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Recognising shapes

“Shapes and objects”

2-11

Level 1 Exercise 1

Aims - Go from volume to plane - Practice in schematisation. - Practice in describing and defining. - Beginning elementary geometric shapes.

Applications (examples)

In class: beginning or reminder of simple geometric shapes and the vocabulary used to describe them. At work: understanding instructions, indications or information given as a pictogram or diagram (safety precautions, for example). In everyday life and for leisure: understanding everything that requires the use of a diagram (pictograms, instruction manuals, assembly instructions, etc.).

Materials

A page showing simple geometric shapes and objects, some drawn in perspective, others not.

Instructions

The pupils match each object with the geometric shape that corresponds best (or each shape to the object that corresponds best). This exercise lends itself very well to the discovery of the instructions by the pupils. The teacher will make sure s/he does not influence the way they try to work out what the instructions are (some look first at the objects and then look for the shapes, others do the opposite, yet others go back and forth between the two without necessarily starting with one or the other).

Remarks When the results are being pooled, the pupils can try to describe and define each geometric shape. The teacher will encourage them to use the appropriate vocabulary to describe them (length, width, side, angle, etc.).

Variations (examples)

1. Each pupil can choose an object in the room that corresponds approximately to one of the geometric shapes on the exercise sheet and show the shape to the group, who will try to find the object in question. 2. One pupil designates an object in the room and another pupil tries to draw on the board the geometric shape or shapes which most closely corresponds to it.

Individualisation Yes.

Answers Yes.

Euro Cordiale, a not-for-profit Association creating teaching tools - European Leonardo da Vinci Programme - www.euro-cordiale.lu

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Recognising shapes

“Shapes and objects” 2-11


WORK IT OUT

Recognising shapes

“Shapes and objects” 2-11

Answers

1 2

3

4

5

1

5

4

2

3 2 3


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Recognising shapes

“The joiner’s tools”

2-12

Level 1 Exercise 2

Aims

- Going from volume to plane. - Practice in schematisation. - Compare with an aim to inclusion, superposition or rotation.


In class: any mental operation consisting in recognising shapes in order to match, compare, or superpose them. At work: improving the arrangement of the workstation for better practicality, efficiency, ergonomics, etc. In everyday life and for leisure: arranging furniture in a room, fittings in a kitchen or bathroom, etc.

Materials

A page with drawings of a joiner’s tools on one half and on the other half a storage rack for these tools with the approximate shape of each one.

Instructions

The pupils have to find the right place for each tool on the storage rack.

Remarks

The pupils can work together to find the use for each tool and try to name them.

Variation(s) (examples)

The pupils who have a workstation, in a workshop or on an assembly line in a company, can make suggestions to improve the organisation of their workstation and the arrangement of the tools or materials that they use: together they can look for criteria for improvement (efficiency, time saving, safety, reduction in the number of defects, reduction of effort, convenience, etc.). This kind of variation could be applied to the space in which a pupil does his/her homework or the way he organises his/her desk in the classroom. Similarly, it could be extended to the arrangement of the house.

Individualisation

Yes.

Answers

Yes, suggested.


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Recognising shapes

“The joiner’s tools” 2-12


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Recognising shapes

“The joiner’s tools” 2-12

Answers

7 11 6 10 3 8 9

5 2 1 4


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Recognise shapes

“Use what’s to hand”

2-13

Level 1 Exercise 3

Aims

- Compare shapes, identify their similarities and their differences in order to match them. - Compare with rotation and superposition. - Being more practical. - Getting to understand messages transmitted as codes or signals.


In class: any mental operation consisting in matching similar shapes; realising that a message is not necessarily expressed in words, but in many other ways as well. At work: correctly interpreting the different signs which mark out a company’s workshops or premises; identifying their exact meaning, recognising their role, their importance (safety, for example). In everyday life and for leisure: correctly interpreting the different signs which transmit information in public places, on the roads, etc. Identifying their exact meaning, recognising their role, their importance, etc.

Materials

A page with drawings of signs, and the same signs made with twigs or stones.

