一:數字不是孤立的46Please respect copyright.PENANAlGKJ5f81dt
上一課我們學了數線:46Please respect copyright.PENANAZWrMkhAU74
> 0 —— 1 —— 2 —— 3 —— 4 —— 546Please respect copyright.PENANAJ5azJzOlzL
每一個數都有位置。
今課我們不只看一個數在哪裏,而是看:46Please respect copyright.PENANAkhsw2lIjev
> 它的旁邊是甚麼數?46Please respect copyright.PENANArumnnv8J1U
例如:46Please respect copyright.PENANAdEUeovVAQn
> 3 的右邊是 446Please respect copyright.PENANA0uV5zkeRJj
> 3 的左邊是 246Please respect copyright.PENANAvyEoXof9lY
所以可以講:46Please respect copyright.PENANAmArbnXz7AK
> 4 比 3 多一46Please respect copyright.PENANANHUettRfN5
> 2 比 3 少一46Please respect copyright.PENANAROiuBNb0zC
今日的核心就係:46Please respect copyright.PENANAHYkQc5G9l4
> 多一 | One More46Please respect copyright.PENANAo5bltPUBs5
> 少一 | One Less46Please respect copyright.PENANAdAAuSAD3o3
二:多一是甚麼?46Please respect copyright.PENANAbKc1BhqSSr
如果你有 3 粒糖果:46Please respect copyright.PENANA2Dgi4qIzj5
> 🍬🍬🍬46Please respect copyright.PENANAUwx31fOz15
再多 1 粒:46Please respect copyright.PENANAbOP95WYB0x
> 🍬🍬🍬🍬46Please respect copyright.PENANApU5Eni03an
就變成 4 粒。
所以:46Please respect copyright.PENANAjDeKBNWJ9g
> 3 多一是 4
用數線看:46Please respect copyright.PENANAHy2gWdQEV2
> 0 —— 1 —— 2 —— 3 —— 4 —— 546Please respect copyright.PENANARsFJJP5KZE
> 3 → 446Please respect copyright.PENANAWmaQAI4y2s
由 3 向右行一格,就去到 4。
所以:46Please respect copyright.PENANAa3KXCGds65
> 多一 = 數線上向右行路
三:少一是甚麼?
如果你有 3 粒糖果:46Please respect copyright.PENANACNWk82aDit
> 🍬🍬🍬46Please respect copyright.PENANAAtnBJQgS5Q
少了 1 粒:46Please respect copyright.PENANAMI9go7yJeH
> 🍬🍬46Please respect copyright.PENANAlDrJzgfuwZ
就變成 2 粒。
所以:46Please respect copyright.PENANA4wXS2nGKF5
> 3 少一是我
用數線看:46Please respect copyright.PENANAQ2Qt2XktP9
> 0 —— 1 —— 2 —— 3 —— 4 —— 546Please respect copyright.PENANAYWgUa7tQ8g
> 2 ← 346Please respect copyright.PENANA3JYZnShEJr
由 3 向左行一格,就去到 2。
所以:46Please respect copyright.PENANAzdy1QgGrAo
> 少一 = 數線上向左行一格46Please respect copyright.PENANAxv1IDfzq1q
四:後繼數與前一個數
數學入面有兩個有用的詞語。
1. 後繼數 | Successor
一個數的後繼數,就是它右邊下一個數。
例如:46Please respect copyright.PENANAPwbesSmooN
> 2 的後繼數是 346Please respect copyright.PENANAMNcjDwL79Q
> 5 的後繼數是 646Please respect copyright.PENANAUiVacnChM7
> 9 的後繼數是 1046Please respect copyright.PENANAZ0cONkeSzp
//
2. 前一個數 | Predecessor46Please respect copyright.PENANABNG5MUj031
一個數的前一個數,就是它左邊上一個數。
例如:46Please respect copyright.PENANAKWDjZTMJaC
> 4 的前一個數是 346Please respect copyright.PENANAX8c0G7zzju
> 8 的前一個數是 746Please respect copyright.PENANAeMqkPWaudN
> 10 的前一個數是 946Please respect copyright.PENANA90SXxS7ZGz
五:簡單例子46Please respect copyright.PENANARem2FnQL11
例子 1:5 多一是幾多?46Please respect copyright.PENANAAlvNkLCHG8
用數線:46Please respect copyright.PENANAfJZy1fM68R
> 0 —— 1 —— 2 —— 3 —— 4 —— 5 —— 646Please respect copyright.PENANA3B7Onq39zm
由 5 向右行一格:46Please respect copyright.PENANAHrUGFWV9k0
> 5 → 646Please respect copyright.PENANADGL608ig1B
所以:46Please respect copyright.PENANAPPQV7pZ6Cl
> 5 多一是 646Please respect copyright.PENANAKN0ZjDaZtw
//
例子 2:5 少一是幾多?46Please respect copyright.PENANAfQliEm8pLv
由 5 向左行一格:46Please respect copyright.PENANA15ZE8K9wwn
> 4 ← 546Please respect copyright.PENANAZprO13klhw
所以:46Please respect copyright.PENANA3THhmLzvgq
> 5 少一是 446Please respect copyright.PENANAEjiKpfuD9P
//
例子 3:0 多一是幾多?
