📚 Year 7 AQA Mathematics: Summer Preview and Bridging Course | AQA Year 7 数学暑期预习与衔接课程
Moving from primary to secondary school is a big step, and mathematics is a subject where solid foundations make all the difference. This summer bridging course is designed to help you revisit key topics from Key Stage 2 and introduce you to the style of thinking you will need in Year 7, aligned with the AQA framework. You will explore number, algebra, geometry, statistics and problem solving in a structured way, building confidence before the term begins.
从小学升入中学是一个重大转变，数学这⻔学科特别需要扎实的根基。本暑期衔接课程旨在帮助你重温关键阶段 2 的重点知识，同时带你熟悉 Year 7 所需的思维方式，整个安排与 AQA 课程框架保持一致。你将系统地接触数、代数、几何、统计以及问题解决，在开学前建立充分的自信。
1. Place Value and Ordering Numbers | 位值与数字排序
In Year 7 you will work with numbers up to at least ten million, including decimals to three decimal places. Understanding place value means knowing that the position of a digit determines its worth. For example, in 3, 045, 782, the digit 3 represents three million, while the 7 is seven hundred. You should also be able to order, compare and round numbers confidently.
在 Year 7 你会接触到至少千万级别的整数，以及保留三位的小数。理解位值就是知道数字所在的位置决定了它的价值。例如，在 3,045,782 中，数字 3 代表三百万，而 7 表示七百。你还需要能自信地进行数字的排序、比较和四舍五入。
It is helpful to think in terms of powers of ten: thousands, millions and beyond. Decimals work the same way, with tenths, hundredths and thousandths. You may also meet negative numbers in real‑life contexts like temperature and bank balances, so being able to order negative and positive values on a number line is essential.
用十的幂次来思考很有帮助：千、百万，以及更大的数位。小数也是同理，分为十分位、百分位和千分位。你还会在温度、银行余额等实际情境中遇到负数，因此在数轴上能排列负数和正数是一项基本技能。
1 million = 10⁶, 1 billion = 10⁹ (in standard form: 1 × 10⁶, 1 × 10⁹)
1 百万 = 10⁶, 10 亿 = 10⁹（标准形式：1 × 10⁶, 1 × 10⁹）
- Recognise the value of each digit in numbers up to 10 million
- Order and compare numbers with up to three decimal places
- Round any whole number to the nearest 10, 100, 1000 etc.
- 识别千万以内每个数字的位值
- 排序和比较至多三位小数的数
- 将任意整数四舍五入到最近的十、百、千等
2. Addition and Subtraction Strategies | 加减法策略
Efficient addition and subtraction form the backbone of secondary maths. Year 7 expects you to move from counting on fingers to using mental strategies and formal column methods for larger integers and decimals. For example, when calculating 5762 + 3894, you can use the column method, carrying digits where the sum exceeds 9 in a column. Similarly, subtraction often requires regrouping (borrowing) when the top digit is smaller.
高效的加减法是中学数学的脊梁。Year 7 要求你摆脱数手指，转而使用心算策略和正式的竖式计算方法来处理较大的整数和小数。例如，在计算 5762 + 3894 时，可以使用竖式加法，当某一位上的和大于 9 时就进位。同样，减法则经常需要在被减数较小时进行借位。
Mental arithmetic also plays a huge part. Bridging through ten, adjusting (compensating) and using number bonds are skills you should practise. For decimals, aligning the decimal points in columns is crucial — never try to align digits from the right without considering the decimal point.
心算也至关重要。凑十法、补偿调整法以及利用数对关系都是你需要练习的技能。对于小数的加减，竖式必须对齐小数点——切勿单纯从右对齐数字而忽略小数点。
Example: 7.35 - 2.8 = 7.35 - 2.80 = 4.55
示例：7.35 - 2.8 = 7.35 - 2.80 = 4.55
- Use column methods fluently for whole numbers and decimals
- Apply mental strategies: partitioning, compensating, number bonds
- Check calculations using inverse operations
- 熟练运用竖式方法处理整数和小数
- 运用心算策略：拆分、补偿、数对
- 用逆运算检查计算结果
3. Multiplication and Division Foundations | 乘法与除法基础
antly. From there, you extend to multiplying and dividing by 10, 100, 1000 and understand the effect of moving digits. Long multiplication and short division for four‑ d. You should also begin to identify factors, multiples, prime numbers and square numbers.
