一、加法不一定逐步數
上一課我們學了:13Please respect copyright.PENANAzbf3XHs0R0
> 8 + 313Please respect copyright.PENANAIUuJwocGYy
可以由 8 開始接住數:13Please respect copyright.PENANArsAkt6YtML
> 8 → 9 → 10 → 11
所以:13Please respect copyright.PENANADbE5RSLGnV
> 8 + 3 = 1113Please respect copyright.PENANALYmn5F5wd6
這個方法很有用。
但如果數字再大一些,每次都一步一步數,仍然會慢。
例如:13Please respect copyright.PENANASNIjnmkIBW
> 8 + 713Please respect copyright.PENANAILQShCfGUm
你可以由 8 開始數 7 步,但有沒有更聰明的方法?
今課我們會開始找加法規律,尤其是一個很重要的技巧:13Please respect copyright.PENANAPnnBOab1N0
> 湊十 | Making Ten13Please respect copyright.PENANAJFpk8DU3eB
二、為何 10 很重要?
我們日常用的數字系統很依賴 10。
例如:13Please respect copyright.PENANAHpHUJu4NVU
> 10、20 、30、100、100013Please respect copyright.PENANA97hBedy4Q5
好多大數都是圍繞 10 而建立。
所以如果你熟悉哪些數可以湊成 10,之後做加法會快好多。
例如:13Please respect copyright.PENANAhrE7s9kN9d
> 8 + 2 = 1013Please respect copyright.PENANA9hw5mNw01S
> 7 + 3 = 1013Please respect copyright.PENANAK46gxsw6Av
> 6 + 4 = 1013Please respect copyright.PENANAmVyZxVtMmp
> 5 + 5 = 1013Please respect copyright.PENANAuAZZFJUx4O
這些叫:13Please respect copyright.PENANAWLhG1ar5CA
> 湊十組合 | Number bonds to 1013Please respect copyright.PENANArrPkbsBDMh
可以理解成:13Please respect copyright.PENANArH0XwlUZUt
> 兩個部分合起來,剛好成為 10。13Please respect copyright.PENANAOxcRhJCcpX
三、先記住 10 的組合
以下是最基本的湊十組合:13Please respect copyright.PENANAMD1ADUUw05
> 0 + 10 = 1013Please respect copyright.PENANASwY2pBiB0S
> 1 + 9 = 1013Please respect copyright.PENANA1ruqAJ1dYE
> 2 + 8 = 1013Please respect copyright.PENANAImMryL2SKb
> 3 + 7 = 1013Please respect copyright.PENANA2Xbh6FDByP
> 4 + 6 =1013Please respect copyright.PENANAPb8xp8gvAN
> 5 + 5 = 1013Please respect copyright.PENANAvj46mdT2Ki
> 6 + 4 = 1013Please respect copyright.PENANADTtavICQdr
> 7 + 3 = 1013Please respect copyright.PENANAWiWs3psO7r
> 8 + 2 = 1013Please respect copyright.PENANASuqolGz3W8
> 9 + 1 = 1013Please respect copyright.PENANAmFrmN3ZJgQ
> 10 + 0 = 1013Please respect copyright.PENANAu7RDbKdgZd
你會見到:13Please respect copyright.PENANAZm5inolaGF
> 1 配 913Please respect copyright.PENANASBdVl7Aa7a
> 2 配 813Please respect copyright.PENANAdsOt3WSpBh
> 3 配 713Please respect copyright.PENANA5qEF56zdR3
> 4 配 613Please respect copyright.PENANAIvBNjmDQCG
> 5 配 513Please respect copyright.PENANAqINkQdFejH
如果交換次序,答案仍然一樣。
例如:13Please respect copyright.PENANAYmXG2zPvxQ
> 3 + 7 = 1013Please respect copyright.PENANAoikbClFzet
> 7 + 3 = 1013Please respect copyright.PENANAtIJNnDaIRB
四、簡單例子:直接湊十
例子 1:8 + 213Please respect copyright.PENANAu5n952alqR
