READING COMPREHENSION A · 阅读理解 A

阅读理解 A · 文章精读

Number Sense · 数学学习中“数感”的重要性(说明文)

IELTS 4.0 基础使用者 · Unit 25 题 · 同色定位词参考答案,供核对
数学学习主题插画
NUMBER SENSE
图例 Q1 定位词 Q2 定位词 Q3 定位词 Q4 定位词 Q5 定位词 波浪线= 答案依据 红下划线= 绝对词(错误特征) 点击文中的彩色定位词可跳到对应题目;点击任意英文生词可查词典

阅读原文

Passage · 先通读标出定位词,再逐题回读对应段

P1Maths is a subject that many students find challenging, but it doesn't have to be that way! The secret to learning maths well is to have fun in learning it and understand it deeply.

P2There is a common and harmful misunderstanding about maths. Some people think that top maths students are those who can quickly remember maths facts, like the multiplication table (乘法表). However, research shows that this isn't true. They don't just remember; they understand numbers in a proper way. This is called "number sense". Number sense means you can understand numbers and how they work together in different ways.

P3The new curriculum standards are helping students learn maths better by paying less attention to remembering and more to understanding numbers. This is important because number sense is the key for all higher-level maths learning.

P4Why is number sense so important? Here are three big reasons: With practice of number sense, you will get better at solving maths problems. You can think more creatively and find solutions more easily. Developing number sense helps you feel more confident about maths. When you understand numbers, you're glad to try new things and not be afraid of making mistakes. When you pay attention to understanding numbers, maths becomes more interesting. You start to see how cool numbers can be and how they work together.

P5So, number sense is so important. With number sense, maths can be a lot easier and a lot more fun!

1
What is the common misunderstanding about top maths students?

关于顶尖数学学生,常见的误解是什么?

细节理解
  • A. They have fun in learning maths.他们学习数学很开心。

    这是正确做法,不是“误解”。

  • B. They practise maths problems every day.他们每天练习数学题。

    无中生有:文中没提“每天练习”。

  • C. They are born with a talent for maths.他们天生有数学天赋。

    无中生有:文中没说天赋论。

  • D. They can quickly remember maths facts.他们能快速记住数学知识。

    原文原句:有些人认为顶尖学生“能快速记住数学知识”,答案 D。

定位Q1 定位词:common misunderstanding / top maths students → P2。
依据P2 “Some people think that top maths students are those who can quickly remember maths facts.” 原句复现。
答案D。注意题干问“misunderstanding(误解)”,先看定位段中 think 引导的观点。
2
What do the new curriculum standards focus more on?

新课标更注重什么?

细节理解
  • A. Understanding numbers.理解数字

    原文:更少关注记忆、更多关注理解数字,答案 A。

  • B. Solving difficult maths problems.解决难题

    偷换概念:新课标强调的是“理解”,不是“做难题”。

  • C. Building problem-solving skills.培养解题技能

    这是数感带来的结果,不是新课标的重点。

  • D. Making maths interesting for students.让数学变有趣

    偏离:有趣是理解后的结果,不是新课标聚焦点。

定位Q2 定位词:new curriculum standards → P3。
依据P3 “paying less attention to remembering and more to understanding numbers” —— 更多关注理解。
答案A。less ... more ... 结构锁定“more to”后面的内容。
3
We can infer from this passage that students with good number sense may ___.

我们可以推断:数感好的学生可能会……

推断题
  • A. stop using the multiplication table停止使用乘法表

    无中生有:文中没说不用乘法表。

  • B. perform better in higher-level maths在更高层次的数学中表现更好

    原文:数感是“所有更高层次数学学习的关键”,答案 B。

  • C. be afraid of making mistakes in maths害怕在数学中犯错

    原文相反:数感好的人“不怕犯错”。

  • D. spend more time doing maths exercises花更多时间做练习

    无中生有:文中没提“花更多时间”。

定位Q3 定位词:number sense / higher-level → P3。
依据P3 “number sense is the key for all higher-level maths learning” —— 数感是更高层次数学的关键。
答案B。推断题从原文“key for”推导出“表现更好”。
4
What is the best title for the passage?

这篇文章的最佳标题是什么?

主旨大意 · 标题
  • A. Study Maths in Groups小组学数学

    无中生有:全文没提小组学习。

  • B. Develop Number Sense in Maths在数学中培养数感

    全文围绕“数感是什么、为什么重要、怎么培养”,答案 B。

  • C. Change Standards in Maths改变数学标准

    以偏概全:新课标只是其中一个支撑点。

  • D. Find New Maths Teaching Methods寻找新的数学教学法

    偏离:文章面向学生学习,不是讲教学方法。

定位标题题 → 找中心词:number sense 反复出现。
依据P2 提出概念 → P3 重要性 → P4 三大理由 → P5 总结,全文主线就是“培养数感”。
答案B。标题要概括全文主线,排除以偏概全与无中生有。
5
Who is the passage mainly written for?