Instructions

The pupils match the two sorts of signs (drawings and shaped from stones or twigs). To match the two, the pupils will use the code that they find the most practical (numbers, arrows, coloured stickers, etc.)

Remarks

It is interesting for the pupils to wonder about the context and use of the signs made with "what’s to hand", in this case taken from nature.


1. With pencils or rubbers, for example, ("what’s to hand"), the pupils make up a sign that the rest of the group has to find (highway code, various pictograms, etc.). 2. The pupils can find different codes that are commonly used and that do not require the use of language; this can be an excellent opportunity to work on the importance of gestures in communication, for example. 3. To make it more amusing, the teacher can also refer to games, such as "Pictionary" where you have to draw a concrete object, a verb or an adjective, so that your partner can guess what the drawing has to express.


Answers Yes.


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Recognise shapes

“Use what’s to hand” 2-13


WORK IT OUT

Recognise shapes

“Use what’s to hand” 2-13

Answers


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Recognise shapes

“Objects and shapes”

2-21

Level 2 Exercise 1

Aims

- Practise identifying geometric shapes that are made up of everyday objects. - Identify different simple geometric shapes. - Find what several different drawings have in common.


In class, at work or in everyday life: understand or make by yourself a shape in diagram form; enlarge the field of vision so as not to limit yourself to the details but to have an overall view. This practice can be extended to reading, with a view to improving their skills (comprehension, speed, etc.).

Materials A page with four series of drawings and four geometric shapes.

Instructions The pupils will match a geometric shape to a series of objects all or part of which is comparable to the geometric shape.

Remarks

- When the solutions are being pooled, the pupils should describe in as much detail as possible the strategy they used; this exercise shows just how many different approaches and methods of investigation there can be. - Certain pupils will only identify the most obvious objects in each line or those that most resemble the shapes below, for example the watch in row A. It is also easy to imagine the objects from different angles than those shown in the drawings; for example the glass vase seen from below: the shape would therefore be close to the circle but for a different reason, as it is seen from a different angle. - Certain pictures show shapes that can belong to several of those shown at the bottom of the page, like the house which could belong to the square, with the front wall, or the trapezium with the roof (see extension 1).


1. The pupils can look for other shapes in the objects drawn, corresponding to the geometrical shapes 1, 2, 3 or 4 than the one suggested in the answers (unless the solutions were very varied). 2. One pupil chooses an object in the room and shows it to the group from different perspectives. The other pupils will determine each time the different geometric shapes that they sees. 3. At this stage, the teacher can probably begin to talk of the hidden side of objects, for example the dice or the weight in the pictures shown here; the pupils will then try to imagine or to represent the invisible sides. 4. The teacher can try to initiate the pupils in the idea of perspective with, for example, the stool whose legs are not the same length in the picture.


Answers Yes.


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Recognise shapes

“Objects and shapes” 2-21

A

B

C

D

1 2 3 4


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Recognise shapes

“Objects and shapes” 2-21

Answers

A 3

B 4

C 2

D 1

1 2 3 4


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Recognise shapes

“Volumes”

2-22

Level 2 Exercise 2

Aims

- Get used to representing objects and shapes in volume. - Get used to schematisation. - Recognise a geometric shape shown in volume. - Compare by using rotation.


In class: any mental operation consisting in finding shapes represented by volume with a view to matching, comparing or superimposing them (geometry, drawing and technical drawing with views in perspective and work on the non visible sides). At work: improving the layout of the workstation in order to make it more practical, more efficient or more ergonomic. In everyday life and for leisure: arranging furniture in a room, equipment in a kitchen or a bathroom, etc.

Materials A page with, in the left-hand column, the volumes of 5 geometrical shapes (cube, prism, etc.) and in the right-hand column the drawings of 5 objects in perspective.

Instructions The pupils will match volumes and objects whose shapes seem fairly similar.

Remarks

- This exercise lends itself well to the discovery of the instructions by the pupils. However, the teacher should make sure s/he does not influence the pupils’ methods of investigation while they are looking for and formulating the instructions (some look first at the objects then look for the shapes; others do the opposite; still others go back and forth constantly between the two with no preference for which comes first). - As always when using WORK IT OUT, during the pooling of solutions, the pupils give as much detail as possible when describing how they proceeded. This exercise shows just how numerous and varied the methods can be.


