📚 Summer Bridging Course: Year 7 AQA Mathematics | 暑期衔接课程：Year 7 AQA 数学
Welcome to your Year 7 AQA Mathematics summer bridging course! This programme is designed to help you make a confident and smooth transition from primary school mathematics to the demands of Key Stage 3. We will revisit essential number skills, introduce early algebra, explore geometry, measurement and statistics, and build the problem-solving habits you need to thrive in Year 7. Work through each section at your own pace, try the examples and make sure you can explain each idea in your own words before moving on.
欢迎参加Year 7 AQA数学暑期衔接课程！本课程旨在帮助您自信、平稳地从小学数学过渡到Key Stage 3的要求。我们将重温关键的数的技能，引入早期代数，探究几何、测量与统计，并培养您在Year 7取得成功所需的解决问题习惯。请按照自己的进度学习每一部分，尝试范例，并在进入下一部分之前确保您能用自己的话解释每一个概念。
1. Place Value and Ordering Numbers | 位值与数字排序
In Year 7 you will work with numbers into the millions and beyond, and with decimals to three decimal places. A firm grasp of place value is the foundation for all written arithmetic, rounding and estimation.
在Year 7，您将接触百万乃至更大的数，以及精确到三位小数的小数。扎实掌握位值是所有笔算、取整和估算的基础。
Each digit in a number has a value depending on its column. In the number 3 508 162, the '3' is in the millions place, the '5' is in the hundred thousands, and the '2' is in the units column. For decimals, the first place to the right of the decimal point is tenths, then hundredths, then thousandths.
数字中的每一位数字根据其所在数位具有不同数值。在数字3 508 162中，“3”位于百万位，“5”位于十万位，“2”位于个位。对于小数，小数点右边第一位是十分位，然后是百分位、千分位。
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Units | . | Tenths | Hundredths |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 4 | 9 | 0 | 5 | 3 | . | 7 | 8 |
This table shows 1 249 053.78: one million, two hundred and forty-nine thousand, fifty-three point seven eight. The digit 7 means seven tenths and the 8 means eight hundredths.
上表显示1 249 053.78：一百二十四万九千零五十三点七八。数字7表示7个十分之一，8表示8个百分之一。
To order a set of decimals, compare the whole number part first, then the tenths, then the hundredths. For instance, 0.45, 0.405 and 0.5: 0.5 is largest because it has 5 tenths, the others have 4 tenths; then compare hundredths.
排序一组小数时，先比较整数部分，再比十分位，再比百分位。例如0.45、0.405和0.5：0.5最大，因为它有5个十分位，其余只有4个十分位；然后比较百分位。
Rounding makes calculations quicker. To round to the nearest thousand, look at the hundreds digit: 5 or more means round up. For example, 23 678 rounds to 24 000 (because the hundreds digit is 6).
取整可使计算更快。取整到最近的千位时，看百位数字：大于等于5则进位。例如23 678取整为24 000（因为百位是6）。
2. Addition and Subtraction Strategies | 加法与减法策略
Confident mental and written methods for addition and subtraction underpin much of secondary mathematics. Always align digits according to their place value when using column methods.
自信的心算和笔算加减法是中学数学的重要基础。使用竖式方法时，务必按位值对齐数字。
e 3 in units, carry 1 to tens; then 7+9+1=17, write 7, carry 1 to hundreds; 4+6+1=11. Result: 1173.
竖式加法从个位开始。若某列之和超过9，向前一位进位。例如478+695：8+5=13，个位写3，进1到十位；然后7+9+1=17，十位写7，进1到百位；4+6+1=11。结果为1173。
Subtraction often requires borrowing. When a digit is too small to subtract from, exchange 1 from the next left column. Example: 502 - 168. In the units column, 2 is less than 8, so borrow 1 from the tens column (turning the 0 into 9 after borrowing from hundreds). The result is 334.
减法常需借位。当某位数字不够减时，从左边一位借1。例如502-168。个位2小于8，从十位借1（原本0从百位借1后变成9）；结果为334。
Always check subtraction by adding the answer to the subtracted number; the sum should equal the starting number. For the example above, 334 + 168 should give 502.
始终用加法检验减法：将答案与减数相加，应等于被减数。如上例，334+168应得502。
ations. For 37 + 48, think of 37 + 40 = 77, then add 8 to get 85. Or use 37 + 50 - 2 = 85.
心算策略如拆分、凑十或调整可提速。对于37+48，可先算37+40=77，再加8得85。或者用37+50-2=85。
3. Multiplication and Division Methods | 乘法与除法方法
nd division are inverse operations; understanding this helps with checking answers and solving missing-number problems.
熟练背出12×12以内的乘法表至关重要。乘法与除法互为逆运算；理解这一点有助于验算和解决缺失数字问题。
0 and 7. Multiply: 30×20=600, 30×7=210, 4×20=80, 4×7=28. Add the parts: 600+210+80+28=918.
两位数乘法可使用网格法。对于34×27，将34拆为30和4，27拆为20和7。相乘：30×20=600，30×7=210，4×20=80，4×7=28。将各部分相加：600+210+80+28=918。
Short division ('bus stop' (write 1, remainder 2), the 2 is brought next to the 4 making 24; 24 ÷ 4 = 6. Answer: 216.
短除法（“公交站法”）用于除以一位数。864÷4：4除8商2（写2），4除6商1（写1，余2），余数2与
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