这篇文章主要写给谁看?

写作对象
  • A. Teachers who teach maths.教数学的老师

    全文用 you / students 直接呼吁学生,非教学指导。

  • B. Students who learn maths.学数学的学生

    “students”“you’re glad to try new things”等直接指向学生,答案 B。

  • C. Parents who help with maths.辅导数学的家长

    文中没有给家长的辅导建议。

  • D. Researchers who study maths.研究数学的研究者

    内容浅显,是面向学生的科普,非研究论文。

定位写作对象题 → 看人称与语气(you / students)。
依据P4 直接用 you:you will get better / you're glad to try new things,明显面向学生。
答案B。对象题抓第二人称 you 和身份词。

文章精读

INTENSIVE READING · 词性标注 + 句型分析

按词性标注颜色读句子:绿色=动词,粉字=形容词,蓝字=副词,紫字=介词,橙字=连词,带底纹=词形变化。点击生词仍可查词典。

P1 · 数学不必可怕

S1Maths is a subject that many students find challenging, but it doesn't have to be that way!数学是一门许多学生觉得有挑战性的科目,但数学不一定是那样的!

S2The secret to learning maths well is to have fun in learning it and understand it deeply.学好数学的秘诀是在学习中找到乐趣,并深入理解它。

P2 · 误解与真相

S1There is a common and harmful misunderstanding about maths.关于数学有一个常见而有害的误解。

S2Some people think that top maths students are those who can quickly remember maths facts, like the multiplication table.有些人认为顶尖的数学学生是那些能快速记住数学知识(比如乘法表)的人。

S3However, research shows that this isn't true.然而,研究表明事实并非如此。

S4They don't just remember; they understand numbers in a proper way.他们不只是记忆,而是以恰当的方式理解数字。

S5This is called "number sense".这就叫“数感”。

S6Number sense means you can understand numbers and how they work together in different ways.数感意味着你能理解数字,以及数字如何以不同方式协同运作。

P3 · 新课标

S1The new curriculum standards are helping students learn maths better by paying less attention to remembering and more to understanding numbers.新课程标准正帮助学生更好地学习数学——少关注记忆,多关注理解数字。

S2This is important because number sense is the key for all higher-level maths learning.这很重要,因为数感是所有更高层次数学学习的关键。

P4 · 三大理由

S1Why is number sense so important?为什么数感如此重要?

S2Here are three big reasons: With practice of number sense, you will get better at solving maths problems.这里有三大理由:通过数感练习,你会更擅长解决数学问题。

S3You can think more creatively and find solutions more easily.你能更创造性地思考,更容易找到解决办法。

S4Developing number sense helps you feel more confident about maths.培养数感能帮助你更自信地面对数学。

S5When you understand numbers, you're glad to try new things and not be afraid of making mistakes.当你理解数字时,你乐于尝试新事物,不怕犯错。

S6When you pay attention to understanding numbers, maths becomes more interesting.当你专注于理解数字时,数学变得更有趣。

S7You start to see how cool numbers can be and how they work together.你开始发现数字可以多么酷,它们如何协同运作。

P5 · 总结

S1So, number sense is so important.所以,数感非常重要。

S2With number sense, maths can be a lot easier and a lot more fun!有了数感,数学可以变得容易得多、有趣得多!

作文金句仿写

WRITING BOOST · 黑色为框架,灰色底纹为可替换词

把文中的好句子拆成“句型框架”,换上你自己的词,就能写出漂亮的句子。

金句 1The secret to learning maths well is to have fun in learning it.

The secret to learning maths / learning English / success is to have fun / keep trying / be patient.

仿写:The secret to learning English is to keep trying. 学好英语的秘诀是坚持。

适用:议论文开头揭示“秘诀”。

金句 2Number sense is the key for all higher-level maths learning.

Practice / Confidence / Teamwork is the key for / to success / good grades / friendship.

仿写:Confidence is the key to success. 自信是成功的关键。

适用:表达“某因素很重要”。

金句 3You're glad to try new things and not be afraid of making mistakes.

You're glad to try new things / ask questions / help others and not be afraid of making mistakes / facing difficulties.

仿写:You're glad to ask questions and not be afraid of facing difficulties. 你乐于提问,不怕面对困难。

适用:写积极的学习态度。

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