1. Work can be done on the hidden sides of the objects shown (how many hidden sides are there? What might they look like? Can we try to draw them? Etc.) 2. As the scale to which the objects are drawn are totally different (the pyramids and the die for example), the group can look at drawings or photos, diagrams in a magazine for example, or an encyclopaedia, the map of a region or country, road map, etc. and think of the proportions and scale. 3. The teacher can emphasise the le principle of perspective in drawing using the 3 pyramids drawn in different sizes, to give an idea of depth of field. The pupils can practise by drawing a rough outline of 3 trees on 3 different planes, from the closest to the observer to the furthest away.


Answers Yes.


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Recognise shapes

“Volumes” 2-22


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Recognise shapes

“Volumes” 2-22

Answers

1

4

2

1

3

5

4

2

5

3


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Recognise shapes

“Shapes and patterns”

2-23

Level 2 Exercise 3

Aims

- Distinguish geometric shapes – shown in isolation or interwoven – count them and name them. - Get used to enlarging the field of vision to obtain an overall view rather than a fragmented one of what is shown.


In class: initiation into the different simple geometric shapes, discovery of their different characteristics and the vocabulary linked to them ("side, angle, length, width") Possibly and by extension, discovery or rediscovery of a few measurements of these shapes (perimeter, area). At work: any operation consisting in recognising and counting similar shapes (putting away, filing, packing, labelling, layout of shelves and departments in a supermarket, etc.). Possibly and by extension, taking measurements in a building in order to put in wallpaper, carpets or floor tiles. In everyday life and for leisure: arranging furniture in a room, equipment in a kitchen or bathroom, simple DIY, putting wallpaper or carpeting, cutting material for curtains, etc.

Materials

- A page with different geometric shapes, each with a different pattern inside. - A second page with samples of the patterns as they can be seen on the first page.

Instructions

1. The pupils look at the first page and write the number of different shapes they see. 2. On the second page, the pupils work together to try to find, then to write next to each sample, the name of the shape it corresponds to.

Remarks

- The second part of the exercise supposes that the pupils (or at least some of them) have received some form of initiation in learning geometric shapes. If they have difficulty writing the names, the teacher can help them. - If the pupils do not have the necessary pre-requirements to allow them to find the names of the shapes, the group can simply do the first part of the exercise. To get the best use of the tool WORK IT OUT, the authors recommend that the teacher does not supply all the elements him/herself (like the names of the shapes, for example) if none of the pupils is able to use his own knowledge nor work out his own approach, method or strategy.


1. The group can be encouraged to approach the vocabulary used to describe geometric shapes ("side, length, width, angle", etc.), to look for the particularities of each shape and to practise describing them clearly. One pupil can, for example, describe – in more or less detail, especially for the dimensions – a shape for the group to try and reproduce. They can compare the results obtained. 2. The teacher can have the group discover or rediscover the elementary calculations for the simplest shapes (measuring the perimeter or the area) and take examples of practical applications (calculating how much paint, carpet, curtain material, etc. is needed).


Answers Yes.


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Recognise shapes

“Shapes and patterns” 2-23

(Page 1)


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Recognise shapes



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Recognise shapes


Answers

circle half circle square square triangle triangle triangle lozenge rectangle trapezium trapezium


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Recognise shapes

“Stained glass windows”

2-31

Level 3 Exercise 1

Aims

- Combine shapes to form a given set. - Find the different parts which go to make up a set using geometric shapes. - Begin inclusion. - Begin reconstruction.


In class: any mental operation consisting in recognising the different shapes that make up a set (in geometry, for example, find the different shapes that make up a complex form). At work: any task of flat assembly requiring the identification of shapes and their inclusion in a set (printed circuits, for example). In everyday life and for leisure: any domestic task or leisure activity implying the choice and arranging of shapes (laying floor tiles, doing jigsaw puzzles, etc.).

