Topicm466148a0f82afea7_1528449000663_0Topic

The cuboidcuboidcuboid

Levelm466148a0f82afea7_1528449084556_0Level

Second

Core curriculumm466148a0f82afea7_1528449076687_0Core curriculum

XI. Solid geometry. The student:

1) recognizes prisms and pyramids – including right regular and regular,

2) calculates the volumes and the surface area of right regular and regular prisms and also the ones that are not right at the level of difficulty not higher than the example task: The base of the right regular prism is an isosceles triangle, whose two equal angles are 45° each, and the longest side has the length of $6\sqrt{2}$ dm. One of the sides of a rectangle, which is the face with the largest area, is 4 dm long. Calculate the volume and the total surface area of this prism.

Timingm466148a0f82afea7_1528449068082_0Timing

45 minutes

General objectivem466148a0f82afea7_1528449523725_0General objective

Using simple, well‑known mathematical objects, interpretation of mathematical concepts and operating mathematical objects.

Specific objectivesm466148a0f82afea7_1528449552113_0Specific objectives

1. Recollecting the structure elements of the cuboid.

2. Calculating the surface area and the volume of the cuboid.

3. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

Learning outcomesm466148a0f82afea7_1528450430307_0Learning outcomes

The student:

- indicates the structure elements of the cuboid,

- calculates the surface area and the volume of the cuboidcuboidcuboid.

Methodsm466148a0f82afea7_1528449534267_0Methods

1. Discussion.

2. Learning stations.

Forms of workm466148a0f82afea7_1528449514617_0Forms of work

1. Group work.

2. Whole class.

Lesson stages

Introductionm466148a0f82afea7_1528450127855_0Introduction

The teacher informs the students that during the class they will recollect information about the cuboid and the cubecubecube. They will also calculate the surface area and the volume of these solids.

Procedurem466148a0f82afea7_1528446435040_0Procedure

Task
The students work individually, using the computer. Their task is to observe the most important elements of the cuboid. Then, they draw a mind map in their notebooks, including: the vertices, the base edges, the face edges, the base diagonals, the face diagonals and the diagonals of the cuboid.

[Geogebra applet]

The students cooperate to find the properties of the cuboidcuboidcuboid and the cube.

The properties of the cuboid:

- it has 6 faces,
- all the faces are rectangles,
- it has 8 vertices,
- it has 12 edges,
- there are 3 edges from each vertex.

The properties of the cubecubecube:

- The cube is a cuboid, whose all faces have the same length.

The students recollect the formulae for the surface area and the volume of the cuboid and the cube.

The surface area of the cuboidsurface area of the cuboidsurface area of the cuboid whose edge lengths are a, b, c:

The volume of the cuboidvolume of the cuboidvolume of the cuboid whose edge lengths are a, b, c:

The surface area of the cube with edge length is a:

The volume of the cubevolume of the cubevolume of the cube with edge length a:

The surface area and the volume of the cube after cutting out the corners.

[Illustration 1]

Task
Calculate the surface area and the volume of the cube with a face length of 4 cm, if a corner whose face is 1 cm long has been cut out.m466148a0f82afea7_1527752263647_0Calculate the surface area and the volume of the cube with a face length of 4 cm, if a corner whose face is 1 cm long has been cut out.

The students work in groups to solve the tasks, using the learning stations technique.

Task - Station 1
The cuboid, whose edges are 3, 4, 5 long, is given. Draw three different nets of this cuboid.m466148a0f82afea7_1527752256679_0The cuboid, whose edges are 3, 4, 5 long, is given. Draw three different nets of this cuboid.

Task - Station 2

[Illustration 2]

Calculate the volume and the surface area of the cuboid, whose net is presented in the diagram. The edges without dimensions are respectively 2 and 4 times longer than the edge with given length.m466148a0f82afea7_1527712094602_0Calculate the volume and the surface area of the cuboid, whose net is presented in the diagram. The edges without dimensions are respectively 2 and 4 times longer than the edge with given length.

Task - Station 3
The sum of the lengths of all the edges of the cuboid equals 76 cm.

What is the altitude of this cuboid, if the square whose area is 49 cmIndeks górny 2² is the base of this cuboid?

Task - Station 4
Can you put 10 litres of water into the cuboid‑shaped aquarium, whose dimensions are 2,5 dm x 3 dm x 1,5 dm?

Task - Station 5
Calculate the surface area of the cubesurface area of the cubesurface area of the cube if the sum of all its edges equals 37,5 cm.

Task - Station 6
Calculate the sum of all the edge lengths of the cube, if its surface area is 11,76 cmIndeks górny 2²

The teacher summarizes and assesses the groups’ work, explaining any doubts.

An extra task:
A cube‑shaped box has the volume of $3\frac{3}{8}$ litra. What is the volume of the box, whose edges are three times longer? How much more paper will we use to get the bigger box glued together?

Lesson summarym466148a0f82afea7_1528450119332_0Lesson summary

The students do the additional tasks.

Finally, they summarize the class and formulate the conclusions that they need to remember.

The properties of the cuboidcuboidcuboid:

- it has 6 faces,
- all the faces are rectangles,
- it has 8 vertices,
- it has 12 edges,
- there are 3 edges from each vertex.

The properties of the cubecubecube:

- The cube is a cuboid, whose all faces have the same length.

The surface area of the cuboidsurface area of the cuboidsurface area of the cuboid whose edge lengths are a, b, c:

The volume of the cuboidvolume of the cuboidvolume of the cuboid whose edge lengths are a, b, c:

The surface area of the cubesurface area of the cubesurface area of the cube with edge length is a:

The volume of the cubevolume of the cubevolume of the cube with edge length a:

Selected words and expressions used in the lesson plan

cubecubecube

cuboidcuboidcuboid

face of the cuboidface of the cuboidface of the cuboid

net of the cuboidnet of the cuboidnet of the cuboid

surface area of the cubesurface area of the cubesurface area of the cube

surface area of the cuboidsurface area of the cuboidsurface area of the cuboid

volume of the cubevolume of the cubevolume of the cube

volume of the cuboidvolume of the cuboidvolume of the cuboid