📚 Cambridge Primary Mathematics Stage 5: Core Skills and Exam Tips | 剑桥小学数学第五阶段：核心技能与备考技巧
Cambridge Primary Mathematics Stage 5 builds strong number sense, geometry skills and data handling. This revision guide summarises the key topics from the Learner's Book 5, including place value, operations, fractions, decimals, percentages, geometry, measurement and statistics. Use the paired English and Chinese notes to check understanding and prepare for assessments.
剑桥小学数学第五阶段帮助学生建立扎实的数感、几何技能和数据处理能力。本复习指南总结了学生用书第五册的核心主题，包括位值、四则运算、分数、小数、百分数、几何、测量和统计。请使用中英对照笔记检查理解并备考。
1. Number and Place Value | 数与位值
In Stage 5, learners read, write, order and compare whole numbers up to one million. Each digit has a value based on its place. In 245 781, the digit 4 has a value of 40 000, not just 4.
在第五阶段，学生需要读写、排序和比较高达一百万的整数。每个数字的值由它的位置决定。在 245 781 中，数字 4 的值是 40 000，而不仅仅是 4。
Rounding is also important. To round to the nearest 1000, look at the hundreds digit: 5 or more rounds up, 4 or less rounds down. For example, 23 650 rounds to 24 000.
四舍五入也很重要。四舍五入到最接近的 1000 时，看百位数字：5 或以上进位，4 或以下舍去。例如，23 650 四舍五入为 24 000。
Negative numbers appear in real-life contexts such as temperature. A temperature of -5 °C is colder than 3 °C, and the difference between them is 8 °C.
负数出现在温度等真实情境中。温度 -5 °C 比 3 °C 更冷，它们之间的差是 8 °C。
2. Addition and Subtraction | 加法与减法
Column addition and subtraction can be used for numbers up to one million, including decimal numbers. Align place values carefully before adding or subtracting.
列式加法和减法可用于高达一百万的数，包括小数。在加减之前要对齐位值。
estimate 5 000 + 2 000 = 7 000. The exact answer is 6 923, which is close to the estimate.
估算是一种有用的检查方法。对于 4 789 + 2 134，估算为 5 000 + 2 000 = 7 000。精确答案是 6 923，与估算接近。
ions help verify results: if 8 300 - 2 750 = 5 550, then 5 550 + 2 750 should equal 8 300.
逆运算有助于验证结果：如果 8 300 - 2 750 = 5 550，那么 5 550 + 2 750 应该等于 8 300。
3. Multiplication and Division | 乘法与除法
ive law breaks a problem into smaller parts: 23 × 6 = (20 × 6) + (3 × 6) = 120 + 18 = 138.
学生需要熟记到 12 × 12 的乘法表，并运用它们进行较大数的乘法。分配律将问题拆分为较小部分：23 × 6 = (20 × 6) + (3 × 6) = 120 + 18 = 138。
Short division is introduced for dividing two- and three-digit numbers by one-digit numbers. For 864 ÷ 4, divide hundreds, tens and ones in turn to get 216.
短除法用于两位数或三位数除以一位数。计算 864 ÷ 4 时，依次除以百位、十位和个位，得到 216。
are number such as 7² = 49 and a cube number such as 3³ = 27 should be recognised quickly.
因数、倍数、平方数和立方数也是第五阶段的内容。平方数如 7² = 49，立方数如 3³ = 27，需要快速辨认。
g or dividing by 10, 100 and 1000, digits move place values. For example, 4.6 × 100 = 460.
乘以或除以 10、100 和 1000 时，数字的位值会移动。例如，4.6 × 100 = 460。
4. Fractions, Decimals and Percentages | 分数、小数与百分数
dividing the numerator and denominator by the same number. For example, 3/4 = 6/8 = 9/12.
等值分数可以通过将分子和分母同时乘以或除以同一个数得到。例如，3/4 = 6/8 = 9/12。
ent denominators, first write them with a common denominator. 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
异分母分数加减时，先化为同分母。1/2 + 1/4 = 2/4 + 1/4 = 3/4。
e 0.75 is equivalent to 75/100 = 3/4. Adding decimals requires aligning the decimal point.
小数可以写到三位小数。像 0.75 等于 75/100 = 3/4。小数加减时需要对小数点。
Percentages compare amounts out of 100. Common conversions include 50% = 0.5 = 1/2, 25% = 0.25 = 1/4 and 10% = 0.1 = 1/10.
百分数表示以 100 为基准的比。常见转换包括 50% = 0.5 = 1/2，25% = 0.25 = 1/4，10% = 0.1 = 1/10。
To find a percentage of a quantity, multiply by the decimal or fraction form. 20% of 80 = 0.2 × 80 = 16.
求一个数的百分数时，用小数或分数形式相乘。80 的 20% = 0.2 × 80 = 16。
5. Geometry: Shapes and Angles | 几何：图形与角
Triangles are classified by side length: equilateral (all equal), isosceles (two equal) and scalene (none equal). They are also classified by angle: acute, right and obtuse.
三角形按边长分类：等边三角形（三边相等）、等腰三角形（两边相等）和不等边三角形（三边不等）。也按角分类：锐角、直角和钝角。
Key angle facts include: on a straight line, angles sum to 180°; around a point, angles sum to 360°; a right angle is exactly 90°.
重要的角事实包括：直线上角之和为 180°；绕一点角之和为 360°；直角恰好是 90°。
The sum of interior angles in a triangle is 180°, and in a quadrilateral it is 360°. This can be used to find missing angles.Published by TutorHao | Mathematics Revision Series | aleveler.com
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