《一年级上册20以内的加减法口诀思维导图》

中心主题：20以内加减法

一级分支：加法口诀

• 主题：10以内加法

  • 分支：基础加法 (1+1 to 5+0)
    • 1 + 1 = 2
    • 1 + 2 = 3, 2 + 1 = 3
    • 1 + 3 = 4, 2 + 2 = 4, 3 + 1 = 4
    • 1 + 4 = 5, 2 + 3 = 5, 3 + 2 = 5, 4 + 1 = 5
    • 1 + 5 = 6, 2 + 4 = 6, 3 + 3 = 6, 4 + 2 = 6, 5 + 1 = 6
    • 1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7, 4 + 3 = 7, 5 + 2 = 7, 6 + 1 = 7
    • 1 + 7 = 8, 2 + 6 = 8, 3 + 5 = 8, 4 + 4 = 8, 5 + 3 = 8, 6 + 2 = 8, 7 + 1 = 8
    • 1 + 8 = 9, 2 + 7 = 9, 3 + 6 = 9, 4 + 5 = 9, 5 + 4 = 9, 6 + 3 = 9, 7 + 2 = 9, 8 + 1 = 9
    • 1 + 9 = 10, 2 + 8 = 10, 3 + 7 = 10, 4 + 6 = 10, 5 + 5 = 10, 6 + 4 = 10, 7 + 3 = 10, 8 + 2 = 10, 9 + 1 = 10
  • 分支：进位加法 (凑十法)
    • 9 + 2 = 9 + 1 + 1 = 10 + 1 = 11
    • 9 + 3 = 9 + 1 + 2 = 10 + 2 = 12
    • 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13
    • 9 + 5 = 9 + 1 + 4 = 10 + 4 = 14
    • 9 + 6 = 9 + 1 + 5 = 10 + 5 = 15
    • 9 + 7 = 9 + 1 + 6 = 10 + 6 = 16
    • 9 + 8 = 9 + 1 + 7 = 10 + 7 = 17
    • 9 + 9 = 9 + 1 + 8 = 10 + 8 = 18
    • 8 + 3 = 8 + 2 + 1 = 10 + 1 = 11
    • 8 + 4 = 8 + 2 + 2 = 10 + 2 = 12
    • 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13
    • 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14
    • 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15
    • 8 + 8 = 8 + 2 + 6 = 10 + 6 = 16
    • 8 + 9 = 8 + 2 + 7 = 10 + 7 = 17
    • 7 + 4 = 7 + 3 + 1 = 10 + 1 = 11
    • 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12
    • 7 + 6 = 7 + 3 + 3 = 10 + 3 = 13
    • 7 + 7 = 7 + 3 + 4 = 10 + 4 = 14
    • 7 + 8 = 7 + 3 + 5 = 10 + 5 = 15
    • 7 + 9 = 7 + 3 + 6 = 10 + 6 = 16
    • 6 + 5 = 6 + 4 + 1 = 10 + 1 = 11
    • 6 + 6 = 6 + 4 + 2 = 10 + 2 = 12
    • 6 + 7 = 6 + 4 + 3 = 10 + 3 = 13
    • 6 + 8 = 6 + 4 + 4 = 10 + 4 = 14
    • 6 + 9 = 6 + 4 + 5 = 10 + 5 = 15
    • 5 + 6 = 5 + 5 + 1 = 10 + 1 = 11
    • 5 + 7 = 5 + 5 + 2 = 10 + 2 = 12
    • 5 + 8 = 5 + 5 + 3 = 10 + 3 = 13
    • 5 + 9 = 5 + 5 + 4 = 10 + 4 = 14

• 主题：10以上加法 (11+1 to 19+1)

  • 分支：不进位加法
    • 11 + 1 = 12
    • 11 + 2 = 13, 12 + 1 = 13
    • 11 + 3 = 14, 12 + 2 = 14, 13 + 1 = 14
    • 11 + 4 = 15, 12 + 3 = 15, 13 + 2 = 15, 14 + 1 = 15
    • 11 + 5 = 16, 12 + 4 = 16, 13 + 3 = 16, 14 + 2 = 16, 15 + 1 = 16
    • 11 + 6 = 17, 12 + 5 = 17, 13 + 4 = 17, 14 + 3 = 17, 15 + 2 = 17, 16 + 1 = 17
    • 11 + 7 = 18, 12 + 6 = 18, 13 + 5 = 18, 14 + 4 = 18, 15 + 3 = 18, 16 + 2 = 18, 17 + 1 = 18
    • 11 + 8 = 19, 12 + 7 = 19, 13 + 6 = 19, 14 + 5 = 19, 15 + 4 = 19, 16 + 3 = 19, 17 + 2 = 19, 18 + 1 = 19
    • 11 + 9 = 20, 12 + 8 = 20, 13 + 7 = 20, 14 + 6 = 20, 15 + 5 = 20, 16 + 4 = 20, 17 + 3 = 20, 18 + 2 = 20, 19 + 1 = 20
  • 分支：凑20法 (11+9, 12+8...)
    • 关注和为20的组合，例如：11 + 9 = 20, 12 + 8 = 20, 13 + 7 = 20, 14 + 6 = 20, 15 + 5 = 20, 16 + 4 = 20, 17 + 3 = 20, 18 + 2 = 20, 19 + 1 = 20. 突出这些组合的记忆，有助于快速计算。