8 距離 10 差幾多?13Please respect copyright.PENANAITtNtiXxnH
> 8 → 9:第 1 步13Please respect copyright.PENANAaKVeeyIBgB
> 9 → 10:第 2 步13Please respect copyright.PENANA5tBSin21s6
所以 8 差 2 到 10。
因此:13Please respect copyright.PENANAxfUmLD6IfN
> 8 + 2 = 1013Please respect copyright.PENANAgEDHXNj09n
//
例子 2:6 + 4
6 距離 10 差幾多?13Please respect copyright.PENANATKACLshYO3
> 6 → 7:第 1 步13Please respect copyright.PENANAZzASsFxsiC
> 7 → 8:第 2 步13Please respect copyright.PENANAmSViO2YYzw
> 8 → 9:第 3 步13Please respect copyright.PENANAM1QPPliIyt
> 9 → 10:第 4 步13Please respect copyright.PENANA3LsEctBF59
所以 6 差 4 到 10。
因此:13Please respect copyright.PENANAwR821UxEOZ
> 6 + 4 = 1013Please respect copyright.PENANA4duEUfDspF
//
例子 3:9 + 1
9 只差 1 就到 10:13Please respect copyright.PENANAwhjyoceRYf
> 9 → 1013Please respect copyright.PENANAuw5tqlXuHF
所以:13Please respect copyright.PENANAcE4nVXSmfs
> 9 + 1 = 1013Please respect copyright.PENANAupUWeNmjps
五、湊十如何幫助加法?
如果題目是:13Please respect copyright.PENANAw0egi9ex3t
> 8 + 513Please respect copyright.PENANA0HkttBs29q
你可以逐步數:13Please respect copyright.PENANAskh5o8jqfh
> 8 → 9 → 10 → 11 → 12 → 1313Please respect copyright.PENANAxeltt30Ixq
答案是 13。
但湊十可以令思考更清楚。
步驟 1:先問 8 差幾多到 1013Please respect copyright.PENANAWldHXCMHWj
> 8 差 2 到 10
所以將 5 拆開成:13Please respect copyright.PENANAzZjqzU26gP
> 2 + 313Please respect copyright.PENANAd7tpdUPWDq
因為:13Please respect copyright.PENANAOZzeAZZ9Tx
> 5 = 2 + 313Please respect copyright.PENANAtTn67t0SPC
步驟 2:先用 2 湊成 1013Please respect copyright.PENANAWxAqiTaGIa
> 8 + 2 = 1013Please respect copyright.PENANA2RvhmdfiUx
步驟 3:再加剩低的 313Please respect copyright.PENANAXaOf7CsAa0
> 10 + 3 = 1313Please respect copyright.PENANA0nCKHy5nuP
所以:13Please respect copyright.PENANA6CHpOm2Uiw
> 8 + 5 = 1313Please respect copyright.PENANA9U3O9E0jZ5
完整想法:13Please respect copyright.PENANABDlegCWPrF
> 8 + 513Please respect copyright.PENANAsBGKjiykCj
> = 8 + 2 + 313Please respect copyright.PENANA4k19o8p8R3
> = 10 + 313Please respect copyright.PENANAishvgxicQa
> = 1313Please respect copyright.PENANAtldszMYKaA
湊十的核心是:13Please respect copyright.PENANAX4lNwrkYQH
> 先去到 10,再接住加剩低那部分。
六、數字拆分:將一個數分成兩部分
要湊十,通常要將一個數拆開。13Please respect copyright.PENANAkXmwNTj84v
例如:13Please respect copyright.PENANAKFGWub5Jhm
> 5 可以拆成 2 + 313Please respect copyright.PENANAJdRpbkBPXX
> 6 可以拆成 1 + 513Please respect copyright.PENANA7W7gN1tgty
> 7 可以拆成 2 + 513Please respect copyright.PENANA4RrCjGYevm
> 4 可以拆成 1 + 313Please respect copyright.PENANAv47u4RFsiM
