GB2214694A - Teaching apparatus - Google Patents

Abstract

Teaching apparatus comprises a plurality of sets of tokens for use with a balance, all of the tokens in each set being of equal mass and marked distinctively by means other than a direct indication of said mass to indicate their membership of that set, different sets having tokens of different mass, the different masses being an integer multiple of a unit of mass. Membership of a set may be marked by shape, colour or alphabetical indicia. The balance may have arms of unequal length.

Description

TEACHING APPARATUS This invention concerns teaching apparatus for use in the teaching of mathematics.

According to the present invention there is provided teaching apparatus comprising a plurality of sets of tokens, all of the tokens in each set being of equal mass and marked distinctively by means other than an indication of said mass to indicate their membership of that set, different sets having tokens of different mass, the different masses being an integer multiple of a unit of mass, and for use with at least one balance to determine or demonstrate known mathematical principles empirically.

Additional sets, though appearing different from said sets aforesaid, may have the same mass.

The tokens may be marked by being of distinctive shape.

The tokens may be marked by being of distinctive colour.

The tokens may be marked by carrying alphabetic indicia.

The shapes of the tokens may be such as to make it difficult to make a visual comparison of the relative masses of tokens from different sets.

The invention will be further apparent from the following description with reference to the figures of the accompanying drawings, which show, by way of example only, parts of one form of teaching apparatus embodying same.

Of the drawings Figure 1 shows a number of tokens selected from different sets thereof; and Figure 2 shows a balance for use with the apparatus.

The apparatus comprises in this example ten sets of tokens. There are about fifty tokens in each set.

All of the tokens in any one set are identical with one another but different from those in any other set. Each token is marked by being of a distinctive shape characteristic of the set of which it is a member. The shapes may be prisms of simple geometric cross-section such as circles, triangles, squares and so on or in the form of silhouettes of known objects. Alternatively some or all of the shapes may be manufactured as other regular geometric shapes or as three dimensional models of known objects such as apples, pears and so on.

Examples of the different possibilities are as illustrated in Figure 1.

At least some of the sets will have tokens of different mass. All of the tokens will have a mass which is an integer multiple of a unit of mass N, which might conveniently be twenty grammes. The mass of each token in the different sets is as given in the following table: Sets Mass 1 N 2 2N 3 2N 4 3N 5 3N 6 4N 7 5N 8 6N 9 8N 10 lON The shapes of the tokens of the different sets are selected so that it is difficult to make a visual assessment of their different volumes and hence comparison of their relative masses.

The tokens are used with a simple balance 10 (see Figure 1) having pans 11 and 12 mounted on opposite ends of a beam 14 supported on a fulcrum 15.

The tokens are distributed to the pupils who perform experiments in accordance with instructions provided on a series of experiment cards.

An elementary set of experiments might be as follows: Al 1 WRITE EXPERIMENT Al COMPARING 4 SHAPES 2 WRITE The names of any 4 shapes chosen from the list of 10.

3 COLLECT One of each of the 4 shapes.

4 Make sure the balance is level.

5 DO Find out as much about the weight of the shapes as you can, using the balance.

6 WRITE All that you have found.

7 Show your work.

8 RETURN To number 1. Choose a different 4 shapes.

A2 1 WRITE EXPERIMENT A2 COMPARING 4 SHAPES 2 WRITE The names of any 4 shapes chosen from the list of 10.

3 COLLECT One of each of the 4 shapes.

4 Make sure the balance is level.

5 DO Find out as much about the weight of the shapes as you can, using the balance.

6 WRITE All that you have found, but use as little writing as possible, eg shorthand,abbreviate using symbols 7 Show your work.

8 RETURN To number 1. Choose a different 4 shapes.

B 1 WRITE EXPERIMENT B 2 SHAPES (date) 2 WRITE The names of 2 shapes.

