课程： 6.6 字母代表数字-interactive

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字母代表数字

How do you use angles in a game of pool?
::你如何在游泳池游戏中使用角度?

In the interactive below, find the different ways you can make a 90 degree angle on the pool table. Later in this lesson, you will use varying number values (including angle measures) and represent them with letters.
::在下文互动的表格中,找到在集合桌上可以做90度角度的不同方式。在此课后,您将使用不同的数字值(包括角度量度),并用字母表示这些数值。

INTERACTIVE

Angles in the Game of Pool

In the game of pool, the player hits a white cue ball with the cue stick. If the cue ball strikes another ball, that ball and the cue ball will continue to move in directions that form a right angle with one another.

::在球池游戏中, 球员会用球杆击入一个白色球。如果球杆打到另一个球, 球和球杆会继续向右移动, 从而形成一个对齐的角度。

Move the ends of the arrows to show the results of different hits.
::移动箭头的结尾以显示不同点击的结果。

The white arrow shows the path that the cue ball will follow.
::白色箭头显示提示球将跟随的路径。

Note that the white arrows show one path, but think about what might happen if the cue ball was hit at another angle.
::请注意,白箭头显示一条路径, 但想想如果球被另一角度击中, 会发生什么。

How do you make a kaleidoscope?
::你怎么做乳胶囊的?

A kaleidoscope makes beautiful symmetrical patterns by reflecting an image multiple times between angled mirrors.
::乳胶显影镜通过在角度镜面之间多次映射图像,使对称图案变得美极了。

Use the interactive below to design your own kaleidoscope. Notice how many reflected images you get as you change the angle of the mirrors.
::使用下面的交互效果来设计您自己的千兆字节镜。当您更改镜面角度时, 注意您得到多少反射图像。

INTERACTIVE

Kaleidoscope

Drag the red circle to create a design.
::拖曳红色圆以创建设计。

Drag the slider to change the angle of the mirrors.
::拖动滑块以改变镜像的角度。

Use the dropdown menu to change the color.
::使用下拉菜单更改颜色。

Press the buttons to clear the screen.
::按下按钮清除屏幕。

Discussion Questions
::讨论问题讨论问题

1. As you change the angle of the mirrors in the kaleidoscope, you get varying numbers of reflected images. When the value of something varies, you can use a variable to represent the changing number. What symbol or letter would you use to represent the changing numbers of reflections ?
::1. 当您改变千兆字节镜镜镜的角度时,会得到不同数量的反射图像。当某物的价值变化时,您可以使用变量来表示数字的变化。您将使用什么符号或字母来表示反射数字的变化?

2. One way to represent the changing numbers of image reflections is with the letter $\begin{aligned} r . \end{aligned}$ What different values of $\begin{aligned} r \end{aligned}$ can you identify in the interactive?
::2. 反映图像反射数字变化的一种方式是用字母 r。在互动中,您可以辨别 r 的不同值是什么?

3. The two angles come together to form an angle. As the angle between the mirrors gets smaller, what happens to the value of $\begin{aligned} r ? \end{aligned}$
::3. 两个角度合在一起形成一个角度:随着镜面之间的角越来越小,r的价值会怎样?

4. There are 360 degrees in a full circle. You can find the angle measure between the two mirrors by dividing 360 by $\begin{aligned} r . \end{aligned}$ Replace $\begin{aligned} r \end{aligned}$ in the expression $\begin{aligned} \frac{360}{r} \end{aligned}$ with each number to find the angle measures .
::4. 全圆为360度。通过将360除以 r. 将表达式360 r 改为 360 r ,可以找到两面镜面之间的角度量。每个数字中将 r 替换为 360 r ,以找到角度量。

$\begin{aligned} r = 2 \end{aligned}$
::r=2

$\begin{aligned} r = 4 \end{aligned}$
::rm=4

$\begin{aligned} r = 6 \end{aligned}$
::r=6

$\begin{aligned} r = 8 \end{aligned}$
::r=8

$\begin{aligned} r = 10 \end{aligned}$
::r=10

$\begin{aligned} r = 12 \end{aligned}$
::r=12 r=12

$\begin{aligned} r = 14 \end{aligned}$
::r=14

Extension
::延长

M ake your own kaleidoscope using mirrors facing each other! A ngle the mirrors to try to get 16, 18, 20, 22 or 24 images. U se the variable expression $\begin{aligned} \frac{360}{r} \end{aligned}$ to find the angle measures for the given numbers of images. You may also use a protractor to measure the angles of the mirrors and check your work. If the mirrors are small enough, you might try to tape or glue them inside of cardboard toilet paper rolls to make a portable kaleidoscope! You should tape paper over the back of one end of the roll and fill it with candy or other small objects. You c an spin your kaleidoscope and look through at the reflected objects moving inside.
::使用相对镜镜制作自己的千字眼; 将镜子切开以试图获取 16、 18、 20、 22 或 24 张图像。使用变量表达式 360 来为给定的图像数量找到角度量度。您也可以使用一个推线来测量镜的角度并检查您的工作。如果镜子足够小, 您可以尝试在纸板卫生纸卷内粘贴或粘贴它们, 以便制作一个便携式千字眼 ! 您应该将纸贴在滚动的一端的背面, 并用糖果或其他小物件填满它。您可以旋转您的千字镜, 并查看里面移动的反射对象。

Can you make line designs?
::你能做线条设计吗?

