Number Bonds to 20: Make Ten Strategy | 20以内数的组合：凑十法

📚 Number Bonds to 20: Make Ten Strategy | 20以内数的组合：凑十法

Number bonds are a key building block for mental arithmetic. A number bond shows how a number can be split into two or more parts. In this lesson, we focus on bonds within 20 and the make ten strategy, which helps students solve addition and subtraction quickly and accurately.

数的组合是心算的重要基石。一个数的组合表示这个数如何被拆分成两个或更多部分。本课我们重点学习 20 以内的数的组合以及凑十法，这将帮助学生快速、准确地进行加减运算。

1. What Are Number Bonds? | 什么是数的组合？

A number bond is a simple diagram or equation that shows the relationship between a whole and its parts. For example, the number 10 can be split into 6 and 4, 7 and 3, or 5 and 5.

数的组合是展示整体与部分之间关系的简单图示或等式。例如，数字 10 可以拆分为 6 和 4、7 和 3，或者 5 和 5。

Whole: 10; Parts: 6 and 4 | 整体：10；部分：6 和 4
Whole: 10; Parts: 7 and 3 | 整体：10；部分：7 和 3
Whole: 10; Parts: 5 and 5 | 整体：10；部分：5 和 5

The whole is the total, and the parts are the two numbers that add up to make the whole. In equation form, we write 6 + 4 = 10.

整体是总数，部分是两个相加得到整体的数。用等式表示，我们写作 6 + 4 = 10。

Number bonds are not just for addition. They also help with subtraction because if you know 6 + 4 = 10, you immediately know 10 – 4 = 6 and 10 – 6 = 4.

数的组合不仅用于加法。它们还有助于减法，因为如果你知道 6 + 4 = 10，你马上就知道 10 – 4 = 6 和 10 – 6 = 4。

2. Why Number Bonds to 20 Matter | 为什么 20 以内数的组合重要

Mastering number bonds to 20 gives students a strong foundation for mental math. It reduces the need to count on fingers and helps with subtraction by thinking of missing parts.

掌握 20 以内数的组合为心算打下坚实基础。它减少了掰手指计算的需要，并通过思考缺失的部分来帮助减法。

In IGCSE mathematics, quick recall of number facts supports algebra, fractions, and problem solving. A student who instantly knows 8 + 7 = 15 can focus on more complex steps later.

在 IGCSE 数学中，快速回忆数字事实有助于代数、分数和解题。一个能立即知道 8 + 7 = 15 的学生可以在后续更复杂的步骤中集中注意力。

Number bonds to 20 also build number sense. Students learn that numbers can be composed and decomposed in many ways, which is essential for understanding place value, regrouping, and later operations with larger numbers.

20 以内数的组合还能培养数感。学生学会数字可以通过多种方式组合和分解，这对于理解位值、进位以及后续更大数的运算至关重要。

3. The Make Ten Strategy | 凑十法

The make ten strategy is a mental math technique used when adding two numbers where one addend is close to 10. We take part of the smaller number to complete ten, then add the rest.

凑十法是一种心算技巧，用于两个数相加且其中一个加数接近 10 的情况。我们从较小的数中取出一部分补成 10，然后再加上剩余部分。

For example, to solve 9 + 4, we split 4 into 1 and 3. First, 9 + 1 = 10, then 10 + 3 = 13.

例如，计算 9 + 4 时，我们将 4 拆分为 1 和 3。先算 9 + 1 = 10，再算 10 + 3 = 13。

9 + 4 = 9 + 1 + 3 = 10 + 3 = 13

This strategy works with any number close to 10, such as 8, 9, or 7. The key is to know how much the larger addend needs to make 10.

这种方法适用于任何接近 10 的数，例如 8、9 或 7。关键是知道较大的加数需要多少才能凑成 10。

For 8 + 6, 8 needs 2 to make 10. Split 6 into 2 and 4. Then 8 + 2 = 10 and 10 + 4 = 14.

对于 8 + 6，8 需要 2 才能凑成 10。将 6 拆分为 2 和 4。先算 8 + 2 = 10，再算 10 + 4 = 14。

8 + 6 = 8 + 2 + 4 = 10 + 4 = 14

4. Doubles and Near Doubles | 双倍与近双倍

Doubles are number bonds with two equal parts, such as 6 + 6 = 12 or 8 + 8 = 16. Knowing doubles helps solve near doubles like 6 + 7, which is one more than 6 + 6.

双倍是两个相等部分的数的组合，例如 6 + 6 = 12 或 8 + 8 = 16。掌握双倍有助于解决近双倍问题，如 6 + 7 比 6 + 6 大 1。

6 + 6 = 12 | 6 + 6 = 12
6 + 7 = 13 | 6 + 7 = 13
7 + 7 = 14 | 7 + 7 = 14
7 + 8 = 15 | 7 + 8 = 15

Near doubles build fluency because students can adjust from a known fact instead of counting from scratch. For example, if 7 + 7 = 14, then 7 + 8 is one more, so 15.

近双倍可以培养流畅性，因为学生可以从已知事实进行调整，而不是从头开始数。例如，如果 7 + 7 = 14，那么 7 + 8 多 1，所以是 15。

This strategy reduces mental load and helps students see relationships between addition facts, which strengthens overall number sense.

这种策略减轻了心算负担，帮助学生看到加法事实之间的关系，从而增强整体数感。

5. Using a Ten Frame | 使用十格框

A ten frame is a rectangular grid with 10 spaces used to visualize numbers up to 10. By filling one frame completely and using a second frame for the rest, students see numbers up to 20 as ‘ten and some more’.

