一、不一定要由 1 數起33Please respect copyright.ＰＥＮＡＮＡBqU4PPQXHX
上一課我們學了加法：33Please respect copyright.ＰＥＮＡＮＡzxru068ggq
> 2 + 3 = 533Please respect copyright.ＰＥＮＡＮＡgkdX5lxqvK
可以理解成：33Please respect copyright.ＰＥＮＡＮＡbUfEys42O4
> 兩堆物件合在一起，變成總數。33Please respect copyright.ＰＥＮＡＮＡLScJHHpvAX
但如果數量開始變大，每次都由 1 數起會很慢。
例如：33Please respect copyright.ＰＥＮＡＮＡgiNHOu3eTr
> 你已經知道盒入面有 8 粒糖果。33Please respect copyright.ＰＥＮＡＮＡ7SZl8y3Gls
> 朋友再給你 3 粒糖果。33Please respect copyright.ＰＥＮＡＮＡd2vY6EvY0w
你不需要重新數：33Please respect copyright.ＰＥＮＡＮＡa1m762PhZg
> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1133Please respect copyright.ＰＥＮＡＮＡHwDO3Go917
你可以由已知的 8 開始，接住數新加的 3 粒：33Please respect copyright.ＰＥＮＡＮＡ9oERuDYL8G
> 9, 10, 1133Please respect copyright.ＰＥＮＡＮＡXQ2kd9Guk4
所以：33Please respect copyright.ＰＥＮＡＮＡiF9qjfvHSh
> 8 + 3 = 1133Please respect copyright.ＰＥＮＡＮＡDZuXwSg5l9
這個方法叫：33Please respect copyright.ＰＥＮＡＮＡMRISF57JXe
> 接住數 | Counting On33Please respect copyright.ＰＥＮＡＮＡLl0OFkjD9v
二、接住數是甚麼？33Please respect copyright.ＰＥＮＡＮＡhESCsQgszL
接住數的意思是：33Please respect copyright.ＰＥＮＡＮＡpV18I6j5pF
> 已經知道一部分有幾多，就由那個數開始，向前數另一部分。33Please respect copyright.ＰＥＮＡＮＡ6n6o0eR8c0
例如：33Please respect copyright.ＰＥＮＡＮＡWD24yCRP5K
> 6 + 233Please respect copyright.ＰＥＮＡＮＡlzTRQX2aEw
你可以由 6 開始，向前行 2 步：33Please respect copyright.ＰＥＮＡＮＡin2lienrIB
> 第 1 步：6 → 733Please respect copyright.ＰＥＮＡＮＡsPsL6XOrQp
> 第 2 步：7 → 833Please respect copyright.ＰＥＮＡＮＡ3Qyo3MMIyJ
所以：33Please respect copyright.ＰＥＮＡＮＡKy5P8IqMke
> 6 + 2 = 833Please respect copyright.ＰＥＮＡＮＡxwfpIO3T8K
重點是：33Please respect copyright.ＰＥＮＡＮＡOXbuyVxPqZ
> 6 是起點，不是第一步。33Please respect copyright.ＰＥＮＡＮＡSRaUN8Mi11
> 加 2，意思是行 2 步。33Please respect copyright.ＰＥＮＡＮＡ1CnGrbzadj
三、接住數和數線33Please respect copyright.ＰＥＮＡＮＡTf3jWGZSic
用數線看：33Please respect copyright.ＰＥＮＡＮＡcXP0pYXM4e
> 0 —— 1 —— 2 —— 3 —— 4 —— 5 —— 6 —— 7 —— 833Please respect copyright.ＰＥＮＡＮＡATnyrwqwyH
做：33Please respect copyright.ＰＥＮＡＮＡBIXspPcf48
> 5 + 333Please respect copyright.ＰＥＮＡＮＡWWzIOZvI6V
即是：33Please respect copyright.ＰＥＮＡＮＡYw7YOoVZNH
> 由 5 開始，向右行 3 步。33Please respect copyright.ＰＥＮＡＮＡGqZmilkfNl