Materials

-One page with several geometric shapes, such as triangles, squares, parallelograms, like the elements of a stained glass window. -Another page on which there are drawings of sometimes complex shapes, including several shapes among those from the first page.

Instructions

The pupils will try to find which shapes from the first page can be used to reconstitute the shapes on the second page by writing the letters corresponding to their choice in the place where the shapes should be.

Remarks

-Some pupils might think of making the task easier by cutting out the shapes and trying to adapt them to the shapes on the second page like a jigsaw puzzle. The teacher can decide if this method can be used to solve the problem, or whether it should only be used as a checking procedure. -Those who wish can of course use a ruler.


1. Since the authors of this tool recommend that, as often as possible, the pupils should be encouraged to be creative, this is a good opportunity to suggest that each one imagines a form, draws it and shows the group a number of shapes that would enable them to reproduce the shape. Basically, the pupils create a similar exercise to the one here, using their own creations. Thus the new exercises could be numbered (2-34, 2-35, 2-36, etc.) and included in the tool. 2. Using photocopies of a photo of the group, each pupil could cut his copy into simple geometric shapes (squares, triangles, rectangles, etc.) and give the pieces to another pupil. The pieces will be placed face down so there is no visual aid, and each pupil will try to reconstruct the photo back to front, on a piece of picture glass, for example. By placing a piece of cardboard on the completed puzzle, the pupils can turn it over and judge their results. If there were several possibilities for reconstructing the photo, the results can be surprising and even very amusing!


Answers Yes, but only suggested, as several solutions are possible.


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Recognise shapes

“Stained glass windows” 2-31

(Page 1)

A B

C

D

E

F

G


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Recognise shapes


(Page 2)


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Recognise shapes


Answers

B

G A F C B

E G F A


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Recognise shapes

“Complements”

2-32

Level 3 Exercise 2

Aims

Associate complementary abstract forms using comparison and rotation.


In class: any mental operation consisting in identifying shapes and looking for characteristics in order to complete a representation, a diagram, a drawing or graphics (in technology, for example). At work: any mental operation consisting in identifying shapes and looking for characteristics with a view to fitting together, assembling or packaging parts (assembly lines or packaging units, especially). In everyday life and for leisure: any mental operation consisting in identifying shapes and looking for characteristics in order to put together furniture in kits or kitchen equipment (food processors with different parts, for example).

Materials

A page with: - 4 abstract shapes on the left, - other abstract shapes on the right likely to fit into the shapes on the left.

Instructions

For each of the four lines, the pupils have to find the shape from those on the right which seems to fit exactly into the shape on the left.

Remarks

-The pupils could be asked to look for one or more infallible ways of checking their answers (cutting out, checking against the light, for example). -As for all the exercises in this tool, when the solutions are being pooled, the pupils should explain their methods in as much detail as possible and show the group the signs and characteristics which led them to their solutions.


This type of exercise encourages creativity. Each pupil could think of a shape, draw it, then draw 2 or 3 other shapes, only one of which would complete the first. The exercises thus obtained could be photocopied and given to the group, who would look for the answers following the teaching method inherent to this tool. The exercises could then be included, thus enriching WORK IT OUT.


Answers Yes.


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Recognise shapes

“Complements” 2-32


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Recognise shapes

“Complements” 2-32

Answers


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Recognise shapes

“Folding and unfolding”

2-33

Level 3 Exercise 3

Aims

- Go from volume to plane. - Recognise a shape in perspective. - Reconstruct a shape in your mind. - Manipulate using stickers to copy a pattern.


In class: in geometry, studying opened-out shapes, like the right-angle parallelepiped. In handiwork, making objects out of paper or cardboard, models, etc. At work: assembling cardboard boxes for packaging, making up objects or boxes from flat, cutting out clothes from patterns, etc. In everyday life and for leisure: making decorations out of paper or cardboard, making models, cutting out clothes from patterns, etc.

Materials

One page with 5 geometric figures shown in volume form. A second page with the same figures shown in their ‘unfolded’ or opened-out form. This page can be photocopied on an A3 sheet, giving one to each pupil. A pair of scissors for each pupil. A set of stickers. Adhesive tape.

