📚 Math Practice Animation: G-3-7 Question Type Breakdown | 数学练习动画：G-3-7 题型解析
Animated math practice has revolutionised the way learners engage with problem-solving. The G-3-7 series, a specially curated set of question types across arithmetic, algebra, geometry, and data handling, uses visual storytelling to break down complex concepts. This article dissects the core question types found in the G-3-7 animated exercises, offering step-by-step strategies so that students can approach similar problems with confidence and clarity.
数学练习动画彻底改变了学习者参与解题的方式。G-3-7 系列是一套精心编排的题型合集，涵盖算术、代数、几何与数据处理，它运用视觉化的叙事手法来拆解复杂概念。本文深入解析 G-3-7 动画练习里的核心题型，提供逐步解题策略，帮助学生自信、清晰地解决类似问题。
1. Fraction Addition with Unlike Denominators | 异分母分数加法
y demonstrating the need for a common denominator. The least common multiple (LCM) of 3 and 4 is shown as 12, and both fraction bars are subdivided accordingly. The sum then becomes (8/12) + (3/12) = 11/12, with the overlapping shaded regions reinforcing the concept.
在动画形式中，G-3-7 练习以两个分数（如 2/3 和 1/4）开始。屏幕将分数拆分为阴影面积模型，直观地展示了通分的必要性。3 和 4 的最小公倍数（LCM）显示为 12，两个分数条被相应地细分。其和随后变为 (8/12) + (3/12) = 11/12，重叠的阴影区域强化了这一概念。
2/3 + 1/4 = 8/12 + 3/12 = 11/12
Key insight: Always find the LCM of the denominators before adding. The animation often colour-codes the equivalent fractions to avoid confusion.
关键洞察：始终在相加前求出分母的最小公倍数。动画常用颜色区分等值分数，避免混淆。
2. Mixed Number Operations Using Area Models | 用面积模型进行带分数运算
Mixed numbers like 2 1/2 and 1 2/3 appear as combined whole units and fractional pieces. The G-3-7 animation converts each mixed number into an improper fraction with a click-through sequence: 2 1/2 becomes 5/2, and 1 2/3 becomes 5/3. Then, the product or sum is computed using fraction multiplication or addition, with the final result converted back to a mixed number, all visualised on a rectangular area grid.
诸如 2 1/2 和 1 2/3 这样的带分数以整体单位与分数片段的组合出现。G-3-7 动画通过点击顺序将每个带分数转换为假分数：2 1/2 变为 5/2，1 2/3 变为 5/3。随后，利用分数乘法或加法计算积或和，最后将结果转换回带分数，整个过程在矩形面积网格上可视化呈现。
2½ → 5/2, 1⅔ → 5/3; 5/2 × 5/3 = 25/6 = 4 1/6
Students often forget to reconvert the improper fraction to a mixed number. The animation highlights the remainder step, making the process intuitive.
学生常忘记将假分数重新转换为带分数。动画高亮显示了求余数的步骤，使过程直观易懂。
3. Solving Two-Step Linear Equations | 解两步线性方程
from both sides, showing the scale rebalancing. Then it divides both sides by 3, isolating x. The visual feedback reinforces the ‘do the same to both sides’ principle.
G-3-7 代数部分展示了对每一步操作都作出反应的天平。对于诸如 3x + 5 = 20 的方程，动画先从两边减去 5，展示天平重新平衡。然后两边除以 3，分离出 x。视觉反馈强化了“等式两边同做同一运算”的原则。
3x + 5 = 20 → 3x = 15 → x = 5
This approach prevents the common error of forgetting to apply operations to the constant term as well. The animation mirrors the algebraic steps with physical movement.
这种方法避免了常见错误——忘记对常数项也进行运算。动画通过物理运动映射代数步骤。
4. Angle Relationships in Parallel Lines | 平行线中的角度关系
Using animated transversal lines cutting a pair of parallel lines, the G-3-7 geometry set highlights corresponding, alternate, and co-interior angles. For instance, given an angle of 65°, the corresponding angle is also 65°, while the alternate interior angle equals 65° and the co-interior angle sums with the given angle to 180°. The animation rotates a protractor overlay, confirming the measures dynamically.
通过动画展示一条截线切割一对平行线，G-3-7 几何题组凸显了同位角、内错角和同旁内角。例如，给定一个 65° 的角，同位角也是 65°，内错角等于 65°，而同旁内角与给定角之和为 180°。动画旋转一个量角器覆盖层，动态确认这些度数。
If ∠A = 65°, then corresponding ∠B = 65°, alternate ∠C = 65°, co-interior ∠D = 115°
Students often confuse alternate and co-interior angles. The colour-coded arcs in the animation help memorise the relationships: F-shape for corresponding, Z-shape for alternate, and C-shape for co-interior.