Year 7 学生必须能对 12 × 12 以内的乘法表脱口而出。在此基础上，你需要延伸到乘 10、100、1000 的运算，理解数字移动的含义。四位数的长乘法和短除法是常规要求。与此同时，你还应该学会找因数、倍数、质数和平方数。
When you multiply by 0.1 or 0.01, you are effectively dividing by 10 or 100. This idea links to place value and helps when working with decimals. Similarly, division can be seen as repeated subtraction or sharing, and the link between multiplication and division should be used to solve missing number problems.
当你乘以 0.1 或 0.01 时，实际上就相当于除以 10 或 100。这种想法与位值直接相连，对处理小数很有帮助。同样，除法可以看作多次相减或均分，而乘法与除法的互逆关系应该用于解决带未知数的问题。
a × b = c ⇔ c ÷ b = a
- Recall all multiplication facts to 12 × 12
- Use long multiplication (e.g. 324 × 58) and short division (e.g. 964 ÷ 8)
- Understand factors, multiples, primes and square numbers (e.g. 7² = 49)
- 熟记 12 × 12 乘法口诀
- 使用长乘法（如 324 × 58）和短除法（如 964 ÷ 8）
- 理解因数、倍数、质数和平方数（如 7² = 49）
4. Understanding Fractions | 理解分数
/4) and convert between improper fractions and mixed numbers. The key is to see the fraction bar as division: 3/4 = 3 ÷ 4 = 0.75.
分数常常让人忧虑，但 Year 7 正是把它们形象化的好时机。你需要能辨认等值分数、约分（如 6/8 = 3/4），并在假分数与带分数之间进行转换。关键是把分数线当作除法：3/4 = 3 ÷ 4 = 0.75。
Comparing and ordering fractions with different denominators requires finding a common denominator. Once you are comfortable with that, adding and subtracting fractions becomes straightforward. You will also multiply a fraction by a whole number and later encounter fractions of amounts in real‑world problems.
比较和排序分母不同的分数需要先找到公分母。一旦你掌握了这一点，分数的加减就会变得简单。你还会学习整数乘以分数，然后在实际问题中遇到“一个数量的几分之几”这类题目。
1/2 + 1/3 = 3/6 + 2/6 = 5/6
- Simplify fractions and list equivalent fractions
- Convert mixed numbers to improper fractions and back
- Add and subtract fractions with different denominators
- 约分并列举等值分数
- 在带分数和假分数之间转换
- 加减分母不同的分数
5. Decimals and Their Operations | 小数及其运算
Decimals are an extension of our number system and appear everywhere — money, measurements, statistics. In Year 7, you will work with numbers up to three decimal places and perform addition, subtraction, multiplication and division. Multiplying a decimal by a whole number can be done by ignoring the decimal point initially, then putting it back based on the total decimal places.
小数是我们数系的延伸，无处不在——钱、测量、统计数据。在 Year 7，你将处理到三位小数的数，并进行加减乘除。小数乘以整数时，可以先忽略小数点计算，再根据小数位数确定积的小数点位置。
Fairness and proportional reasoning are behind this operation. You should also be able to link decimals back to fractions: 0.125 = 1/8.
在小数除法中，可以将除数和被除数同时乘以十的幂，把除数化为整数。例如 4.2 ÷ 0.6 变为 42 ÷ 6 = 7。这种操作背后的原理是等比变形。你还应将小数与分数联系起来：0.125 = 1/8。
0.25 × 3 = 0.75 and 1.5 ÷ 0.5 = 3
- Add and subtract decimals with up to three decimal places
- Multiply a decimal by a whole number and by another decimal
- Divide a decimal by a whole number, and by converting to a simple whole number division
- 加减至多三位小数的数
- 小数乘以整数及小数乘以小数
- 小数除以整数，以及通过转换化为整数的除法
6. Introduction to Percentages | 百分数入门
Percent means 'per hundred' inator 100. In Year 7 you will convert between fractions, decimals and percentages. For example, 25% also find percentages of amounts without a calculator, using benchmark percentages like 50%, 25%, 10% and 1%.
百分数意思是“每一百份”，其实就是分母为 100 的分数。在 Year 7，你将学习分数、小数和百分数之间的相互转换。例如 25% = 0.25 = 1/4。你还会在没有计算器的情况下求一个量的百分之几，借助 50%、25%、10% 和 1% 等基准百分数。
Building 10% first (divide by 10) and then scaling is a powerful mental method. If you need 30%, find 10% and multiply by 3. If you need 5%, take half of 10%. Understanding percentage increase and decrease in simple contexts, like discounts and price rises, starts here.
