一、不一定要真的畫出物件再拿走
上一課我們學減法最直觀的意思:6Please respect copyright.PENANAslR50ya2DX
> 有一個數量,取走一部分,看剩餘多少。
例如:6Please respect copyright.PENANAT35ELX4Q1z
> 7 - 3
可以想像成有 7 粒糖果,吃了 3 粒,剩餘 4 粒。
但如果數字大一些,每次都要畫出所有物件再劃走,就會很慢。
所以今日我們學一個更方便的方法:6Please respect copyright.PENANAfhMKDegwkz
> 倒後數 | Counting Back
即是:6Please respect copyright.PENANAC5cuf5Q4dU
> 由原本數量開始,向後數取走的數量。
例如:6Please respect copyright.PENANAdB91HLj7aH
> 7 - 3
由 7 開始,倒後行 3 步:6Please respect copyright.PENANAPvWkgLI5jY
> 7 → 6 → 5 → 4
所以:6Please respect copyright.PENANAj8sLldAask
> 7 - 3 = 4
二、倒後數為甚麼是減法?
減法:6Please respect copyright.PENANAo1v7F9ff0u
> 8 - 2
意思是:6Please respect copyright.PENANAcmkLdNK84Y
> 原本有 8 個,取走 2 個。
每取走 1 個,數量就少 1。
所以可以倒後數:6Please respect copyright.PENANAUjkK8oraQo
> 8 → 7:取走第 1 個6Please respect copyright.PENANAXAJhwhX21z
> 7 → 6:取走第 2 個
最後剩餘6Please respect copyright.PENANA2r9cO6bwLB
> 6
所以:6Please respect copyright.PENANA7gAxxvkqiA
> 8 - 2 = 6
主旨:6Please respect copyright.PENANAUzPWVFwKDO
> 減多少,就由原本的數開始,向後行多少步。
三、用數線看倒後數
數線:6Please respect copyright.PENANAmEmXHD9Ss2
> 0 —— 1 —— 2 —— 3 —— 4 —— 5 —— 6 —— 7 —— 8
做:6Please respect copyright.PENANARMOn5nKnDQ
> 8 - 3
由 8 開始,向左行 3 步:6Please respect copyright.PENANAPEwDB26vkm
> 8 → 7:第 1 步6Please respect copyright.PENANArBNuBur8IE
> 7 → 6:第 2 步6Please respect copyright.PENANAkcTEHgbexd
> 6 → 5:第 3 步
所以:6Please respect copyright.PENANAXWAPYQwu79
> 8 - 3 = 5
留意:6Please respect copyright.PENANAIPUCOxPH4w
> 起點 8 不是第 1 步。6Please respect copyright.PENANAqCdVbrXGRl
> 減 3,是要行 3 步。
四、簡單例子
例子 1:5 - 1
由 5 開始,倒後行 1 步:6Please respect copyright.PENANAdEYCFqeu1A
> 5 → 4
所以:6Please respect copyright.PENANA3AgxGsWNVB
> 5 - 1 = 4
這個就是:6Please respect copyright.PENANAh4iEdF4OhX
> 5 少一是 4
//
例子 2:6 - 2
由 6 開始,倒後行 2 步:6Please respect copyright.PENANAMJUnQJSpSH
> 6 → 5:第 1 步6Please respect copyright.PENANAjPCEKQPEGT
> 5 → 4:第 2 步
所以:6Please respect copyright.PENANAx4mQ3MCx6g
> 6 - 2 = 4
//
例子 3:9 - 4
由 9 開始,倒後行 4 步:6Please respect copyright.PENANANA1Iraj0tb
> 9 → 8:第 1 步6Please respect copyright.PENANAkjWMV8V5sH
> 8 → 7:第 2 步6Please respect copyright.PENANAojblXCC4aw
> 7 → 6:第 3 步6Please respect copyright.PENANAL15AkSK6Xm
> 6 → 5:第 4 步
所以:6Please respect copyright.PENANAv9T4cSyBWh
> 9 - 4 = 5
五、易錯的地方:數「數字」和數「步」不同
題目:6Please respect copyright.PENANAyuyiAXuver
> 7 - 3
錯誤的做法可能是:6Please respect copyright.PENANAusN1tTYDu0
> 7, 6, 5
然後回答:6Please respect copyright.PENANAkZf7asZMVT
> 5
但這個是數了三個出現的數字:6Please respect copyright.PENANAn8OHTgoHPN
> 7、6、5
真正要做的是:6Please respect copyright.PENANA40Ljk5qjdG
> 由 7 開始,行 3 步。
正確:6Please respect copyright.PENANABJp5SwChkU
> 7 → 6:第 1 步6Please respect copyright.PENANAOSucH8G9l4
> 6 → 5:第 2 步6Please respect copyright.PENANAaNU79PFwIv
> 5 → 4:第 3 步
所以:6Please respect copyright.PENANA4bADvmQK6N
> 7 - 3 = 4
