculus—relies on a solid understanding of numbers and their relationships.

欢迎来到我们K年级（Grade K）数学系列的第15-6课！在本课中，我们将探索100以内数字的精彩世界。学会数数、认读和书写100以内的数字，是数学中最基础也是最重要的技能之一。这项知识将陪伴你从幼儿园一路走到IGCSE乃至更远的未来，因为从代数到微积分的每一个高级主题，都建立在对数字及其关系的扎实理解之上。

1. Counting to 100 | 数到100

Counting to 100 is like taking a journey through the number system. We start at 1 and move forward one step at a time: 1, 2, 3, 4, 5… all the way to 100. When we count, we are actually adding 1 each time. This simple pattern of “adding one” is the foundation of the entire number system. Try counting aloud: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. After 10, we enter a new pattern: 11, 12, 13, and so on.

数到100就像踏上一段穿越数字系统的旅程。我们从1开始，一次向前走一步：1、2、3、4、5……一直到100。当我们数数时，实际上每次都是在加1。这种”加1″的简单规律是整个数字系统的基础。试试大声数一数：1、2、3、4、5、6、7、8、9、10。数到10以后，我们进入新的规律：11、12、13，依此类推。

As you count higher, you will notice that numbers follow a repeating pattern. The ones digit (个位) goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and then starts over, while the tens digit (十位) increases by 1. For example: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Can you see the pattern? Each group of ten is called a “ten” or a “decade.”

当你数到更大的数字时，会发现数字遵循一种重复的规律。个位数按0、1、2、3、4、5、6、7、8、9排列，然后重新开始，而十位数每次增加1。例如：20、21、22、23、24、25、26、27、28、29、30。你能看出这个规律吗？每十个数字组成一组，称为一个”十”（decade）。

1, 2, 3, …, 10 | 11, 12, 13, …, 20 | 21, 22, 23, …, 30 | … | 91, 92, 93, …, 100

Practice counting by tens first: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. These are the “milestones” on our number journey. Once you know the tens, counting by ones becomes much easier!

先练习以十为单位数数：10、20、30、40、50、60、70、80、90、100。这些是我们数字旅程中的”里程碑”。一旦你掌握了整十数，逐个计数就变得容易多了！

2. Tens and Ones (Place Value) | 十位和个位（位值）

Every two-digit number is made up of tens and ones. In the number 47, the digit 4 is in the tens place, meaning it represents 4 tens, or 40. The digit 7 is in the ones place, meaning it represents 7 ones, or just 7. So 47 = 40 + 7. This concept is called “place value,” and it is one of the most powerful ideas in all of mathematics.

每一个两位数都由十位和个位组成。在数字47中，数字4位于十位，代表4个十，也就是40。数字7位于个位，代表7个一，也就是7。所以47 = 40 + 7。这个概念叫做”位值”（place value），它是整个数学中最强大的思想之一。

Let us look at a few more examples. The number 63 has 6 tens and 3 ones: 63 = 60 + 3. The number 85 has 8 tens and 5 ones: 85 = 80 + 5. What about 100? The number 100 has 1 hundred, 0 tens, and 0 ones. We can write this as: 100 = 100 + 0 + 0.

我们再来看几个例子。数字63有6个十和3个一：63 = 60 + 3。数字85有8个十和5个一：85 = 80 + 5。那么100呢？数字100有1个百、0个十和0个一。我们可以写成：100 = 100 + 0 + 0。

Number	Tens (十位)	Ones (个位)	Expanded Form (展开式)
23	2	3	20 + 3
58	5	8	50 + 8
72	7	2	70 + 2
100	10 (or 1 hundred)	0	100 + 0 + 0

Understanding place value helps us read numbers correctly and prepare for addition and subtraction with larger numbers. In IGCSE mathematics, place value extends to thousands, millions, and even decimals!

