生成适合4生5年纪学上的，生动有趣的教学视频，且能与生活、解决实际问题关联。对基础概念采用动画图的形式进行有趣的解读。---**Extraction Content:**
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**Section: 图形与几何 (Figures and Geometry)**
**Topic: 专题五 (Topic Five)**
**Calculations & Answers:**
**Calculation Block 1:**
* **体积 (Volume):**
* 20 × 3 × 3
* = 60 × 3
* = 180 (cm³)
* **(2) 表面积 (Surface Area):**
* 5 ÷ 2 = 2.5 (dm)
* 3.14 × 5 × 10 + 3.14 × 2.5² × 2
* = 3.14 × 5 × 10 + 3.14 × 6.25 × 2
* = 157 + 39.25
* = 196.25 (dm²)
**Calculation Block 2:**
* **体积 (Volume):**
* 3.14 × 2.5² × 10
* = 3.14 × 6.25 × 10
* = 19.625 × 10
* = 196.25 (dm³)
**Answers to Problems (based on calculations above):**
* **【答案】(1)** 这个长方体的表面积为 258 cm³，体积是 180 cm³。
* **(Answer (1))** The surface area of this cuboid is 258 cm³, and its volume is 180 cm³.
* **(2)** 这个圆锥体的表面积是 196.25 dm²，体积是 196.25 dm³。
* **(2)** The surface area of this cone is 196.25 dm², and its volume is 196.25 dm³.
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**Section: 真题解析 (Real Exam Analysis)**
**Question Stem:**
(湖北小考)一个圆锥体，底面周长是 12.56 厘米，高 2.4 厘米，它的体积是______立方厘米。(π取3.14)
*(Translation: (Hubei Primary Exam) A cone has a base circumference of 12.56 cm and a height of 2.4 cm. Its volume is ______ cubic centimeters. (Take π as 3.14))*
**Solution Explanation:**
**【解答】**
由题可得，圆锥的底面半径为 12.56 ÷ 3.14 ÷ 2 = 2 (厘米)，则圆锥的体积为 1/3 × 3.14 × 2² × 2.4 = 10.048 (立方厘米)。
*(Translation: **[Solution]**
From the problem, the base radius of the cone is 12.56 ÷ 3.14 ÷ 2 = 2 (cm). Then the volume of the cone is 1/3 × 3.14 × 2² × 2.4 = 10.048 (cubic centimeters).)*
**Answer:**
**【答案】** 10.048
*(Translation: **[Answer]** 10.048)*
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**Section: 第三节 图形与运动 (Section Three: Figures and Movement)**
**Subtitle: 考点一 平移 (Key Point One: Translation)**
**Textual Information:**
1. **平移的概念 (Concept of Translation)**
* (1) 在平面内，将一个图形上的所有点都沿着某个直线方向移动相同的距离，这样的图形运动叫做平移。→ 一种直线运动。
*(Translation: (1) In a plane, moving all points on a figure along a straight line direction by the same distance is called translation. → A type of linear motion.)*
* (2) 图形平移后各对应点之间的距离叫做图形平移的距离。
*(Translation: (2) The distance between corresponding points after a figure is translated is called the translation distance of the figure.)*
* (3) 平移三要素：原位置、平移方向和平移距离。
*(Translation: (3) Three elements of translation: original position, translation direction, and translation distance.)*
**Chart/Diagram Description (实例讲解 - Example Explanation):**
* **Title:** 平移 (Translation)
* **Type:** Grid-based geometric figure illustration.
* **Main Elements:**
* A grid of squares serves as the background.
* **Original Figure:** An isosceles triangle is drawn on the grid, with its base aligned horizontally along a grid line.
* **Translation 1 (Upwards):**
* An upward-pointing arrow indicates a translation from the original triangle to a new triangle located directly above it.
* **Label:** "向上平移4格" (Translate upwards 4 units).
* The translated triangle is congruent to the original and is positioned 4 grid units vertically above the original figure's corresponding points.
* **Translation 2 (Rightwards):**
* A rightward-pointing arrow indicates a translation from the original triangle to another new triangle located to its right.
* **Label:** "向右平移5格" (Translate rightwards 5 units).
* The translated triangle is congruent to the original and is positioned 5 grid units horizontally to the right of the original figure's corresponding points.
* **Overall:** The diagram illustrates two examples of geometric translation on a grid, showing how a figure moves along a straight line by a specified number of grid units in a particular direction.
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Here is the extracted content from the image:
**Header:**
小学生知识通 小学数学
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**Section: 学之舟 (Learning Boat)**
**重点说明 (Key Explanation):**
图形平移后，它们的形状、大小和方向都不改变，只是位置发生了变化。
**图解知识 (Knowledge Illustration):**
* **Chart/Diagram Description:**
* **Type:** Simple illustrative diagrams.
