WORK IT Understand a rotation 7-11 · 2013-01-29 · WORK IT OUT Understand a rotation “The...

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Understand a rotation

“The position of the cards”

7-11

Level 1 Exercise 1

Aims

- Practise finding an element in a series after diverse manipulations. - Find where you are in a series of elements after they have been turned face down. - Find where you are in a series of elements after they have been inverted.

Applications (examples)

In class: geometry and arithmetic: notions of symmetry and inversion. At work: anything that concerns work on your own work environment, relations with neighbouring workstations or activities; look for breakdowns or the causes of various incidents. In everyday life and for leisure: finding your way on a map during travel or even walks; ability to keep your self-awareness in the middle of changes (of people, places, or situations) and ability to reorganise yourself after happy or unhappy events.

Materials

A page with some playing cards. The teacher can also use real cards for this exercise, which will probably be more practical.

Instructions

The teacher shows the pupils the first three cards (the pupils should be close enough to see the cards well). The teacher will give the position of the cards for the pupils, from right to left, and name them: first card: jack of diamonds, second card: 7 of spades, etc. The cards are then turned face down and upside down (by turning the page over then upside down). The pupils then have to say where the ace of hearts is (first, second or third card). The same exercise will be done again with 4 then 5 then 6 cards, always picking the ace of hearts to look for.

Comments

The pupils will perhaps notice that when the card they must look for is right in the middle of the series (as in the series of 5 cards), the position of the ace remains the same no matter how you manipulate the series, without dissociating the series.

Variations (examples)

- With a real pack of cards, the teacher can vary the game indefinitely. - With a real pack of cards, the teacher can ask the pupils to create their own series of cards and to make one or more pupils look for a card after manipulation.

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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“The position of the cards” 7-11


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“The position of the cards” 7-11

Answers

1. 1st position

2. 3rd position

3. 3rd position

4. 3rd position


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“What time is it?”

7-12

Level 1 Exercise 2

Aims

- See where you are in a round dial. - Manipulate as instructed. - Transpose time from one code to another (4.00 = 16.00).


In class: learn to tell the time, begin fractions; also in geometry: questions about angles. At work: initiation to group work; differentiation between oneself (the centre) and the others, when taking into account the work of colleagues or in other sectors. In everyday life and for leisure: learn to tell the time, find your bearings in relation to the points of the compass.

Materials

- A page showing a diagram of the face of a clock or alarm clock with numbers but no hands. - Two matches or two sticks per pupil, one of them should be broken so it is shorter than the others. They will represent the hands of the clock.

Instructions

The pupils place the clock hands so as to show the time indicated by the teacher (8.10 – 10.15 – 17.30 – 22.08 – etc.). They must then determine the new time if asked to do:

- a quarter of a turn to the right (or clockwise) - a quarter of a turn to the left (or anticlockwise) - half a turn to the right - a third of a turn to the left

This rotation should be done by manipulation.

Comments

The pupils may find it difficult to see the quarters and especially the thirds on the screen. The teacher will have to make sure that the notions of half, quarter and third are understood. If necessary, the third can be omitted.


- The teacher can ask the pupils to take turns giving a manipulation to be done (half a turn, a quarter of a turn, a third of a turn, etc.) after one pupil has suggested a precise time. - This might also be a good opportunity to work with the two different codes for telling the time (4.00 = 16.00 in the 24-hour clock), by asking the pupils to give their results both ways whenever possible.

Individualisation

No.

Answers

No.


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“What time is it?” 7-12


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“The corkscrew”

7-13

Level 1 Exercise 3

Aims

- Find the direction of a rotation. - Imagine a manipulation.


In class: transform a rotation into linear progression: geometry, syntax. Advance in successive approaches. Distinguish between linear progression and successive progression, in drawing for example. At work: understand spiral progression, which is frequently found in tools and assembly. Understand the direction of the rotation with the thread to the right (the most common) and the thread to the left (less frequent). In everyday life and for leisure: anything related to assembling kits, with right thread and left thread. Understand spiral staircases in historical monuments (for defence purposes, they turned so as to shelter the defender: turning to the left going up, or to the right if the attacker is going down).

Materials

A page with a picture of a corkscrew.

Instructions

The teacher will ask the pupils to indicate by means of an arrow the direction in which the corkscrew must be turned to push it into the cork.

Comments

The teacher can bring in a real corkscrew to help the demonstration when the results are pooled.