先求 10%（除以 10）再进行缩放是一种强大的心算方法。如果需要 30%，先求 10% 再乘 3。如果需要 5%，就取 10% 的一半。理解简单的百分比增减，如折扣和加价，也是从这一阶段起步的。
30% of £200 = (10% of £200) × 3 = £20 × 3 = £60
- Convert between fractions, decimals and percentages
- Find percentages of quantities using mental benchmarks
- Solve simple percentage increase and decrease problems
- 在分数、小数和百分数之间进行转换
- 使用心算基准求一个量的百分之几
- 解决简单的百分数增减问题
7. Algebraic Thinking and Expressions | 代数思维与表达式
Algebra in Year 7 is about expressing general rules using letters. You will write simple expressions like 3n + 2, substitute numbers into formulas and understand that letters represent variables or unknowns. This is the start of moving from arithmetic to symbolic reasoning.
Year 7 的代数主要是使用字母表达一般规则。你会写出像 3n + 2 这样的简单表达式，把数字代入公式，理解字母代表变量或未知数。这是从算术迈向符号推理的开端。
this thinking. For example, the pattern 5, 8, 11, 14, ... increases by 3 each time. The nᵗʰ term can be written as 3n + 2. You will also explore one‑step equations like x + 5 = 12, using inverse operations to find the value of the unknown.
研究数列有助于发展这种思维。例如，模式 5, 8, 11, 14, ... 每次增加 3，它的第 n 项可以写成 3n + 2。你还会探索一步方程，如 x + 5 = 12，运用逆运算求出未知数的值。
If y = 2x + 1 and x = 4, then y = 2×4 + 1 = 9
- Use letter symbols to represent unknown numbers
- Simplify simple expressions (collect like terms, e.g. a + a = 2a)
- Substitute numbers into expressions and formulas
- 用字母符号代表未知数
- 简化简单表达式（合并同类项，如 a + a = 2a）
- 将数字代入表达式和公式
8. Geometry: Angles and Shapes | 几何：角与形状
In Year 7 geometry, you will classify and measure angles using a protractor, learning about acute, obtuse, reflex and right angles. The sum of angles on a straight line is 180°, and the sum around a point is 360°. You will use these facts to find missing angles without measuring every time.
在 Year 7 的几何中，你将用量角器对角度进行分类和测量，学习锐角、钝角、优角和直角。直线上邻补角的和为 180°，而绕一个点的周角和为 360°。你将利用这些性质求未知角，而不必每次都用测量。
You will also explore properties of 2D shapes: triangles (equilateral, isosceles, scalene) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium). Knowing about parallel and perpendicular lines, symmetry and diagonals will allow you to describe and sort shapes logically.
你还会探究二维图形的性质：三角形（等边、等腰、不等边）和四边形（正方形、长方形、平行四边形、菱形、梯形）。理解平行线、垂直线、对称性和对角线，能帮助你合乎逻辑地描述和分类图形。
Angle sum of a triangle = 180°, angle sum of a quadrilateral = 360°
- Measure and draw angles accurately with a protractor
- Use angle facts on a straight line and around a point
- Identify and describe triangles and quadrilaterals by their properties
- 使用量角器精确测量和绘制角
- 运用直线上和周角的角度关系
- 根据性质识别和描述三角形和四边形
9. Measurement: Perimeter, Area and Volume | 测量：周长、面积与体积
iangles. For a rectangle, area = length × width, while for a triangle it is (base × height) ÷ 2. The area of a parallelogram is found using base and perpendicular height, leading to the same formula as a rectangle but with a slanted shape.
Year 7 的测量内容超越了简单的长方形。你将计算直线多边形的周长以及平行四边形和三角形的面积。对于长方形，面积 = 长 × 宽；三角形则为（底 × 高）÷ 2。平行四边形的面积也是底乘垂直高，这与长方形公式一致，只不过形状是倾斜的。
.g. 1 m = 100 cm, 1 litre = 1000 cm³) and solve compound measurement problems in everyday contexts.
