一、加法不一定逐步數
上一課我們學了:12Please respect copyright.PENANAcUKXKEcT2X
> 8 + 312Please respect copyright.PENANABP5gQOys2O
可以由 8 開始接住數:12Please respect copyright.PENANAOsxHkuLept
> 8 → 9 → 10 → 11
所以:12Please respect copyright.PENANAYnyjPUXh9Q
> 8 + 3 = 1112Please respect copyright.PENANAHoF6GZgZEd
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:12Please respect copyright.PENANAzGQ1w1mZhe
> 8 + 712Please respect copyright.PENANAs0BjjUTWO3
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:12Please respect copyright.PENANAcsyvIabNKq
> 湊十 | Making Ten12Please respect copyright.PENANAgL9s23LEt8
二、為何 10 很重要?
我們日常用的數字系統很依賴 10。
例如:12Please respect copyright.PENANAjJ3Wzy9sWv
> 10、20 、30、100、100012Please respect copyright.PENANAHlKAbie5Pb
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:12Please respect copyright.PENANAWocoytx7Rw
> 8 + 2 = 1012Please respect copyright.PENANACN4lFlm0Qx
> 7 + 3 = 1012Please respect copyright.PENANAJz4eeZBez0
> 6 + 4 = 1012Please respect copyright.PENANAKioH15wtcM
> 5 + 5 = 1012Please respect copyright.PENANAYyE7Cvi9gX
這些叫:12Please respect copyright.PENANATFwTWr26xX
> 湊十組合 | Number bonds to 1012Please respect copyright.PENANA3gBKaWEttL
可以理解成:12Please respect copyright.PENANAwrkHHIGmUx
> 兩個部分合起來,剛好成為 10。12Please respect copyright.PENANAz1bTmaAs5L
三、先記住 10 的組合
以下是最基本的湊十組合:12Please respect copyright.PENANAsPHk2cIA7h
> 0 + 10 = 1012Please respect copyright.PENANA5FiNxgUfWN
> 1 + 9 = 1012Please respect copyright.PENANAxsNYYi1kxM
> 2 + 8 = 1012Please respect copyright.PENANA1BNUlWKKTo
> 3 + 7 = 1012Please respect copyright.PENANANScFPBYSYn
> 4 + 6 =1012Please respect copyright.PENANAbatlTBRNwt
> 5 + 5 = 1012Please respect copyright.PENANAY02DaxDgih
> 6 + 4 = 1012Please respect copyright.PENANAdgYRwBAH7L
> 7 + 3 = 1012Please respect copyright.PENANABy9VmjH4GD
> 8 + 2 = 1012Please respect copyright.PENANArDCDtPGqdB
> 9 + 1 = 1012Please respect copyright.PENANA7lnQR4oWGK
> 10 + 0 = 1012Please respect copyright.PENANAOWLewGqS97
你會見到:12Please respect copyright.PENANAU4N2X3VCxJ
> 1 配 912Please respect copyright.PENANAY7SyZhcafB
> 2 配 812Please respect copyright.PENANAlLK8RLEVQj
> 3 配 712Please respect copyright.PENANAiiCXzz7DDo
> 4 配 612Please respect copyright.PENANAhr8Up7xvDw
> 5 配 512Please respect copyright.PENANAuTjD2IHa01
如果交換次序,答案仍然一樣。
例如:12Please respect copyright.PENANAvGyEolnweI
> 3 + 7 = 1012Please respect copyright.PENANAli34euGbsf
> 7 + 3 = 1012Please respect copyright.PENANAJMcQLibozR
四、簡單例子:直接湊十
例子 1:8 + 212Please respect copyright.PENANAOJNUxAMIcC
8 距離 10 差幾多?12Please respect copyright.PENANAiynD4pZPET
> 8 → 9:第 1 步12Please respect copyright.PENANAIdzCOzy1xp
> 9 → 10:第 2 步12Please respect copyright.PENANA3OSxW5hdRv
所以 8 差 2 到 10。
因此:12Please respect copyright.PENANAyKALEfa6iH
> 8 + 2 = 1012Please respect copyright.PENANAkfOroaFBVO
//
例子 2:6 + 4
6 距離 10 差幾多?12Please respect copyright.PENANAsLomSS1SSW
> 6 → 7:第 1 步12Please respect copyright.PENANA0Vj2a8zVUB
> 7 → 8:第 2 步12Please respect copyright.PENANAgdiQWpQ2af
> 8 → 9:第 3 步12Please respect copyright.PENANAmAUs2FhfEK
> 9 → 10:第 4 步12Please respect copyright.PENANAoO3pWkrnlW
所以 6 差 4 到 10。
因此:12Please respect copyright.PENANAWMb6G6K7ak
> 6 + 4 = 1012Please respect copyright.PENANAxDJ3cyQmJ6
//
例子 3:9 + 1
9 只差 1 就到 10:12Please respect copyright.PENANA739zGXblon
> 9 → 1012Please respect copyright.PENANAsrZWJPn3Ol
所以:12Please respect copyright.PENANA9EzsVpJpZN
> 9 + 1 = 1012Please respect copyright.PENANAKZi7rr8CCW
五、湊十如何幫助加法?