由 0 向右行一格:46Please respect copyright.PENANA4k89dxmOKL
> 0 → 146Please respect copyright.PENANAhkntVDvI5c
所以:46Please respect copyright.PENANAzeH6AM8mec
> 0 多一是 146Please respect copyright.PENANA6yXEqU3dlJ
意思:46Please respect copyright.PENANAImnnMrnVk5
> 由沒有任何一個,變成有一個。46Please respect copyright.PENANAIzzQTgv4D0
六:0 可不可以少一?46Please respect copyright.PENANAntI43Ln9fa
現在我們的數線:46Please respect copyright.PENANABYU44BU9Ku
> 0 —— 1 —— 2 —— 3 —— 446Please respect copyright.PENANAiDWb1HDMDe
問題:46Please respect copyright.PENANAwB0evDeDI5
> 0 少一是幾多?46Please respect copyright.PENANAJP5WqQy0Vx
如果只講「物件數量」,0 已經代表沒有任何一件。
那麼「少一」就好像在問:46Please respect copyright.PENANAy7j1N5yhc2
> 沒有粒糖,再少一粒糖果,會變成如何?46Please respect copyright.PENANAROzR5F9BQm
在目前的數量世界入面,答案是:46Please respect copyright.PENANAB9tmKbPpeT
> 做不到。46Please respect copyright.PENANA5ZivPav8qN
因為你沒有糖果可以再拎走。
所以在現在這個階段:46Please respect copyright.PENANAkRpQjVqGjE
> 0 沒有前一個自然數。46Please respect copyright.PENANArOy2Q7IRrq
將來學習負數時,我們會擴展數線:46Please respect copyright.PENANAsxwJ71yF1T
> -1 —— 0 —— 1 —— 246Please respect copyright.PENANApGTRZHhgyj
那時 0 少一就會是:46Please respect copyright.PENANACOIXdicg5f
> -146Please respect copyright.PENANAxmypd7Ysyq
七:多一和少一是相反方向46Please respect copyright.PENANABdEEFzOMqN
如果由 3 多一:46Please respect copyright.PENANAVDSwUiSYEh
> 3 → 446Please respect copyright.PENANA4EqhHVFnOb
再少一:46Please respect copyright.PENANAfi8PodD3n6
> 4 → 346Please respect copyright.PENANAsNZsgnHq6a
就返到原本的 3。
相反,如果由 3 少一:46Please respect copyright.PENANAPufzXo08IJ
> 3 → 246Please respect copyright.PENANAmYO56lv1Ha
再多一:46Please respect copyright.PENANAQHzuFHBYuT
> 2 → 346Please respect copyright.PENANA1vllJsX7y3
都返到原本的 3。
所以:46Please respect copyright.PENANABFnBXI4Ccw
> 多一和少一是相反動作。46Please respect copyright.PENANAUiNRhrRvFv
八:連續多一46Please respect copyright.PENANADoRve0l9AL
問題:46Please respect copyright.PENANAW1Zl5AwdjR
> 由 2 開始,多一、再多一、再多一,最後是幾多?46Please respect copyright.PENANAF0dD9gibix
步驟一:由 2 開始46Please respect copyright.PENANAonTI8WHGlb
> 246Please respect copyright.PENANAoYyPzhC1se
步驟二:第一次多一46Please respect copyright.PENANAwxk1yiDM5d
> 2 → 346Please respect copyright.PENANAZV0gaUcBfp
步驟三:第二次多一46Please respect copyright.PENANASEPdORwCJZ
> 3 → 446Please respect copyright.PENANApiTHxighZA
步驟四:第三次多一46Please respect copyright.PENANAo4WjvGofH0
> 4 → 546Please respect copyright.PENANAwxRFJF6CA9
所以最後是:46Please respect copyright.PENANAbag6vhRJSN
> 5