記住:6Please respect copyright.PENANA3tYfBnAMg5
> 減 3 = 行 3 步,不是讀出 3 個數字。
六、倒後數和取走物件是同一件事
例如:6Please respect copyright.PENANArR50SanVMt
> 6 - 2
物件方法
有 6 粒糖果:6Please respect copyright.PENANAy165hME1Eo
> 🍬🍬🍬🍬🍬🍬
拿去 2 粒:6Please respect copyright.PENANAoM5Z8pmpNB
> 🍬🍬
剩餘:6Please respect copyright.PENANAfZxS1ak5Ml
> 🍬🍬🍬🍬
所以:6Please respect copyright.PENANA4LOJ3PJx9n
> 6 - 2 = 4
//
倒後數方法
由 6 開始,倒後 2 步:6Please respect copyright.PENANASmJKrUKmvn
> 6 → 5 → 4
所以:6Please respect copyright.PENANAiKQ6SaHKXi
> 6 - 2 = 4
兩個方法答案一樣,因為它們在描述同一件事:6Please respect copyright.PENANAvXDryJNA45
> 每取走一個,就少一。
七、倒後數到 06Please respect copyright.PENANAFS1PO0OaL2
如果你有 4 粒糖果,吃光 4 粒:6Please respect copyright.PENANAnqW4H0sEkV
> 4 - 46Please respect copyright.PENANAUfbNpmwdKr
由 4 開始倒後行 4 步:6Please respect copyright.PENANAslqAv7Uyjd
> 4 → 3:第 1 步6Please respect copyright.PENANAVpDotxm6oZ
> 3 → 2:第 2 步6Please respect copyright.PENANAa7KZtkcKXp
> 2 → 1:第 3 步6Please respect copyright.PENANA5F2lZRk0Tn
> 1 → 0:第 4 步
所以:6Please respect copyright.PENANAeDie7FSMZ1
> 4 - 4 = 06Please respect copyright.PENANAhJQCbUt8zH
意思是:6Please respect copyright.PENANApqJBCnH6oE
> 全部取走,剩餘沒有任何一個。6Please respect copyright.PENANAvLhNJPHcpI
八、減 0:一步都不行
如果是:6Please respect copyright.PENANAZTEZhxDXlr
> 5 - 06Please respect copyright.PENANAlxgIKsBprs
意思是:6Please respect copyright.PENANAK32d1mpSwu
> 由 5 開始,倒後行 0 步。6Please respect copyright.PENANAdtzrfrQfk9
所以仍然是:6Please respect copyright.PENANAkSCh1PP463
> 56Please respect copyright.PENANAv7M91XQeNB
因此:6Please respect copyright.PENANAQJKdkIaXgK
> 5 - 0 = 56Please respect copyright.PENANAANlRkViHGN
再例如:6Please respect copyright.PENANA52rAU9XVq0
> 9 - 0 = 96Please respect copyright.PENANAKHGzVKBiiv
> 3 - 0 = 36Please respect copyright.PENANAkRao4hcf8y
> 0 - 0 = 06Please respect copyright.PENANA3U60LX8WZY
核心意思:6Please respect copyright.PENANA7qNKjqguE7
> 減 0,數量不變。6Please respect copyright.PENANAPalrnqBW52
九、暫時不倒後過 06Please respect copyright.PENANAEiZFIRoouf
現在我們的數線暫時是:6Please respect copyright.PENANA1tEnvoNWZv
> 0 —— 1 —— 2 —— 3 —— 4 —— 56Please respect copyright.PENANAnBsIDH7MWh
如果題目是:6Please respect copyright.PENANAIeQSXBAWZV
> 3 - 56Please respect copyright.PENANApszKK5BHti
即是由 3 開始向左行 5 步。
但目前數線去到 0 就停:6Please respect copyright.PENANA1F4bK3yCKx
> 3 → 2:第 1 步6Please respect copyright.PENANAUFMMwudUWD
> 2 → 1:第 2 步6Please respect copyright.PENANADQTnuRDu4t
> 1 → 0:第 3 步6Please respect copyright.PENANAuj55KQeaut
之後還要行 2 步,但在現在「數量世界」入面,已經沒有得再少。
所以目前階段會話:6Please respect copyright.PENANAvvnaxz8nIQ
> 3 - 5 暫時未能處理。6Please respect copyright.PENANA7c5d3KaIyf
將來學負數時,數線會向左延伸:6Please respect copyright.PENANA65nMMCRuBp
> -3 —— -2 —— -1 —— 0 —— 1 —— 2 —— 36Please respect copyright.PENANAVlzbZIsdPy
到那時可以正式做:6Please respect copyright.PENANAIogl75qzkb
