📚 Functional Skills Maths Levels Explained: What You Learn at Each Level | 英国功能性技能数学各级别学什么内容
Functional Skills Maths is the UK's practical alternative to GCSE Mathematics. It is offered at five levels - Entry Level 1, Entry Level 2, Entry Level 3, Level 1 and Level 2 - and each level has its own clearly defined subject content set by the Department for Education and regulated by Ofqual in England. This guide explains, level by level, exactly what number skills, measures, shape, space and data handling you are expected to master, how each level is assessed, and where each qualification can take you.
功能性技能数学（Functional Skills Maths）是英国GCSE数学的实用型替代资格，共分为五个级别：入门级1、入门级2、入门级3、一级（Level 1）和二级（Level 2）。每个级别都有由英国教育部制定、由Ofqual监管的明确教学内容大纲。本文将逐级说明：你需要掌握哪些数与运算、度量、图形与空间、数据处理技能，每级如何考核，以及该资格能带你去哪里。
1. What Functional Skills Maths Actually Is | 什么是功能性技能数学
Functional Skills Maths is an applied qualification. Instead of abstract algebra and formal proof, it tests whether you can use maths confidently in real situations: working out a wage, comparing supermarket prices, reading a utility bill, interpreting a graph in a news report, or measuring materials for a job.
功能性技能数学是一门"应用型"资格。它不考抽象代数与形式化证明，而是考查你能否在真实情境中自信地使用数学：计算工资、比较超市价格、看懂水电账单、解读新闻中的图表，或为一项工作测量材料。
Every level is built on three content strands, plus a problem-solving strand that runs through all of them:
每个级别都建立在三大内容板块之上，并贯穿一条"解题与决策"主线：
- Using numbers and the number system - 数与数系的使用（整数、小数、分数、百分数、比与比例）
- Using common measures, shape and space - 常用度量、图形与空间（长度、质量、容量、时间、货币、周长、面积、体积、角度）
- Handling information and data - 信息与数据处理（表格、图表、平均数、概率）
- Solving mathematical problems and decision making - 数学解题与决策（选择方法、检验答案、判断结果是否合理）
The reformed qualifications were introduced in England from September 2019, and assessment is now more demanding than the pre-2019 versions, with a stronger emphasis on multi-step problems and on explaining or checking your reasoning.
改革后的资格自2019年9月起在英格兰实施，考核难度高于2019年之前的版本，更强调多步骤问题以及解释、检验推理过程的能力。
2. The Five Levels at a Glance | 五个级别一览
The table below summarises how the levels compare in terms of GCSE equivalence and typical learners.
下表概括了各级别与GCSE的对应关系以及典型学习者群体。
| Level 级别 | GCSE equivalence 对应关系 | Typical learner 典型学习者 |
| Entry Level 1 入门级1 | Pre-GCSE, very early numeracy 远低于GCSE，早期数感 | Learners with SEND, supported learning 特殊教育需求或支持性学习的学生 |
| Entry Level 2 入门级2 | Pre-GCSE 远低于GCSE | Foundation learners, ESOL learners 基础阶段学生、英语非母语学生 |
| Entry Level 3 入门级3 | Pre-GCSE, close to foundation GCSE 接近GCSE基础卷水平 | Adults returning to study, vocational learners 成人回归学习、职业课程学生 |
| Level 1 一级 | Broadly GCSE grades 1-3 (D-G) 大致相当于GCSE 1-3分 | Apprentices, college students, job seekers 学徒、学院学生、求职者 |
| Level 2 二级 | Broadly GCSE grade 4 (C) and above 大致相当于GCSE 4分（旧C）及以上 | Apprenticeship applicants, university applicants, employees 学徒申请者、大学申请者、在职人员 |
These equivalences are the ones used by employers, colleges and apprenticeship frameworks. Level 2 Functional Skills Maths is the level most often accepted in place of GCSE Maths grade 4 for course entry.
上述对应关系是雇主、学院和学徒制框架普遍采用的标准。二级功能性技能数学是最常被接受、可替代GCSE数学4分成绩的级别。
3. Entry Level 1: Early Number and Everyday Routines | 入门级1：基础数与日常常规
Entry Level 1 is about functional numeracy in the immediate environment. The numbers involved are small, the contexts are familiar, and practical resources such as coins, counters and rulers are usually available.