* **Main Elements:**
* **Left Diagram:** Shows a red flag (likely the Chinese national flag with five stars) on a flagpole. An upward-pointing arrow is positioned to the right of the flagpole, indicating an upward vertical movement.
* **Right Diagram:** Shows a rectangular window with horizontal blinds. A rightward-pointing arrow is positioned on the window, indicating a rightward horizontal movement.
* **Labels and Annotations:** None directly on the diagrams, but the accompanying text explains their meaning.
* **Textual Information for 图解知识:**
五星红旗的上下移动可以看作是一种竖直方向上的平移；推拉窗的移动可以看作是一种水平方向上的平移。
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**Main Content:**
**温馨提示 (Warm Reminder):**
升国旗、拉开抽屉、绕车的运动、电梯上下等，都属于生活中的平移现象。
**2. 平移的性质 (Properties of Translation):**
(1) 平移不改变图形的形状、大小和方向 (平移前后的两个图形是全等形)。平移是由平移的方向和平移的距离决定的。
(2) 图形平移后，对应点所连的线段平行 (或共线) 且相等，对应的角大小相等。
**3. 平移的作图步骤和方法 (Steps and Methods for Drawing Translation):**
(1) 确定平移方向和平移距离。
(2) 找到构成图形的关键点。
(3) 沿平移的方向，按平移距离描出图形每个关键点的对应点。
(4) 用线段顺次连接各对应点，画出平移后的图形，并标明各点对应的字母。
**考点二 旋转 (Key Point Two: Rotation)**
**1. 旋转的概念 (Concept of Rotation):**
(1) 在平面内，把一个图形围绕某一定点按顺时针或逆时针方向转动一定角度的过程，叫做旋转。这个定点叫做旋转中心，旋转的角度叫做旋转角。
(2) 决定旋转后图形位置的三要素：一是旋转中心，二是转方向 (逆时针或顺时针)，三是旋转角度。
**重点说明 (Key Explanation - Related to Rotation):**
描述旋转现象时，要描述成“某物体或图形沿某一点按某方向旋转了多少度”。
**2. 旋转的特征 (Characteristics of Rotation):**
旋转前后的图形 (或物体) 在形状、大小方面不发生变化，唯一改变的就是它的位置。
**重点说明 (Key Explanation - Related to Rotation):**
图形绕某一点旋转一定的角度，图形中的对应点，对应线段都旋转相同的角度。
**3. 画旋转后图形的方法 (Methods for Drawing Rotated Figures):**
(1) 定中心：确定旋转中心。
(2) 定方向：确定图形的旋转方向，即按顺时针旋转还是逆
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**Footer:**
学之舟 128 知识通
The provided image contains educational content related to graphics and geometry, specifically focusing on rotation and axial symmetry. There are no explicit questions or options in the traditional sense, but rather explanations, definitions, and examples.
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**Top Banner Content:**
* **Topic:** 图形与几何 (Graphics and Geometry)
* **Module:** 专题五 (Topic Five)
* **Publisher/Series:** 学之舟 (Boat of Learning)
**Section: 时针旋转 (Clockwise Rotation)**
* (3) 定角度: 确定旋转角度的大小。(Determine angle: Determine the size of the rotation angle.)
* (4) 按要求画出要旋转的图形的各个顶点旋转后对应点的位置,再用线段把这些对应点顺次连接起来。(Draw the positions of the corresponding points after rotating each vertex of the figure according to the requirements, and then connect these corresponding points sequentially with line segments.)
**Section: 温馨提示 (Warm Reminder)**
* **Title:** 旋转和平移的异同点 (Similarities and Differences between Rotation and Translation)
* (1) 共同点: 图形的位置发生变化,形状和大小不变。(Common points: The position of the figure changes, but its shape and size remain unchanged.)
* (2) 不同点: 平移时,物体沿直线运动,自身方向不发生变化;旋转时,物体沿曲线运动,自身方向发生变化。(Different points: During translation, the object moves along a straight line, and its own orientation does not change; during rotation, the object moves along a curve, and its own orientation changes.)
**Section: 重点说明 (Key Explanation)**
* **Content:** 判断平移还是旋转,关键在于图形在运动时是绕一个定点运动还是沿直线运动,以及图形运动时角度有没有改变。(To judge whether it's translation or rotation, the key is whether the figure moves around a fixed point or along a straight line during its movement, and whether the angle of the figure changes during its movement.)
