📚 Math G6 Workbook: Core Practice and Skills | 数学 G6 练习册：核心练习与技能
This workbook article summarises the core Grade 6 mathematics topics students need to practise. It includes place value, fractions, ratios, integers, expressions, geometry, statistics and measurement. Each section gives clear explanations and examples so learners can build confidence before assessments.
本练习册文章总结了六年级数学需要练习的核心主题，包括位值、分数、比、整数、表达式、几何、统计和测量。每个小节都提供清晰的讲解和例题，帮助学习者在评估前建立信心。
1. Number Sense and Place Value | 数感与位值
Grade 6 students should read, write, compare and round multi-digit whole numbers and decimals to thousandths. They need to understand that each place value is ten times the value of the place to its right. A number such as 4,307.56 can be expanded as 4×1000 + 3×100 + 0×10 + 7×1 + 5×0.1 + 6×0.01.
六年级学生应该会读、写、比较多位数整数以及千分位小数。他们需要理解每个数位的值是右边数位的十倍。像 4,307.56 这样的数可以展开为 4×1000 + 3×100 + 0×10 + 7×1 + 5×0.1 + 6×0.01。
Common workbook tasks include writing numbers in standard form, word form and expanded form. Students also practise rounding decimals such as 3.276 to the nearest hundredth, giving 3.28. Comparing decimals requires lining up the decimal points and checking digits from left to right.
常见练习包括写出数字的标准形式、文字形式和展开形式。学生还要练习将小数四舍五入，例如把 3.276 四舍五入到百分位得到 3.28。比较小数需要对齐小数点，并从左到右检查数位。
2. Operations with Whole Numbers and Decimals | 整数与小数运算
Fluent multi-digit multiplication and long division are central to Grade 6 arithmetic. Students should use the standard algorithm and check results with estimation or inverse operations. For example, 1,248 ÷ 12 gives 104 because 104 × 12 = 1,248.
熟练进行多位数乘法和长除法是六年级算术的核心。学生应使用标准算法，并用估算或逆运算检查结果。例如，1,248 ÷ 12 等于 104，因为 104 × 12 = 1,248。
Decimal operations require careful placement of the decimal point. When multiplying 0.6 × 0.3, the result is 0.18 because 6 × 3 = 18 and there are two decimal places in total. In division, 7.2 ÷ 0.8 can be rewritten as 72 ÷ 8 = 9 after moving the decimal point one place to the right in both numbers.
小数运算需要仔细确定小数点的位置。计算 0.6 × 0.3 时，结果是 0.18，因为 6 × 3 = 18，并且一共有两位小数。在除法中，7.2 ÷ 0.8 可以把两个数的小数点都向右移动一位，变成 72 ÷ 8 = 9。
3. Fractions: Concepts, Equivalence and Operations | 分数：概念、等值与运算
Students must find equivalent fractions and use the greatest common factor and least common multiple to simplify or compare fractions. For example, 8/12 simplifies to 2/3 because 4 is the greatest common factor of 8 and 12. Comparing 2/3 and 3/5 uses the common denominator 15, giving 10/15 and 9/15.
学生必须会找等值分数，并运用最大公因数和最小公倍数来化简或比较分数。例如，8/12 化简为 2/3，因为 4 是 8 和 12 的最大公因数。比较 2/3 和 3/5 时使用公分母 15，得到 10/15 和 9/15。
For addition and subtraction, students convert to common denominators first. To subtract 5/6 − 1/4, use 12 as the common denominator: 10/12 − 3/12 = 7/12. For multiplication, multiply numerators and denominators directly: 3/4 × 2/5 = 6/20 = 3/10. For division, multiply by the reciprocal: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
进行加减法时，学生先化为公分母。计算 5/6 − 1/4 时，用 12 作为公分母：10/12 − 3/12 = 7/12。进行乘法时，直接将分子相乘、分母相乘：3/4 × 2/5 = 6/20 = 3/10。进行除法时，乘以倒数：3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8。
| Fraction 分数 | Decimal 小数 | Percent 百分数 |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
4. Ratios, Rates and Percent | 比、比率与百分数
A ratio compares two quantities and can be written in three ways: a:b, a to b, or a/b. Grade 6 students simplify ratios and find equivalent ratios. The ratio 12:18 simplifies to 2:3 because both terms can be divided by 6.
比用于比较两个量，可以用三种方式书写：a:b、a 比 b 或 a/b。六年级学生需要化简比并找出等值比。比 12:18 化简为 2:3，因为两项都可以除以 6。
A unit rate shows the amount per one unit. If a student reads 120 pages in 4 hours, the unit rate is 120 ÷ 4 = 30 pages per hour. Percent means per hundred, so 15% of 80 is 0.15 × 80 = 12. Workbooks also include converting between fractions, decimals and percents.
单位比率表示每一单位的量。如果一名学生 4 小时阅读 120 页，那么单位比率是 120 ÷ 4 = 每小时 30 页。百分数表示每一百份中的几份，因此 80 的 15% 是 0.15 × 80 = 12。练习册还包括分数、小数和百分数之间的转换。
5. Integers and the Coordinate Plane | 整数与坐标平面
Integers include positive whole numbers, negative whole numbers and zero. Students must compare integers and find absolute value. For example, −7 has a smaller value than −3, but the absolute value of −7 is 7, written |−7| = 7.
整数包括正整数、负整数和零。学生必须会比较整数并求绝对值。例如，−7 的值小于 −3，但 −7 的绝对值是 7，写作 |−7| = 7。
The coordinate plane is formed by a horizontal x-axis and a vertical y-axis. Points are written as ordered pairs (x, y). The point (−3, 4) lies in Quadrant II because x is negative and y is positive. Workbooks often ask students to plot points, reflect shapes, and solve problems involving distance between points on the same axis.
