1.3视觉模式

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 视觉模式

  Collapse Expand

  视觉模式

  

  [Figure 1]

  播放段落

  Whitney is on a school trip to Italy. The fifth day there her group visits Venice where she gets to see the Doge's Palace. She notices a visual pattern in the architecture and snapped the photo above. How could Whitney describe this visual pattern? What type of visual pattern is it?
  ::惠特尼正在前往意大利的学校旅行。 第五天,她的团体前往威尼斯,在那里她可以看到Doge的宫殿。她注意到建筑中的视觉图案,并拍下了上面的照片。惠特尼如何描述这种视觉图案?这是什么样的视觉图案?

  播放段落

  In this concept, you will learn to recognize, describe, and extend visual patterns.
  ::在此概念中,您将学会识别、描述和扩展视觉模式。

  播放段落

  Visual Patterns
  ::视觉模式

  播放段落

  A  visual pattern  is a sequence of pictures or geometric objects that have been created based on some rule. There are two categories of visual patterns that you will learn about here.
  ::视觉模式是指根据某种规则创建的图片或几何天体序列。这里将学习两类视觉模式。

  播放段落
  1. Some visual patterns are made up of a sequence of pictures or geometric objects that repeat over and over. These types of patterns are called  repeating patterns . The sequence of pictures that repeat is called the  pattern unit .
     ::一些视觉图案由一系列连续重复的图片或几何物体组成。这些图案称为重复图案。重复图案的顺序称为图案单位。
  播放段落
  2. Some visual patterns are based on a picture or geometric object that keeps increasing or decreasing in size in a specific way. These types of patterns have a  pattern rule  that help to describe how the picture or object is growing or shrinking.
     ::某些视觉图案以图象或几何物体为基础,该图象或几何物体以某种特定方式不断增减。这些图案类型有一个模式规则,有助于描述图象或物体是如何成长或缩小的。

  播放段落

  Here is an example of a visual pattern that is a repeating pattern.
  ::这里的例子是一个重复模式的视觉模式。

  播放段落

  Find the pattern unit for the pattern below.
  ::为下面的图案查找模式单位。

  

  [Figure 2]

  播放段落

  First, notice that this visual pattern is made up of circles, squares, and triangles.
  ::首先,请注意这个视觉图案是由圆圈、方形和三角形组成的。

  播放段落

  Next, look carefully to see how the shapes have been placed. After each  circle  is a  square , after each square is two triangles, and after each pair of triangles is another circle. This is a repeating pattern because the same  set  of four pictures repeats over and over.
  ::下一步, 请仔细查看形状是如何放置的 。 每个圆之后是一个正方形, 每个正方形之后是两个三角形, 每个三角形之后是另一个圆。 这是一个重复模式, 因为相同的四张图象会反复重复 。

  播放段落

  The pattern unit for this visual pattern is the set of pictures that repeats.
  ::此视觉图案的图案单位是重复的图片集。

  播放段落

  The answer is that the pattern unit is "circle, square,  triangle , triangle":
  ::答案是图案单位是“圆圈、方形、三角形、三角形”

  

  [Figure 3]

  播放段落

  Once you understand the pattern and know the pattern unit, you can extend the pattern. The next picture in our sequence of pictures would be a triangle.
  ::一旦您了解图案图案和图案单位, 您可以扩展图案。 我们相片序列中的下一个图案将是一个三角形 。

  播放段落

  Here is an example of an increasing visual pattern.
  ::以下是视觉图案不断增长的例子。

  播放段落

  Find a pattern rule to describe the pattern below. What will the next step in the pattern look like?
  ::查找一个模式规则来描述下面的模式。 模式的下一步将是什么样子 ?

  

  [Figure 4]

  播放段落

  As you can see, this pattern is different from a repeating pattern because the geometric objects keep getting bigger and bigger. There is not a pattern unit that repeats, but you can find a pattern rule to describe what is happening.
  ::正如你所看到的,这个模式与重复模式不同, 因为几何天体越来越大。 没有一个模式单位重复, 但是您可以找到一个模式规则来描述正在发生的事情 。

  播放段落

  To find the pattern rule, look to see how the steps in the pattern are related. Each new big triangle is made up of more and more smaller triangles. In fact, each new big triangle is made up of the previous big triangle plus an additional row of small triangles.
  ::要找到模式规则, 请查看图案中的步骤是如何关联的 。 每个新的大三角由越来越多的小三角组成 。 事实上, 每个新的大三角由前一个大三角组成, 再加上一列小三角。

  播放段落
  • The first step in the pattern has just one row of 1 triangle.
    ::该图案的第一步只有一行一三角形。
  播放段落
  • The second step in the pattern has two rows of 1 triangle, then 3 triangles.
    ::模式的第二步是两行 1 三角形,然后是 3 三角形。
  播放段落
  • The third step in the pattern has three rows of 1 triangle, then 3 triangles, then 5 triangles.
    ::模式的第三步有三行 1三角形, 然后3三角形, 然后5三角形。