你可以見到:46Please respect copyright.PENANAylX13vrgvw
> 多一做三次,就是向右行三格。46Please respect copyright.PENANAUiGLPYtABL
將來我們會將這件事寫成:46Please respect copyright.PENANAHkmrmu2xrB
> 2 + 3 = 546Please respect copyright.PENANAbeFcMQKU3R
九:連續少一46Please respect copyright.PENANATM9gLlvf4H
問題:46Please respect copyright.PENANA8bF13lTH0t
> 由 6 開始,少一、再少一,最後是幾多?46Please respect copyright.PENANAhG6BLZgD56
步驟 1:由 6 開始46Please respect copyright.PENANAYL9VAPf9Nn
> 646Please respect copyright.PENANAvEhcyNGQU8
步驟 2:第一次少一46Please respect copyright.PENANAxcAtFfoUDB
> 6 → 546Please respect copyright.PENANAOcANDinNcc
步驟 3:第二次少一46Please respect copyright.PENANAyk6rgJfmgn
> 5 → 446Please respect copyright.PENANAHU4ylvokTd
所以最後是:46Please respect copyright.PENANAOIJZOEjns1
> 446Please respect copyright.PENANAdy9FwoeutN
將來我們會寫成:46Please respect copyright.PENANAQQVwckAnKC
> 6 - 2 = 446Please respect copyright.PENANAQwH4NlefYg
十:多一、少一和「相鄰數」46Please respect copyright.PENANACogYuaiKHh
兩個相鄰的整數,相差一定是 1。
例如:46Please respect copyright.PENANAJ8OU5q9szA
> 4 和 5 相鄰46Please respect copyright.PENANAjpqQI8KkqU
> 5 比 4 多一46Please respect copyright.PENANAETPLuj7Qrh
> 4 比 5 少一46Please respect copyright.PENANAuaEHoz3vtY
又例如:46Please respect copyright.PENANAASr6cRa6Ku
> 8 和 9 相鄰46Please respect copyright.PENANAyL2mALasAw
> 9 比 8 多一46Please respect copyright.PENANAuvUxfvVZMA
> 8 比 9 少一46Please respect copyright.PENANAN07vEBjcba
所以,如果有人問:46Please respect copyright.PENANAKeSZYD6ZZv
> 哪兩個數是相鄰?46Please respect copyright.PENANA04TNZrE3b4
你可以看它們是不是只相差 1。
例如:46Please respect copyright.PENANAZxLQmnJ5m4
> 6 和 7:相鄰46Please respect copyright.PENANAoP55Jqxcq4
> 6 和 8:不相鄰,因為中間還有 7
十一:搵缺失的數46Please respect copyright.PENANA7J9CGf1CLO
數線其中一段是:46Please respect copyright.PENANA6eqlFB98rF
> 3 —— ? —— 546Please respect copyright.PENANAWevoQqnbOf
問題:46Please respect copyright.PENANApzvmcLx41R
> ? 應該是幾多?46Please respect copyright.PENANAoyLWAAfwSJ
步驟 1:由 3 向右一格46Please respect copyright.PENANAPJvF9Gv2X0
3 後面下一個數是:46Please respect copyright.PENANAf4cU3hva19
> 446Please respect copyright.PENANA7XPvm0npfC
步驟 2:由 5 向左一格46Please respect copyright.PENANAui6MfO3B2W
5 前面上一個數都是:46Please respect copyright.PENANAbbXr3SCcLG
> 446Please respect copyright.PENANAwPhGZZco9C
所以:46Please respect copyright.PENANAONbJGUIplh
> ? = 446Please respect copyright.PENANATOeUzXMSrD
完整數線為:46Please respect copyright.PENANAUKUHnYba22
> 3 —— 4 —— 546Please respect copyright.PENANAGzAKCmlzoV
十二:為何 9 多一是 10?
