3D SHAPES

Material for learners

3D SHAPES There are many types of three-dimensional shapes. You've surely seen spheres and cubes before. In this lesson, you'll learn about POLYHEDRA — three-dimensional shapes whose faces are POLYGONS and you'll also learn about two special types of polyhedra: PRISMS AND PYRAMIDS. POLYHEDRA These shapes are all EXAMPLES OF POLYHEDRA. - A die is in the shape of a CUBE. The faces of a cube are squares.

- A box of cookies is in the shape of a RECTANGULAR PRISM. The faces of a rectangular prism are rectangles.

- A soccer ball is in the shape of a TRUNCATED ICOSAHEDRON. The faces of a truncated icosahedron are pentagons and hexagons.

A three-dimensional shape whose faces are polygons is known as a POLYHEDRON. This term comes from the Greek words poly, which means "many," and hedron, which means "face." So, quite literally, a polyhedron is a three-dimensional object with many faces. The other parts of a polyhedron are its EDGES, the line segments along which two faces intersect, and its VERTICES, the points at which three or more faces meet.

TYPES OF 3D SHAPES

ACTIVITIES:

1.- Match the name of the shapes with the pictures and objects. Draw lines

1. Cone

Hat

2. Cylinder

Ball

3. Cube

Drink can

4. Pyramid

Egyptian Pyramids

5. Sphere

Dice

POLYHEDRA (all surfaces are

flat)

PRISM

PYRAMID

PLATONIC

SOLIDS (there are only five of them)

NON POLYHEDRA (SOLIDS OF

REVOLUTION)

(at least one surface is not

flat)

CILINDER

CONE

SPHERE

2.- Make statements matching the words from each column in the next table:

A cone

is a

Polyhedron

solid, it means,

there is at least one surface

which is not flat A prism

A sphere

Non-polyhedron

all its surfaces are flat

A cylinder

A pyramid

1) A __________________ is a ___________________________ solid, it means, __________ __________________________________________________________________________

2) A __________________ _____ ___________________________ solid, it means, ________ __________________________________________________________________________

3) A __________________ _____ ___________________________ solid, it means, ________ __________________________________________________________________________

4) A __________________ _____ ___________________________ solid, it means, ________ __________________________________________________________________________

5) A __________________ _____ ___________________________ solid, it means, ________

__________________________________________________________________________

POLYHEDRA

3.- Complete The following sentences with this words:

EDGE

LATERAL FACE

POLYGONS

BASE

VERTEX

a) A POLYHEDRON is a three dimensional figure whose faces are…………………………….

b) The four ELEMENTS OF A POLYHEDRON are:

…………………………. …………………………. …………………………. ………………………….

c) Filling the missing data (elements of a polyhedron):

EXPLORE PRISMS

4.- Fill in the following table with the missing data. Use the following words:

PRISM - SQUARE - RECTANGLE - TRIANGLE - PENTAGON - HEXAGON – OCTAGON

RECTANGULAR – CUBE - TRIANGULAR- PENTAGONAL – HEXAGONAL - OCTAGONAL

NAME NUMBER OF FACES

TYPE OF FACES

NUMBER OF

VERTICES

NUMBER OF

EDGES

SHAPE NET

5.- Fill in the empty gaps with the missing words or numbers:

a) The net of a TRIANGULAR PRISM consists of two ................. and three .................. Triangles are the .................. of the prism and rectangles are the ..........................

b) The net of a RECTANGULAR PRISM consists of six ................... Both the .............. and the ........................... of this shape are ...............................

c) The net of a CUBE consist of six....................................... Both the ........................and the.........................of this sape are...............................................

d) The net of a PENTAGONAL PRISM consists of two ........................and five ........................ Pentagons are the ....................... of the prism and ......................... are the lateral faces.

e) The net of an OCTAGONAL PRISM consists of two ............................ and eight .................................... Octagons are ......................... of the prism and rectangles are the ..............................................

6.- Look at the prisms above and use the following substitution table to build one sentence of each prism

that explains the characteristics of each one of them.

The net of a

RECTANGULAR HEXAGONAL HEPTAGONAL OCTAGONAL TRIANGULAR PENTAGONAL CUBE

prism consist of

TWO SIX

SQUARES RECTANGLES

and THREE FOUR FIVE SIX SEVEN EIGHT

PENTAGONS SQUARES HEXAGONS HEPTAGONS RECTANGLES OCTAGONS TRIANGLES

7.- Draw a rectangular prism and a triangular prism. a)How many vertices and edges have each one? b) What kind of polygons form the base and faces in each of them? c) What are the differences and similarities between both of them? 8.- What are the differences between a prism and a cube?

9.- Categorize these prisms depending on the polygon that form the base

10.- Draw the net of a triangular prism.

11.- Draw a rectangular prism and a triangular prism.

How many vertices and edges have each one?

12.- Calculate the name of vertices, edges and faces of a prism which base is a regular hexagon.