一级分支：减法口诀

• 主题：10以内减法

  • 分支：基础减法 (从 1-1 to 10-0)
    • 1 - 1 = 0
    • 2 - 1 = 1, 2 - 2 = 0
    • 3 - 1 = 2, 3 - 2 = 1, 3 - 3 = 0
    • 4 - 1 = 3, 4 - 2 = 2, 4 - 3 = 1, 4 - 4 = 0
    • 5 - 1 = 4, 5 - 2 = 3, 5 - 3 = 2, 5 - 4 = 1, 5 - 5 = 0
    • 6 - 1 = 5, 6 - 2 = 4, 6 - 3 = 3, 6 - 4 = 2, 6 - 5 = 1, 6 - 6 = 0
    • 7 - 1 = 6, 7 - 2 = 5, 7 - 3 = 4, 7 - 4 = 3, 7 - 5 = 2, 7 - 6 = 1, 7 - 7 = 0
    • 8 - 1 = 7, 8 - 2 = 6, 8 - 3 = 5, 8 - 4 = 4, 8 - 5 = 3, 8 - 6 = 2, 8 - 7 = 1, 8 - 8 = 0
    • 9 - 1 = 8, 9 - 2 = 7, 9 - 3 = 6, 9 - 4 = 5, 9 - 5 = 4, 9 - 6 = 3, 9 - 7 = 2, 9 - 8 = 1, 9 - 9 = 0
    • 10 - 1 = 9, 10 - 2 = 8, 10 - 3 = 7, 10 - 4 = 6, 10 - 5 = 5, 10 - 6 = 4, 10 - 7 = 3, 10 - 8 = 2, 10 - 9 = 1, 10 - 10 = 0
  • 分支：破十法 (11-2 to 19-9)
    • 11 - 2 = 11 - 1 - 1 = 10 - 1 = 9
    • 11 - 3 = 11 - 1 - 2 = 10 - 2 = 8
    • 11 - 4 = 11 - 1 - 3 = 10 - 3 = 7
    • 11 - 5 = 11 - 1 - 4 = 10 - 4 = 6
    • 11 - 6 = 11 - 1 - 5 = 10 - 5 = 5
    • 11 - 7 = 11 - 1 - 6 = 10 - 6 = 4
    • 11 - 8 = 11 - 1 - 7 = 10 - 7 = 3
    • 11 - 9 = 11 - 1 - 8 = 10 - 8 = 2
    • 12 - 3 = 12 - 2 - 1 = 10 - 1 = 9
    • 12 - 4 = 12 - 2 - 2 = 10 - 2 = 8
    • 12 - 5 = 12 - 2 - 3 = 10 - 3 = 7
    • 12 - 6 = 12 - 2 - 4 = 10 - 4 = 6
    • 12 - 7 = 12 - 2 - 5 = 10 - 5 = 5
    • 12 - 8 = 12 - 2 - 6 = 10 - 6 = 4
    • 12 - 9 = 12 - 2 - 7 = 10 - 7 = 3
    • 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9
    • 13 - 5 = 13 - 3 - 2 = 10 - 2 = 8
    • ... (继续列举到19-9，但为了简洁省略部分)

• 主题：20以内减法 (20-1 to 11-1)

  • 分支：20减几
    • 20 - 1 = 19
    • 20 - 2 = 18
    • 20 - 3 = 17
    • 20 - 4 = 16
    • 20 - 5 = 15
    • 20 - 6 = 14
    • 20 - 7 = 13
    • 20 - 8 = 12
    • 20 - 9 = 11
    • 20 - 10 = 10
  • 分支：十多减几 (19-1 to 11-1)
    • 19-1 = 18
    • 19-2 = 17
    • ...
    • 11-1 = 10

一级分支：加减法应用

• 主题：解决问题

  • 分支：加法应用题
    • 类型：求总数 (合并), 求增加 (增加), 求部分 (整体-部分)。
    • 示例：有3个苹果，又拿来2个，一共有几个苹果？ (3+2=5)
    • 示例：小明有5本书，小红比小明多2本，小红有几本书？ (5+2=7)
  • 分支：减法应用题
    • 类型：求剩余 (减少), 求比较 (相差), 求部分 (整体-部分)。
    • 示例：有5个苹果，吃掉2个，还剩几个苹果？ (5-2=3)
    • 示例：小明有5本书，小红有3本书，小明比小红多几本书？ (5-3=2)
  • 分支：混合运算
    • 加减混合应用题 (先加后减，先减后加)。
    • 示例：先有5个苹果，吃掉2个，又拿来3个，现在有几个苹果？ (5-2+3=6)

一级分支：学习技巧

• 主题：记忆方法

  • 分支：口诀记忆
    • 反复诵读，熟能生巧。
    • 利用游戏，寓教于乐。
    • 小组合作，互相帮助。
  • 分支：理解算理
    • 理解加减法的意义。
    • 利用实物进行操作。
    • 将抽象算式具体化。
  • 分支：练习方法
    • 每天坚持练习。
    • 从易到难，循序渐进。
    • 错题分析，及时纠正。

• 主题：工具辅助

  • 分支：计数器
    • 帮助理解加减法过程。
  • 分支：手指
    • 辅助计算，简单易用。
  • 分支：画图
    • 将算式可视化，方便理解。

总结：

掌握20以内的加减法是小学数学的基础，通过理解算理，熟记口诀，并辅以练习，可以帮助学生轻松掌握这一知识点。 运用凑十法、破十法等技巧，可以提高计算速度和准确率。同时，将加减法应用于实际问题中，可以培养学生的数学思维和解决问题的能力。本思维导图旨在为一年级学生提供一个系统而全面的学习框架，帮助他们更好地掌握20以内的加减法。