📚 Year 7 Support Homework 7: Core Skills Check | 七年级支持作业7：核心技能检查
This article guides Year 7 students through a typical support homework set. It focuses on building confidence in number work, early algebra, geometry, and data handling. Support homework is designed to reinforce classroom learning, so work through each section slowly and check your answers.
本文帮助七年级学生完成一份典型的支持作业。重点在于建立数感、初步代数、几何和数据处理的信心。支持作业旨在巩固课堂所学，因此请逐节练习并检查答案。
1. What Is Support Homework? | 什么是支持作业？
Support homework is a set of carefully graded questions that help you secure the basics before moving to harder problems. It usually covers several topics from recent lessons and is not meant to be a test.
支持作业是一组精心设计的分层练习题，帮助你在进入更难的题目之前打好基础。它通常涵盖最近几节课的多个主题，并不是一次测验。
In Year 7, a support homework often includes about ten to fifteen short questions. You should attempt every question and show your working, even when the answer seems obvious. This helps your teacher see where you need extra help.
在七年级，一份支持作业通常包含十到十五道简答题。你应该尝试每一道题并写出过程，即使答案看起来很明显。这有助于老师了解你需要额外帮助的地方。
2. Place Value and Ordering | 位值与排序
Understanding place value is the foundation of all number work. In a number such as 4 372, the digit 4 has a value of 4 000, 3 has a value of 300, 7 has a value of 70, and 2 has a value of 2.
理解位值是所有数字运算的基础。在 4 372 这个数中，数字 4 的值是 4 000，3 的值是 300，7 的值是 70，2 的值是 2。
4 372 = 4 × 1000 + 3 × 100 + 7 × 10 + 2 × 1
When ordering decimals, compare the digits from left to right. For example, 0.45 is greater than 0.405 because the hundredths digit 5 is greater than 0.
在比较小数时，从左到右逐位比较。例如 0.45 大于 0.405，因为百分位的 5 大于 0。
- 0.45 means 4 tenths + 5 hundredths | 0.45 表示 4 个十分之一 + 5 个百分之一
- 0.405 means 4 tenths + 0 hundredths + 5 thousandths | 0.405 表示 4 个十分之一 + 0 个百分之一 + 5 个千分之一
3. Mental Addition and Subtraction | 心算加减法
sense. Use partitioning: to calculate 236 + 48, think 236 + 40 = 276, then 276 + 8 = 284.
心算方法有助于快速计算并培养数感。使用拆分法：计算 236 + 48 时，先算 236 + 40 = 276，再算 276 + 8 = 284。
236 + 48 = 236 + 40 + 8 = 284
3: 67 + 33 = 100, 100 + 400 = 500, 500 + 3 = 503, so the difference is 33 + 400 + 3 = 436.
对于 503 − 67 这样的减法，可以从 67 往上数到 503：67 + 33 = 100，100 + 400 = 500，500 + 3 = 503，因此差是 33 + 400 + 3 = 436。
503 − 67 = 436
4. Multiplication and Division Strategies | 乘法与除法策略
ion for larger numbers. For example, 23 × 6 can be split as (20 + 3) × 6 = 120 + 18 = 138.
熟记 12 × 12 以内的乘法表能让笔算更容易。对于较大的数，使用网格法或短乘法。例如 23 × 6 可以拆分为 (20 + 3) × 6 = 120 + 18 = 138。
23 × 6 = (20 × 6) + (3 × 6) = 120 + 18 = 138
Division is the inverse of multiplication. To work out 144 ÷ 12, think 'what number times 12 gives 144?' Since 12 × 12 = 144, the answer is 12.
除法是乘法的逆运算。要计算 144 ÷ 12，可以想 '什么数乘以 12 等于 144？' 因为 12 × 12 = 144，所以答案是 12。
144 ÷ 12 = 12
5. Fractions: Simplifying and Equivalent Forms | 分数：化简与等值形式
To simplify a fraction, divide the numerator and denominator by their highest common factor.
分数表示整体的一部分。等值分数表示相同的量。例如 1/2 = 2/4 = 4/8。化简分数时，将分子和分母同时除以它们的最大公因数。
12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4
me denominator, add the numerators and keep the denominator. For example, 3/8 + 2/8 = 5/8.
