Section outline

  • General

    Collapse all Expand all

  • 固体数字分类

    lesson content

    When Arthur is at a birthday party, he enjoys sorting the gifts by their different shapes as a strategy to help him guess what is inside each package.  He observes the similar and different attributes of the gifts to put them into categories. Looking at the characteristics of the gifts, what are the shapes of the sides of each gift, and how many sides, edges, and corners does each have?
    ::当亚瑟在生日聚会上,他享受按不同形状对礼物进行分类,作为帮助他猜到每个包裹内是什么的策略。他观察礼物的相似和不同属性,把它们分为不同的类别。看看礼物的特性,每件礼物的侧面的形状,以及每个礼物的侧面、边缘和角有多少?

    In this concept, you will learn how to classify three-dimensional solids according to their common attributes. 
    ::在这个概念中,你会学习如何根据三维固体的共同特性进行分类。

    Classifying Solid Figures
    ::分类固体数字

    are three-dimensional objects, meaning they have length, width, and height .  Because they have three dimensions , they have depth and take up space in our universe.  Solid figures are identified according to the features that are unique to each type of solid.  Specifically, you can observe the numbers of faces, edges, and vertices , as well as the shape of the base . 
    ::它们是三维的物体, 意思是它们有长度、 宽度和高度。 因为它们有三个维度, 它们具有深度, 并占据了宇宙中的空间。 固态数字是根据每种固体的特有特征确定的。 具体地说, 您可以观察面、 边缘和脊椎的数量, 以及基座的形状 。

    The flat surfaces of a are its faces , or sides as they are commonly called.  The base is the face on which the figure rests.  The edge of a solid figure is the line segment where two faces meet.  A vertex (plural: vertices) is the corner that is formed where the ends of the line segments of two or more faces meet.
    ::一个平面的平面是它的脸,或它们通常被称为的两边。 基数是图的底数。 固态图的边缘是两面相交的线段。 顶部( 柱形: 顶部) 是两面或更多面线段相交的角。

    A sphere is a solid figure that has no faces, edges, or vertices. This is because it is completely round; it has no flat sides or corners.
    ::球体是一个没有面孔、边缘或脊椎的坚固数字。 这是因为球体是完全圆的,没有平面或角。

    lesson content

    A cone has one face, but no edges or vertices. Its face is in the shape of a circle . Because a circle is a flat, plane shape, it is a face. But because it is round around the outside, it does not form any edges or vertices. 
    ::锥体有一个面孔, 但没有边缘或脊椎。 它的面孔是圆形的。 因为圆环是平的, 平面形状, 它是一个面孔。 但是因为它环绕着外部, 它不会形成任何边缘或脊椎 。

    lesson content

    A cylinder has two circular faces but also no edges or vertices.
    ::圆柱体有两个圆形面,但没有边缘或脊椎。

    lesson content

    A pyramid has one base and at least three triangular faces.  It has edges where faces meet each other or the base, vertices where two faces meet the base, and a vertex at the top where all of the triangular faces meet.  A pyramid is named by the shape of its base.
    ::金字塔有一个底部,至少有三个三角面。它有面部相交的边缘,有面部相交的边缘,有两面相交的顶部的顶部,还有所有三角面相交的顶部的顶部的顶部。金字塔按其底部的形状命名。

    A triangular pyramid has a triangle-shaped base and three other triangular faces, or four in all.
    ::三角金字塔有一个三角形的底部和其他三个三角面孔,或总共四个面孔。

    lesson content
              

    A rectangular pyramid has a rectangle-shaped base and a square-based pyramid has a square-shaped base.  They both have four triangular faces, five faces in all. 
    ::矩形金字塔有矩形形基,以方形金字塔有方形基。两个金字塔都有四张三角面,五张面。

                            

              Rectangular Pyramid                             Square Pyramid
    ::矩形金字塔广场金字塔

    A  prism is a solid figure that has two congruent parallel faces and any number of sides. In other words, it can have any number of faces, but at least two of them must be parallel. The shape of the two parallel faces can be a triangle , square, rectangle , pentagon , hexagon , or any other kind of polygon . Prisms are named by the shape of their bases. Here are three examples of different prisms:
    ::棱晶是一个坚实的数字, 具有两个相似的平行面和任何多个侧面。 换句话说, 它可以拥有任何多个面, 但其中至少有两个面必须平行。 两个平行面的形状可以是三角形、 方形、 矩形、 五角形、 六角形或其他任何类型的多边形。 棱晶按其底部的形状命名。 以下三个不同棱镜的例子 :

    lesson content

    is a prism where all the faces are square. cube A
    ::是一个棱镜,所有面孔都是正方形。 立方体A

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Arthur and his gift reorganization.
    ::早些时候,你得到一个问题 关于亚瑟和他的礼物重组。

