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数轴习题——新初一 教材衔接预习

数轴习题——新初一 教材衔接预习

数轴 完整知识整理(小升初衔接)

一、核心概念

1. 数轴定义

规定了原点、正方向、单位长度的一条直线叫做数轴

满足以下三个条件:

要素
说明
原点
直线上表示数字0 的点
正方向
一般向为正方向,向为负方向,用箭头标出
单位长度
选取统一长度作为一格,原点右侧依次标1,2,3,…;左侧依次标-1,-2,-3,…

2. 数轴三要素(缺一不可)

原点、正方向、单位长度 —— 三条同时具备才是数轴,少一条都不是。

这三点是判断“是不是数轴”的唯一标准,考试中经常以图形辨析题出现。

3. 数轴四步画法

步骤
操作
一画
画一条水平直线
二取
在直线上选取一点标记原点,写数字0
三定
画出箭头确定正方向,规定单位长度(统一标准)
四标
均匀标注整数刻度(…,-2,-1,0,1,2,…)

4. 数轴判断易错点

错误类型
说明
❌ 没有箭头
缺少正方向,不是数轴
❌ 单位长度不一致
每格长短不统一,不是数轴
❌ 数字标注错乱
顺序标反、负数标错位置
❌ 直线未向两端延伸
数轴是直线,应向两端无限延伸

二、常考题型

题型1:在数轴上描数

步骤:先画数轴 → 确定原点、正方向、单位长度 → 在对应位置标出数字。

注意

  • 整数直接标;
  • 分数、百分数、小数先统一成小数再找点(如 ( 3/4 = 0.75 ),在0和1之间靠近1的位置);
  • 负分数同理,在负数区间内找对应位置。

题型2:行程类数轴应用题(邮递员、货车送货)

解题步骤

步骤
操作
以起点为原点,规定正方向,设定单位长度,画出数轴
标出各个地点对应的数字
两点距离 = 终点数 − 起点数(取正值
总路程
:把每一段行驶的长度全部相加(不计方向,只算绝对值)

⚠️ 关键区分

  • “最终位置”看终点对应的数
  • “总路程”把所有移动距离加在一起(不管向左还是向右)。

题型3:数轴点移动 ⭐(高频易错)

移动规则

方向
运算
移动
数字变大,原数+ 移动单位长度
移动
数字变小,原数 移动单位长度

⚠️ 重点警告: 题目只说移动距离,没有说明方向时,一定要分向右、向左两种情况讨论防止漏解

示例: 表示-2 的点移动7 个单位:

方向
计算
结果
向右
-2 + 7 = 5
5
向左
-2 − 7 = -9
-9

答案:5 或 -9(两个都要写!)

三、高频易错警示

易错点 TOP 3

序号
易错点
正确做法
1
画数轴忘记画箭头、单位长度长短不一
三要素逐一核对:原点、箭头、单位长度
2
数轴上点平移,只考虑向右,漏掉向左
看到“移动m个单位”无方向,必分左右讨论
3
求路程时把正负数字直接相加
路程 = 各段绝对值之和,方向不计入总和

四、小升初衔接关键提醒

小学基础
初中延伸
只在直线上标0和正数
数轴上同时标负数、0、正数
用“刻度的直尺”表示数
抽象为“数轴”,建立数形结合思想
距离就是“大数减小数”
升级为绝对值 的概念,为后续学习绝对值做铺垫

💡 本节核心就是三件事

  1. 会画(三要素一个不少)
  2. 会标(给数能找点,给点能读数)
  3. 会用(距离、平移、行程问题)

三件事搞定了,数轴这一关就彻底过了。

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  1. CONNECT:[ UseTime:0.000564s ] mysql:host=127.0.0.1;port=3306;dbname=wenku;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000818s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000407s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000274s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000618s ]
  6. SELECT * FROM `set` [ RunTime:0.000232s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000667s ]
  8. SELECT * FROM `article` WHERE `id` = 849993 LIMIT 1 [ RunTime:0.000495s ]
  9. UPDATE `article` SET `lasttime` = 1783782156 WHERE `id` = 849993 [ RunTime:0.010412s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.000309s ]
  11. SELECT * FROM `article` WHERE `id` < 849993 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000582s ]
  12. SELECT * FROM `article` WHERE `id` > 849993 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000484s ]
  13. SELECT * FROM `article` WHERE `id` < 849993 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.001011s ]
  14. SELECT * FROM `article` WHERE `id` < 849993 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000878s ]
  15. SELECT * FROM `article` WHERE `id` < 849993 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000974s ]
0.107023s