Topicm1800d8c87fed0034_1528449000663_0Topic

Nets and models of solids

Levelm1800d8c87fed0034_1528449084556_0Level

Third

Core curriculumm1800d8c87fed0034_1528449076687_0Core curriculum

X. Plane geometry. The student:

6) calculates the volume and the surface area of a prismprismprism, pyramidpyramidpyramid, cylindercylindercylinder, coneconecone, sphere using trigonometry and theorems.

Timingm1800d8c87fed0034_1528449068082_0Timing

45 minutes

General objectivem1800d8c87fed0034_1528449523725_0General objective

Using and interpreting the representation. Using mathematical objects and manipulating them, interpreting mathematical concepts.

Specific objectivesm1800d8c87fed0034_1528449552113_0Specific objectives

1. Recognising and drawing the nets of solids.

2. Application of a net to calculating the surface area of a solidsolidsolid.

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

Learning outcomesm1800d8c87fed0034_1528450430307_0Learning outcomes

The student:

- recognises and draws nets of solids,

- applies nets to calculate the surface area of solids.

Methodsm1800d8c87fed0034_1528449534267_0Methods

1. Discussion.

2. Snowball.

Forms of workm1800d8c87fed0034_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm1800d8c87fed0034_1528450127855_0Introduction

The teacher informs the students that during this lesson they will improve their skills connected with recognising nets of solids. They will also use nets to calculate the surface area of solids.

The students recollect what net of a polyhedronpolyhedronpolyhedron is.

Procedurem1800d8c87fed0034_1528446435040_0Procedure

The student work in groups using the “snowball” technique. The students’ task is to draw all possible (11) nets of a cubecubecube.

The first group draws one of the nets on a piece of paper and passes it to another group. This group draws another net of a cubecubecube and passes it on. In this way the piece of paper goes between the groups. The last group presents the results. If the students managed to draw 11 different nets of a cubecubecube, they finish this stage of the class. If not, there is a discussion leading to discovering the missing nets and presenting arguments, which prove why some of the suggested drawings aren’t nets of a cube.

The diagram below shows possible answers. The coloured figures are nets of a cubecubecube.

[Illustration 1]

Working in groups, the students use their computers to check if they can recognise nets of given solids (prismprismprism, pyramidpyramidpyramid, cylindercylindercylinder and coneconecone).

Task
Open Geogebra applet: „Nets of solids”. Solve the suggested task. Discuss your doubts with your partner or the teacher. Repeat the task until all your answers are correct.

[Geogebra applet]

Using the nets in the applet suggest the formula for the total surface area of:
- a cube whose side is a,
- a cuboid whose sides of the base are a and b and altitude c,
- a regular quadrangular pyramid whose side of the base is a and the lateral edges are b,
- a cylinder whose base radius is r and altitude is H,
- a cone whose base radius is r and slant height is I.m1800d8c87fed0034_1527752263647_0Using the nets in the applet suggest the formula for the total surface area of:
- a cube whose side is a,
- a cuboid whose sides of the base are a and b and altitude c,
- a regular quadrangular pyramid whose side of the base is a and the lateral edges are b,
- a cylinder whose base radius is r and altitude is H,
- a cone whose base radius is r and slant height is I.

Compare your ideas with the information in the table:

[Table]

The students do the task individually, present their results and explain the doubts.

Task
Draw the net of a regular hexagonal prismprismprism. The side of the base equals 5 cm and the altitude of the prism is 4 cm. Calculate the total surface area of this prism.

Task
Draw the net of a regular tetrahedronregular tetrahedronregular tetrahedron whose edge length is 4 cm. Calculate the total surface area of this tetrahedron.

Task
The total surface area of a coneconecone is $75\pi$ cmIndeks górny 2² and the slant height is 10 cm long. Calculate the base radius of this cone.

An extra task:
Draw the net of a coneconecone whose base radius is 6 cm and the slant height is 9 cm.

Lesson summarym1800d8c87fed0034_1528450119332_0Lesson summary

The students do the consolidation tasks.

They summarize the class by formulating the conclusions to memorize.

- Nets of polyhedrons, cylinder and cone are presentations of these solids on a plane. The nest are useful for calculating the surface areas of solids.m1800d8c87fed0034_1527752256679_0- Nets of polyhedrons, cylinder and cone are presentations of these solids on a plane. The nest are useful for calculating the surface areas of solids.

Selected words and expressions used in the lesson plan

coneconecone

cubecubecube

cylindercylindercylinder

net of solidnet of solidnet of solid

polyhedronpolyhedronpolyhedron

prismprismprism

pyramidpyramidpyramid

regular tetrahedronregular tetrahedronregular tetrahedron

solidsolidsolid

surface area of solidsurface area of solidsurface area of solid