拆分不代要改變數量,只是將同一個數分成兩部分。
例如 5 粒糖果:13Please respect copyright.PENANAnNOKJk2wCA
> 🍬 🍬 | 🍬 🍬 🍬13Please respect copyright.PENANAWg9dkMOwOJ
左邊 2 粒,右邊 3 粒。
所以:13Please respect copyright.PENANAsZsJB3ttss
> 5 = 2 + 313Please respect copyright.PENANAclu28CkmNX
但總數仍然是 5。
七:簡單例子:9 + 4
問題:13Please respect copyright.PENANAYqLMO9VcFs
> 9 + 4= ?13Please respect copyright.PENANArTGHiCSD93
步驟 1:9 差幾多到 10?13Please respect copyright.PENANAlA8Vk1D37D
> 9 差 1 到 10
步驟 2:將 4 拆成 1 + 313Please respect copyright.PENANAJJ8XJaqPvD
> 4 = 1 + 3
步驟 3:先湊十13Please respect copyright.PENANAY5T6OwXACC
> 9 + 1 = 1013Please respect copyright.PENANAmXqw8IlTkl
步驟 4:再加剩低的 313Please respect copyright.PENANAEcFmysnJbI
> 10 + 3 = 1313Please respect copyright.PENANA7sBYHkXxfx
所以:13Please respect copyright.PENANAXHMq9HZUrq
> 9 + 4 = 1313Please respect copyright.PENANADuQjXkpGUi
完整:13Please respect copyright.PENANAdomLwi0BEM
> 9 + 413Please respect copyright.PENANAVrTFcbtFnJ
> = 9 + 1 + 313Please respect copyright.PENANANdEqSwQKGu
> = 10 + 313Please respect copyright.PENANA5NJwpE85ye
> = 1313Please respect copyright.PENANAMxsrPkHQdz
八、7 + 5
問題:13Please respect copyright.PENANAJC5f7KiYyl
> 7 + 5 = ?13Please respect copyright.PENANAozTcHyzxjR
步驟 1:7 差幾多到 10?13Please respect copyright.PENANA6y0SgBrVCQ
由 7 到 10:13Please respect copyright.PENANAFXdXJSvFhT
> 7 → 8:第 1 步13Please respect copyright.PENANAqZRVohjszH
> 8 → 9:第 2 步13Please respect copyright.PENANAsMDMSdejPO
> 9 → 10:第 3 步13Please respect copyright.PENANANw5BkMISI1
所以:13Please respect copyright.PENANAMI05LH5uYj
> 7 差 3 到 1013Please respect copyright.PENANAxffvcW40uS
步驟 2:將 5 拆成 3 + 213Please respect copyright.PENANAHZhTXQyald
> 5 = 3 + 213Please respect copyright.PENANA7km3bs2P6j
步驟 3:先湊十13Please respect copyright.PENANAiFmxRgovyH
> 7 + 3 = 1013Please respect copyright.PENANANAtFoUEERi
步驟 4:再加剩低的 213Please respect copyright.PENANAA6dSBbH2lS
> 10 + 2 = 1213Please respect copyright.PENANAmukfJ7vt5W
所以:13Please respect copyright.PENANAEUp1HqzEsB
> 7 + 5 =1213Please respect copyright.PENANAkr2W2t5zHB
九、6 + 8
問題:13Please respect copyright.PENANAISquLX45Qw
> 6 + 8 = ?13Please respect copyright.PENANAXgR13L5bj8
這條題目有兩個方向。
方向 A:由 6 湊十13Please respect copyright.PENANAOCYvvkk3BF
6 差 4 到 10。13Please respect copyright.PENANAAAyXudkq35
所以將 8 拆成:13Please respect copyright.PENANAykDReo5K5E
> 4 + 4
然後:13Please respect copyright.PENANApaEGCrmWfD
> 6 + 813Please respect copyright.PENANAHUu0X6nEtH
> = 6 + 4 + 413Please respect copyright.PENANAHxtbVmVbp0