理解位值帮助我们正确读数字，也为大数的加减法做好准备。在IGCSE数学中，位值会扩展到千位、百万位，甚至小数！

3. Comparing Numbers | 比较数字的大小

When we compare two numbers, we decide which one is bigger, which one is smaller, or whether they are equal. We use special symbols: “greater than” (>) means the number on the left is bigger, “less than” (<) means the number on the left is smaller, and "equal to" (=) means both numbers are the same.

当我们比较两个数字时，我们要判断哪个更大、哪个更小，或者它们是否相等。我们使用特殊符号：”大于”（>）表示左边的数字更大，”小于”（<）表示左边的数字更小，"等于"（=）表示两个数字相同。

For example: 25 > 18 because 25 has 2 tens, while 18 only has 1 ten. When comparing two-digit numbers, always look at the tens digit first. The number with the larger tens digit is bigger. If the tens digits are the same, then compare the ones digits. For example: 34 and 38 both have 3 tens, so we compare the ones: 4 is less than 8, therefore 34 < 38.

例如：25 > 18，因为25有2个十，而18只有1个十。比较两位数时，先看十位数字。十位数字较大的数更大。如果十位数字相同，就比较个位数字。例如：34和38都有3个十，所以我们比较个位：4小于8，因此34 < 38。

45 > 39 — Because 4 tens is more than 3 tens (因为4个十大于3个十)
67 < 71 — Because 6 tens is less than 7 tens (因为6个十小于7个十)
82 = 82 — Both numbers are exactly the same (两个数字完全相同)
99 > 90 — Same tens digit (9), but 9 ones > 0 ones (十位相同为9，但9个一大于0个一)

4. Counting by 2s, 5s, and 10s | 以2、5、10为单位跳数

Skip counting means counting forward by a number other than 1. When we count by 2s, we say: 2, 4, 6, 8, 10, 12… When we count by 5s, we say: 5, 10, 15, 20, 25… And when we count by 10s, we say: 10, 20, 30, 40, 50… Skip counting helps us understand multiplication and division, which are key topics in later grades and in IGCSE mathematics.

跳数（skip counting）是指以1以外的数字为单位向前数数。当以2为单位数数时，我们说：2、4、6、8、10、12……当以5为单位数数时，我们说：5、10、15、20、25……当以10为单位数数时，我们说：10、20、30、40、50……跳数帮助我们理解乘法和除法，这些是高年级和IGCSE数学中的关键主题。

Skip counting also reveals beautiful patterns. When counting by 2s, all the numbers end in 0, 2, 4, 6, or 8 — the even numbers. When counting by 5s, all numbers end in 5 or 0. When counting by 10s, all numbers end in 0. Recognizing these patterns makes mental math much faster.

跳数还揭示了美丽的规律。以2为单位数数时，所有数字都以0、2、4、6或8结尾——也就是偶数。以5为单位数数时，所有数字都以5或0结尾。以10为单位数数时，所有数字都以0结尾。识别这些规律使心算更快。

Counting by 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Counting by 5s: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

In Grade K, we practice skip counting up to 100. This skill will directly help you when you learn the 2-times table, 5-times table, and 10-times table in Grade 2 and beyond.

在K年级，我们练习数到100以内的跳数。这个技能在你二年级及以后学习2的乘法表、5的乘法表和10的乘法表时，将直接为你提供帮助。

5. Number Patterns | 数字规律

Numbers can form patterns, just like shapes and colors can. A number pattern is a sequence of numbers that follows a rule. For example, the sequence 5, 10, 15, 20, 25 follows the rule “add 5 each time.” The sequence 30, 25, 20, 15 follows the rule “subtract 5 each time.”

数字可以形成规律，就像形状和颜色可以形成规律一样。数字规律是遵循某种规则的数列。例如，数列5、10、15、20、25遵循”每次加5″的规则。数列30、25、20、15遵循”每次减5″的规则。

Finding the rule is like solving a mystery! Look at the numbers and ask yourself: What is happening from one number to the next? Are we adding? Subtracting? The answer to this question is the rule of the pattern.