如果題目是:12Please respect copyright.PENANA0VxO4AeYMT
> 8 + 512Please respect copyright.PENANA7bBTUgyRb5
你可以逐步數:12Please respect copyright.PENANADs7CqeqIaX
> 8 → 9 → 10 → 11 → 12 → 1312Please respect copyright.PENANANVcKpdTJB2
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 1012Please respect copyright.PENANA3cr05MWO5a
> 8 差 2 到 10
所以將 5 拆開成:12Please respect copyright.PENANAodEDAj0AKH
> 2 + 312Please respect copyright.PENANAnWvbJMHYBT
因為:12Please respect copyright.PENANAyIJVlstH2H
> 5 = 2 + 312Please respect copyright.PENANAeTId5Nulm4
步驟 2:先用 2 湊成 1012Please respect copyright.PENANAAQaDxGwS2y
> 8 + 2 = 1012Please respect copyright.PENANAch8djtUBKM
步驟 3:再加剩低的 312Please respect copyright.PENANATEKgd9ER2D
> 10 + 3 = 1312Please respect copyright.PENANABdKG08tWT1
所以:12Please respect copyright.PENANAKL3M2MTJdz
> 8 + 5 = 1312Please respect copyright.PENANAOZKiSlF4l3
完整想法:12Please respect copyright.PENANARb2FOUkgoI
> 8 + 512Please respect copyright.PENANAvqPHcrU3U4
> = 8 + 2 + 312Please respect copyright.PENANAC3odry893e
> = 10 + 312Please respect copyright.PENANAhuiZSMoAnP
> = 1312Please respect copyright.PENANAhQ0l0smZBF
湊十的核心是:12Please respect copyright.PENANAJBf8uPZw9r
> 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。12Please respect copyright.PENANAEgQbslmUV7
例如:12Please respect copyright.PENANArgLN3i1qWu
> 5 可以拆成 2 + 312Please respect copyright.PENANA8DFjOocVMl
> 6 可以拆成 1 + 512Please respect copyright.PENANAP7VIZ4HVnr
> 7 可以拆成 2 + 512Please respect copyright.PENANAChiQqNY4xv
> 4 可以拆成 1 + 312Please respect copyright.PENANALUCGHvnmQY
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:12Please respect copyright.PENANAgBcdsJAsc3
> 🍬 🍬 | 🍬 🍬 🍬12Please respect copyright.PENANAz2AscIfDIN
左邊 2 粒,右邊 3 粒。
所以:12Please respect copyright.PENANAEv7aonBX6j
> 5 = 2 + 312Please respect copyright.PENANAwvC6JygYpF
但總數仍然是 5。
七:簡單例子:9 + 4
問題:12Please respect copyright.PENANAADYJ5j7kaw
> 9 + 4= ?12Please respect copyright.PENANAIefj6nLMpn
步驟 1:9 差幾多到 10?12Please respect copyright.PENANAtbMkYlB39u
> 9 差 1 到 10
步驟 2:將 4 拆成 1 + 312Please respect copyright.PENANArl08z0N5bZ
> 4 = 1 + 3
步驟 3:先湊十12Please respect copyright.PENANATtOQmwTf49
> 9 + 1 = 1012Please respect copyright.PENANAnLNiG8axK0
步驟 4:再加剩低的 312Please respect copyright.PENANAtYHG27wUYc
> 10 + 3 = 1312Please respect copyright.PENANAIRbAaf9En3
所以:12Please respect copyright.PENANAs4u88QbTvv
> 9 + 4 = 1312Please respect copyright.PENANA7tBryAwV9z
完整:12Please respect copyright.PENANAdm1EzMX9WH
> 9 + 412Please respect copyright.PENANAPFOa0GyuLg
> = 9 + 1 + 312Please respect copyright.PENANAbrQAM5QPyK
> = 10 + 312Please respect copyright.PENANAeKus9b3B07
> = 1312Please respect copyright.PENANAa4hafl07X9
八、7 + 5
問題:12Please respect copyright.PENANAlauIQsbZAn
> 7 + 5 = ?12Please respect copyright.PENANAHk838QGOjI
步驟 1:7 差幾多到 10?12Please respect copyright.PENANA3EWwAaXLnf
由 7 到 10:12Please respect copyright.PENANA798TS5Xb0y