13.- Calculate the total area of these prisms:

14.- How much plastic is needed to build this garbage?

15.- (GROUPS) With the information provided by your classmate, calculate the area of the following shapes:

Name Height= Side of the base= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Apothem= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Apothem= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Lateral Area= Base Area= Total area=

16.- Name some prisms in everyday life and describe them.

EXPLORE PYRAMIDS

17.- Fill in the following table with the missing data. Use the following words:

PYRAMID - SQUARE - RECTANGLE - TRIANGLE - PENTAGON - HEXAGON – OCTAGON

RECTANGULAR – TRIANGULAR- PENTAGONAL - HEXAGONAL OCTAGONAL

NAME NUMBER OF FACES

TYPE OF FACE NUMBER OF

VERTICES

NUMBER OF EDGES

SHAPE PLANE DEVELOPTMENT

18.- Fill in the empty gaps with the missing words or numbers:

a) The net of a triangular pyramid consists of four ................................................................

The base of the pyramid is a .................., and the lateral faces are also ...........................

b) The net of a rectangular pyramid consists of one ...................... and four ........................

The rectangle is the .............. of the pyramid, and the triangles are the ...........................

c) The net of a pentagonal pyramid consists of one ......................... and five ......................

The pentagon is the ................... of the pyramid, and the triangles are the .....................

d) The net of a hexagonal pyramid consists of one ...................... and six ............................

The hexagon is the .................. of the pyramid, and the triangles are the ........................

19.- Draw a regular pentagonal pyramid and an irregular triangular pyramid

Indicate the number of edges and vertices of each one of them.

20.- Draw the net of a triangular prism and the net of a quadrangular pyramid

21.- Draw the development of a regular quadrangular pyramid with base edge 4 cm and height 8 cm. Calculate the lateral and total area.

22.- Calculate the total area of these regular pyramids.

23.- (GROUPS) With the information provided by your classmate, calculate the area of the following

shapes

Name Height= Side of the base= Base Height= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Apothem= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Apothem= Lateral Area= Base Area= Total area=

Name Height= Side of the base= Apothem= Lateral Area= Base Area= Total area=

24.- Name some pyramids in everyday life and describe them.

25.- Look at this picture (The Big Ben, in London), and answer:

The Big Ben, London

A

B

C

a) Complete the sentences using the words below:

Square pyramid Square prism Cube

The figure A is a __________________________________________.

The figure B is a __________________________________________.

The figure C is a __________________________________________.

b) Take notes to explain to your classmates the differences and similarities among the three different

3D shapes you can see on it.

(In pairs)

Notes:

Differences: _________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

Similarities: __________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

26.- Evaluate the advantages and disadvantages of the following constructions. Try to justify it including

historical, cultural and climatic reasons.

Some questions to think:

On a house, why might a pyramid-shaped roof be better than a flat roof? Why are there houses with flat roofs? Do you think it is convenient in countries that rain a lot ?. And in countries that do not rain and sun? Evaluate advantages and disadvantages. Are there historical and / or cultural reasons that influenced the construction of pyramids in Egypt and castles with a prism shape in Spain? Research the internet. What shape do you think is the best? VOCABULARY: Roof – rain- sun –run off- snow – weather – cheaper – expensive – easy – difficult

a) SWEDEN b) EGYPT

b) PERU d) MEDITERRANEA HOUSE

e) DENMARK f) ARABIC CASTLE (LLEIDA)

ASSESSMENT

Teacher Name: Remei Gil Student Name: ________________________________________

CATEGORY 4 3 2 1 TOTAL

Distinguish between polyhedra and non-polyhedra

Thorough and complete

Substantially complete

Partially complete Serious misconceptions

Know similarities and differences between different geometric figures

Thorough and complete

Substantially complete

Partially complete Serious misconceptions

Draw a geometric figure in 3D

Thorough complete and accurate

Substantially complete and accurate

Partially complete and accurate

No accurate and unclear

Construct with cardboard a 3D shape

Thorough complete and accurate

Substantially complete and accurate

Partially complete and accurate

No accurate and unclear

Calculate total area of a 3D shape

All calculations are shown and the resultats are correct

Some calculations are shown and the resultats are correct

Some calculations are shown and the resultats are with minor inaccuracies

No calculations are shown or results are inaccurate and with numerous errors

Calculate the volume of a 3D shape

All calculations are shown and results are correct

Some calculations are shown and results are correct

Some calculations are shown and results are with minor inaccuracies

No calculations are shown or results are inaccurate and with numerous errors

Explain the shapes that form a building, monument, etc. and compare with others

Thorough, complete and accurate

Substantially complete

Partially complete Serious misconceptions

Solve problems of areas and volumes of real life

All calculations and drawings are shown and results are correct

Some calculations and drawings are shown and results are correct

Some calculations and drawings are shown or results are with minor inaccuracies

No calculations and drawings are shown or results are inaccurate and with numerous errors

FINAL SCORE