同分母分数相加，分母不变，分子相加。例如 3/8 + 2/8 = 5/8。
3/8 + 2/8 = 5/8
6. Decimals and Percentages | 小数与百分数
Decimals are another way of writing fractions with denominators 10, 100, 1000, and so on. For example, 0.7 means 7/10 and 0.25 means 25/100.
小数是分母为 10、100、1000 等的分数的另一种写法。例如 0.7 表示 7/10，0.25 表示 25/100。
0.25 = 25/100 = 1/4
f 100. To convert a decimal to a percentage, multiply by 100. For example, 0.85 × 100 = 85%.
百分数表示每一百份中的数量。将小数转换为百分数，只需乘以 100。例如 0.85 × 100 = 85%。
0.85 = 85%
percentage of an amount, convert the percentage to a decimal and multiply. For example, 20% of 60 = 0.20 × 60 = 12.
求一个数的百分之几，先将百分数转换为小数再相乘。例如 60 的 20% = 0.20 × 60 = 12。
20% of 60 = 0.2 × 60 = 12
7. Introduction to Algebra | 代数初步
In algebra, letters stand for unknown numbers. An expression such as 3a + 2 means 'multiply a by 3, then add 2.' When a = 4, the value is 3 × 4 + 2 = 14.
在代数中，字母表示未知数。像 3a + 2 这样的表达式表示 'a 乘以 3，再加 2'。当 a = 4 时，值是 3 × 4 + 2 = 14。
If a = 4, then 3a + 2 = 3 × 4 + 2 = 14
2x = 7x, but 5x + 2y cannot be simplified further because x and y are different variables.
同类项可以合并。例如 5x + 2x = 7x，但 5x + 2y 不能进一步化简，因为 x 和 y 是不同的变量。
5x + 2x = 7x
8. Solving Simple Equations | 解简单方程
you must do to the other. To solve x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7.
方程就像天平。对一边做什么运算，另一边也要做同样的运算。解 x + 5 = 12 时，两边同时减去 5：x = 12 − 5 = 7。
x + 5 = 12 → x = 12 − 5 → x = 7
For a multiplication equation such as 4n = 32, divide both sides by 4: n = 32 ÷ 4 = 8.
对于 4n = 32 这样的乘法方程，两边同时除以 4：n = 32 ÷ 4 = 8。
4n = 32 → n = 32 ÷ 4 → n = 8
9. Geometry: Angles and Shapes | 几何：角与图形
An angle is a measure of turn, measured in degrees (°). A right angle is 90°, a straight line is 180°, and a full turn is 360°. Angles on a straight line add up to 180°.
角是转动的度量，以度（°）为单位。直角是 90°，平角是 180°，周角是 360°。直线上的角之和为 180°。
Angles on a straight line: a + b = 180°
add up to 180°. If two angles are 50° and 60°, the third angle is 180° − 50° − 60° = 70°.
三角形的三个内角之和总是 180°。如果两个角分别是 50° 和 60°，第三个角就是 180° − 50° − 60° = 70°。
Third angle = 180° − 50° − 60° = 70°
In any quadrilateral, the four interior angles add up to 360°. This is useful when you are asked to find a missing angle in a rectangle, parallelogram, or trapezium.
任意四边形的四个内角之和为 360°。当你需要求矩形、平行四边形或梯形中的未知角时，这个规则很有用。
10. Data Handling: Averages and Charts | 数据处理：平均数与图表
e are. For the data set 3, 5, 7, 9, 11, the mean is (3 + 5 + 7 + 9 + 11) ÷ 5 = 35 ÷ 5 = 7.
平均数是将所有数值相加后除以数值的个数。对于数据集 3、5、7、9、11，平均数是 (3 + 5 + 7 + 9 + 11) ÷ 5 = 35 ÷ 5 = 7。
Mean = (3 + 5 + 7 + 9 + 11) ÷ 5 = 7
The median is the middle value when the numbers are in order. The mode is the most frequent value. The range is the difference between the largest and smallest values.
中位数是将数据按顺序排列后位于中间的数。众数是出现次数最多的数。极差是最大值与最小值之差。