十格框是一个有 10 个格子的长方形网格，用于直观表示 10 以内的数。当填满一个十格框，再用第二个十格框表示剩余部分时，学生可以看到 20 以内的数是 ‘十加几个’。

For 13, one full ten frame and 3 counters on the next frame show 10 + 3 = 13.

对于 13，一个满的十格框和下一个框上的 3 个计数片表示 10 + 3 = 13。

Ten frames support the make ten strategy because students can physically move counters to complete a frame. For 9 + 4, a student fills 9 spaces on the first frame, moves 1 counter from the 4 to complete ten, and then sees 10 and 3 remaining.

十格框支持凑十法，因为学生可以实际移动计数片来填满一个框。对于 9 + 4，学生先在第一框放 9 个计数片，从 4 中移 1 个到第一框补成 10，然后看到 10 和剩下的 3。

Using ten frames repeatedly helps students internalize the make ten strategy without needing physical objects, building strong mental images of numbers.

反复使用十格框有助于学生在无需实物的情况下内化凑十法，建立清晰的数字心像。

6. Addition within 20 | 二十以内加法

To add numbers within 20, combine the parts using number bonds. When the sum crosses 10, use the make ten strategy to split the second addend.

计算 20 以内加法时，利用数的组合将各部分合起来。当和超过 10 时，使用凑十法拆分第二个加数。

Example: 8 + 5. Split 5 into 2 and 3. Then 8 + 2 = 10 and 10 + 3 = 13.

示例：8 + 5。将 5 拆分为 2 和 3。先算 8 + 2 = 10，再算 10 + 3 = 13。

8 + 5 = 8 + 2 + 3 = 10 + 3 = 13

Another example: 7 + 6. Split 6 into 3 and 3. Then 7 + 3 = 10 and 10 + 3 = 13.

另一个示例：7 + 6。将 6 拆分为 3 和 3。先算 7 + 3 = 10，再算 10 + 3 = 13。

If both addends are less than 10 but the sum exceeds 10, always decide which addend is closer to 10 and split the other addend. This makes the process consistent and efficient.

如果两个加数都小于 10 但和超过 10，始终选择更接近 10 的加数，并拆分另一个加数。这样可以使过程一致且高效。

7. Subtraction within 20 | 二十以内减法

Subtraction within 20 can be solved by thinking of the missing part in a number bond. For 15 – 8, ask: ‘What do I add to 8 to make 15?’ Since 8 + 7 = 15, the answer is 7.

20 以内的减法可以通过思考数的组合中缺失的部分来解决。例如 15 – 8，问自己：’8 加上什么数等于 15？’ 因为 8 + 7 = 15，所以答案是 7。

For subtraction crossing 10, use the make ten strategy in reverse: 13 – 5 = 13 – 3 – 2 = 10 – 2 = 8.

对于跨 10 的减法，反向使用凑十法：13 – 5 = 13 – 3 – 2 = 10 – 2 = 8。

This works because we first subtract enough to reach 10, then subtract the remaining part from 10. It makes the calculation easier and avoids counting backwards from 13 one by one.

这种方法可行，因为我们先减到 10，然后从 10 中减去剩余部分。它使计算更容易，避免从 13 开始逐个数倒数。

14 – 6 = 8 | 14 – 6 = 8
12 – 7 = 5 | 12 – 7 = 5
17 – 9 = 8 | 17 – 9 = 8

8. Word Problems | 应用题

Word problems require translating a real-life situation into a number sentence. Identify the whole and the parts before choosing an operation.

应用题需要将实际情境转化为数字表达式。先找出整体和部分，再选择运算。

Example: ‘Tom has 9 pencils. He buys 4 more. How many does he have now?’ The parts are 9 and 4; the whole is 9 + 4 = 13.

示例：’Tom 有 9 支铅笔。他又买了 4 支。现在他一共有多少支？’ 部分是 9 和 4；整体是 9 + 4 = 13。

Example: ‘There are 16 apples. 7 are eaten. How many are left?’ This is 16 – 7 = 9.

示例：’有 16 个苹果。吃了 7 个。还剩多少个？’ 这是 16 – 7 = 9。

When reading word problems, look for clue words: ‘in all’, ‘altogether’, and ‘more’ often signal addition; ‘left’, ‘fewer’, and ‘take away’ signal subtraction.

读应用题时，注意关键词：’一共’、’总共’ 和 ‘更多’ 通常表示加法；’剩下’、’少了’ 和 ‘拿走’ 表示减法。

9. Common Misconceptions | 常见误区

Students sometimes count all objects starting from 1 instead of counting on from the larger number. This slows down mental math and leads to errors.

学生有时从 1 开始逐一数所有物体，而不是从较大的数接着数。这会降低心算速度并导致错误。

Another misconception is forgetting to split the smaller number correctly when making ten. For 9 + 5, some students split 5 into 2 and 3, which gives 9 + 2 = 11, not 10, so they get stuck.

另一个误区是在凑十时没有正确拆分较小的数。例如 9 + 5，有些学生将 5 拆分为 2 和 3，这样 9 + 2 = 11，而不是 10，于是就算错了。

The correct split for 9 + 5 is 1 and 4 because 9 needs 1 to make 10.

对于 9 + 5，正确的拆分是 1 和 4，因为 9 需要 1 才能凑成 10。

Some students also confuse the operations in word problems, adding when they should subtract. Regular practice with drawing number bonds can help clarify whether the whole or a part is missing.

有些学生还会在应用题中混淆运算，应该减法时却用了加法。经常练习画数的组合图可以帮助弄清是整体还是部分缺失。

10. Practice Questions | 练习题目

Try these questions to build fluency. Solve each using number bonds or the make ten strategy.

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

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Number Bonds to 20: Make Ten Strategy | 20以内数的组合：凑十法