3 COLLECT About 8 of each of the 2 shapes.

4 Make sure the balance is level.

5 REM Keep the 2 shapes in separate buckets on the balance.

6 DO Use the shapes to make the balance level.

7 WRITE Details of how you made the balance level.

8 DO Find another way of making the balance level.

9 COLLECT More shapes, if needed.

10 WRITE Details of this new balance under the last one.

11 REPEAT 8, 9, 10. Do try to write first any others you think are possible.

12 CHECK Show your work.

13 RETURN To 1 and try another 2 shapes.

D 1 WRITE EXPERIMENT D 3 SHAPES (date) 2 WRITE The names of 3 shapes.

3 COLLECT About 8 of each of the 3 shapes.

4 Make sure the balance is level.

5 DO Find the heaviest.

6 DO Put 1 heavy shape in 1 bucket.

7 DO Put the other shapes in the other bucket so that the balance is level. Use them separately and mixed. Find all possibilities.

8 WRITE All these possibilities (None, if none).

9 WRITE Any more possibilities you would expect to be true.

10 DO Put another heavy shape with the other heavy shapes.

11 REPEAT 7, 8, 9, 10, checking any your have written.

12 LOOK For patterns and follow them through.

13 WRITE Your results in columns to show pattern.

14 CHECK Your results in columns to show patterns.

15 RETURN To 1 and try another 3 shapes.

C 1 WRITE EXPERIMENT C 3 SHAPES (date) 2 CHOSE 2 of the shapes and write down WRITE their names eg, apples and cubes.

Choose a 3rd shape and write this this name separately.

3 COLLECT About 8 of each of the 2 shapes.

Only 1 of the 3rd shape.

4 Make sure the balance is level.

5 REM You must always use at least one of each shape. Don't forget - you only have ONE of the 3rd shape.

6 DO Use the shapes to make the balance level.

7 WRITE Which shapes you used to make the balance level.

8 USE Find another balance.

9 COLLECT More shapes, if needed.

10 WRITE Details of this new balance under the last one.

11 REPEAT 8, 9, 10. Do try to write first any others you think are possible.

12 CHECK Show your work.

13 RETURN To 1 and try other shapes.

Experiments can be devised to demonstrate the principles of Ratio, Proportionality, Measurement, and numerous algebraic operations including the solution of simultaneous linear equations and graph work.

It will be appreciated that it is not intended to limit the invention to the above example only, many variations, such as might readily occur to one skilled in the art, being possible, without departing from the scope thereof as defined by the appended claims.

Thus for example, the balance may be of different kind and/or have arms of unequal length.

Claims (10)

1. Teaching apparatus comprising a plurality of sets of tokens, all of the tokens in each set being of equal mass and marked distinctively by means other than an indication of said mass to indicate their membership of that set, different sets having tokens of different mass, the different masses being an integer multiple of a unit of mass, and for use with at least one balance to determine or demonstrate known mathematical principles empirically.

2. Teaching apparatus according to claim 1, including at least one additional set, which though appearing different from the other sets, has tokens of the same mass as those of one of the other sets.

3. Teaching apparatus according to claim 1 or claim 2, wherein the tokens are marked by being of distinctive shape.

4. Teaching apparatus according to claim 3, wherein at least some of the shapes are prisms.

5. Teaching apparatus according to claim 3 or claim 4, wherein at least some of the shapes are regular geometric shapes other than prisms.

6. Teaching apparatus according to any one of claims 3 - 5, wherein at least some of the shapes are models of known objects.

7. Teaching apparatus according to claim 1 or claim 2, wherein the tokens are marked by being of distinctive colour.

8. Teaching apparatus according to claim 1 or claim 2, wherein the tokens are marked by carrying alphabetic indicia thereon.

9. Teaching apparatus according to claim 3, wherein the shapes are selected so as to make it difficult to make a visual comparison of the relative masses of tokens from different sets.

10. Teaching apparatus according to any preceeding claim including a balance.