立方体和长方体的体积引入公式 V = 长 × 宽 × 高，单位使用 cm³ 和 m³。你还要进行常用公制单位间的换算（如 1 m = 100 cm, 1 升 = 1000 cm³），并在日常生活情境中解决组合测量问题。
Area of triangle = ½ × b × h, Volume of cuboid = l × w × h
- Calculate perimeter of compound rectilinear shapes
- Compute area of rectangles, parallelograms and triangles
- Find volume of cubes and cuboids and convert metric units
- 计算组合直线多边形的周长
- 计算长方形、平行四边形和三角形的面积
- 求立方体和长方体的体积，进行公制单位换算
10. Statistics: Interpreting Data | 统计：数据解读
Statistics in Year 7 focuses on collecting, representing and interpreting data. You will read and draw bar charts, pictograms and line graphs, as well as begin to use pie charts with simple fractions. The mean, mode, median and range are introduced as measures of average and spread.
Year 7 的统计侧重于数据的收集、展示与解读。你将阅读和绘制条形图、象形图和折线图，并开始使用简单分数来解读饼图。平均数、众数、中位数和极差作为度量集中趋势和离散程度的指标被引入。
Being able to choose the most appropriate average is a key skill: the mode for categorical data, the median when there are outliers, and the mean for symmetrical data. You will also compare two sets of data by looking at shape and spread, and ask critical questions about graphs.
能够选择最合适的平均数是关键技能：类别数据用众数，存在异常值时用中位数，对称数据用平均数。你还会通过查看分布形态和离散程度来比较两组数据，并对统计图提出批判性问题。
Mean = sum of values ÷ number of values, Range = highest − lowest
- Construct and interpret bar charts, line graphs and pie charts
- Calculate mean, median, mode and range from a set of numbers
- Compare datasets using appropriate statistics
- 绘制并解读条形图、折线图和饼图
- 计算一组数据的平均数、中位数、众数和极差
- 使用恰当的统计量来比较数据集
11. Mathematical Problem Solving | 数学问题解决
Problem solving is woven through every topic. In Year 7 you will meet multi‑step word problems that require you to pick out the maths, decide on operations and interpret the result. Modelling with bars or part‑whole diagrams is a powerful strategy carried over from primary, and now extended to fractions, percentages and algebra.
问题解决贯穿每个主题。在 Year 7 你会遇到需要多步运算的应用题，必须从中提炼数学信息，确定运算，并解释结果。条形模型或部分‑整体图是从小学延续下来的强大策略，现在扩展到分数、百分数和代数。
You should practise explaining your reasoning in writing, using correct mathematical language. For example, instead of just giving an answer, describe 'I added the two amounts because I needed to find the total' or 'I divided by 6 because there are 6 equal groups'. This clarity helps deepen understanding.
你要练习用正确的数学语言书面解释推理过程。例如，不要只给出答案，而要说“我把两个数量加起来是因为需要求总和”或“我除以 6 是因为共有 6 个相等的组”。这种清晰的表达有助于深化理解。
- Break down multi‑step problems into small stages
- Use bar models, number lines and diagrams to support thinking
- Explain reasoning clearly using accurate vocabulary
- 将多步问题分解成小阶段
- 使用条形模型、数轴和图示辅助思考
- 用准确的词汇清晰地解释推理过程
12. Transition Tips and Study Habits | 过渡建议与学习习惯
Starting secondary mathematics can feel fast‑paced, but good habits make the journey smoother. Keep your work organised, show all steps neatly and always check answers. Spend a little time each day on quick recall of number facts and times tables so that your working memory is free for new ideas.
刚接触中学数学时可能会觉得节奏很快，但良好的习惯能让学习之旅更加顺畅。保持作业条理，清晰写出每一步并始终检查答案。每天花一点时间快速回忆数对和乘法口诀，你的工作记忆就能腾出来吸收新知识。
Ask questions whenever you are uncertain. In Year 7, teachers expect you to think about why a method works, not just how to do it. Use online videos, practice worksheets and games to reinforce learning. Finally, treat mistakes as learning opportunities — every error shows a gap that can be filled before it widens.
一旦不确定就要提问。在 Year 7，老师希望你能思考方法为什么有效，而不仅仅是怎么做。利用在线视频、练习卷和游戏来巩固学习。最后，把错误当作学习的机会——每一个错误都揭示了一个可修补的知识漏洞，以免它越变越大。
- Organise a regular revision timetable from the start
- Practise explaining concepts aloud as if teaching someone
- Keep a maths journal to note down tricky problems and solutions
- 从一开始就制定定期的复习时间表
- 练习像给别人讲解一样大声解释概念
- 写一本数学日志，记下棘手的问题及其解法
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