Instructions

The pupils have to find their own individual code to match each opened-out form to its corresponding geometric figure. They will check one of the figures. To do this, the teacher should have an A3 photocopy of the second sheet for each pupil. The pupils are then asked to cut out one figure of their choice, and fold it to obtain the geometric figure chosen.

Remarks

To obtain the shape in volume, the pupils can use what is available (stickers or adhesive tape) to stick the sides together. Some may think to add an extra edge while cutting out, so that the finished shape is correctly stuck together.


1. The teacher draws an opened-out shape on the board other than those already shown (e.g. a cone, a six-sided prism, etc.). The pupils reproduce the figure on a blank piece of paper, in the size they choose but keeping more or less the same proportions. They then cut out the figure and try to fold it to obtain the shape intended by the teacher. They can of course readjust the proportions by redrawing or cutting out again. The teacher can also give indications of size, to avoid too much difficulty in reproducing the proportions. 2. The teacher can draw a shape in volume (e.g. a glass, vase or jug) and ask the pupils to draw the shape as they would imagine it opened out, then to cut out the drawing and fold it to recreate the object in paper. 3. The teacher can get the group to work together, pooling all their ideas and suggestions, to make up a model of a famous monument (for example the Eiffel Tower, Big Ben, etc.).


Answers Yes.


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Recognise shapes

“Folding and unfolding” 2-33

Page 1


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Recognise shapes


Page 2


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Recognise shapes


Answers

Page 1

A B

C

D

E


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Recognise shapes


Answers

Page 2

C

E

B

A

D


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Recognising shapes

“Screws”

2-41

Level 4 Exercise 1

Aims

- Recognising shapes seen from different angles. - Comparing from different angles. - Reconstructing a shape in your mind.


In class: in geometry, studying unfolded shapes like a parallelepiped rectangle; in manual work, constructing objects from paper or cardboard, models, etc. At work: putting together cardboard boxes for packing, making objects or boxes from a “flat” support, cutting out clothes from a pattern… In everyday life and leisure: using boxes bought at the Post Office to put up yourself, making decorations out of paper, model making, cutting out clothes from patterns …

Materials

A sheet of paper with: - 6 six screws and bolts seen from above - the same 6 screws and bolts seen from the side.

Instructions

By using a code that they choose individually, the pupils will match the screws (or bolts) and the heads.

Comments

One of the main interests of this exercise is to ask the pupils, when pooling solutions, to be very precise as to the method used and to explain as clearly and in as much detail as possible the marks which helped find the match.


1. The teacher draws on the board a different “unfolded” shape from those shown in the exercise (for example a cone, or a six-pointed prism). The students reproduce the shape on a blank sheet of paper, in whatever dimension they like, but keeping more or less the same proportions. They will then cut out this shape and try to fold the paper to find the shape, in three dimensions, that the teacher was thinking of. They can of course readjust the proportions of their shape by drawing it again or cutting out more. The teacher can also give ideas of measurements to avoid too great a disproportion in reproducing the proportions. 2. The teacher can draw a shape en volume (for example a glass, a decanter, a jug) and ask them to do the drawing first as they might imagine it "unfolded" then to cut it out and fold it to recreate the object using paper. 3. The teacher can have the group pool all their ideas and suggestions, to make a much-simplified model of a well-known monument (for example Marble Arch, an obelisk, the Eiffel Tower…)

Individualisation

Yes

Answers

Yes


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Recognising shapes

“Screws” 2-41


WORK IT OUT

Recognising shapes

“Screws” 2-41

Answers

A

Z

B

A

C

B

D

C

E

E

F

D


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Recognising shapes

“Jigsaw puzzle grid”

2-42

Level 4 Exercise 2

Aims

- Recognising shapes using symbols. - Using mental rotation to recognise a shape. - Comparing. - Reconstituting. - Visual scanning without taking into account any particular criteria.