**Section: 考点二 轴对称 (Knowledge Point Two: Axial Symmetry)**
**1. 轴对称图形 (Axially Symmetric Figures)**
* **Definition:** 如果一个图形沿着一条直线对折,两侧的图形能够完全重合,这个图形就是轴对称图形。折痕所在的这条直线叫作对称轴。(If a figure is folded along a straight line, and the figures on both sides can completely overlap, then this figure is an axially symmetric figure. The line where the fold crease is located is called the axis of symmetry.)
* **Annotation/Hint:** 分割线,两边相同。(Dividing line, both sides are identical.)
**2. 常见的轴对称图形及其对称轴的条数 (Common Axially Symmetric Figures and the Number of Their Axes of Symmetry)**
* 正方形有4条对称轴。(A square has 4 axes of symmetry.)
* 长方形有2条对称轴。(A rectangle has 2 axes of symmetry.)
* 等边三角形有3条对称轴。(An equilateral triangle has 3 axes of symmetry.)
* 等腰三角形有1条对称轴。(An isosceles triangle has 1 axis of symmetry.)
* 圆有无数条对称轴。(A circle has infinitely many axes of symmetry.)
* 菱形有2条对称轴。(A rhombus has 2 axes of symmetry.)
* 扇形有1条对称轴。(A sector has 1 axis of symmetry.)
**3. 对称轴和轴对称图形的画法 (Drawing Axes of Symmetry and Axially Symmetric Figures)**
* (1) 找对称轴的方法: 如果把图形沿一条直线对折,两边的图形完全重合,那么这条直线就是图形的对称轴。(Method to find the axis of symmetry: If the figure is folded along a straight line and the figures on both sides completely overlap, then this line is the axis of symmetry of the figure.)
* (2) 补全轴对称图形的方法: 找出图形的关键点,画出关键点关于对称轴的对称点,把对称点用线段顺次连接,就能得到完整的轴对称图形。(Method to complete an axially symmetric figure: Find the key points of the figure, draw the symmetric points of these key points with respect to the axis of symmetry, and then connect the symmetric points sequentially with line segments to obtain a complete axially symmetric figure.)
**Section: 图解知识 (Illustrated Knowledge)**
* **Sub-heading:** 轴对称图形 (Axially Symmetric Figures)
**Chart/Diagram Description:**
* **Type:** Two simple illustrative figures.
* **Figure 1 (Left):** A five-pointed star. It is colored orange with a black outline. It is vertically symmetrical.
* **Figure 2 (Right):** A stylized Christmas tree. It is colored green with a brown trunk and a black outline. It is vertically symmetrical.
**Section: 重点说明 (Key Explanation)**
* **Content:** 一个图形放大n倍,它的各边也要随之放大n倍。(If a figure is enlarged by n times, all its sides must also be enlarged by n times.)
**Section: 温馨提示 (Warm Reminder)**
* **Content:** 一个图形被一条直线分成两边完全相同的图形,这个图形不一定是轴对称图形。例如:一个邻边不相等的平行四边形被对角线分成了两个完全相同的两部分,但是沿着对角线对折后,两边的图形并不能完全重合,因此该图形并不是轴对称图形。(If a figure is divided into two completely identical parts by a straight line, this figure is not necessarily an axially symmetric figure. For example: A parallelogram with unequal adjacent sides is divided into two completely identical parts by a diagonal line, but if folded along the diagonal, the figures on both sides cannot completely overlap, therefore, this figure is not an axially symmetric figure.)
**Page Footer:**
* 学之舟 129 知识通 (Boat of Learning 129 Knowledge Pass)
**General Information:**
* **Title:** 小学生知识通 / 小学数学 (Elementary Student Knowledge Pass / Elementary Mathematics)
* **Section:** 学之舟 (Learning Boat)
* **Page Number:** 学之舟 130 知识圈 (Learning Boat 130 Knowledge Circle)
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**Section: 图解知识 (Illustrated Knowledge)**
**Textual Information:**
* 我们使用的一寸、二寸照片就是按照一定的比例缩放的。(Our one-inch and two-inch photos are scaled proportionally.)
**Chart/Diagram Description:**
* **Scene 1:** A girl sitting on a stool next to a potted plant, with a camera and a tripod. The camera is pointing towards a small framed picture on a stand to the right. This illustrates the concept of photography and scaling.
* **Scene 2 (Title: 图形缩放 - Figure Scaling):** A horizontal arrangement of four pairs of items. Each pair shows an item in two sizes:
* A green T-shirt icon (small and large).
* A red tomato icon (small and large).
* A red umbrella icon (small and large).
* A black and white soccer ball icon (small and large).
* This visually demonstrates the concept of scaling (enlargement and reduction) of common objects.
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**Section: 考点四 图形的缩放 (Key Point 4: Scaling of Figures)**
**Textual Information:**
* **Subtitle:** 图形大小比例发生改变 (Figure size and proportion change).
