第七单元

Unit seven

Packaging box - cuboid and cube

(包装盒——长方体和正方体)

Lesson one

1. What are the features of a cuboid?

长方体有哪些特征？

2. We do this with the aid of tools.

我们借助学具来研究。

3. The line where two faces intersect is called an edge, and the point where three edges intersect is called a vertex.

两个面相交的线叫作棱，三条棱相交的点叫作顶点。

4. Tell me, what did you find?

说一说，你有什么发现？

5. Discovery: A cuboid has eight vertices.

发现：长方体有8个顶点。

6. A cuboid has six faces.

长方体有6个面。

7. A cuboid has 12 edges, which can be divided into 3 groups according to their length.

长方体有12条棱，按长度可以分成3组，相对的4条棱……

8. When a cuboid is viewed from one direction, a maximum of three faces can be seen simultaneously.

从一个方向观察一个长方体，最多能同时看到3个面。

9. The length of three edges intersecting a vertex is called the length, width and height of a cuboid respectively.

相交于一个顶点的三条棱的长度，分别叫作长方体的长、宽、高。

10. What are the features of a cube?

正方体有哪些特征？

11. We do this with the aid of tools.

我们借助学具来研究。

12. A cube has six faces. They are identical squares.

正方体有6个面，它们是完全相同的正方形。

13. A cube has 8 vertices and 12 edges, each of which has the same length.

正方体有8个顶点、12条棱，每条棱的长度都相等。

14. What are the connections and differences between cuboids and cuboids?

正方体与长方体有什么联系与区别？

15. A square is a special rectangle. Is a cube a special cuboid?

Let's tidy it up.

正方形是特殊的长方形，正方体是不是特殊的长方体呢？

16. Let's tidy it up.

我们整理一下吧。

17. A cube is a special kind of cube.

The relationship between cuboids and cuboids can be represented by the figure on the right.

正方体是特殊的长方体。可以用右图表示正方体和长方体的关系。

Lesson two

1. At least how many square centimeters of cardboard is required to make such a computer packing box?

制作这样一个电脑包装箱至少需要多少平方厘米纸板？

2. How many square centimeters of cardboard do you need?

求需要多少平方厘米的纸板就是求什么？

3. Let's study this with the aid of an expansion of a cuboid surface.

我们借助长方体表面的展开图来研究吧。

4. Can you find the other 3 faces in the expansion?

你能在展开图上找到其他的3个面吗？

5. Which surfaces have the same area?

哪些面的面积相等？

6. Find the areas of the opposite sides and add them together.

分别求出相对面的面积，再相加。

7. Add front and back.

前、后面相加。

8. Add left and right.

左、右面相加。

9. Add the top and the bottom.

上、下面相加。

10. Find the total area.

求出总面积。

11. What else can we do?

还可以用什么方法呢？

12. Find the sum of the areas of the front, right and top surfaces, then multiply by 2.

先求前面、右面、上面3个面的面积之和，再乘2。

13. You try to solve the problem!

你来试着解决问题吧！

14. How many square centimeters of cardboard do you need to make a cosmetic box at least?

做一个化妆品盒子至少需要多少平方厘米纸板？

15. For what? It's really just what?

求什么？实际就是求什么？

16. You try to solve the problem!

你来试着解决问题吧！

17. The total area of six faces of a cuboid or cube is called its surface area.

长方体或正方体6个面的总面积，叫作它的表面积。

Lesson three

1. What is volume?

什么是体积？

2. Let's do an experiment.

我们做个试验吧。

3. What did you find when you put the stone into the water?

将石块放入水中，你发现什么了？

4. Put the block into the empty cup. What do you find?

将木块放入空杯中，你发现什么了？

5. The amount of space a body takes up is called the volume of the body.

物体所占空间的大小叫作物体的体积。

6. Who has the bigger volume, the cuboid or the cube?

下面的长方体和正方体，谁的体积大？

7. I know that the area of a rectangle or square can be measured by a small square.

我知道用小正方形能计量出长方形、正方形的面积。

8. Conjecture: volume can be measured with small cubes.

猜想：可以用小正方体计量体积。

9. Let's have a try!

咱们来试一试！

10. The unit of area is square centimeter, square decimeter...

What are the units of volume?