- The teacher can ask the pupils to give other examples of a similar mechanism, used in everyday life or at work. - The teacher can ask the pupils to draw a screw and, according to their drawing, put an arrow to show the direction it must be turned to screw in.

Individualisation

Yes.

Answers

Yes.


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“The corkscrew” 7-13


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“The corkscrew” 7-13

Answers


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“Shapes in circles”

7-21

Level 2 Exercise 1

Aims

Acquire a sense of rotation by manipulating geometric shapes.


In class: work on orientation, introduction to geometry (triangles and hexagons, squares and octagons), as the circle is the basis for understanding all regular polygons; understand gearing. At work: training for fitters: orientation of one part in relation to a whole). In everyday life and for leisure: child’s game: shapes and forms.

Materials

- A reference page with drawings of circles with marks. - A second page showing 5 independent geometric shapes for the pupils to cut out. - A pair of scissors for each pupil.

Instructions

The teacher asks the pupils to cut out the geometric shapes and to place them in the corresponding circles using the marks.

Comments

The pupils can move the shapes around in the circles to find the exact place, but they must not move or pivot the page itself.


The teacher can ask the pupils if it is possible de superpose several shapes in one circle, to try it out and show their work to the group.

Individualisation

No.

Answers

No.


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“Shapes in circles” 7-21


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“Shapes in circles” 7-21

Page 2


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“The ace of hearts”

7-22

Level 2 Exercise 2

Aims

Practise mentally finding the position of an element which is part of a whole when one or more elements are added.


In class: syntax: where to place the verb (or the direct object) in a written sentence. At work: anything concerning understanding mechanisms, repairs, maintenance, looking for causes of breakdowns; also storage. In everyday life and for leisure: anything concerning children’s games, as well as searching or exploring (for example looking for a document in a file, or a child in a crowd, etc.).

Materials

- A reference page with a picture of 5 playing cards. - A second page with pictures of cards that have been added, and those just next to them.

Instructions

The pupils look at the page with the 5 cards and work on the page where the cards have been added. To the right of each new series, they must write la position of the ace of hearts in the configuration where one card has been added each time. The added cards are cumulative. For example: to find the position of the ace of hearts when the fourth card is added, the cards added previously must be taken into account in the position they held in the series when they were inserted. To make the work more fun, the teacher can use a real pack of cards. He will say which card has been added to the series and where, but without placing it in the series.

Comments

If the exercise seems difficult, the teacher can suggest exercise 7-11 first.


Using a real pack of cards, the teacher can ask the pupils to choose a series and add the cards they want. The pupils who have already done 7-11 might suggest turning the series around or upside down.

Individualisation

Yes.

Answers

Yes.


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“The ace of hearts” 7-22

Page 1


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Page 2


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Answers

1. 4th position

2. 5th position

3. 5th position

4. 7th position


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“The alarm clock”

7-23

Level 2 Exercise 3

Aims

Practise deducing the direction of a rotation from the point of view of the observer.


In class: anything related to decentring. Symmetry in geometry, observation. At work: any job requiring you to situate yourself in relation to a movement, depending on whether you are on the right or the left, of a vehicle, for example, when assembling in the factory or repairing. Fit in with a team. Understand the way things move during training in safety, repairs, maintenance, etc. In everyday life and for leisure: understanding another person’s movement, in sport (for example send the ball to a beginner’s racket hand in tennis or table tennis).

Materials

A reference page with a picture of two similar alarm clocks. These clocks are shown in perspective, on a flat surface, one opposite the other. The clock further away from the observer is seen with the dial facing; the other is shown from behind (the dial is therefore not visible).

Instructions

The pupils draw an arrow showing the direction of the rotation of the hands on each alarm clock from their own point of view.

Comments

If the exercise seems difficult, the teacher can suggest doing exercises from the series of “Find – Find yourself”.


The pupils can reflect on everything that moves or turns always in the same direction and think about the direction of the rotation when the object is turned round or the observer’s point of view is moved. Assembly lines in a factory give many examples.

Individualisation

Yes.

Answers

Yes.


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“The alarm clock” 7-23


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“The alarm clock” 7-23

Answers


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“The notched wheel”

7-31

Level 3 Exercise 1

Aims

Practise working out the direction of a rotation using the notion of a quarter.


In class: understand the transformation of a rotation in progression, in geometry, in mechanics. In mathematics, initiation into fractions. But also work on the logic of a presentation (succession of demonstrations which lead to understanding, for example). At work: any job involving repairs, maintenance; use of unusual tools and work on a grinder. In everyday life and for leisure: assembling furniture or equipment sold in kit form. On a bicycle, look for the place that knocks when the wheel makes a noise at each turn…

Materials

A page showing a diagram of a wheel with 4 notches which moves on a tige which has 4 marks.