找出规则就像破解一个谜题！观察这些数字，问问自己：从一个数字到下一个数字发生了什么变化？我们在加还是减？这个问题的答案就是规律的规则。

2, 4, 6, 8, ? — The rule is “add 2,” so the next number is 10 (规则是”加2″，所以下一个数是10)
10, 20, 30, 40, ? — The rule is “add 10,” so the next number is 50 (规则是”加10″，所以下一个数是50)
50, 45, 40, 35, ? — The rule is “subtract 5,” so the next number is 30 (规则是”减5″，所以下一个数是30)
1, 3, 5, 7, ? — The rule is “add 2,” so the next number is 9 (规则是”加2″，所以下一个数是9)

Number patterns teach us to think logically and predict what comes next. This is an important skill for algebra, where you will use rules to generate sequences and find unknown terms.

数字规律教会我们逻辑思考和预测接下来会发生什么。这是代数学习的重要技能，在代数中你将使用规则来生成数列并找出未知项。

6. Addition: Putting Together | 加法：合在一起

Addition is the process of putting two or more groups together to find the total. The symbol for addition is “+” (plus). For example, if you have 3 apples and your friend gives you 2 more, you now have 3 + 2 = 5 apples. The answer to an addition problem is called the “sum” (和).

加法是把两个或多个组合并在一起，求出总数的过程。加法的符号是”+”（加号）。例如，如果你有3个苹果，你的朋友又给了你2个，你现在就有3 + 2 = 5个苹果。加法问题的答案叫做”和”（sum）。

In Grade K, we practice addition facts with sums up to 10. These basic facts are the building blocks for all future mathematics. Memorizing them will make you a faster and more confident mathematician.

在K年级，我们练习和不超过10的加法事实。这些基本事实是所有未来数学的基石。记住它们会使你成为更快、更自信的数学家。

Addition Fact	Sum (和)
2 + 3	5
4 + 4	8
6 + 3	9
5 + 5	10

One helpful strategy for addition is “counting on.” If you need to solve 3 + 2, start at 3 and count forward 2 numbers: 4, 5. The answer is 5. Another strategy is using your fingers or objects like blocks and counters to help you visualize the problem.

一个有用的加法策略是”接着数”（counting on）。如果需要计算3 + 2，从3开始向前数2个数：4、5。答案是5。另一个策略是用手指或积木、计数器等物体来帮助你在脑海中形象化问题。

7. Subtraction: Taking Away | 减法：拿走

Subtraction is the opposite of addition. When we subtract, we take away from a group or find the difference between two numbers. The symbol for subtraction is “−” (minus). For example, if you have 7 cookies and you eat 3 of them, you have 7 − 3 = 4 cookies left. The answer to a subtraction problem is called the “difference” (差).

减法与加法相反。当我们做减法时，我们从一组中拿走一些，或者求两个数字之间的差。减法的符号是”−”（减号）。例如，如果你有7块饼干，吃掉了3块，你还剩7 − 3 = 4块饼干。减法问题的答案叫做”差”（difference）。

Subtraction can also mean comparing two groups. If one group has 8 toys and another has 5 toys, the difference is 8 − 5 = 3 toys. How many more does the first group have? The answer 3 tells us the difference between the groups.

减法也可以表示比较两组。如果一组有8个玩具，另一组有5个玩具，差是8 − 5 = 3个玩具。第一组多几个？答案3告诉我们两组之间的差。

9 − 4 = 5 — Start with 9, take away 4, left with 5 (从9开始，拿走4，剩5)
10 − 6 = 4 — Start with 10, take away 6, left with 4 (从10开始，拿走6，剩4)
7 − 0 = 7 — Taking away nothing leaves the original group (什么都不拿走，剩原来的组)
8 − 8 = 0 — Taking away everything leaves zero (全部拿走，剩下0)

Just like addition, subtraction facts with numbers up to 10 should be practiced until they become automatic. In IGCSE mathematics, subtraction appears everywhere—from solving equations to calculating differences in statistics.