入门级1关注的是身边环境中的功能性数感。涉及的数字很小，情境是熟悉的，通常可以使用硬币、计数器和尺子等实物教具。
What you are expected to do at Entry Level 1:
入门级1需要掌握的能力：
- Count reliably up to 20 items - 能可靠地数到20个物品
- Read, write, order and compare numbers up to 20 - 读写、排序并比较20以内的数字
- Add and subtract single-digit numbers within 20 - 在20以内进行一位数的加减法
- Recognise coins and notes and use them in simple shopping situations - 认识硬币与纸币并在简单购物情境中使用
- Recognise and name common 2-D and 3-D shapes - 认识并说出常见平面图形与立体图形的名称
- Use everyday positional and directional language such as under, next to, behind - 使用如"下面""旁边""后面"等日常方位与方向词汇
- Sort and classify objects by a single criterion - 按单一标准对物品进行分类
- Read simple lists, tables and pictograms to find information - 阅读简单清单、表格与象形图以获取信息
Assessment at this level is highly practical and usually centre-based, with tasks linked to daily routines such as shopping, cooking or travel.
该级别的考核高度注重实操，通常由学习中心组织实施，任务与购物、烹饪、出行等日常活动挂钩。
4. Entry Level 2: Money, Measures and Simple Charts | 入门级2：货币、度量与简单图表
Entry Level 2 widens the number range and introduces standard units of measure. Learners begin to work with two-digit numbers and to record information in simple charts.
入门级2扩大了数字范围并引入标准度量单位。学习者开始处理两位数运算，并用简单图表记录信息。
Core content at Entry Level 2:
入门级2的核心内容：
- Count reliably up to 100 items and read, write, order and compare numbers up to 200 - 可靠地数到100，并读写、排序、比较200以内的数字
- Add and subtract two-digit whole numbers - 进行两位数整数的加减法
- Recognise multiples of 2, 5 and 10 and simple fractions such as ½, ¼, ¾ and ⅓ - 认识2、5、10的倍数以及 ½、¼、¾、⅓ 等简单分数
- Round numbers to the nearest 10 - 将数字四舍五入到最接近的10
- Use money up to £100 and work out change - 处理100英镑以内的货币并计算找零
- Read and record time in analogue and digital form, including half and quarter hours - 读取并记录指针式与数字式时间，包括半点与一刻钟
- Use standard units of length, mass and capacity: mm, cm, m, g, kg, ml, l - 使用长度、质量、容量的标准单位：毫米、厘米、米、克、千克、毫升、升
- Recognise lines of symmetry and right angles - 认识对称轴与直角
- Record data using tally charts, pictograms, bar charts and simple tables - 用计数表、象形图、条形图和简单表格记录数据
A typical Entry Level 2 question might ask you to read a price list, add two items and state the change from £20. Estimation and checking are already part of the mark scheme.
典型的入门级2题目可能是：阅读一份价目表，把两件商品相加，并算出用20英镑付款后的找零。估算与检验能力从这一级起就纳入评分要求。
5. Entry Level 3: Three-Digit Numbers, Fractions and Data | 入门级3：三位数、分数与数据
Entry Level 3 is the bridge to Level 1. Number work moves into three-digit calculations, fractions of amounts and simple percentages, and shape work introduces perimeter and area.