步驟：33Please respect copyright.ＰＥＮＡＮＡvIKcWnpwnH
> 5 → 6：第 1 步33Please respect copyright.ＰＥＮＡＮＡhrACAtx69B
> 6 → 7：第 2 步33Please respect copyright.ＰＥＮＡＮＡn6hNrNBxby
> 7 → 8：第 3 步33Please respect copyright.ＰＥＮＡＮＡw2XlsPbauQ
所以：33Please respect copyright.ＰＥＮＡＮＡy1Inh69VPG
> 5 + 3 = 833Please respect copyright.ＰＥＮＡＮＡD0jKnl1YNH
四、簡單例子33Please respect copyright.ＰＥＮＡＮＡZGtbpYszcZ
例子 1：4 + 2
由 4 開始，向前行 2 步：33Please respect copyright.ＰＥＮＡＮＡUaJbu8OIfa
> 4 → 5：第 1 步33Please respect copyright.ＰＥＮＡＮＡqBZ6xswnhB
> 5 → 6：第 2 步33Please respect copyright.ＰＥＮＡＮＡfWe2dCDpqh
所以：33Please respect copyright.ＰＥＮＡＮＡlSmjP0SffD
> 4 + 2 = 633Please respect copyright.ＰＥＮＡＮＡxreOv7jQ8s
//
例子 2：7 + 1
由 7 開始：向前行 1 步：33Please respect copyright.ＰＥＮＡＮＡM2VtjGUm1X
> 7 → 833Please respect copyright.ＰＥＮＡＮＡHJQ3fEyCbz
所以：33Please respect copyright.ＰＥＮＡＮＡnYMDDqcrVF
> 7 + 1 = 833Please respect copyright.ＰＥＮＡＮＡtRVhTlcBMk
其實這個就是：33Please respect copyright.ＰＥＮＡＮＡUvaXrXvXdB
> 7 多一是 833Please respect copyright.ＰＥＮＡＮＡku08SQ8SwX
//
例子 3：3 + 4
由 3 開始，向前行 4 步：33Please respect copyright.ＰＥＮＡＮＡ47SDfJYA4e
> 3 → 4：第 1 步33Please respect copyright.ＰＥＮＡＮＡiZL2B9MDZW
> 4 → 5：第 2 步33Please respect copyright.ＰＥＮＡＮＡqm1y33FZ0S
> 5 → 6：第 3 步33Please respect copyright.ＰＥＮＡＮＡgvUxlKdEsx
> 6 → 7：第 4 步33Please respect copyright.ＰＥＮＡＮＡ9TAIUBFWT3
所以：33Please respect copyright.ＰＥＮＡＮＡzZq9qThcEk
> 3 + 4 = 733Please respect copyright.ＰＥＮＡＮＡFInH7l5JpV
五、接住數可能會有的錯誤33Please respect copyright.ＰＥＮＡＮＡI1JmM1xXSk
錯誤：將起點計成第一步
例如：33Please respect copyright.ＰＥＮＡＮＡtCpVDBvpCB
> 6 + 333Please respect copyright.ＰＥＮＡＮＡBFFJYOnpER
錯誤數法：33Please respect copyright.ＰＥＮＡＮＡprn58PgdtA
> 6, 7, 833Please respect copyright.ＰＥＮＡＮＡxvonTfpMZt
然後答：33Please respect copyright.ＰＥＮＡＮＡD7oxO3CoGu
> 833Please respect copyright.ＰＥＮＡＮＡ21f0XAMXqa
但這個其實只是數了 3 個「出現的數」，不是行了 3 步。
正確做法：33Please respect copyright.ＰＥＮＡＮＡc231uLDHWN
> 6 → 7：第 1 步33Please respect copyright.ＰＥＮＡＮＡ9OUP66zBSL
> 7 → 8：第 2 步33Please respect copyright.ＰＥＮＡＮＡPKEVLwYsRn
> 8 → 9：第 3 步33Please respect copyright.ＰＥＮＡＮＡi9U8fshz2l
所以：33Please respect copyright.ＰＥＮＡＮＡS81O6odw87