坐标平面由水平的 x 轴和竖直的 y 轴构成。点写成有序数对 (x, y)。点 (−3, 4) 位于第二象限，因为 x 为负、y 为正。练习册经常要求学生描点、作图形对称，并解决同一坐标轴上点与点之间的距离问题。
6. Expressions and One-Step Equations | 表达式与一步方程
An expression combines numbers, variables and operations without an equals sign. Students learn to write and evaluate expressions such as 3x + 5 when x = 4, giving 3(4) + 5 = 17. Exponents are used to show repeated multiplication, so 2³ = 2 × 2 × 2 = 8.
表达式由数字、变量和运算组成，不含等号。学生学习书写和求值表达式，例如当 x = 4 时，3x + 5 = 3(4) + 5 = 17。指数用来表示重复乘法，因此 2³ = 2 × 2 × 2 = 8。
A one-step equation is solved by using an inverse operation. To solve x + 5 = 12, subtract 5 from both sides to get x = 7. To solve 6x = 42, divide both sides by 6 to get x = 7. Workbooks often include the check step: substitute the solution back into the original equation.
一步方程通过逆运算求解。解 x + 5 = 12 时，两边同时减去 5，得到 x = 7。解 6x = 42 时，两边同时除以 6，得到 x = 7。练习册通常包含检验步骤：把解代回原方程。
Example: 6x = 42 → x = 7
7. Geometry: Area, Surface Area and Volume | 几何：面积、表面积与体积
Grade 6 geometry focuses on area of triangles, parallelograms and composite figures. The area of a triangle is A = ½ bh, where b is base and h is height. A triangle with base 8 cm and height 5 cm has area ½ × 8 × 5 = 20 cm².
六年级几何重点是三角形、平行四边形和组合图形的面积。三角形面积公式为 A = ½ bh，其中 b 是底，h 是高。底为 8 厘米、高为 5 厘米的三角形面积是 ½ × 8 × 5 = 20 cm²。
Students also find the volume of rectangular prisms using V = l × w × h. Surface area is the total area of all faces. For a box with length 4 m, width 3 m and height 2 m, volume is 4 × 3 × 2 = 24 m³. Each face is measured and added to find surface area.
学生还要用 V = l × w × h 求长方体体积。表面积是所有面的总面积。一个长 4 米、宽 3 米、高 2 米的长方体，体积是 4 × 3 × 2 = 24 m³。每个面都要测量并相加以求出表面积。
A = ½ bh and V = l × w × h
8. Data, Graphs and Statistics | 数据、图表与统计
Statistical thinking in Grade 6 includes finding mean, median, mode and range. The mean is the average, the median is the middle value in ordered data, and the mode is the most frequent value. For the data set 4, 7, 7, 9, 13, the mean is (4+7+7+9+13) ÷ 5 = 8, the median is 7, and the mode is 7.
六年级的统计思维包括求平均数、中位数、众数和极差。平均数是所有数据的总和除以数据个数，中位数是有序数据中的中间值，众数是出现次数最多的值。对于数据集 4, 7, 7, 9, 13，平均数是 (4+7+7+9+13) ÷ 5 = 8，中位数是 7，众数是 7。
Students also display data using dot plots, box plots and histograms. They describe distributions as symmetric, skewed left or skewed right. Interquartile range measures the spread of the middle 50% of a data set, helping to compare variability between groups.
学生还要用点图、箱线图和直方图展示数据。他们需要描述分布是对称、左偏还是右偏。四分位距衡量一组数据中间 50% 的离散程度，有助于比较不同组之间的变异性。
9. Units of Measurement and Conversions | 测量单位与换算
Measurement problems require converting units within the same system. In the metric system, 1 km = 1000 m, 1 m = 100 cm, and 1 kg = 1000 g. In customary units, 1 foot = 12 inches and 1 yard = 3 feet. Grade 6 students use ratio reasoning to convert between units.
测量问题需要在同一单位制内进行单位换算。在公制中，1 千米 = 1000 米，1 米 = 100 厘米，1 千克 = 1000 克。在英制中，1 英尺 = 12 英寸，1 码 = 3 英尺。六年级学生运用比率推理进行单位换算。
Workbook questions often connect measurement to real life. Converting 3.5 km to meters gives 3500 m because 1 km = 1000 m. Converting 2 hours and 15 minutes to minutes gives 2 × 60 + 15 = 135 minutes. Students should include the correct unit in every final answer.
练习册中的题目通常将测量与现实生活联系起来。把 3.5 千米换算成米，结果是 3500 米，因为 1 千米 = 1000 米。把 2 小时 15 分钟换算成分钟，是 2 × 60 + 15 = 135 分钟。学生应在每个最终答案中写出正确的单位。
10. Problem Solving and Practice Strategies | 问题解决与练习策略
Effective practice involves reading a word problem carefully, identifying known and unknown quantities, and drawing a model when needed. Students should look for keywords but also use mathematical reasoning. Writing each step clearly helps avoid careless mistakes in multi-step problems.
有效练习需要仔细阅读应用题，找出已知量和未知量，并在需要时画图。学生既要关注关键词，也要运用数学推理。每一步都写清楚有助于避免多步问题中的粗心错误。
A useful routine is read, represent, solve and check. After solving, ask whether the answer makes sense and whether it answers the original question. Common errors include misplacing decimal points, mixing up area and perimeter, and forgetting to convert units before calculating.
一个有效的解题步骤是：阅读、表示、求解和检查。求出答案后，要问答案是否合理，是否回答了原来的问题。常见错误包括小数点位置错误、混淆面积和周长、以及计算前忘记统一单位。
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