> = 10 + 413Please respect copyright.PENANAhyu9peIAqw
> = 1413Please respect copyright.PENANABWcmbVK2EV
答案:13Please respect copyright.PENANAZ4zSu9wlmC
> 1413Please respect copyright.PENANAXRa5A098zk
//
方法 B:由 8 湊十13Please respect copyright.PENANAbWTUlcNC76
8 差 2 到 10。
所以將 6 拆成:13Please respect copyright.PENANA0aGytPo6gF
> 2 + 413Please respect copyright.PENANA6nNOfdo8Yr
然後:13Please respect copyright.PENANAwnM5PGYQ8g
> 8 + 613Please respect copyright.PENANA6CTCHpxx1A
> = 8 + 2 + 413Please respect copyright.PENANAUs397uFsHh
> = 10 + 413Please respect copyright.PENANAq6ghcDhEP8
> = 14
答案一樣13Please respect copyright.PENANArG63G2Ll48
> 1413Please respect copyright.PENANAnhRrGZ0SxZ
//
哪個方法更自然?13Please respect copyright.PENANAhX8sX2Dq7i
通常由較接近 10 的數開始會容易一些。13Please respect copyright.PENANAHxxI7WDMNs
8 比 6 更接近 10,所以:13Please respect copyright.PENANAGBX4WoCdrw
> 8 + 613Please respect copyright.PENANAakXhonJnxI
會比較容易思考:13Please respect copyright.PENANACL7v4gpRZe
> 8 差 2,到 10,再剩 4。13Please respect copyright.PENANAciKlqR76Ic
所以:13Please respect copyright.PENANAtnYBaQA9gd
> 8 + 6 = 1413Please respect copyright.PENANAlyh1IO3G9v
十、加法規律:雙倍
有一類加法特別容易記:13Please respect copyright.PENANApDTmuC2S58
> 1 + 1 = 213Please respect copyright.PENANApZTIKr6mGd
> 2 + 2 = 413Please respect copyright.PENANAnIZ52tWJ3v
> 3 + 3 = 613Please respect copyright.PENANAzRNRkTfa0A
> 4 + 4 = 813Please respect copyright.PENANAqQrzJ7zjEF
> 5 + 5 = 1013Please respect copyright.PENANA1N8KoZUdCl
> 6 + 6 = 1213Please respect copyright.PENANApWFM7tTZmg
> 7 + 7 = 1413Please respect copyright.PENANA6BVjSaFZ6m
> 8 + 8 = 1613Please respect copyright.PENANA9ey8Q31m4T
> 9 + 9 = 1813Please respect copyright.PENANAWDgUjoxL5d
> 10 + 10 = 2013Please respect copyright.PENANAwmSk2j8pJf
這些叫:13Please respect copyright.PENANAROLJhmKPuV
> 雙倍數 | Doubles13Please respect copyright.PENANAimfvfCfrUi
意思是:13Please respect copyright.PENANAPUIu2MR5F6
> 同一個數加自己。13Please respect copyright.PENANArRY0uSYbry
例如:13Please respect copyright.PENANAwSWGbm3eMw
> 6 + 6 = 12
雙倍數加法很重要,因為好多加法都可以靠近它。
十一、接近雙倍數:Near Doubles
例如:13Please respect copyright.PENANAKdFH3S3NBX
> 6 + 713Please respect copyright.PENANAnk7QGpsJi8
7 比 6 多 1。
你可以先想:13Please respect copyright.PENANAtvjiqFsYHr
> 6 + 6 = 1213Please respect copyright.PENANANcUw7ao0K9
再加 1:13Please respect copyright.PENANAo2542jvbH7
> 12 + 1 = 13
所以:13Please respect copyright.PENANASjVQYWyEos
> 6 + 7 = 1313Please respect copyright.PENANAysdFerPgpX
//
又例如:13Please respect copyright.PENANAPAXm72sCer