> 6 + 3 = 933Please respect copyright.ＰＥＮＡＮＡhj3MDFRhkl
一個簡單的檢查方法是：33Please respect copyright.ＰＥＮＡＮＡPGvjiBsbyZ
> 加 3，應該比原本大 3。33Please respect copyright.ＰＥＮＡＮＡeIcScZkRfj
> 6 變 9，剛好大 3。33Please respect copyright.ＰＥＮＡＮＡvNu12L3a4W
六、如何選擇起點更快？33Please respect copyright.ＰＥＮＡＮＡKJixVe3wv8
因為加法可以交換次序：33Please respect copyright.ＰＥＮＡＮＡ0bA6mXXicZ
> 2 + 8 = 8 + 233Please respect copyright.ＰＥＮＡＮＡD06BEjxDIn
所以接住數時，通常可以由較大的數開始，數較小的數。
例如：33Please respect copyright.ＰＥＮＡＮＡxj5a5BiPIa
> 2 + 833Please respect copyright.ＰＥＮＡＮＡRndHgmZcZp
方法 A：由 2 開始，行 8 步。33Please respect copyright.ＰＥＮＡＮＡP5jEldV7SR
> 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → 1033Please respect copyright.ＰＥＮＡＮＡIHjfvdd7km
答案：33Please respect copyright.ＰＥＮＡＮＡrutXuFH1HK
> 1033Please respect copyright.ＰＥＮＡＮＡJJYxp0jfhG
方法 B：換一換次序，想成：33Please respect copyright.ＰＥＮＡＮＡxJMwrTM6Ef
> 8 + 233Please respect copyright.ＰＥＮＡＮＡvi5sXiywdM
由 8 開始，行 2 步：33Please respect copyright.ＰＥＮＡＮＡSOySzXCxb1
> 8 → 9 → 1033Please respect copyright.ＰＥＮＡＮＡqLsNSZSj1J
答案一樣；33Please respect copyright.ＰＥＮＡＮＡNlWqaLNXIL
> 10
但方法 B 快很多。
所以做加法時可以用這個策略：33Please respect copyright.ＰＥＮＡＮＡJxGDgfaaWT
> 由大數開始，接住數小的數。33Please respect copyright.ＰＥＮＡＮＡ3r5XFe089m
七、1 + 933Please respect copyright.ＰＥＮＡＮＡ16miG4pcu4
問題：33Please respect copyright.ＰＥＮＡＮＡ4IVC2xLTfV
> 1 + 9 = ?33Please respect copyright.ＰＥＮＡＮＡgnfJuP58qS
你可以由 1 開始行 9 步，但很慢。
因為加法可以交換次序：33Please respect copyright.ＰＥＮＡＮＡhxxntZu4Aw
> 1 + 9 = 9 + 133Please respect copyright.ＰＥＮＡＮＡRsi2tjY1gM
由 9 開始，行 1 步：33Please respect copyright.ＰＥＮＡＮＡkTPYvu1Xv3
> 9 → 1033Please respect copyright.ＰＥＮＡＮＡafBm6xEX9A
所以：33Please respect copyright.ＰＥＮＡＮＡgm9dLUqw12
> 1 + 9 = 1033Please respect copyright.ＰＥＮＡＮＡSv3fw37rdN
不是盲目跟左邊開始，而是選擇更容易的方向理解。
八、接住數和「合併」是同一回事33Please respect copyright.ＰＥＮＡＮＡJGoyVDBBwn
有時你可能會問：33Please respect copyright.ＰＥＮＡＮＡjKqGk958ZU
> 加法到底是合併，還是接住數？33Please respect copyright.ＰＥＮＡＮＡ8YEhmxdbB8
答案是：33Please respect copyright.ＰＥＮＡＮＡhwtH5938kE
> 兩個都對，只是角度不同。33Please respect copyright.ＰＥＮＡＮＡ0xdibIziH4
例如：33Please respect copyright.ＰＥＮＡＮＡig73Hi29D2
> 4 + 333Please respect copyright.ＰＥＮＡＮＡs9I6HvwSK7
