Multiplying with Equal Groups: Repeated Addition and Arrays | 等量分组乘法：重复加法与阵列

📚 Multiplying with Equal Groups: Repeated Addition and Arrays | 等量分组乘法：重复加法与阵列

Welcome to this revision lesson on Grade 2, Lesson 16-7. In this lesson, we explore multiplication as equal groups. We will learn how to use repeated addition, arrays, and number lines to multiply small numbers quickly.

欢迎来到本期二年级 Lesson 16-7 复习课。本节课围绕“乘法与等量分组”展开。我们将学习如何利用重复加法、阵列和数轴来快速计算较小数字的乘法。

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1. What Are Equal Groups? | 什么是等量分组？

Equal groups mean that all groups contain exactly the same number of objects. For example, 3 plates with 4 cookies on each plate make 3 equal groups. Another example: 5 bags with 2 pens in each bag make 5 equal groups.

等量分组是指每一组里物体的数量完全相同。例如：3 个盘子，每个盘子上有 4 块饼干，就构成了 3 个等量组；又如：5 个袋子，每个袋子里有 2 支笔，也构成了 5 个等量组。

• The number of groups tells us how many equal sets we have.

• The size of each group tells us how many objects are in one set.

• 组数表示我们一共有几个等量集合。

• 每组大小表示一个集合内有多少个物体。

When we put these two numbers together, we use the multiplication sign ×. For example, 3 plates × 4 cookies = 12 cookies.

把这两个信息合在一起时，我们使用乘法符号 ×。例如：3 个盘子 × 每个盘子 4 块饼干 = 12 块饼干。

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2. Repeated Addition: The Shortcut | 重复加法：乘法的快捷方式

Before you learned multiplication, you could find the total by adding. If 4 groups each have 3 stars, the total is 3 + 3 + 3 + 3 = 12. This is repeated addition.

在学习乘法之前，你通常会用连加来求总数。比如：4 组，每组有 3 颗星，那么总数是 3 + 3 + 3 + 3 = 12。这就是重复加法。

Multiplication is a shortcut for repeated addition of the same number. Instead of writing 3 + 3 + 3 + 3, we write 4 × 3 = 12. We say “4 groups of 3 equals 12.”

乘法是“相同加数连加”的简便写法。我们不用写 3 + 3 + 3 + 3，直接写 4 × 3 = 12，读作“4 个 3 的和是 12”。

4 × 3 = 3 + 3 + 3 + 3 = 12

Notice that the number of groups goes first, and the group size goes second. The product is the total.

要注意：组数写在前面，每组大小写在后面，乘积就是总数。

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3. Arrays: Rows and Columns | 阵列：行与列

An array is an arrangement of objects in rows and columns. Rows go from left to right, and columns go from top to bottom. Arrays help us see multiplication in a picture.

阵列是把物体按“行”和“列”排列的图形。行是横向排列，列是纵向排列。阵列能帮助我们直观地“看到”乘法。

For example, a 2 by 4 array has 2 rows and 4 columns. The total number of dots is 2 × 4 = 8.

例如，一个“2 行 4 列”的阵列共有 2 × 4 = 8 个圆点。

● ● ● ●
● ● ● ●

In the picture above, there are 2 rows and 4 columns. We can count 8 dots. The array shows both 2 × 4 and 4 × 2.

上图中，有 2 行、4 列，一共可以数出 8 个圆点。这个阵列既能表示 2 × 4，也能表示 4 × 2。

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4. Comparing Addition and Multiplication | 加法与乘法的对比

Addition and multiplication are related but not the same. Addition combines any numbers; multiplication is a fast way to add equal groups.

加法和乘法关系密切，但又不完全相同。加法可以合并任意数量；乘法则是“等量分组”时的快速加法。

Addition	Multiplication
5 + 2 = 7	No equal groups: only 5 + 5 = 2 × 5
3 + 3 + 3 + 3 = 12	4 × 3 = 12
2 + 2 + 2 = 6	3 × 2 = 6

In the table, repeated addition and multiplication give the same answer. The multiplication expression is shorter.

表格中的每一行，重复加法与乘法的结果都相同，只是乘法表达式更简洁。

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5. The Commutative Property | 乘法交换律

The commutative property of multiplication says that changing the order of the numbers does not change the product. For example, 3 × 5 = 15 and 5 × 3 = 15.

乘法交换律指出：交换两个乘数的位置，积不变。例如：3 × 5 = 15，5 × 3 = 15。

Think about a 3 by 5 array: it has 3 rows and 5 columns. If we turn it around, it becomes 5 rows and 3 columns. The total is still 15.

想一想一个“3 行 5 列”的阵列：它有 3 行 5 列。转个方向，就变成了“5 行 3 列”，总数仍然是 15。

3 × 5 = 5 × 3

This property helps us learn fewer facts! When you know 2

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