和加法一样，10以内的减法事实应该练习到自动化的程度。在IGCSE数学中，减法无处不在——从解方程到统计中计算差异。

8. Shape Recognition | 图形识别

Shapes are all around us! In mathematics, we learn to identify and name basic two-dimensional (2D) and three-dimensional (3D) shapes. Common 2D shapes include squares, circles, triangles, and rectangles. Common 3D shapes include cubes, spheres, cylinders, and cones.

图形无处不在！在数学中，我们学习识别和命名基本的二维（2D）和三维（3D）图形。常见的二维图形包括正方形、圆形、三角形和长方形。常见的三维图形包括立方体、球体、圆柱体和圆锥体。

A square has 4 equal sides and 4 corners. A rectangle has 4 sides with opposite sides equal, and 4 corners. A triangle has 3 sides and 3 corners. A circle has no corners at all—it is perfectly round. How many sides does a circle have? It has one continuous curved side!

正方形有4条相等的边和4个角。长方形有4条边，对边相等，有4个角。三角形有3条边和3个角。圆形没有任何角——它是完全的圆形。圆形有几条边？它有一条连续的曲线边！

When you look around your classroom or your home, you can find many shapes. A window might be a rectangle, a clock might be a circle, and a book might be a rectangle. Identifying shapes in the real world helps us understand geometry, which is a major topic in IGCSE mathematics.

当你环顾教室或家中，可以找到许多图形。窗户可能是长方形，时钟可能是圆形，书可能是长方形。在现实世界中识别图形帮助我们理解几何，而几何是IGCSE数学中的一个重要主题。

9. Position Words | 位置词

Position words describe where things are located. Words like “above”（上面）, “below”（下面）, “beside”（旁边）, “inside”（里面）, “outside”（外面）, “left”（左边）, and “right”（右边）help us describe the world around us. In mathematics, these words are used to describe positions on graphs, maps, and in space.

位置词描述事物所在的位置。像”上面”（above）、”下面”（below）、”旁边”（beside）、”里面”（inside）、”外面”（outside）、”左边”（left）和”右边”（right）等词语帮助我们描述周围的世界。在数学中，这些词用于描述图形、地图和空间中的位置。

For example: The ball is above the table. The cat is below the chair. The book is beside the lamp. The toy is inside the box. Being able to use position words correctly is the first step toward understanding coordinate geometry, where we use numbers to describe exact positions on a grid.

例如：球在桌子的上面。猫在椅子的下面。书在台灯的旁边。玩具在盒子的里面。正确使用位置词是理解坐标几何的第一步，在坐标几何中我们用数字来描述网格上的精确位置。

Try this game: Place a toy somewhere in your room. Ask a friend or family member to describe where it is using position words. Can they use words like “above,” “below,” “beside,” and “between” to describe its location? This is a fun way to practice!

试试这个游戏：把玩具放在房间的某个位置。让朋友或家人用位置词来描述它在哪里。他们能用”上面”、”下面”、”旁边”和”中间”等词来描述它的位置吗？这是练习的好方法！

10. Measurement Basics | 测量基础

Measurement helps us answer questions like: How long is this object? How heavy is it? How much can it hold? In Grade K, we learn to compare lengths, heights, and weights using words like “longer,” “shorter,” “taller,” “heavier,” and “lighter.”

测量帮助我们回答这样的问题：这个物体有多长？它有多重？它能装多少？在K年级，我们学习用”更长”、”更短”、”更高”、”更重”和”更轻”等词语来比较长度、高度和重量。

We can measure length with our hands, with blocks, or with a ruler. When we say a pencil is “about 3 blocks long,” we are using non-standard units. Later, in IGCSE mathematics, we will use standard units like centimeters (cm), meters (m), grams (g), and kilograms (kg).