有時由 9 去 10 會覺得特別,因為寫法由一個符號變成兩個符號。
但概念上,它和其他「多一」一樣:46Please respect copyright.PENANAYJG2sZFgrg
> 7 多一是 846Please respect copyright.PENANAN0w8HYE1GN
> 8 多一是 946Please respect copyright.PENANA2CowFn0Z1Y
> 9 多一是 1046Please respect copyright.PENANA7qK30GxpDT
意思都是:46Please respect copyright.PENANASvC4Vkl8B9
> 數線上向右行一格。46Please respect copyright.PENANAE5Sl6im7Pn
10 只是寫法變了,數量仍然是「9 再多一」。
例如:46Please respect copyright.PENANAyLTxBEDgoi
> ⭐⭐⭐⭐⭐⭐⭐⭐⭐46Please respect copyright.PENANADwwhMIG5yh
這裏是 9 粒星。
再加一粒:46Please respect copyright.PENANAUsU1bD86Kw
> ⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐46Please respect copyright.PENANAcwAzdUNJxe
就是 10 粒星。46Please respect copyright.PENANAXKCJmjcA6E
所以:46Please respect copyright.PENANATa54Za2OFy
> 雖然寫法變複雜,但「多一」的意思沒有變。46Please respect copyright.PENANAsW2C284hsu
十三:由 4 出發46Please respect copyright.PENANAYdfldOSbDJ
問題:46Please respect copyright.PENANAo62RhqlWxY
1. 4 多一是幾多?46Please respect copyright.PENANAx2i1QVdJ8o
2. 4 少一是幾多?46Please respect copyright.PENANAY8284rkzeA
3. 4 多一之後再少一是幾多?46Please respect copyright.PENANA3DDgK27NAb
4. 4 少一之後再少一是幾多?46Please respect copyright.PENANAjITrLG7paw
第 1 問46Please respect copyright.PENANAwCNnehVWVv
> 4 → 546Please respect copyright.PENANA38NOOmiZ32
所以:46Please respect copyright.PENANAcpOoOXNXrg
> 4 多一是 546Please respect copyright.PENANAs28JAgwl2b
//
第 2 問46Please respect copyright.PENANASiwBnXbTn9
> 4 → 3
所以:46Please respect copyright.PENANAzKlxd8XPrO
> 4 少一是 346Please respect copyright.PENANAyjmC4FFjAT
//
第 3 問46Please respect copyright.PENANA8GUC8r7tk4
4 多一:46Please respect copyright.PENANAhTqFq22nJo
> 4 → 546Please respect copyright.PENANATXVWUcMgs7
再少一:46Please respect copyright.PENANALdKzvKlwRF
> 5 → 446Please respect copyright.PENANAShxTznIhcc
所以最後是:46Please respect copyright.PENANAasWMHBfe0n
> 446Please respect copyright.PENANACWO1oU5MpN
//
第 4 問46Please respect copyright.PENANAV4MZ45eJDj
4 少一:46Please respect copyright.PENANAjOzgDzmhFp
> 4 → 346Please respect copyright.PENANAfl4EM6dbIr
再少一:46Please respect copyright.PENANAUsaSn4A76Y
> 3 → 2
所以最後是:46Please respect copyright.PENANArSz9dLLqWA
> 246Please respect copyright.PENANAJ7d2FH50bo
十四:今日小結46Please respect copyright.PENANAjGvKUDMlhZ
今課你掌握了:
1. 多一即是數線上向右行一格。46Please respect copyright.PENANAxqjdysGff1
2. 少一即是數線上向左行一格。46Please respect copyright.PENANAlZ5Wbghk48
3. 一個數的後繼數,就是它多一之後的數。46Please respect copyright.PENANAYF3QRmd7HO
4. 一個數的前一個數,就是它少一之後的數。46Please respect copyright.PENANA9rHaeOhjAx
5. 多一和少一是相反動作。46Please respect copyright.PENANA5lTb0FGzq4
6. 連續多一,可以理解成將來的加法:連續少一,可以理解成將來的減法。
數學之間不是散開的;每個數都和前後的數連住,而「一」就是最基本的步伐。
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