> 7 → 8:第 1 步12Please respect copyright.PENANAfDAiBPCfYF
> 8 → 9:第 2 步12Please respect copyright.PENANA2FYdYaZNU0
> 9 → 10:第 3 步12Please respect copyright.PENANAKdmlrYTKzz
所以:12Please respect copyright.PENANAOObis2wRhZ
> 7 差 3 到 1012Please respect copyright.PENANAFUNdcUPmOF
步驟 2:將 5 拆成 3 + 212Please respect copyright.PENANA19yFr85UGE
> 5 = 3 + 212Please respect copyright.PENANA6wt9rIvGzE
步驟 3:先湊十12Please respect copyright.PENANALIPf57ue3B
> 7 + 3 = 1012Please respect copyright.PENANAZIhSyfZc5G
步驟 4:再加剩低的 212Please respect copyright.PENANAWbldxLlbOd
> 10 + 2 = 1212Please respect copyright.PENANASjJ0WF46cE
所以:12Please respect copyright.PENANAH6KJpHJnCY
> 7 + 5 =1212Please respect copyright.PENANAoRr0CKaIWe
九、6 + 8
問題:12Please respect copyright.PENANAuIu3qbmaPz
> 6 + 8 = ?12Please respect copyright.PENANAYRhVQuZlNj
這條題目有兩個方向。
方向 A:由 6 湊十12Please respect copyright.PENANACr9oUXtz4S
6 差 4 到 10。12Please respect copyright.PENANAG7sQcfMLPm
所以將 8 拆成:12Please respect copyright.PENANAS4EdnLsDoY
> 4 + 4
然後:12Please respect copyright.PENANA46GHq8TPa4
> 6 + 812Please respect copyright.PENANA2no7RcXwuX
> = 6 + 4 + 412Please respect copyright.PENANA3qH6eWHtPB
> = 10 + 412Please respect copyright.PENANAknyaoSCrgQ
> = 1412Please respect copyright.PENANAlAXAnP4Aew
答案:12Please respect copyright.PENANA9b5GZno9Ad
> 1412Please respect copyright.PENANANZWcoyVYt5
//
方法 B:由 8 湊十12Please respect copyright.PENANAkbOjtCLJqP
8 差 2 到 10。
所以將 6 拆成:12Please respect copyright.PENANA8O7MkNu6i7
> 2 + 412Please respect copyright.PENANAgiY6D7kCSr
然後:12Please respect copyright.PENANABWoXDnhNkK
> 8 + 612Please respect copyright.PENANAaCtcHkLgCN
> = 8 + 2 + 412Please respect copyright.PENANAIGlAsIeqrb
> = 10 + 412Please respect copyright.PENANACTLgFgEbUY
> = 14
答案一樣12Please respect copyright.PENANAJUIOxaMJdZ
> 1412Please respect copyright.PENANAJXKeVxGL6w
//
哪個方法更自然?12Please respect copyright.PENANAZJE42RmbMH
通常由較接近 10 的數開始會容易一些。12Please respect copyright.PENANAaDhVmu7vNn
8 比 6 更接近 10,所以:12Please respect copyright.PENANAKgzO3fzEhZ
> 8 + 612Please respect copyright.PENANARxOhTy7oUH
會比較容易思考:12Please respect copyright.PENANAZF26x53yhF
> 8 差 2,到 10,再剩 4。12Please respect copyright.PENANAMCsKKmyFoV
所以:12Please respect copyright.PENANAof9eIsw8gj
> 8 + 6 = 1412Please respect copyright.PENANAPIH7K8EU1P
十、加法規律:雙倍
有一類加法特別容易記:12Please respect copyright.PENANALTt2k8gTrg
> 1 + 1 = 212Please respect copyright.PENANAOK07EqA9O5
> 2 + 2 = 412Please respect copyright.PENANAnsDjlnax0q
> 3 + 3 = 612Please respect copyright.PENANAkhYFtbdMLZ
> 4 + 4 = 812Please respect copyright.PENANAenzB9vrFzV
> 5 + 5 = 1012Please respect copyright.PENANAWdV2yythgH
> 6 + 6 = 1212Please respect copyright.PENANA4iXksEJ9n5
> 7 + 7 = 1412Please respect copyright.PENANAzwNYMfOz1J
> 8 + 8 = 1612Please respect copyright.PENANABLntp6Vk8d
> 9 + 9 = 1812Please respect copyright.PENANASW8v7SsrhL