> 8 + 913Please respect copyright.PENANA06hqTPL4A5
先想:13Please respect copyright.PENANArrlQxkdg77
> 8 + 8 = 1613Please respect copyright.PENANAbfkC1Kv0ad
再多 1:13Please respect copyright.PENANADcH25Bumrq
> 16 + 1 = 1713Please respect copyright.PENANAP5RroZmM8G
所以:13Please respect copyright.PENANAJ2JLR8fUEk
> 8 + 9 = 1713Please respect copyright.PENANAZJPnj9Y6IW
這個叫:13Please respect copyright.PENANAP08AOGWGIR
> 接近雙倍數 | Near Doubles13Please respect copyright.PENANABu7vR5QYWz
即是:13Please respect copyright.PENANADe8IFCg4gr
> 兩個數差 1,可以先用雙數,再調整 1。13Please respect copyright.PENANAeW5H4dmpHr
十二、7 + 8
問題:13Please respect copyright.PENANAssoeOU1adf
> 7 + 8 = ?13Please respect copyright.PENANARH4ET1mhHO
可以用湊十,也可以用接近雙倍數。
方法 A:13Please respect copyright.PENANAA4Bm9jadiN
8 差 2 到 10:13Please respect copyright.PENANAl66owlnHXc
將 7 拆成:13Please respect copyright.PENANAkVOuYt7qmh
> 2 + 513Please respect copyright.PENANAzZECilcGl1
所以:13Please respect copyright.PENANAQ8IujL0IP3
> 8 + 713Please respect copyright.PENANAkI4LpTY9L1
> = 8 + 2 + 513Please respect copyright.PENANA4Iphw0F6pY
> = 10 + 513Please respect copyright.PENANAAPvk7sm3L2
> = 1513Please respect copyright.PENANAn7fkmlDszl
//
方法 B:接近雙倍數13Please respect copyright.PENANAvObMxamr94
先想:13Please respect copyright.PENANAfgnEVIDVXg
> 7 + 7 = 1413Please respect copyright.PENANA00KO7cNhLZ
而 8 比 7 多 1。
所以:13Please respect copyright.PENANAO61mSa9D9s
> 7 + 8 = 1513Please respect copyright.PENANAiQl5TLc2Dj
兩個方法都對。
重點是:13Please respect copyright.PENANAAK0Zdev5Md
> 數學可以有多一條合理解題路線。13Please respect copyright.PENANAP2A5Wh1Ijd
十三、加 9 的規律
加 9 可以用很有效率地湊 10。13Please respect copyright.PENANA73LqMSittK
例如:13Please respect copyright.PENANAfqCCSBy3qo
> 6 + 913Please respect copyright.PENANAednERLrxFS
9 差 1 到 10。
可以由 6 借 1 給 9:13Please respect copyright.PENANAl1JQERtsDt
> 9 + 1 = 1013Please respect copyright.PENANAWQaInC3w4g
6 借走 1 之後剩:13Please respect copyright.PENANAMAUuxERV7P
> 513Please respect copyright.PENANAbN62oKRIc4
所以:13Please respect copyright.PENANAYXiDBs05bt
> 6 + 913Please respect copyright.PENANAUWE37SXk6M
> = 5 + 1013Please respect copyright.PENANAJT7wXqgYFF
> = 1513Please respect copyright.PENANAaMxm3acOp6
另一個寫法:13Please respect copyright.PENANAxigYZ5ddGw
> 9 + 613Please respect copyright.PENANARdJw5lDaXm
> = 9 + 1 + 513Please respect copyright.PENANAYOohVg3N0y
> = 10 + 513Please respect copyright.PENANA7b3nfG3GvQ
> = 1513Please respect copyright.PENANAzXJpWZgGai
加 9 的直覺可以是:13Please respect copyright.PENANAvWHkJ9g4jr