    Arthur needs to figure out the characteristics of two gifts. He also wants to characterize the big round helium balloons.
    ::亚瑟需要弄清楚两个礼物的特性

    Arthur considers the first present, a large blue one.
    ::亚瑟考虑第一件礼物 一件蓝色的大礼物

    First, it has 6 faces.  
    ::首先,它有6张面孔。

    Next, they are all square including the base.  
    ::接下来,他们都是平方 包括基地。

    Then, the gift has 8 vertices and 12 edges.  
    ::礼物有8个脊椎和12个边缘

    The answer is that the large blue present is a cube.
    ::答案是,大蓝色的现在是一个立方体。

    Arthur goes on to consider the smaller present.
    ::亚瑟接着考虑小礼物

    First, it has 6 faces.  
    ::首先,它有6张面孔。

    Next, all of the faces are .  
    ::接下来,所有的脸都是。

    Then, the present has 8 vertices and edges.  
    ::然后,现在有8个脊椎和边缘。

    The answer is that the gift on the left side of the table with the dark blue bow is a rectangular prism .
    ::答案是 桌子左侧的礼物 与深蓝的弓 是长方形棱柱。

    Finally, Arthur considers the balloons.
    ::最后,亚瑟考虑气球。

    First, they do not have faces.  
    ::首先,他们没有面孔。

    Next, they do not have edges or vertices.
    ::其次,它们没有边缘或脊椎。

    Then, they are completely round.  
    ::然后,它们就完全圆了。

    The answer is that the balloons are spheres.
    ::答案是气球是球体

    Example 2
    ::例2

    Identify the figure below. Be as specific as you can.
    ::标明下图,尽可能具体。

    First, the figure has 7 faces.  Five of the faces are rectangles; 2 of the faces are pentagons which are parallel and congruent. 
    ::首先,数字有7张面孔。5张面孔是矩形;2张面孔是平行和一致的五边形。

    Next, the base is a pentagon.
    ::下一个是五角形基地

    Then, there are 15 edges and 10 vertices.
    ::然后,有15个边缘和10个顶峰。

    The answer is the solid figure is a pentagonal prism.
    ::答案是,坚固的数字是五角形棱镜。

    Example 3
    ::例3

    Identify the figure.
    ::确定数字。

    lesson content

    First, the figure has 4 faces, all triangular in shape including the base.
    ::首先,这个数字有4张面孔,所有三角形的形状,包括底座。

    Next, there are 6 edges and 4 vertices.
    ::接下来,有6个边缘和4个顶峰。

    Then, 3 of the triangles form a vertex at the top. 
    ::然后,三角形中的3个形成顶部的顶部顶部。

    The answer is the solid figure is a triangular pyramid.
    ::答案是,坚固的数字是三角金字塔。

    Example 4
    ::例4

    Identify the figure.
    ::确定数字。

    lesson content

    First, the figure has 1 face.  
    ::首先,数字有一个面孔。

    Next, the face is in the shape of a circle.
    ::接下来,脸部是圆形的形状。

    Then, it does not have any edges or vertices.
    ::那么,它就没有任何边缘或脊椎。

    The answer is the solid figure is a cone.
    ::答案是,坚固的数字是锥形。

    Example 5
    ::例5

    Identify the figure.
    ::确定数字。

    First, the figure has 6 faces.
    ::首先,这个数字有6张面孔。

    Next, all of the faces are square including the base.
    ::接下来,所有的面孔都是平的,包括基地。

    Then, there are 8 vertices and 12 edges.
    ::然后,有8个脊椎和12个边缘。

    The answer is the solid figure is a cube.
    ::答案是,固态图是一个立方体。

    Example 6
    ::例6

    Identify the figure.
    ::确定数字。

    First, this figure does not have any faces.
    ::首先,这一数字没有任何面孔。

    Next, this figure does not have any edges or vertices.
    ::接下来,这个数字没有边缘或顶点。

    Then, this figure is completely round.
    ::那么,这个数字是完全圆的。

    The answer is the solid figure is a sphere.
    ::答案是,坚固的数字是一个球体。

    Review
    ::回顾

    Identify each figure. Be as specific as possible.
    ::确定每个数字,尽可能具体。

    1. lesson content
    2. lesson content
    3. lesson content
    4. lesson content
    5. lesson content
    6. lesson content
    7. lesson content
    8. lesson content
    9. lesson content
    10. lesson content

    Look at each picture and determine whether each is a prism, pyramid, cylinder, cone or sphere.
    ::看看每张图片,确定每个图片是棱镜、金字塔、圆柱、锥形还是球体。

    1. lesson content
       
    2. lesson content

    Review (Answers)
    ::回顾(答复)

    Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
    ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

    Resources
    ::资源