* **1. 图形缩放的概念 (Concept of Figure Scaling)**
* (1) 不改变图形的形状，把图形的每条边扩大为原来的 $n$ 倍，叫做图形的放大。(Without changing the shape of the figure, enlarging each side of the figure to $n$ times its original size is called enlargement of the figure.)
* (2) 不改变图形的形状，把图形的每条边缩小为原来的 $\frac{1}{n}$ 倍，叫做图形的缩小。(Without changing the shape of the figure, reducing each side of the figure to $\frac{1}{n}$ times its original size is called reduction of the figure.)
* **2. 画放大或缩小图形的方法 (Methods for Drawing Enlarged or Reduced Figures)**
* (1) 把图形按 $n:1$ 放大，先画一条边，使它的长度为原来长度的 $n$ 倍，对应角度不变，再画与它相邻的边，放大后图形与原图形各对应边的比值是 $n$。(To enlarge a figure by $n:1$, first draw one side, making its length $n$ times the original length, keep the corresponding angles unchanged, then draw the adjacent sides. The ratio of corresponding sides of the enlarged figure to the original figure is $n$.)
* (2) 把图形按 $1:n$ 缩小，先画一条边，使它的长度为原来长度的 $\frac{1}{n}$ 倍，对应角度不变，再画与它相邻的边，放大后图形与原图形各对应边的比值是 $\frac{1}{n}$。(To reduce a figure by $1:n$, first draw one side, making its length $\frac{1}{n}$ times the original length, keep the corresponding angles unchanged, then draw the adjacent sides. The ratio of corresponding sides of the enlarged figure to the original figure is $\frac{1}{n}$.)
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**Section: 温馨提示 (Warm Reminder)**
**Textual Information:**
* 图形放大或缩小后，边的长度按比例发生变化，图形的面积也发生了变化，图形的形状和边与边之间的角度不变。(After a figure is enlarged or reduced, the length of its sides changes proportionally, and its area also changes, but the shape of the figure and the angles between its sides remain unchanged.)
**Chart/Diagram Description:**
* A small image of a rolled-up scroll or document, located to the right of the text.
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**Section: 真题回放 (Real Exam Review)**
**Question 1:**
* **Question Stem:** (西藏小考)下列图形中，对称轴最多的是( )。(Tibet Primary Exam) Among the following figures, which one has the most axes of symmetry?
* **Options:**
* A. 长方形 (Rectangle)
* B. 正方形 (Square)
* C. 等腰三角形 (Isosceles triangle)
* D. 圆 (Circle)
* **Answer:** 【答案】D (Answer: D)
**Question 2 (例1):**
* **Question Stem:** 例1 (阜南小考)下列图形中，( )不是轴对称图形。(Example 1 - Funan Primary Exam) Among the following figures, which one ( ) is not an axially symmetric figure?
* **Options:**
* **A.** [Chart/Diagram Description]
* **B.** [Chart/Diagram Description]
* **C.** [Chart/Diagram Description]
* **Chart/Diagram Description (for Options A, B, C):**
* **A. (Image):** Two heart shapes, drawn side-by-side, touching or slightly overlapping at their inner sides. Each heart shape is individually symmetric. The combined figure appears to have one vertical axis of symmetry if treated as a single compound shape.
* **B. (Image):** Two crescent moon-like shapes, arranged symmetrically, resembling two 'C's facing away from each other and touching at their innermost tips, forming a kind of stylized hourglass or 'X' shape. This figure appears to have two axes of symmetry (horizontal and vertical).
* **C. (Image):** A geometric figure resembling a parallelogram, or a highly skewed rectangle, formed by two triangles sharing a common vertex and aligned on a diagonal. It does not appear to have an axis of symmetry.
* **Other Relevant Text (Annotation for Option C):**
* An arrow points from image C to the following explanation: 选项C为中心对称，在平面内，把一个图形绕着某个点旋转180°，如果旋转后的图形能与原来的图形重合，那么这个图形叫作中心对称图形。(Option C is centrally symmetric. In a plane, if a figure is rotated 180° around a certain point, and the rotated figure coincides with the original figure, then this figure is called a centrally symmetric figure.)
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**Section: 解析 (Analysis/Solution)**
**Textual Information:**
* 如果一个平面图形沿着一条直线折叠后，直线两旁的部分能够互相重合，那么这个图形叫作轴对称图形，这条直线叫作 (If a planar figure can be folded along a straight line such that the parts on both sides of the line coincide with each other, then this figure is called an axially symmetric figure, and this straight line is called...)
*(Note: The sentence is incomplete. The line is typically called the "axis of symmetry".)*