这是小学五年级的第三单元，倍数和因数；多使用图形展示---**Overall Title:** 探索活动: 2, 5 的倍数的特征 (Exploration Activity: Characteristics of Multiples of 2 and 5) **Chart/Diagram Description:** The image displays a hundred chart (10x10 grid of numbers from 1 to 100), along with several speech bubbles representing dialogue between cartoon characters illustrating mathematical concepts. **Table Content (Hundred Chart):** | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |---|---|---|---|---|---|---|---|---|----| | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | --- **Section: Multiples of 5** **Question/Instruction:** 在百数表中圈出 5 的倍数，你发现了什么? (Circle the multiples of 5 in the hundred chart, what did you find?) **Student Observations (from speech bubbles):** * **Student 1:** 我发现 5 的倍数末尾只有 0 或 5。 (I found that multiples of 5 only end in 0 or 5.) * **Student 2:** 5 的倍数都在第 5 列、第 10 列。 (Multiples of 5 are all in the 5th column and 10th column.) **Follow-up Question:** 你能向同伴解释一下你的发现吗? (Can you explain your findings to your partner?) **Trial Calculations/Examples (from speech bubbles):** * **Student 1's trial (left bubble):** * 我任意写几个数试试: (Let me try writing a few numbers:) * 65 × 5 = 325 * 132 × 5 = 660 * ... * **Student 2's trial (right bubble):** * 我算算看: (Let me calculate:) * 5 × 1 = 5 * 5 × 2 = 10 * 5 × 3 = 15 * 5 × 4 = 20 * ... **Summary/Explanation (from speech bubble, presumably an expert's or teacher's conclusion):** 实际上，个位上是 0 或 5 的数，都是 5 的倍数。 (Actually, numbers whose unit digit is 0 or 5 are all multiples of 5.) --- **Section: Multiples of 2** **Question/Instruction:** 从上表中找出 2 的倍数，说一说这些数有什么特征。 (Find the multiples of 2 from the table above, and describe the characteristics of these numbers.) **Trial Calculations/Examples & Observations (from speech bubbles):** * **Student 1's trial (left bubble):** * 2 × 1 = 2 * 2 × 2 = 4 * 2 × 3 = 6 * 2 × 4 = 8 * 2 × 5 = 10 * 2 × 6 = 12 * 个位上是…… (The unit digit is...) * **Student 2's observation (right bubble):** * 个位上是 2, 4, 6, 8, 0 的数都是 2 的倍数。 (Numbers whose unit digit is 2, 4, 6, 8, 0 are all multiples of 2.) --- **Section: Recognize (Definitions)** **Title:** 认一认。 (Recognize.) **Definitions:** * 像 2, 4, 6, 8, ……这样的数，是 2 的倍数，也叫偶数； (Numbers like 2, 4, 6, 8, ... are multiples of 2, also called even numbers;) * 像 1, 3, 5, 7, ……这样的数，不是 2 的倍数，也叫奇数。 (Numbers like 1, 3, 5, 7, ... are not multiples of 2, also called odd numbers.) **Main Title:** 探索活动: 3的倍数的特征 (Exploration Activity: Characteristics of Multiples of 3) **Introduction/Initial Discussion:** 我们研究了2, 5的倍数的特征，说一说，3的倍数有什么特征呢？ (We have studied the characteristics of multiples of 2 and 5. Tell us, what are the characteristics of multiples of 3?) **Dialogue 1 (Girl in pink dress):** 我猜个位上是3, 6或9的数是3的倍数。(I guess numbers with 3, 6, or 9 in the ones place are multiples of 3.) **Dialogue 2 (Girl in orange dress):** 不一定，13就不是3的倍数。(Not necessarily, 13 is not a multiple of 3.) **Dialogue 3 (Boy in green shirt):** 3×1=3, 3×2=6, 3×3=9, 3×4=12, ……个位上的数没什么规律啊…… (3×1=3, 3×2=6, 3×3=9, 3×4=12, …… The numbers in the ones place don't seem to follow any pattern...) **Question/Task 1:** 请你在百数表中接着圈出3的倍数，你发现了什么？ (Please continue circling the multiples of 3 in the hundred chart. What did you find?) **Chart Description & Content:** * **Type:** A 10x10 grid, a "hundred chart" or "multiplication table" (for 1 to 100). * **Main Elements:** Numbers from 1 to 100 arranged in 10 rows and 10 columns. * **Data Points:** Some numbers are pre-circled, indicating they are multiples of 3. * **Circled Numbers:** 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. **Table Content (Hundred Chart):** 1 2 ③ 4 5 ⑥ 7 8 ⑨ 10 11 ⑫ 13 14 ⑮ 16 17 ⑱ 19 20 ㉑ 22 23 ㉔ 25 26 ㉗ 28 29 ㉚ 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 **Dialogue 4 (Old man):** 你知道吗？这些数各个数位上数字之和都是3的倍数。(Do you know? The sum of the digits in each place value of these numbers are all multiples of 3.) **Dialogue 5 (Girl in pink dress):** 是这样吗？我找几个数看看: 12, 1+2=3; 15, 1+5=6; 18, 1+8=9; 21… (Is that so? Let me check a few numbers: 12, 1+2=3; 15, 1+5=6; 18, 1+8=9; 21...) **Dialogue 6 (Boy in green shirt):** 2016年又要开奥运会啦，2+0+1+6=9, 是3的倍数，2016=3×672，确实是3的倍数，太神奇啦！(The Olympic Games are coming again in 2016. 2+0+1+6=9, which is a multiple of 3. 2016 = 3 × 672, it really is a multiple of 3, how amazing!) **Question/Task 2:** 根据上面的发现，在下面的数中圈出3的倍数，并与同伴交流。(Based on the above findings, circle the multiples of 3 among the following numbers and discuss with your partner.) **Numbers for Task 2:** 53, 87, 36, 65, 60, 128, 453