合併角度：33Please respect copyright.ＰＥＮＡＮＡ9nrxCnN0e1
> 4 個物件 + 3 個物件 = 7 個物件33Please respect copyright.ＰＥＮＡＮＡuwpGKMEy26
接住數角度：33Please respect copyright.ＰＥＮＡＮＡGrgZNKtw46
> 由 4 開始，向前行 3 步，到 733Please respect copyright.ＰＥＮＡＮＡAgO3Y8SJnd
兩種方法都描述著同一件事：33Please respect copyright.ＰＥＮＡＮＡ2DLIo1gVv5
> 4 + 3 = 733Please respect copyright.ＰＥＮＡＮＡZ66cSVDWX5
所以數學入面，常常會有多個模型解釋同一個概念。
九、用接住數解故事題33Please respect copyright.ＰＥＮＡＮＡUoNlNHbdfj
例子 4：
你有 6 張卡，33Please respect copyright.ＰＥＮＡＮＡl6gv3gAIYb
朋友再給你 4 張。33Please respect copyright.ＰＥＮＡＮＡ9qOj9IljGG
你現在有多少張？33Please respect copyright.ＰＥＮＡＮＡ0cH4JZH8lk
步驟 1：找已經起點33Please respect copyright.ＰＥＮＡＮＡDK96lIMvQj
原本有：33Please respect copyright.ＰＥＮＡＮＡDPTYBs2SNU
> 6 張33Please respect copyright.ＰＥＮＡＮＡG1fjB6rye3
步驟 2：找新增數量33Please respect copyright.ＰＥＮＡＮＡw3KNfvDIMM
朋友給你：33Please respect copyright.ＰＥＮＡＮＡVVdhdJogi0
> 4 張33Please respect copyright.ＰＥＮＡＮＡZcJFVBDQIe
所以是：33Please respect copyright.ＰＥＮＡＮＡuIlCZkWNbl
> 6 + 433Please respect copyright.ＰＥＮＡＮＡNTNXvWRK7K
步驟 3：由 6 接住數 4 步33Please respect copyright.ＰＥＮＡＮＡnkrwDYAycg
> 6 → 7：第 1 步33Please respect copyright.ＰＥＮＡＮＡsv3dhale0h
> 7 → 8：第 2 步33Please respect copyright.ＰＥＮＡＮＡd8q44KbzsZ
> 8 → 9：第 3 步33Please respect copyright.ＰＥＮＡＮＡPsxPO0tHXa
> 9 → 10：第 4 步33Please respect copyright.ＰＥＮＡＮＡVcR1OLHdPA
答案：33Please respect copyright.ＰＥＮＡＮＡeUwLX5uask
> 你現在有 10 張卡。33Please respect copyright.ＰＥＮＡＮＡzRZllmZbAJ
十一、那個方法較簡單？33Please respect copyright.ＰＥＮＡＮＡE4nKwPBTQ7
問題：33Please respect copyright.ＰＥＮＡＮＡncC63pDfs4
> 4 + 933Please respect copyright.ＰＥＮＡＮＡHRUnEotGKw
方法 A：由 4 開始，行 9 步。33Please respect copyright.ＰＥＮＡＮＡXUuLchUDmc
> 4 → 5 → 6 → 7 → 8 → 9 → 10 → 11 → 12 → 1333Please respect copyright.ＰＥＮＡＮＡYLEGoEU03x
答案是：33Please respect copyright.ＰＥＮＡＮＡWaQNVvUpLi
> 1333Please respect copyright.ＰＥＮＡＮＡXCColgLdaC
方法 B：交換次序：33Please respect copyright.ＰＥＮＡＮＡPZdJ600h21
> 4 + 9 = 9 + 433Please respect copyright.ＰＥＮＡＮＡMEbffx6JFZ
由 9 開始，行 4 步：33Please respect copyright.ＰＥＮＡＮＡr815fnRW5K
> 9 → 10：第 1 步33Please respect copyright.ＰＥＮＡＮＡ6LESFRfcpz
> 10 → 11：第 2 步33Please respect copyright.ＰＥＮＡＮＡzyF5XcAZhE