> 3 - 5 = -26Please respect copyright.PENANAoJ8rKNUqXl
十、故事題:用倒後數解減法6Please respect copyright.PENANAy0gWhNBOVw
例子 4
你有 8 張貼紙。6Please respect copyright.PENANAipIkA96wuy
你用了 3 張。6Please respect copyright.PENANA7eLsKqQJ8N
你剩餘多少張?6Please respect copyright.PENANAc1EpHAwbWO
步驟 1:原本有多少?6Please respect copyright.PENANAXLEHKQ7eb0
> 8 張6Please respect copyright.PENANA8MlpfNh3Y1
步驟 2:用了多少?6Please respect copyright.PENANAVJGTrEumgD
> 3 張6Please respect copyright.PENANATJdK2d3z6r
步驟 3:寫成減法6Please respect copyright.PENANA3Syfiw5SZz
> 8 - 36Please respect copyright.PENANAmQFCyf8pfg
步驟 4:由 8 倒後行 3 步6Please respect copyright.PENANApseYALpCaN
> 8 → 7:第 1 步6Please respect copyright.PENANAi0RyCrczxq
> 7 → 6:第 2 步6Please respect copyright.PENANAbXfKPpjRN0
> 6 → 5:第 3 步6Please respect copyright.PENANANcI1eVmFR2
所以:6Please respect copyright.PENANA2kmUGoAf4T
> 8 - 3 = 56Please respect copyright.PENANAcEW6tjEiKz
答案:6Please respect copyright.PENANAfnaKAkqR5N
> 剩低 5 張貼紙。6Please respect copyright.PENANA5cKp8IpwNT
十一、另一故事題:倒後數到 06Please respect copyright.PENANAItvOtAvFIB
盒入面有 6 粒巧克力。6Please respect copyright.PENANAbFLxW4jvqp
你吃了 6 粒。6Please respect copyright.PENANA48WmxqOeII
盒入面剩多少粒?6Please respect copyright.PENANAocmzae185b
步驟 1:寫成減法6Please respect copyright.PENANAf2ltzA7pWx
> 6 - 66Please respect copyright.PENANAzAX24EML9v
步驟 2:倒後行 6 步6Please respect copyright.PENANAZuymVmWrEN
> 6 → 5:第 1 步6Please respect copyright.PENANAXG08FVoP6Q
> 5 → 4:第 2 步6Please respect copyright.PENANA5ESZMOv4y7
> 4 → 3:第 3 步6Please respect copyright.PENANA1ezGTtJLhf
> 3 → 2:第 4 步6Please respect copyright.PENANAruzf9jteBq
> 2 → 1:第 5 步6Please respect copyright.PENANABuTih0CP22
> 1 → 0:第 6 步6Please respect copyright.PENANARPs0aMJgdd
所以:6Please respect copyright.PENANAgOgw4j9wUj
> 6 - 6 = 06Please respect copyright.PENANAcp0cfEHyjc
答案:6Please respect copyright.PENANAQrCyMaC3tE
> 剩低 0 粒巧克力6Please respect copyright.PENANAH5737mAIKh
十二、用倒後數檢查答案6Please respect copyright.PENANAqu6nrfRHev
假設有人話:6Please respect copyright.PENANAy0vGsas6H5
> 9 - 3 = 76Please respect copyright.PENANA6gmz92PQte
我們可以用倒後數檢查。
由 9 倒後行 3 步:6Please respect copyright.PENANAy5eP9EtK0T
> 9 → 8:第 1 步6Please respect copyright.PENANAFXIk453Eq6
> 8 → 7:第 2 步6Please respect copyright.PENANA1Ao0lRIg4i
> 7 → 6:第 3 步6Please respect copyright.PENANA4ktZMzWlu6
最後是:6Please respect copyright.PENANAmscyDaDbW0
> 66Please respect copyright.PENANATJ4FjeTDEJ
所以:6Please respect copyright.PENANA5P6kjCYyUt
> 9 - 3 = 66Please respect copyright.PENANAKrIFg3XXVy
原本的答案 7 錯了,因為只倒後行了 2 步:6Please respect copyright.PENANAe3CoSp1fOL
> 9 → 8 → 76Please respect copyright.PENANASB93zyXx1m
要記住:6Please respect copyright.PENANAWN2DgRiXEd
> 每一條箭嘴代表一步。6Please respect copyright.PENANAqldKzI2PMt
十三、減法和加法可以互相檢查6Please respect copyright.PENANA3EvO1hgB42