我们可以用手、积木或尺子来测量长度。当我们说一支铅笔”大约3块积木长”时，我们使用的是非标准单位。后来，在IGCSE数学中，我们将使用标准单位，如厘米（cm）、米（m）、克（g）和千克（kg）。

1 meter = 100 centimeters | 1 kilogram = 1000 grams | 1 liter = 1000 milliliters

Measuring objects in daily life prepares us for understanding units, conversions, and estimation—all critical skills for IGCSE mathematics. Try measuring the length of your desk using your handspan or paper clips. How many handspans long is it?

在日常生活中测量物体，为我们理解单位、换算和估算做好准备——这些都是IGCSE数学的关键技能。试着用手掌宽度或回形针来测量书桌的长度。它有多少个手掌宽？

11. Word Problems | 应用题

Word problems are stories that contain numbers. They help us understand why mathematics is useful in real life. For example: “Maya has 4 red balloons and 3 blue balloons. How many balloons does she have in total?” To solve this, we need to recognize that “in total” means we should add: 4 + 3 = 7.

应用题是含有数字的故事。它们帮助我们理解为什么数学在现实生活中很有用。例如：”Maya有4个红色气球和3个蓝色气球。她总共有多少个气球？”要解决这个问题，我们需要认识到”总共”意味着我们应该用加法：4 + 3 = 7。

Another example: “There are 10 birds on a fence. 4 birds fly away. How many birds are left?” The words “fly away” tell us this is a subtraction problem: 10 − 4 = 6. Key words like “in total” (总共) help us identify addition, while “left” (剩下) and “take away” (拿走) help us identify subtraction.

另一个例子：”篱笆上有10只鸟。4只飞走了。还剩多少只鸟？”关键词”飞走”告诉我们这是一个减法问题：10 − 4 = 6。像”总共”（in total）这样的关键词帮助我们识别加法，而”剩下”（left）和”拿走”（take away）帮助我们识别减法。

When solving word problems, follow these steps: First, read the problem carefully. Second, identify what numbers are given. Third, decide whether to add or subtract. Fourth, solve the problem and write your answer with a label. For example: “Answer: 6 birds.”

解决应用题时，请遵循以下步骤：第一，仔细阅读问题。第二，识别给出的数字。第三，决定是加还是减。第四，解决问题并写出带标签的答案。例如：”答案：6只鸟。”

12. Connecting to IGCSE Mathematics | 连接IGCSE数学

Everything we learn in Grade K is connected to the mathematics you will study in IGCSE. Counting to 100 becomes the foundation for working with numbers up to millions and beyond. Place value helps you understand decimals, fractions, and percentages. Addition and subtraction become the building blocks for multiplication, division, algebra, and calculus.

我们在K年级学的一切都与你在IGCSE中将要学习的数学相关联。数到100成为处理百万以上数字的基础。位值帮助你理解小数、分数和百分数。加减法成为乘法、除法、代数和微积分的基石。

In IGCSE mathematics, you will encounter topics such as algebra (代数), geometry (几何), trigonometry (三角学), and statistics (统计). A student who has a strong foundation in counting, place value, and basic operations will find these topics much more accessible. Mathematics is like building a house—each floor depends on the floors below it.

在IGCSE数学中，你将遇到代数、几何、三角学和统计等主题。一个在数数、位值和基本运算方面基础扎实的学生，会发现这些主题更容易掌握。数学就像盖房子——每一层都依赖于下面的楼层。

Remember: every expert mathematician was once a child learning to count. The skills you are practicing today in Lesson 15-6—counting, comparing, adding, and subtracting—are the very same skills that will help you succeed in IGCSE and in life. Keep practicing, stay curious, and enjoy the beautiful world of numbers!

请记住：每一位数学专家都曾经是学习数数的孩子。你今天在第15-6课中练习的技能——数数、比较、加法和减法——正是帮助你在IGCSE和生活中取得成功的技能。坚持练习，保持好奇心，享受美妙的数字世界吧！

Published by TutorHao | Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Counting to 100: Building Blocks of Mathematics | 数到100：数学的基石