> 11 → 12：第 3 步33Please respect copyright.ＰＥＮＡＮＡdRxOwhAKo9
> 12 → 13：第 4 步33Please respect copyright.ＰＥＮＡＮＡ3XmpGGMGIn
答案一樣是：33Please respect copyright.ＰＥＮＡＮＡG741ikAK4S
> 1333Please respect copyright.ＰＥＮＡＮＡs0nETJszRu
方法 B 更短。
結論：33Please respect copyright.ＰＥＮＡＮＡAb4z1669Ql
> 接住數不只是計算方法，亦是一種選擇更有效路線的方法。33Please respect copyright.ＰＥＮＡＮＡVOm0XjlYBV
十二、接住數可以跨過 1033Please respect copyright.ＰＥＮＡＮＡQIZAF12ReB
由 8 加 5：33Please respect copyright.ＰＥＮＡＮＡQhWy7zwUbu
> 8 + 533Please respect copyright.ＰＥＮＡＮＡWPi3SIaAKG
有時過了 9 去到 10，會覺得特別。33Please respect copyright.ＰＥＮＡＮＡvlwEUKhQ10
但其實只是繼續向前行。33Please respect copyright.ＰＥＮＡＮＡxGFS4SnWn7
步驟：33Please respect copyright.ＰＥＮＡＮＡFyux3JKMxa
> 8 → 9：第 1 步33Please respect copyright.ＰＥＮＡＮＡwqG6hSxzv6
> 9 → 10：第 2 步33Please respect copyright.ＰＥＮＡＮＡ2cUQRndTEr
> 10 → 11：第 3 步33Please respect copyright.ＰＥＮＡＮＡWv9yvaY6lm
> 11 → 12：第 4 步33Please respect copyright.ＰＥＮＡＮＡjrG8Xkjnwd
> 12 → 13：第 5 步33Please respect copyright.ＰＥＮＡＮＡJd6sVQSYmc
所以：33Please respect copyright.ＰＥＮＡＮＡ1o6cEKmAkK
> 8 + 5 = 1333Please respect copyright.ＰＥＮＡＮＡY38nwg0POq
10 不是牆壁，只是數線上其中一個位置，與其他數一樣。
十三、接住數和「差多少到某個數」
有時接住數可以幫你猜：33Please respect copyright.ＰＥＮＡＮＡzHjUwIJt4B
> 由一個數去到另一個數，要加幾多？33Please respect copyright.ＰＥＮＡＮＡrRFYsGrHWG
例如：33Please respect copyright.ＰＥＮＡＮＡfIxvYAcFcT
> 6 + ? = 1033Please respect copyright.ＰＥＮＡＮＡmdz4IwzmqO
意思是：33Please respect copyright.ＰＥＮＡＮＡz8ZoBeKf0e
> 由 6 開始，要行幾步才到 10？33Please respect copyright.ＰＥＮＡＮＡuuQIYJ9dHK
數線步驟：33Please respect copyright.ＰＥＮＡＮＡWM0nwCRGMS
> 6 → 7：第 1 步33Please respect copyright.ＰＥＮＡＮＡfo7MJFf7TY
> 7 → 8：第 2 步33Please respect copyright.ＰＥＮＡＮＡWZpMFMgK5L
> 8 → 9：第 3 步33Please respect copyright.ＰＥＮＡＮＡsYSNmS309F
> 9 → 10：第 4 步33Please respect copyright.ＰＥＮＡＮＡgbqX2hS9Fy
所以：33Please respect copyright.ＰＥＮＡＮＡ98yiKMincf
> 6 + 4 = 1033Please respect copyright.ＰＥＮＡＮＡPTZuvA5wa0
即是：33Please respect copyright.ＰＥＮＡＮＡJNnWWDobgf
> ? = 433Please respect copyright.ＰＥＮＡＮＡ9fawuHaAaV
十四、三個數相加
問題：33Please respect copyright.ＰＥＮＡＮＡVsKZoGc5NM
> 3 + 2 + 4 = ?33Please respect copyright.ＰＥＮＡＮＡyytAWwaa26
可以逐段接住數。33Please respect copyright.ＰＥＮＡＮＡfQdpMIt8UQ