学生常常混淆内错角与同旁内角。动画中用不同颜色标出的弧线有助于记忆这些关系：同位角呈 F 形，内错角呈 Z 形，同旁内角呈 C 形。
5. Pythagoras' Theorem in Right Triangles | 直角三角形的勾股定理
he legs, the area exactly fills the square on the hypotenuse, visually proving a² + b² = c². Then, typical problems ask for a missing side: if a=5 and c=13, then b=√13² − 5² = 12.
G-3-7 展示一个直角边为 a 和 b、斜边为 c 的直角三角形。动画在每条边上构建正方形。通过重新排列直角边上的正方形，其面积恰好填满斜边上的正方形，直观地证明了 a² + b² = c²。随后的典型问题要求找出缺失边：若 a=5、c=13，则 b = √13² − 5² = 12。
a² + b² = c² → 5² + b² = 13² → b = √169 − 25 = √144 = 12
Remember to identify the hypotenuse correctly; it is always opposite the right angle. The animation highlights the longest side before applying the formula to avoid substitution errors.
务必正确识别斜边；它总是与直角相对。动画在应用公式前会高亮最长边，以避免代换错误。
6. Percentage Increase and Decrease | 百分比增减
The G-3-7 percentage module uses a dynamic slider on a bar model. For a 15% increase on 200, the bar extends proportionally. The animation calculates 10% (20) and 5% r shrinks, and the multiplier method is also shown: multiply by 1.15 for increase, 0.85 for a 15% decrease.
G-3-7 百分比模块在条形模型上使用动态滑块。对于 200 增长 15%，条形按比例延伸。动画计算出 10%（20）和 5%（10），然后将总和加至原数：200 + 30 = 230。对于减少，条形缩短，同时展示乘数法：增长乘 1.15，减少 15% 乘 0.85。
Increase: 200 × 1.15 = 230; Decrease: 200 × 0.85 = 170
The animation reinforces that a 15% decrease does not simply reverse a 15% increase on the new amount. Comparing the two operations side by side prevents the classic misunderstanding.
动画强调 15% 的减少并不能简单地将增长后的新数量反转。将两种运算并排比较，可防止典型的误解。
7. Reading and Interpreting Statistical Graphs | 统计图表的阅读与解读
ights the difference by subtracting the heights: Year 1: 120 units, Year 2: 150 units, so the increase is 30 units. Students are then prompted to calculate the percentage growth: (30/120) × 100% = 25%. The dynamic annotation helps extract exact values from the axes.
G-3-7 包含动态条形图、饼图和折线图。例如，一个双重条形图比较了两年的销售额。动画通过减去高度来突显差异：第一年 120 单位，第二年 150 单位，因此增长为 30 单位。随后提示学生计算增长百分比：(30/120) × 100% = 25%。动态标注有助于从坐标轴上提取精确数值。
Increase = 150 − 120 = 30; Percentage increase = (30 ÷ 120) × 100% = 25%
Always check the scale on the y-axis; uneven scales are often used in tricky questions. The G-3-7 animation pauses to show the scale intervals before asking for a reading.
始终检查 y 轴的比例尺；难题中常使用不均匀的刻度。G-3-7 动画会暂停以显示刻度间隔，然后再要求读数。
8. Probability Tree Diagrams | 概率树状图
nch by branch. The first pick probabilities are 3/5 for red and 2/5 for blue. For the second pick, the denominators change due to non-replacement: if a red was picked, the next probabilities become 2/4 red and 2/4 blue. The animation multiplies along branches to find combined probabilities, e.g., P(red then blue) = (3/5) × (2/4) = 6/20 = 3/10.
对于两阶段概率问题，比如从装有 3 只红色和 2 只蓝色袜子的抽屉里抽出两只，G-3-7 动画逐枝生成树状图。第一次抽取的概率是红色 3/5，蓝色 2/5。第二次抽取时，由于不放回，分母发生变化：若第一次抽到红色，则下一次概率变为红色 2/4，蓝色 2/4。动画沿枝条相乘以求得组合概率，例如 P(先红后蓝) = (3/5) × (2/4) = 6/20 = 3/10。
P(Red, Blue) = 3/5 × 2/4 = 6/20 = 3/10
The animation reminds students to sum the probabilities of all relevant branches for 'at least one' or 'either' type questions. The visual collapsing of branches makes the addition step obvious.