  播放段落

  You can see that the number of rows of triangles corresponds to the step in the pattern. Each time a new row is added, it has 2 more triangles than the row above it.
  ::您可以看到三角形的行数与图案的行数对应。每当添加新行时,其三角形比上方的行多两个。

  播放段落

  The answer for the pattern rule is: to get the next step in the pattern, take the previous step and add another row of small triangles to the bottom with 2 more triangles than the row above it.
  ::模式规则的答案是: 要获得图案的下一步, 采取前一步, 然后在底部再增加一列小三角形, 其三角形比上方的列多两个 。

  播放段落

  Now that you have the pattern rule, you can extend the pattern.
  ::现在你有了模式规则, 你可以扩展模式。

  播放段落

  You'd expect the next step in the pattern to look like the third step in the pattern except with an additional row of triangles.
  ::你会期望图案的下一步 看起来像图案的第三步 除了另外一列三角形之外

  播放段落

  The answer is that the fourth step in the pattern will have four rows of 1 triangle, then 3 triangles, then 5 triangles, then 7 triangles:
  ::答案是,图案的第四步将有一个三角形的4行,然后是3个三角形,然后是5个三角形,然后是7个三角形:

  

  [Figure 5]

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Whitney and her school trip to Italy.
  ::早些时候,你得到一个问题 惠特尼和她去意大利的学校旅行。

  播放段落

  She got to see the Doge's Palace in Venice where she noticed an interesting visual pattern in the architecture.
  ::她看到威尼斯的Doge宫 在那里她注意到一个有趣的视觉图案 在建筑中。

  播放段落

  First, notice that this is a repeating pattern. Objects are being repeated as opposed to increasing/decreasing in size.
  ::首先, 请注意这是一个重复的图案。 对象会重复, 而不是增加/ 减少大小 。

  播放段落

  As this is a repeating pattern, next try to describe the pattern unit.
  ::由于这是一个重复模式, 下次尝试描述模式单位 。

  播放段落

  The same column with railing is being repeated over and over. This is the pattern unit.
  ::同一列有栏杆的栏杆反复重复重复。 这是图案单位 。

  播放段落

  The answer is that this is a repeating pattern with a pattern unit that is a column/railing pair.
  ::答案是,这是一个重复模式,有一个图案单位,即一列/一列/两列。

  播放段落

  Example 2
  ::例2

  播放段落

  What will the next step in the pattern below look like?
  ::下面模式的下一步将是什么样子?

  

  [Figure 6]

  播放段落

  First, notice that this is a decreasing visual pattern.
  ::首先,请注意,这是一个不断下降的视觉模式。

  播放段落

  To find the pattern rule, look to see how the steps in the pattern are related. Each new  rectangle  is made up of fewer and fewer squares. In fact, each new rectangle is made up of half as many squares as the previous rectangle.
  ::要找到模式规则, 请看看图案中的步骤是如何关联的。 每个新的矩形由越来越少的方形组成。 事实上, 每一个新的矩形由与前一个矩形相同的半个方形组成 。

  播放段落
  • The first step in the pattern has 16 squares.
    ::模式中的第一步有16平方。
  播放段落
  • The second step in the pattern has 8 squares.
    ::模式的第二步是8平方。
  播放段落
  • The third step in the pattern has 4 squares.
    ::模式的第三步有4平方。

  播放段落

  You can see that if you take the number of squares in one step of the pattern and divide by 2, you will get the number of squares in the next step of the pattern.
  ::您可以看到,如果在图案的一步中将方形数乘以1,然后除以 2,那么在图案的下一个步骤中将获得方形数。

  播放段落

  The answer is that the pattern rule is to get the number of squares in the next step in the pattern, take the number of squares in the previous step and divide by 2.
  ::答案是,模式规则是,在模式的下一步获得方形数,在前一步取得方形数,再除以2。

  播放段落

  Now that you have the pattern rule, you can extend the pattern.
  ::现在你有了模式规则, 你可以扩展模式。

  播放段落

  You'd expect the next step in the pattern to have half as many squares as the third step. The third step has 4 squares, so the fourth step will have two squares.
  ::第三步有4平方,所以第四步有2平方。

  播放段落

  The answer is that the next step in the pattern will look like:
  ::答案是,这个模式的下一步将看起来像:

  

  [Figure 7]

  播放段落

  Example 3
  ::例3

  播放段落

  Describe the following pattern. What is its pattern unit or pattern rule?
  ::描述以下模式。其模式单位或模式规则是什么?

  

  [Figure 8]

  播放段落

  First notice that this is a repeating pattern. Images are being repeated as opposed to increasing/decreasing in size.
  ::第一个通知是此为重复模式。 图像正在重复, 而不是增加/ 减少大小 。

  播放段落

  Next, look carefully to see how the images have been placed. After each smiley  face  with the mouth on the bottom is a smiley face with the mouth on the left. The same set of two pictures repeats over and over.
  ::接下来, 请仔细看图像是如何放置的 。 在每张微笑的脸和底部的嘴是一张微笑的脸和左边的嘴。 同样的两张图片会反复重复 。

  播放段落

  The answer is that this is a repeating pattern. The pattern unit is:
  ::答案是这是一个重复模式。 模式单位是:

  

  [Figure 9]

  播放段落

  Example 4
  ::例4

  播放段落

  Describe the following pattern. What is its pattern unit or pattern rule?
  ::描述以下模式。其模式单位或模式规则是什么?