面积单位有平方厘米、平方分米……体积单位有哪些呢？

11. Volume is measured in units of volume.

计量体积要用体积单位。

12. Commonly used units of volume are cubic centimeter, cubic decimeter, and cubic meter. What letters are used?

常用的体积单位有立方厘米、立方分米和立方米，用什么字母表示？

13. A cube with an edge of 1 cm and a volume of 1 cubic cm.

Can you give me some examples?

棱长为1厘米的正方体，体积是1立方厘米。你能举例吗？

14. A cube with an edge length of 1 decimeter has a volume of 1 decimeter.

Can you give me some examples?

棱长为1分米的正方体，体积是一立方分米。你能举例吗？

15. A cube with an edge length of 1 meter has a volume of 1 cubic meter.

Can you give me some examples?

棱长为1米的正方体，体积是1立方米。你能举例吗？

16. Think about it. Use small cubes with edges of 1 cm to form the following cuboids and cubes.

想一想，用棱长1厘米的小正方体摆成下面的长方体和正方体。

17. What are their volumes?

它们的体积各是多少？

18. You measure the volume of an object by how many units of volume it contains.

计量一个物体的体积，要看这个物体含有多少个“体积单位”。

19. How many cubic centimeters are there in a decimeter?

1立方分米是多少立方厘米呢?

20. What do you find by swinging?

通过摆一摆，你发现了什么？

21. 1 cubic decimeter =1000 cubic centimeters

1立方分米=1000立方厘米

22. 1 cubic meter =1000 cubic decimeter

1立方米=1000立方分米

23. Which milk carton has more milk?

哪个奶盒装的牛奶多一些？

24. The volume of objects that a container can hold is called their volume.

容器所能容纳物体的体积，叫作它们的容积。

25. Volume is usually measured in units of volume.

计量容积一般用体积单位。

26. But the volume of liquids, such as water and oil, is usually measured in liters and milliliters.

但是计量液体的体积，如水、油等，常用容积单位升与毫升。

27. Liters and milliliters can be written in L and mL, respectively.

升与毫升可以分别写成L和mL。

28. 1 liter =1 decimeter cubed

1升=1立方分米

29. 1 milliliter =1 cubic centimeter

1毫升=1立方厘米

30. 1 litre =1000 milliliters

1升=1000毫升

Lesson four

1. How do you figure out the volume of a Coke box?

怎样求可乐箱的体积呢？

2. The shape of the Coke box is rectangular.

可乐箱的形状是长方形的。

3. Let's study how to find the volume of a cuboid with the aid of some tools.

我们借助学具来研究怎样求长方体的体积。

4. The size of the area is the number of units of area, and the size of the volume is the number of units of volume, right?

面积的大小就是含有“面积单位”的数量，体积的大小应该是含有“体积单位”的数量吧？

5. Give it a try!

动手试一试吧！

6. What did you find?

你发现什么了？

7. The volume of a cuboid = length × width × height

长方体的体积=长×宽×高

8. How do you figure out the volume of beer?

怎样求啤酒的体积呢？

9. The shape of the beer box is cube.

啤酒箱的形状是正方体的。

10. A cuboid is a cube when its length, width and height are equal.

长方体的长、宽、高相等时，就是正方体了。

11. The volume of a cube = length of edges × length of edges × length of edges

正方体的体积=棱长×棱长×棱长

12. The area of the base of cuboids and cubes is called their base area.

长方体和正方体底面的面积叫作它们的底面积。

13. The volume of a cuboid (or cube) = the area of the base × the height

长方体（或正方体）的体积=底面积×高

14. How many litres does the peach juice box contain? (Box wall thickness is not considered)

桃汁饮料盒能乘多少升饮料？（盒壁厚度不计）

15. What do I want? What do I want?

求什么的，也就是求什么？

16. You try to solve the problem!

你试着解决问题吧！

17. The calculation method of cuboid or cube container volume is the same as that of volume, but the length, width and height should be measured from inside the container.

长方体或正方体容器容积的计算方法与体积的计算方法相同，但要从容器里面量长、宽、高。