步驟 1：先做 3 + 233Please respect copyright.ＰＥＮＡＮＡa4BrqUXRSk
由 3 行 2 步：33Please respect copyright.ＰＥＮＡＮＡ7lhEDAxGU1
> 3 → 4：第 1 步33Please respect copyright.ＰＥＮＡＮＡnWXrI3UYv0
> 4 → 5：第 2 步33Please respect copyright.ＰＥＮＡＮＡDgLXRTGb3v
所以：33Please respect copyright.ＰＥＮＡＮＡV1xLpLWa1v
> 3 + 2 = 533Please respect copyright.ＰＥＮＡＮＡ9Nwtk9HZpr
步驟 2：再加 433Please respect copyright.ＰＥＮＡＮＡ6ThdhC7teL
由 5 行 4 步：33Please respect copyright.ＰＥＮＡＮＡnQcLIa3j3H
> 5 → 6：第 1 步33Please respect copyright.ＰＥＮＡＮＡFMuuoHzqOx
> 6 → 7：第 2 步33Please respect copyright.ＰＥＮＡＮＡYeJJbvLGtA
> 7 → 8：第 3 步33Please respect copyright.ＰＥＮＡＮＡHN0qnPgYKK
> 8 → 9：第 4 步33Please respect copyright.ＰＥＮＡＮＡrL5glpC8pa
所以：33Please respect copyright.ＰＥＮＡＮＡN7SSDfxwpM
> 3 + 2 + 4 = 933Please respect copyright.ＰＥＮＡＮＡovBQTvinJw
另一種想法是：33Please respect copyright.ＰＥＮＡＮＡDIQhGtbatW
> 先將 2 + 4 變成 633Please respect copyright.ＰＥＮＡＮＡvLPCeZO7LG
> 再做 3 + 6 變成 933Please respect copyright.ＰＥＮＡＮＡ3XS0L7c2Gn
這個會引出之後的加法結合律。
十五、接住數背後的數學思想33Please respect copyright.ＰＥＮＡＮＡ0shyvr9aU6
接住數表面上很簡單，但背後有三個重要思想：33Please respect copyright.ＰＥＮＡＮＡlWdV5Xj6Uf
第一，數字有順序：33Please respect copyright.ＰＥＮＡＮＡ6NW3ffKsMD
> 6 後面是 7，7 後面是 8。33Please respect copyright.ＰＥＮＡＮＡnrvDCxWGIy
第二，加法可以理解成移動：33Please respect copyright.ＰＥＮＡＮＡUrTD2X3g8C
> 加 3 = 向右行 3 步。33Please respect copyright.ＰＥＮＡＮＡHCPS5rsfwe
第三，已知的數量可以成為起點：33Please respect copyright.ＰＥＮＡＮＡWm8Jg4FLfD
> 不需要每次由 1 重新開始。33Please respect copyright.ＰＥＮＡＮＡh7GRPim2XS
這個思想很重要，因為數學不是每次重新數一次，而是會利用已知的資料，繼續推理。
十六、今日小結33Please respect copyright.ＰＥＮＡＮＡr5TGez3goJ
今課你已掌握：33Please respect copyright.ＰＥＮＡＮＡIKFds4FLJ9
1. 接住數即是由已知數量開始，向前數新增的數量。33Please respect copyright.ＰＥＮＡＮＡeGIILEwOge
2. a + b 可以理解成由 a 開始，向右行 b 步。33Please respect copyright.ＰＥＮＡＮＡz3n9iBxF2t
3. 起點不是第一步：加幾，就要行幾步。33Please respect copyright.ＰＥＮＡＮＡYvR7R8KIJP
4. 加法可以交換次序，所以通常由較大數開始數較小的數會更快。33Please respect copyright.ＰＥＮＡＮＡ1az9BgdBNj
5. 接住數和合併數量是同一個加法概念的兩種理解。33Please respect copyright.ＰＥＮＡＮＡZUHTOVumVR
6. 接住數可以幫我們處理缺失部分，例如 6 + ? = 10。33Please respect copyright.ＰＥＮＡＮＡuhPSs7GPHy
接住數是用已佑數量做起點，將「加法」變成沿數線向前走。
ns216.73.216.75da2
and then Add to home screen.