入门级3是通往一级的桥梁。数字运算扩展到三位数，出现"求某个量的几分之几"以及简单百分数；图形部分引入周长与面积。
Entry Level 3 content includes:
入门级3的内容包括：
- Read, write, order and compare numbers up to 1000 - 读写、排序并比较1000以内的数字
- Add and subtract three-digit numbers; multiply a two-digit number by a one-digit number; divide with remainders - 进行三位数加减法；两位数乘一位数；带余数的除法
- Round to the nearest 10, 100 and 1000 - 四舍五入到最近的10、100、1000
- Find fractions of quantities: ½, ¼, ⅓, ⅕, ⅔, ¾ - 求数量的分数值：½、¼、⅓、⅕、⅔、¾
- Use decimals up to two decimal places in money and measure contexts - 在货币与度量情境中使用两位小数
- Find simple percentages such as 10%, 25%, 50% and 75% - 求10%、25%、50%、75%等简单百分数
- Convert between units of measure: mm ↔ cm ↔ m, g ↔ kg, ml ↔ l - 在度量单位之间换算：毫米↔厘米↔米、克↔千克、毫升↔升
- Use the 12-hour and 24-hour clock and calculate time intervals - 使用12小时制与24小时制并计算时间间隔
- Work out the perimeter and area of rectangles and the volume of cuboids by counting cubes - 计算长方形周长与面积，并用单位立方体计数法求长方体体积
- Use scales, simple coordinates and angles in shapes - 使用比例尺、简单坐标与图形中的角
- Interpret bar charts, line graphs and pie charts; find the mean and range - 解读条形图、折线图和饼图；求平均数与极差
- Express probability as a simple fraction - 用简单分数表示概率
Perimeter of a rectangle 长方形周长 = 2 × (length + width) 长加宽之和的两倍
Area of a rectangle 长方形面积 = length × width 长 × 宽
6. Level 1: Everyday Maths for Work and Study | 一级：工作与学习中的日常数学
Level 1 is where functional maths becomes genuinely multi-step. You are expected to choose the right method yourself, keep track of units, and show that your answer makes sense in context.
一级的功能性数学开始真正进入多步骤运算。你需要自行选择正确方法、注意单位一致性，并说明答案在情境中是否合理。
Number content at Level 1:
一级的"数"部分内容：
- Read, write, order and compare numbers of any size, including negative numbers in context such as temperature - 读写、排序并比较任意大小的数，包括温度等情境中的负数
- Add, subtract, multiply and divide using efficient written and mental methods, and with a calculator - 用高效的笔算、心算及计算器进行四则运算
- Understand and use the order of operations (brackets, indices, division and multiplication, addition and subtraction) - 理解并运用运算顺序（括号、乘方、乘除、加减）
- Round numbers and use estimation to check that an answer is reasonable - 四舍五入并用估算检验答案是否合理
- Find equivalent fractions, convert between improper fractions and mixed numbers - 求等值分数，在假分数与带分数之间转换
- Convert between fractions, decimals and percentages - 在分数、小数、百分数之间转换
- Find a percentage of an amount and express one quantity as a percentage of another - 求某量的百分数，并把一个量表示为另一个量的百分数
- Use ratio and direct proportion, for example scaling a recipe or mixing materials - 使用比与正比例，例如按比例调整食谱或配比材料
Measures, shape, space and data at Level 1:
一级的度量、图形、空间与数据内容：
- Convert between metric units and read scales accurately - 在公制单位之间换算并准确读取刻度
- Calculate with mixed units of time, for example hours and minutes - 对混合时间单位（如小时与分钟）进行计算
- Work out the perimeter and area of rectangles, triangles and composite shapes, and the volume of cuboids - 计算长方形、三角形及组合图形的周长与面积，以及长方体的体积
- Use coordinates in the first quadrant and angles at a point, on a straight line and in triangles - 使用第一象限坐标，以及围绕一点、一条直线和三角形内角的计算
- Construct and interpret tables, bar charts, pie charts and line graphs - 制作并解读表格、条形图、饼图与折线图
- Calculate the mean and range of a set of data and use them to compare two sets - 计算一组数据的平均数与极差，并用它们比较两组数据
- Express probability as a fraction, decimal or percentage - 用分数、小数或百分数表示概率
Mean 平均数 = sum of values ÷ number of values 数值总和 ÷ 数值个数
Range 极差 = largest value − smallest value 最大值 − 最小值
7. Level 2: The GCSE-Equivalent Benchmark | 二级：等同GCSE的关键门槛
Level 2 is the qualification most employers, apprenticeship providers and universities ask for. The content is broader, the numbers larger, and problems frequently require several steps and a judgement about the answer.
二级是大多数雇主、学徒制提供方和大学所要求的资格。内容更广、数字更大，题目往往需要多个步骤并对结果作出判断。
Number content at Level 2:
二级的"数"部分内容：
- Read, write, order and compare positive and negative numbers of any size - 读写、排序并比较任意大小的正数与负数
- Carry out multi-step calculations with numbers of any size, with and without a calculator -
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