> 10 + 10 = 2012Please respect copyright.PENANAtJOKzvnBRJ
這些叫:12Please respect copyright.PENANAX21sL9bBPw
> 雙倍數 | Doubles12Please respect copyright.PENANA5E1dz9l0Pp
意思是:12Please respect copyright.PENANAuPRgRG1FKi
> 同一個數加自己。12Please respect copyright.PENANAn2A5QLJV4M
例如:12Please respect copyright.PENANAqjEpUXLxF7
> 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:12Please respect copyright.PENANACnkGQ9ISVx
> 6 + 712Please respect copyright.PENANA3JMrDQzy5k
7 比 6 多 1。
你可以先想:12Please respect copyright.PENANA8qBvYBfUDZ
> 6 + 6 = 1212Please respect copyright.PENANAPKAjvs1KQW
再加 1:12Please respect copyright.PENANA2lvC1nTgE5
> 12 + 1 = 13
所以:12Please respect copyright.PENANAea2Wbd6Mrv
> 6 + 7 = 1312Please respect copyright.PENANAbYyLeh6Ke3
//
又例如:12Please respect copyright.PENANA8Sqrj8EvIU
> 8 + 912Please respect copyright.PENANAN1B8UyuXaL
先想:12Please respect copyright.PENANAu9FhE3FSR6
> 8 + 8 = 1612Please respect copyright.PENANAVRHAhco78L
再多 1:12Please respect copyright.PENANAjXCWVJwS9C
> 16 + 1 = 1712Please respect copyright.PENANAlLCuDxCkIZ
所以:12Please respect copyright.PENANAcmRrljnxng
> 8 + 9 = 1712Please respect copyright.PENANAoYHLM7m2Fc
這個叫:12Please respect copyright.PENANAbE3URvXdTo
> 接近雙倍數 | Near Doubles12Please respect copyright.PENANAuQruM7hmQk
即是:12Please respect copyright.PENANAYgayRmvYKa
> 兩個數差 1,可以先用雙數,再調整 1。12Please respect copyright.PENANAX9n1aHuPjm
十二、7 + 8
問題:12Please respect copyright.PENANA2Z6JGgonuC
> 7 + 8 = ?12Please respect copyright.PENANAR3ydbN4NTO
可以用湊十,也可以用接近雙倍數。
方法 A:12Please respect copyright.PENANAEVNmdZS3sa
8 差 2 到 10:12Please respect copyright.PENANAqjScRswNYg
將 7 拆成:12Please respect copyright.PENANA2BzXLv9fpg
> 2 + 512Please respect copyright.PENANAkGoUMGFkKC
所以:12Please respect copyright.PENANAjZRdpzqAtE
> 8 + 712Please respect copyright.PENANAGXaHFp6mIc
> = 8 + 2 + 512Please respect copyright.PENANANswrUuQivC
> = 10 + 512Please respect copyright.PENANAO1VrNfDbqw
> = 1512Please respect copyright.PENANAIkXOjAbSp3
//
方法 B:接近雙倍數12Please respect copyright.PENANAb1ifRFWfVr
先想:12Please respect copyright.PENANAFw8WNNjtq7
> 7 + 7 = 1412Please respect copyright.PENANAL2pjXWVhU8
而 8 比 7 多 1。
所以:12Please respect copyright.PENANAzn3wkFCufx
> 7 + 8 = 1512Please respect copyright.PENANAr4fEmYuvxN
兩個方法都對。
重點是:12Please respect copyright.PENANA9XgC48bSne
> 數學可以有多一條合理解題路線。12Please respect copyright.PENANAvGjNLelWLM
十三、加 9 的規律
加 9 可以用很有效率地湊 10。12Please respect copyright.PENANAJihwwehN6K
例如:12Please respect copyright.PENANAQUw4BOsrTc
> 6 + 912Please respect copyright.PENANAGUaNGIUrmz
9 差 1 到 10。
可以由 6 借 1 給 9:12Please respect copyright.PENANA6LFP34Khef
> 9 + 1 = 1012Please respect copyright.PENANAWi5OBNGf6z
6 借走 1 之後剩:12Please respect copyright.PENANAnZDLSMH1jy
> 512Please respect copyright.PENANABKNNGLmBWU
所以:12Please respect copyright.PENANAp7F2Gze9wS
> 6 + 912Please respect copyright.PENANA9LOTkHTQRA
> = 5 + 1012Please respect copyright.PENANAxs0MhgXjwS