In class: increasing the field of vision to identify a document and reading when the text is not straight or in front of the reader; exercise in scanning in all directions to accelerate recognition speed, particularly useful in improving reading ability; exercise in finding a quick and efficient strategy when looking for something visually. At work: Exercise in visualising quickly and reliably, for example in making or checking printed circuit boards; exercise in searching for a rapid and efficient strategy for any post in which the visual predominates and which requires precision. In everyday life and leisure: improving the speed of visual scanning, useful in all domestic tasks, DIY, leisure activities like crosswords, embroidery, etc.

Materials

- One page with a grid in which symbols of playing cards are placed. - A second page with the same grid split up and sometimes inverted in comparison with the original.

Instructions

Les pupils will circle each shape shown on the second page on the grid on the first page after having found it. They must not take into consideration the inversions which sometimes appear in the split grid.

Comments

If some pupils find the exercise too difficult, they can do an intermediate phase consisting in showing them the second page and the answer sheet. The work will then be to find the sets shown on the answer sheet. Once they have done this exercise, the pupils can take the first page again instead of the answers, which they put to one side.


1. An exercise practising visual searching, whose oral formulation would consist of a description, by one of the pupils, of a "piece" of the grid without specifying the types of sign that it contains (for example, they will say: "the piece contains 3 signs" and not "the piece contains two clubs and a heart "); the group will then try to find the piece described. Needless to say, the description must be clear and precise! 2. Using a blank crossword grid, the pupils can practise isolating parts that they describe to the group. It will be interesting to see how many different solutions can be found from the answers given then, in addition to those provided.

Individualisation

Yes.

Answers

Yes.


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Recognising shapes

“Jigsaw puzzle grid” 2-42

Page 1


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Page 2


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Recognising shapes


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Recognising shapes

“Funny-shaped suitcase”

2-43

Level 4 Exercise 3

Aims - Distinguishing geometric forms – fitted into each other – listing them and, possibly, naming them. - Getting used to extending one’s field of vision, to have an overall view rather than a fragmented view of what is shown.


In class: rediscovering simple geometrical forms, their different characteristics and their semantic field and, possibly, discovering or rediscovering how to measure them (circumference or area). At work: any operation consisting in finding and listing similar shapes in tasks such as filing, tidying, packing, labelling, shelf-stocking in a supermarket. By extension, taking measurements in the building industry for wall-papering, carpeting or tiling… In everyday life and leisure: setting out furniture in a room, fittings in a kitchen, a bathroom, simple DIY, laying carpet, cutting curtains …

Materials - One sheet of paper with a drawing made up of different geometrical shapes all mixed up together - One page with questions about the drawing.

Instructions The pupils will observe the shape in order to answer the questions asked on the second sheet. If their reading ability prevents them from understanding the questions, the exercise can be done orally.

Comments If some pupils find the exercise too difficult, they can do an intermediate phase consisting in showing them the second page and the answer sheet. The work will then be to find the sets shown on the answer sheet. Once they have done this exercise, the pupils can take the first page again instead of the answers, which they put to one side.


1. If the group is interested, the teacher can ask them to try to find the name of the different forms distinguished in the exercise, and even to name others which can then be drawn. 2. The pupils can try to find, in the room or from memory, an object or a piece of furniture which is made up of several different geometric forms. 3. If the teacher is asked, he can have the group discover or rediscover the elementary calculations for the shapes (circumference and area) going up to circles and triangles. The pupils can give examples of practical applications.

Individualisation

Yes.

Answers

Yes.


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Recognising shapes

“Funny-shaped suitcase” 2-43

1. In this drawing, how many shapes are drawn several times? 2. How many shapes are drawn only once? 3. How many shapes are there in all?


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Recognising shapes

“Funny-shaped suitcase” 2-43

Answers

1. In this drawing, how many shapes are drawn several times?

4 shapes in all are drawn several times: 2 squares 2 semi-circles 2 circles 4 parallelograms (if you consider the two parallelograms which together form a third) 2. How many shapes are drawn only once?

4 shapes in all are drawn only once: 1 lozenge 1 rectangle (if you consider the two squares which form it) 1 triangle 1 octagon (an 8-sided shape) 3. How many shapes are there in all?

In all, there are 8 shapes.


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