  

  [Figure 10]

  播放段落

  First notice that this is a repeating pattern. Images are being repeated as opposed to increasing/decreasing in size.
  ::第一个通知是此为重复模式。 图像正在重复, 而不是增加/ 减少大小 。

  播放段落

  Next, look carefully to see how the images have been placed. After each set of lines is an arrow. The same set of two pictures repeats over and over.
  ::下一步, 仔细看一看图像是如何放置的 。 在每组线之后, 每组线都是箭头。 相同的两组图片会反复重复 。

  播放段落

  The answer is that this is a repeating pattern. The pattern unit is:
  ::答案是这是一个重复模式。 模式单位是:

  

  [Figure 11]

  播放段落

  Example 5
  ::例5

  播放段落

  Continue the described pattern with the next two shapes.
  ::继续下两个形状的描述模式 。

  播放段落

  Triangle, star, triangle, star, square, square, triangle, star, triangle
  ::三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角 三角

  播放段落

  First notice that this is a repeating pattern. The images haven't been displayed, but they have been described. The images are being repeated as opposed to increasing/decreasing in size.
  ::首先注意此为重复模式。 图像尚未显示, 但已经描述过 。 图像正在重复, 而不是增加/ 缩小大小 。

  播放段落

  Next, look carefully to see how the shapes have been ordered. After "triangle, star, triangle, star" is "square, square". After "square, square" the "triangle, star, ..." sequence seems to repeat. It appears that the same set of six shapes will repeat over and over.
  ::接下来, 仔细看这些形状是如何排列的 。 在“ 三角形, 恒星, 三角形, 恒星” 之后是“ 方形, 方形 ” 。 在“ 方形, 方形 ” 之后是“ 方形, 方形 ” , “ 三角形, 恒星... ” 序列似乎重复。 同样的六种形状似乎会反复重复 。

  播放段落

  The pattern unit is "triangle, star, triangle, star, square, square".
  ::模式单位是"三角 恒星 三角 恒星 方形 方形"

  播放段落

  Now that you have the pattern unit, you can extend the pattern. After the "triangle, star, triangle" at the end of the pattern will be another star, then two squares, and then back to the beginning of the pattern unit with "triangle, star, triangle, star, square, square...".
  ::现在有了图案单位, 您可以扩展图案。 在图案结尾的“ 三角 、 恒星、 三角 ” 之后, 将会是另一颗恒星, 然后是两个方形, 然后回到图案单位的开头, 然后是“ 三角 、 恒星、 三角 、 恒星、 方形、 方形 ” 。

  播放段落

  The answer is that the next two shapes will be "star, square".
  ::答案是,接下来的两种形状 将是"明星,方形"

  播放段落

  Review
  ::回顾

  播放段落

  Write a rule for each number pattern.
  ::为每个数字模式写一个规则。

  1. $\begin{array}{r}4,7,13,25\end{array}$  
  2. $\begin{array}{r}216,196,176,156\end{array}$  
  3. $\begin{array}{r}1,7,19,43\end{array}$  
  4. $\begin{array}{r}10000,1000,100,10\end{array}$  

  播放段落

  Write the next number in each pattern.
  ::在每个模式中写下一个数字 。

  5. $\begin{array}{r}4,7,13,25,\underset{\_}{}\end{array}$  
  6. $\begin{array}{r}216,196,176,156,\underset{\_}{}\end{array}$  
  7. $\begin{array}{r}1,7,19,43,\underset{\_}{}\end{array}$  
  8. $\begin{array}{r}10000,1000,100,10,\underset{\_}{}\end{array}$  

  播放段落

  Write down the next image in each pattern based on the description.
  ::根据描述在每一个图案中写下下一个图像 。

  播放段落
  9. A hexagon, a pentagon, a square, ____
     ::六边形,五边形,方形
  播放段落
  10. Five dots, ten dots, fifteen dots, ____
      ::五点,十点,十五点
  播放段落
  11. Fifteen dots, fourteen dots, twelve dots, ____
      ::15点,14点,12点,___
  播放段落
  12. Two triangles, four triangles, three triangles, six triangles, five triangles, ____
      ::两个三角 四个三角 三个三角 六个三角 五个三角
  播放段落
  13. An octagon, a hexagon, an octagon, a pentagon, an octagon, ____
      ::八边形、六边形、八边形、五边形、八边形、___
  播放段落
  14. One square, 1.5 squares, 2 squares, 2.5 squares, ____
      ::1平方、1.5平方、2平方、2.5平方、____
  播放段落
  15. Eighteen circles, nine circles, four and a half circles ____
      ::十八圈,九圈,四圈半圈