如果:6Please respect copyright.PENANAR5WvScAMzP
> 8 - 3 = 56Please respect copyright.PENANA7QFsyIduoO
那可以用加法檢查:6Please respect copyright.PENANA1vWd1ekeTO
> 5 + 3 = 86Please respect copyright.PENANAnMvOuBR2AH
意思是:6Please respect copyright.PENANA2bhXFhodo7
> 剩餘 5,再加回取走的 3,就會回到原本的 8。6Please respect copyright.PENANAj4wayVkC7e
所以:6Please respect copyright.PENANAQvVSdsoRl4
> 8 - 3 = 56Please respect copyright.PENANA6ITyT95M0A
> 5 + 3 = 86Please respect copyright.PENANANNhsiRT0oY
這兩句是是相連的。
再例如:6Please respect copyright.PENANAWPyerMN3dv
> 10 - 4 = 66Please respect copyright.PENANA7wchWEqtOB
可以檢查:6Please respect copyright.PENANAfb99C3wCOQ
> 6 + 4 = 106Please respect copyright.PENANAf2pnB0vZPa
如果加回之後回到原本數量,減法答案就合理。
十四、需要思考的例子:7 - 46Please respect copyright.PENANAAPJi5LreTP
問題:6Please respect copyright.PENANAJ2ccw3q2bQ
> 7 - 46Please respect copyright.PENANAfT38NurUaQ
方法 A:倒後數6Please respect copyright.PENANAbpHboLDGe2
由 7 倒後行 4 步:6Please respect copyright.PENANAOQ9LbyyDXa
> 7 → 6:第 1 步6Please respect copyright.PENANAy1UdhoRfH5
> 6 → 5:第 2 步6Please respect copyright.PENANA9iJi7rjg3w
> 5 → 4:第 3 步6Please respect copyright.PENANAj70YQbjotP
> 4 → 3:第 4 步6Please respect copyright.PENANAeWwYFSN9xI
所以:6Please respect copyright.PENANAoBwERL9Ied
> 7 - 4 = 36Please respect copyright.PENANAmeGTqbwuLW
//
方法 B:用加法檢查6Please respect copyright.PENANAYfw4DYG7Sa
問:6Please respect copyright.PENANAR6SuMwBuz1
> 3 + 4 是不是等於 7?6Please respect copyright.PENANAtOrFz1G2gx
由 3 向前行 4 步:6Please respect copyright.PENANARy3M2e8FM0
> 3 → 4 → 5 → 6 → 76Please respect copyright.PENANA4U4Rj7kPl0
是,會回到 7。
所以:6Please respect copyright.PENANA08Ug5MtSvB
> 7 - 4 = 36Please respect copyright.PENANAdOqTivpNLk
兩個方法互相支持。
十五、需要思考的例子:10 - 6
問題:6Please respect copyright.PENANAxhBMDgWjOr
> 10 - 66Please respect copyright.PENANASSBdptXvit
方法 A:倒後數6Please respect copyright.PENANAlTyw2IkHlt
由 10 倒後 6 步:6Please respect copyright.PENANAZpX4A9mSNb
> 10 → 9:第 1 步6Please respect copyright.PENANAJuLYb7EvOi
> 9 → 8:第 2 步6Please respect copyright.PENANAxdke5DZqU4
> 8 → 7:第 3 步6Please respect copyright.PENANANH7k70R4MX
> 7 → 6:第 4 步6Please respect copyright.PENANAfeD1BGJjTC
> 6 → 5:第 5 步6Please respect copyright.PENANA1o2w5E3HR4
> 5 → 4:第 6 步6Please respect copyright.PENANAuyxPh57Sb6
所以:6Please respect copyright.PENANAb5k65YJzwO
> 10 - 6 = 46Please respect copyright.PENANA1ntMyHxLeI
//
方法 B:用湊十的反向想法6Please respect copyright.PENANAhoYRbek7IM
之前我們知道:6Please respect copyright.PENANAowRtsssmIN
> 6 + 4 = 106Please respect copyright.PENANA3TX85JlTIS
所以如果整體是 10,取走 6,剩低就是:6Please respect copyright.PENANAeqLEyTyFyv
> 46Please respect copyright.PENANAd0nmvcTA86
因此:6Please respect copyright.PENANAFecw5f5r1C
> 10 - 6 = 46Please respect copyright.PENANAGDTeyL9mCW