> 加 10 再少 113Please respect copyright.PENANARurXDbC3ba
例如:13Please respect copyright.PENANAQ2TwgIHbEc
> 6 + 10 = 1613Please respect copyright.PENANANUzDlA0otW
> 6 + 9 = 1513Please respect copyright.PENANANH5JBPPLif
因為 9 比 10 少 1。
十四、加法規律不是魔法
今課有很多技巧:13Please respect copyright.PENANAd0NEGYNmND
> 湊十、雙倍數、接近雙倍數、加 913Please respect copyright.PENANA7I6cTZbnR2
但所技巧都要回到同一個基礎:13Please respect copyright.PENANA2OFIkHErpF
> 數量沒有改變,只是拆分與重組。13Please respect copyright.PENANAbsu95M15hj
例如:13Please respect copyright.PENANA4c7QshDnia
> 8 + 513Please respect copyright.PENANANxrSYEOM2x
改成:13Please respect copyright.PENANACRieMMk3yr
> 8 + 2 + 313Please respect copyright.PENANAj67BM3kR0X
這裏沒有偷偷地改答案,因為:13Please respect copyright.PENANABiKL2Gxjlx
> 5 = 2 + 313Please respect copyright.PENANADJst0FAlgO
數學技巧可靠,因為每一步都保持數量相等。
十五、綜合例子:選擇一個好方法
題目 1:9 + 713Please respect copyright.PENANAoT3hP9rlE7
9 接近 10,所以用湊十。
9 差 1 到 10。13Please respect copyright.PENANAs6Z2oxhDcL
將 7 拆成:13Please respect copyright.PENANAlwy4BBvrCp
> 1 + 613Please respect copyright.PENANAbRFW4NZLUX
所以:13Please respect copyright.PENANAvAoVhYj6ih
> 9 + 713Please respect copyright.PENANAKPMrWCGIV5
> = 9 + 1 + 613Please respect copyright.PENANAx7Ch4N8gJp
> = 10 + 613Please respect copyright.PENANAfzxlEWcDgd
> = 1613Please respect copyright.PENANABFN74AybmW
答案:13Please respect copyright.PENANAfbTHDL5DFH
> 1613Please respect copyright.PENANAZkWIZfi41s
//
題目 2:6 + 613Please respect copyright.PENANA4jyhknhjw1
兩個數一樣,用雙倍數:13Please respect copyright.PENANARxKw1ydGvj
> 6 + 6 = 1213Please respect copyright.PENANAKLXTLVKAhm
答案:13Please respect copyright.PENANAXGOf3Hx5nU
> 1213Please respect copyright.PENANAKJIVTW6GOq
//
題目 3:6 + 713Please respect copyright.PENANA1oczt48tdC
兩個數差 1,用接近雙倍數13Please respect copyright.PENANAiFCsa19wHT
> 6 + 6 = 1213Please respect copyright.PENANAKTXvfFoqN4
> 再多 1 = 13
所以:13Please respect copyright.PENANAjTM867oro4
> 6 + 7 = 1313Please respect copyright.PENANAfYkuhHiZlA
十六、今日小結
今課你掌握了:13Please respect copyright.PENANAjVCcScWb1U
1. 10 是重要標準,熟悉湊十可以加法更法。13Please respect copyright.PENANAvUGXFsITFr
2. 湊十組合包括:1 + 9、2 + 8、3 + 7、4 + 6、5 + 5。13Please respect copyright.PENANAhgzAyP3X5s
3. 做湊十時,可以將一個數拆成兩部分。13Please respect copyright.PENANA4RYCy17QgS
4. 例如 8 + 5 可以想成 8 + 2 + 3 = 10 + 3 = 13。13Please respect copyright.PENANAo82jeUTRha
5. 雙倍數加法是同一個數加自己,例如 6 + 6 = 12。13Please respect copyright.PENANAYVEDQZH4cF
6. 接近雙倍數可以先用雙倍數,再多一或少一。13Please respect copyright.PENANA1evHWH0TPq
7. 所有加法技巧都要保持原本數量不變。
湊十是將加法重新安排,先去到 10,再從 10 繼續前進。
ns216.73.216.75da2