> = 1512Please respect copyright.PENANAKWfcOPn5SM
另一個寫法:12Please respect copyright.PENANATVsd9hosQX
> 9 + 612Please respect copyright.PENANAX8K2W0i7Pl
> = 9 + 1 + 512Please respect copyright.PENANAadp5e0k6hp
> = 10 + 512Please respect copyright.PENANA7yIrGPCQXB
> = 1512Please respect copyright.PENANAzbaQG0cPMV
加 9 的直覺可以是:12Please respect copyright.PENANAoh51ABxUlU
> 加 10 再少 112Please respect copyright.PENANATwhOZg2alr
例如:12Please respect copyright.PENANAlAy9uSnpdU
> 6 + 10 = 1612Please respect copyright.PENANAXN5MfPICTS
> 6 + 9 = 1512Please respect copyright.PENANArneIzNIJYY
因為 9 比 10 少 1。
十四、加法規律不是魔法
今課有很多技巧:12Please respect copyright.PENANAgAowPGJUAi
> 湊十、雙倍數、接近雙倍數、加 912Please respect copyright.PENANAlXRrfO01Uq
但所技巧都要回到同一個基礎:12Please respect copyright.PENANA3WJYNjQATO
> 數量沒有改變,只是拆分與重組。12Please respect copyright.PENANAWq4O1TM2BR
例如:12Please respect copyright.PENANAEOI92we9qm
> 8 + 512Please respect copyright.PENANAHE8XGp11mX
改成:12Please respect copyright.PENANAxdOYee5f75
> 8 + 2 + 312Please respect copyright.PENANAYkmLQOaY6T
這裏沒有偷偷地改答案,因為:12Please respect copyright.PENANAbZleLBAsTx
> 5 = 2 + 312Please respect copyright.PENANAijj6uJKHWb
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 + 712Please respect copyright.PENANAmNuyBPVbXN
9 接近 10,所以用湊十。
9 差 1 到 10。12Please respect copyright.PENANAaCxFLSocHe
將 7 拆成:12Please respect copyright.PENANA8CC4FyyGOK
> 1 + 612Please respect copyright.PENANAaFAwKw3JaD
所以:12Please respect copyright.PENANAFFr0HhkMBT
> 9 + 712Please respect copyright.PENANAt2uW1pnBQQ
> = 9 + 1 + 612Please respect copyright.PENANAohIRt6yutr
> = 10 + 612Please respect copyright.PENANABUm7q91CIm
> = 1612Please respect copyright.PENANAAu8bcYnKLY
答案:12Please respect copyright.PENANACjwzj5FIah
> 1612Please respect copyright.PENANA5fv186knmL
//
題目 2:6 + 612Please respect copyright.PENANA3PQAUYPxyn
兩個數一樣,用雙倍數:12Please respect copyright.PENANAzi9m2lNYD1
> 6 + 6 = 1212Please respect copyright.PENANAV1txWNdjTr
答案:12Please respect copyright.PENANAf4sUS0Y0fL
> 1212Please respect copyright.PENANAKV4QBuSWql
//
題目 3:6 + 712Please respect copyright.PENANAC4gHojJrLY
兩個數差 1,用接近雙倍數12Please respect copyright.PENANAaM8vj6y4Ir
> 6 + 6 = 1212Please respect copyright.PENANAscDNLF34sz
> 再多 1 = 13
所以:12Please respect copyright.PENANA9mFwe2Nnh4
> 6 + 7 = 1312Please respect copyright.PENANAB3mk98M9Yb
十六、今日小結
今課你掌握了:12Please respect copyright.PENANA7AW18qGPGf
1. 10 是重要標準,熟悉湊十可以加法更法。12Please respect copyright.PENANAO0fBb4YhRL
2. 湊十組合包括:1 + 9、2 + 8、3 + 7、4 + 6、5 + 5。12Please respect copyright.PENANArDMnjDjt94
3. 做湊十時,可以將一個數拆成兩部分。12Please respect copyright.PENANArJbLpKfGxo
4. 例如 8 + 5 可以想成 8 + 2 + 3 = 10 + 3 = 13。12Please respect copyright.PENANA59IZp6CPwE
5. 雙倍數加法是同一個數加自己,例如 6 + 6 = 12。12Please respect copyright.PENANAbsr5E1tKBS
6. 接近雙倍數可以先用雙倍數,再多一或少一。12Please respect copyright.PENANARDBbMcTJPI
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