這個開始接近「部分與整體」的想法:6Please respect copyright.PENANAHxhplkPkb7
> 整體 - 一部分 = 另一部分6Please respect copyright.PENANAH9ajV1em3z
十六、倒後數適合甚麼情況?6Please respect copyright.PENANADOzNWsgLnz
倒後數特別適合:6Please respect copyright.PENANAqGwtBUYYzx
> 減的數比較小6Please respect copyright.PENANAdhHLB9HsRB
例如:6Please respect copyright.PENANAtRcuQjmh4E
> 9 - 26Please respect copyright.PENANAvQQLjEDAHo
由 9 倒後 2 步:6Please respect copyright.PENANAHXQyfUVNF8
> 9 → 8 → 7
很快。
但如果是:6Please respect copyright.PENANAiw9GJAWjU1
> 15 - 86Please respect copyright.PENANAC4RXTiQyaS
倒後數 8 步就會比較長。
之後我們會學另一種減法意思:6Please respect copyright.PENANA6GEUC2oMz0
> 減法:比較差距 | Subtraction as Difference6Please respect copyright.PENANAKDML2Buknj
到那時可以用「由 8 數上去 15」的方法,可能會更快。
今日先集中掌握:6Please respect copyright.PENANAqCCaxd4pss
> 取走多少,就倒後多少步。6Please respect copyright.PENANAWRt3WUSPDY
十七、綜合例子:先加後減6Please respect copyright.PENANADXZaGzYV4g
你有 4 粒波子。6Please respect copyright.PENANA69HRPGSqyG
朋友送你 5 粒。6Please respect copyright.PENANA65I19QYhae
你之後送走 2 粒。6Please respect copyright.PENANAWVfDbSfC6q
問題:6Please respect copyright.PENANA7ZycsElsMl
> 最後有多少粒波子?6Please respect copyright.PENANAoB8iMw9yZO
步驟 1:先處理增加6Please respect copyright.PENANAeJMe93GHXr
原本有 4 粒,朋友給 5 粒:6Please respect copyright.PENANABL9dJ6TBm4
> 4 + 56Please respect copyright.PENANAhtjyzhaBuJ
由 5 開始數 4 步,或者由 4 開始數 5 步都可以。6Please respect copyright.PENANADS3zJtOAuF
用較快方法:6Please respect copyright.PENANAlvALtB898B
> 5 → 6 → 7 → 8 → 96Please respect copyright.PENANAYF0iuKadOW
所以:6Please respect copyright.PENANA6VAo41r5SR
> 4 + 5 = 96Please respect copyright.PENANAvNo9W5Vvrc
現在有:6Please respect copyright.PENANA2Abq0H7bfZ
> 9 粒6Please respect copyright.PENANApwFRX30DM2
步驟 2:再處理取走6Please respect copyright.PENANA9T8dr7jvRq
送走 2 粒:6Please respect copyright.PENANAAjVstFUL2q
> 9 - 2
由 9 倒後行 2 步:6Please respect copyright.PENANAbUyzKl62Eu
> 9 → 8:第 1 步6Please respect copyright.PENANAymsnHEgsAL
> 8 → 7:第 2 步6Please respect copyright.PENANAWIayih5TBw
所以:6Please respect copyright.PENANA2MCTMkvZYD
> 9 - 2 = 76Please respect copyright.PENANAkyKNDnz5Oq
答案:6Please respect copyright.PENANAInt1awBCYx
> 最後有 7 粒波子。6Please respect copyright.PENANAhVLz2FYVOn
十九、今日小結6Please respect copyright.PENANA6WWT7yG218
今課你掌握了:6Please respect copyright.PENANAk7tZEhfBRF
1. 倒後數是做減法的方法。6Please respect copyright.PENANAxalocFoJbB
2. 「a - b」可以理解成由「a」,向左行「b」步。6Please respect copyright.PENANAmBjnHO823Q
3. 起點不是第一;每一次移動才是一步。6Please respect copyright.PENANA3GhZiFMXwN
4. 減 0,即是行 0 步,答案不變。6Please respect copyright.PENANA2aZgrc7YpK
5. 一個數減自己,會倒後到 0。6Please respect copyright.PENANAx71QIk9pom
6. 減法可以用加法檢查:如果「a - b = c」,那「c + b = a」。6Please respect copyright.PENANA20yOfj0WK8
7. 目前階段倒後數不越過 0:負數會之後再學。6Please respect copyright.PENANAi9IaAVzWRs
減法可以理解成由原本數量開始,沿數線向左一步一步倒後行。
ns216.73.216.133da2