动画提醒学生，对于“至少一个”或“任一”类型的问题，要将所有相关枝条的概率相加。树枝的视觉折叠使加法步骤显而易见。
9. Coordinate Transformations: Translation and Reflection | 坐标变换：平移与反射
Using a dynamic grid, the G-3-7 geometry set shows a triangle with vertices (2,1), (5,1), (4,4). A translation vector (3, -2) slides the shape three units right and two down. The animation traces the path of each vertex, producing new coordinates (5,-1), (8,-1), (7,2). For reflection across the y-axis, the x-coordinates change sign: (-2,1), (-5,1), (-4,4). The visual transformation reinforces the invariant properties of shape and size.
利用动态网格，G-3-7 几何题组展示了一个顶点为 (2,1)、(5,1)、(4,4) 的三角形。平移向量 (3, -2) 将图形向右滑动 3 个单位、向下 2 个单位。动画追踪每个顶点的路径，产生新坐标 (5,-1)、(8,-1)、(7,2)。对于沿 y 轴的反射，x 坐标变号：(-2,1)、(-5,1)、(-4,4)。视觉变换强化了形状与大小不变的性质。
Translation by (3, -2): (x, y) → (x+3, y-2); Reflection in y-axis: (x, y) → (-x, y)
Students often confuse the direction of vectors or reflections. The animation's colour-coded arrows and ghost images help internalise the mapping rules.
学生常混淆向量方向或反射轴。动画中用彩色箭头和虚影图像帮助内化映射规则。
10. Volume and Surface Area of Cuboids | 长方体体积与表面积
×3 = 72 cubic units. The surface area is animated by unfolding the net: it shows three pairs of rectangles with areas lw (24), lh (18), and wh (12). The total surface area is 2×(24+18+12) = 108 square units.
G-3-7 测量模块旋转一个长 l=6、宽 w=4、高 h=3 的长方体。通过数单位立方体计算体积：V = l × w × h = 6×4×3 = 72 立方单位。表面积通过展开图进行动画演示：展示了三对矩形，面积分别为 lw (24)、lh (18) 和 wh (12)。总表面积为 2×(24+18+12) = 108 平方单位。
V = 6 × 4 × 3 = 72; SA = 2(6×4 + 6×3 + 4×3) = 2(24+18+12) = 108
Pay attention to units: volume in cubic units, area in square units. The animation flashes the correct unit label after each calculation to prevent omission.
注意单位：体积用立方单位，面积用平方单位。动画在每次计算后闪烁正确的单位标签，以防遗漏。
11. Algebraic Expansion Using Area Models | 运用面积模型进行代数展开
For expressions like (x+3)(x+2), the G-3-7 algebra set fills a rectangular grid with sides x+3 and x+2. The composition yields four sub-areas: x², 2x, 3x, and 6. Summing these gives x² + 5x + 6. The animation then connects this to the FOIL method, showing that the middle term 5x comes from adding 2x and 3x. This dual representation solidifies the distributive law.
对于像 (x+3)(x+2) 这样的表达式，G-3-7 代数题组填充了一个边长为 x+3 和 x+2 的矩形网格。组合后产生四个子区域：x²、2x、3x 和 6。将这些相加得到 x² + 5x + 6。动画随后将其与 FOIL 方法联系起来，表明中间项 5x 来自 2x 和 3x 相加。这种双重表示巩固了分配律。
(x+3)(x+2) = x² + 2x + 3x + 6 = x² + 5x + 6
The visual grid prevents the common error of forgetting to multiply the constant terms or missing the cross terms. Students can literally see the product taking shape.
视觉网格防止了常见的错误，如忘记乘以常数项或遗漏交叉项。学生可以真切地看到乘积如何形成。
12. Direct and Inverse Proportion | 正比例与反比例
ies concludes with proportion, using animated graphs and tables. For a direct proportion y ∝ x doubles, y doubles, creating a straight line through the origin. An inverse proportion y ∝ ains constant at 12. The animation morphs the table into a curve, emphasising the shape difference.
G-3-7 系列以比例收尾，使用了动态图表和表格。对于正比例 y ∝ x，当 x 加倍时 y 也加倍，形成一条过原点的直线。反比例 y ∝ 1/x 展示一条双曲线：当 x=2 时，y=6；x=4 时，y=3；x=6 时，y=2；乘积 xy 恒为 12。动画将表格变形为曲线，强调形状差异。
Direct: y = kx (k=3 → points (2,6), (4,12)); Inverse: y = k/x (k=12 → points (2,6), (4,3))
Identifying the constant of proportionality is key. The G-3-7 animation highlights the invariant product or ratio, helping students recognise real-world problems like speed-time relationships or currency conversion.
识别比例常数是关键。G-3-7 动画高亮显示不变的乘积或比值，帮助学生识别现实问题，如速度-时间关系或货币兑换。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图