Instructions

The pupils will indicate the position of the small shaded circle on the wheel at each movement of the wheel on the marks.

Comments

The answers can be formulated in different ways, for example: - with arrows linking each mark to the correct median on the wheel - with identical numbers or letters for the marks and the corresponding positions on the wheel - by numbering the marks and indicating the position of the shaded circle by “middle to the right”, “middle at the top”, “middle to the left” or “middle at the bottom”. It is better to let the pupils choose how to formulate their answers.


The pupils can give instructions to the other pupils, such as: The wheel makes two quarter turns to the right and one to the left; which mark does the notched circle arrive at?

Individualisation

Yes.

Answers

Yes.


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“The notched wheel” 7-31


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“The notched wheel” 7-31

Answers

1 2 3 4 5

1 5

2

3

4


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“The wheel is turning”

7-32

Level 3 Exercise 2

Aims

Practise working out the direction of a rotation using the notion of quarters.


In class: learn multiplication tables in relation to fractions and operations using fractions; initiation to the notion of cycles in geography… At work: any job involving repairs, maintenance; use of unusual tools and work on a grinder. In everyday life and for leisure: assembling furniture or equipment sold in kit form. On a bicycle, look for the place that knocks when the wheel makes a noise at each turn…

Materials

A page showing a diagram of a wheel divided into 4 quarters, each with a distinct symbol. A small circle outside the wheel is the mark.

Instructions

The pupils will indicate by how many quarter turns the wheel must be turned for a symbol to be opposite the mark.

Comments

The teacher can begin by giving instructions like: “In this position, how many quarter turns are needed for the heart to be opposite the mark?” then the pupils can take over and indicate the symbols.


This exercise can be done using a ball divided into 4 quarters, each of which will be marked with a symbol. A light source could be used as a reference point. It would then be possible to talk about the rotation of the Earth and about time zones.

Individualisation

No.

Answers

No.


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“The wheel is turning” 7-32


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“Cogwheels”

7-33

Level 3 Exercise 3

Aims

Acquire a sense of rotation.


In class: work on distinguishing right from left with decentring. Any work involving the action of one thing on another, or the prejudices one can have, or hasty judgements made at first sight. At work: any job to do with gearing, or automatic systems. Any task involving the action of one element on another, of one machine on another, of a succession in a chain. In everyday life and for leisure: any DIY or handy work where one element has an action on another.

Materials

A page showing a diagram of two interdependent cogwheels.

Instructions

The pupils must:

- work out the direction of the rotation of wheel B after deciding (themselves or by the teacher) that of wheel A;

- indicate whether the two wheels turn at the same speed and justify the answer.

Comments

The teacher can take two round objects, one large and one small, for the pupils to demonstrate the rotation, if they wish.


The answer to the second question can lead to extensions such as: if the diameter of wheel B is twice as big as that of the drawing, will it turn more quickly or less quickly than wheel B in the drawing? Same question if the diameter of wheel B is twice as small as that of wheel B in the drawing. And what if there were a third wheel?

Individualisation

Yes.

Answers

Yes.


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“Cogwheels” 7-33


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“Cogwheels” 7-33

Answers


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“Rotating shapes”

7-41

Level 4 Exercise 1

Aims - Acquire a sense of rotation. - Find yourself in your environment. - Reproduce a shape exactly by moving it around.


In class: solid geometry, introduction to negative values and algebra (for the last shape, a three-quarter turn to the right equals a quarter turn to the left). At work: training in repairs and maintenance, reading maps, identifying a part from whatever angle it appears, in a picture or in reality. In everyday life and for leisure: introduction to origami (which is in itself a very good tool for logical thinking - different stages of completion to be identified, a progression to work out, missing steps to fill in, etc.). Using models before moving furniture in a house or flat.

Materials A page showing: . 5 shapes to reproduce . 5 arrows indicating a half, quarter or three-quarter turn to be done . 5 blank squares

Instructions The pupils have to reproduce the shapes on the left as precisely as possible in the space on the right, making them rotate by a quarter, a half or a three-quarter turn, according to the arrows.

Comments The exercise as it is requires a lot of time to reproduce all the shapes given. If the teacher does not have enough time, or is worried that the pupils will get bored, he can ask them to choose three shapes to reproduce from those given. The pupils can use any means to reproduce the shapes exactly with the required rotation. For example, they might decide to cut out their page and turn the original shape around.