Use the interactive below to connect each dot on the inner ring of the circle to another dot with double its value. Notice that sometimes the second dot will be on the outer ring of the circle.
::使用下面的交互效果将圆圈内环上的每个点连接到一个值翻倍的点上。请注意, 有时第二点会出现在圆圈外环上。

INTERACTIVE

Line Designs

Drag the red point to the point of the number that is two times its value.
::拖曳红色点到数字的点,该点是其值的两倍。

The next red point will appear when the previous one is placed correctly.
::当前一红点被正确定位时, 下一个红点将会出现。

In the interactive below, the total number of points around the circle is either 32, 64 or 96 and is represented with the variable, $\begin{aligned} m . \end{aligned}$ The number multiplying each number can change from 2 to 7 and is represented with the variable, $\begin{aligned} n . \end{aligned}$
::在下文互动部分,圆周周围的点数总数为32、64或96,与变量 m 一起表示。每个数字的乘数从2个改为7个,与变量 n 一起表示。

INTERACTIVE

Drawing Lines with Modular Multiplication

Drag the sliders to change the number of points around the circle and the number that you multiply each of the point numbers by.
::拖动滑动键以改变圆周周围的点数和乘以每个点数的数字。

CK-12 PLIX Interactive: Neighborhood Block
::CK-12 PLIX 互动:邻居区块

In this PLIX interactive, you will use a neighborhood map to make calculations about a bike ride using a variable.

::在此 PLIX 互动中, 您将使用邻居地图使用变量计算骑自行车的乘数。

Can you decode a secret message?
::你能解码一条秘密信息吗?

Riddle: "I can fly but have no wings. I can cry but I have no eyes. Wherever I go, darkness follows me. What am I?"
::鲁德尔说:我能飞,却没有翅膀,我哭,我的眼睛却看不见。我走到哪里,黑暗就跟着我。我是什么人呢?

The answer to the riddle is in code:
::谜语的答案是代码:

A SVWYB
::A SVWYB (A SVWYB)

Use the interactive to decode the answer using the decryption key: $\begin{aligned} 3 x - 2. \end{aligned}$
::使用交互方式解码解密密密钥: 3x-2。

INTERACTIVE

Can you decode a secret message?

F ind the relationship between the letters and numbers using the diagram and decryption key.
::使用图表和解密密密钥查找字母和数字之间的关系。

Convert the letters "ASVWYB" into numbers.
::将字母“ ASVWYB” 转换为数字。

Then move the red points to manipulate the equations.
::然后移动红点来操纵方程。

Find the value of each letter by counting to its place in the alphabet. For example A = 1, D = 4, and Z = 26.
::查找每字母的值, 计算字母中的字母位置。例如 A = 1, D = 4, Z = 26 。

Multiply the number by 3 .
::乘以数字乘以 3。

Subtract 2
::减减2

If the number is greater than 26, subtract 26 from the number. Repeat if necessary.
::如果数字大于26,则从数字中减去26。如有必要,请重复。

Finally, use the coded number to identify the letter by finding its place in the alphabet.
::最后,使用编码编号来识别字母,在字母表中找到字母位置。

Practice the decoding process with the question below:
::采用以下解码程序:

CK-12 PLIX Interactive: Water Bottle Expression
::CK-12 PLIX 互动:水瓶表达式

In this PLIX Interactive you will measure water into different sized water bottles and work with two variables.
::在本次PLIX互动中,您将测量不同大小的水瓶中的水量,并使用两个变量开展工作。

Summary

To solve real world problems, write equations with an unknown value and solve for that value.
::为了解决现实世界的问题写出价值未知的方程式并解决这个价值

Use a number to represent the unknown value. Substitute values into the letter to find different values for the expression.
::使用数字来表示未知值。在字母中替换值以查找表达式的不同值。

章节大纲

常规

字母代表数字

How do you use angles in a game of pool? ::你如何在游泳池游戏中使用角度?

How do you make a kaleidoscope? ::你怎么做乳胶囊的?

Can you make line designs? ::你能做线条设计吗?

Can you decode a secret message? ::你能解码一条秘密信息吗?

How do you use angles in a game of pool?
::你如何在游泳池游戏中使用角度?

How do you make a kaleidoscope?
::你怎么做乳胶囊的?

Can you make line designs?
::你能做线条设计吗?

Can you decode a secret message?
::你能解码一条秘密信息吗?