The teacher can ask the pupils to reproduce an object placed in front of them by rotating them by a quarter or a half turn. The pupils can choose a shape from those given and give oral indications for the rotation and direction (a half turn to the right, a quarter turn to the left, etc.). At a certain moment, a pupil will be asked to indicate the rotation and the direction so that the shape regains its original position on the exercise sheet.

Individualisation

Yes.

Answers

Yes.


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“Rotating shapes” 7-41


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“Rotating shapes” 7-41

Answers


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“The three wheels”

7-42

Level 4 Exercise 2

Aims

- Work out the direction and the amplitude of a rotation. - Develop the sense of wider observation of a complex whole. - Develop the ability to estimate size.


In class: in geometry, study the link (the wherefore of 3.1415926 etc.) between diameter and circumference. At work: understand certain mechanisms, and also any job to do with gearing, or automatic systems. Any task involving the action of one element on another, of one machine on another, of a succession in a chain. In everyday life and for leisure: any DIY or handy work where one element has an action on another.

Materials

- A page showing 3 circles of different sizes (r = 2 cm, 2.5 cm and 3 cm): there are two models available: the one with the marks enables the pupils to do the exercise more easily. - An exercise sheet with a series of closed questions.

Instructions

The pupils must answer the questions on the exercise sheet by ticking the square which they think corresponds to the right answer.

Comments

The teacher can first give out the page without the marks and, if the pupils find it too difficult, give them the page with the marks.


The answer to the second question can lead to extensions such as: if the diameter of wheel B is twice as big as that of the drawing, will it turn more quickly or less quickly than wheel B in the drawing? Same question if the diameter of wheel B is twice as small as that of wheel B in the drawing. This type of extension can also been done with a circumference twice as big or twice as small, which will help them work out the difference between diameter and circumference.

Individualisation

Yes.

Answers

Yes.


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“The three wheels” 7-42

Model A


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Model B


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Page 2

1. If A turns in the direction of the arrow, B will turn:

1. in the same direction as the arrow aXa

2. in the opposite direction to the arrow aXa

3. anticlockwise aXa 2. If A turns in the direction of the arrow, C will turn:



3. it’s impossible to know aXa 3. If C turns full circle, A will do:

1. a full circle too aXa

2. 5 turns aXa

3. 2 turns aXa 4 If A turns full circle, C will do:

1. less than one turn aXa

2. 4 turns aXa

3. 1 and a half turns aXa 5. If A turns full circle, B will do:

1. 2 turns aXa

2. ½ a turn aXa

3. 5 turns aXa


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Answers

1. If A turns in the direction of the arrow, B will turn:



3. anticlockwise aXa 2. If A turns in the direction of the arrow, C will turn:



3. it’s impossible to know aXa 3. If C turns full circle, A will do:

1. a full circle too aXa

2. 5 turns aXa

3. 2 turns aXa 4 If A turns full circle, C will do:

1. less than one turn aXa

2. 4 turns aXa

3. 1 and a half turns aXa 5. If A turns full circle, B will do:

1. 2 turns aXa

2. ½ a turn aXa

3. 5 turns aXa


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“Rolling the dice”

7-43

Level 4 Exercise 3

Aims

Practise identifying a side after a rotation.


In class: anything relating to decentring, identifying the non-visible surfaces of a geometric shape, observation. At work: any job requiring you to situate yourself in relation to a movement, depending on whether you are on the right or the left, of a vehicle, for example, when assembling in the factory or repairing. Fit in with a team. Understand the way things move during training in safety, repairs, maintenance, etc In everyday life and for leisure: anything concerning children’s games, as well as searching or exploring (for example looking for a document in a file, or a child in a crowd, etc.).

Materials

A page with a die seen from different angles, the fourth one missing. Below, 4 numbered dice.

Instructions

The pupils choose, from the 4 numbered dice, the one that, if the rotation is continued in the same direction, would complete the series above.

Comments

The teacher can use a real die to make explanations easier when the solutions are pooled.


The pupils can each make a die with paper and adhesive tape, and put the numbers or dots in a different order to the one in the exercise. The other pupils have to find the hidden side of each die shown to them when they can see the other three sides.

Individualisation

Yes.

Answers

Yes.


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“Rolling the dice” 7-43

1 2 3 4


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“Rolling the dice” 7-43

Answers

1 2 3 4


WORK IT Understand a rotation 7-11 · 2013-01-29 · WORK IT OUT Understand a rotation “The...

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