Arithmetic – PRECOUNTING STAGE

Arithmetic – PRECOUNTING STAGE

Counters on Cards

(ii) Knife, razor-blade or scissors, ruler.
(i) Cardboard (an old carton will do), 2 colours of paint, paste.

Plan

Instructions for making
Cut out base and paint it in one of the colours. Cut out two sets of counters and paint them in the second colour. Paste box. one set on the cardboard. Put the spare counters in a match-
Quantity
At least six needed for each classroom.
Use
(i) Children can match the loose set with those pasted on the card and so gain some idea of relationship of sizes and the meaning of bigger’ and ‘ smaller ‘.
6.
(ii) For later practice in interpreting the meaning of first, second, third, etc.

When to be used – EQUIPPING THE CLASSROOM

(i) For matching, and for practice in bigger’ and ‘smaller’, in the first few weeks at school, before actual numbers are encountered.
(ii) When acquainting the pupils with the meaning of first, second, third, etc. towards the end of the second year at school.
Materials required
(i) Cardboard.
2 Templates
(ii) Knife, razor-blade or scissors, ruler.

Plan

Note
These sizes should be doubled if children have the necessary blackboard space.
Quantity
One or two of each

Use
Children draw round templates on the blackboard or in their exercise books and then colour in the enclosed space. In this way they gain some experience in discrimination of shape. When to be used In the early weeks at school before number work begins.

Jigsaw Puzzles (For more advanced types see pages 14 and 41)

Materials required
Simple coloured pictures of children, animals, cars, lorries, ships, trains, aeroplanes or other objects with which the child- ren are familiar. Old posters from information agencies are often useful. If no pictures are available they can be drawn.

Plan

Size

As large as possible and not smaller than 24″ x 21″.
Instructions for making
Paste the pictures on cardboard which has been cut to size. When paste is dry, cut out the jigsaws as shown by the dotted lines. Straight lines only should be used at this stage.

Quantity – EQUIPPING THE CLASSROOM

As many as possible, with a minimum of six.
Use
The children should build up the picture from the parts. In this way they gain experience in the elements of pattern making by fitting the parts together, and practice in manipu- lative work.
When to be used
In the early weeks at school before the number work begins.
Materials required
4 Formboards
(i) Thick cardboard, hardboard or three-ply wood, 24″ x 18″. ii) Knife, scissors or razor-blade, if cardboard is being used. Fret-saw, brace and bit if wood is being used.

Plan

Instructions for making
The shapes are cut out of the cardboard or wood as shown in A. A more advanced type is shown in B in which the shapes are halved after being cut out. If wood is used great care must be taken to cut accurately.
Quantity
One of each in the first-year class.

The children fit the cut-out shapes into their corresponding holes and in this way become acquainted with sizes and shapes and with similarities and differences.
When to be used
In the first term of the first year at school.
Materials required
5 Stick Board
(i) Wood, base 12″ x 4″ x 1″; sticks as shown, paint.
(ii) Saw, chisel or brace and bit.
Plan

Instructions for making
The base measuring 12″ x 4″ is cut out of 1″ or thicker timber. The holes are then cut to the shape of the sticks to be inserted. If they are round, use a brace and bit, if square use a chisel. The sticks should be about 1″ wide. Care must be taken that the holes cut are such that the sticks can fit in easily yet firmly.
When cutting the sticks the thickness of the base must be added

on to the given length of the stick.
The appearance of the apparatus will be improved if it is given a coat of bright paint.
Quantity
Two for the first-year class.

EQUIPPING THE CLASSROOM
The children insert the sticks in order of size-either the shortest first or the longest first-and build up the series. In this way they gain experience in relationship of sizes and learn the meaning of the terms long and short, longer and shorter.
When to be used
In the first term of the first year at school before work on counting begins.
Materials required
2 COUNTING
I Flash Cards
(i) Cardboard, 2 contrasting colours of paint or white paper, paste and ink.
(ii) Knife or scissors, paint-brush.
Plan
The cards should not be less than 4″ x 4″.
Instructions for making
If paint is available, use one colour for the background and the other for the dots. If no paint is available and the card- board is a dingy colour, paste white paper over. If nothing else is available, lined paper from exercise books will

suffice. When the paste is dry, draw and fill in the dots which should be reasonably large. Various arrangements of the same number of dots should be used-at least three of each number except one. In no case should the number of dots exceed six.
Quantity
At least one set of each-two, if sufficient cardboard is available.

Use To give children practice in naming groups of objects.

The cards can be used both for teaching and revision work. They can be used by the teacher or by pupils working in groups.
When to be used
When the children are forming mental images of groups and learning something of the range of numbers-probably about the latter half of the first term.
Materials required
2 Matching Designs
(i) Cardboard, 4 colours of tempera paint or 2 of ink. (ii) Ruler, pencil, scissors, pen.
Plan

Other suitable pictures: house, railway engine, canoe (or local fishing craft), lorry.
Instructions for making
The picture is drawn on cardboard and the squares marked off as shown. Each group of squares is painted a different colour. Separate cardboard squares are then cut out to match those in the pictures in size and colour.
Quantity
At least four of each.

Use
Children place the loose cardboard squares on the correspond- ing ones in the picture. Each group of these is counted and checked from the picture and the number either written or
said aloud.
When to be used
When children are building up early number concepts in the latter half of the first term in the first year. They may also be used for revision at later periods.
3 Matchboxes and Counters
Materials required
(i) 6 matchboxes, scrap cardboard, ink. (ii) Scissors, pen.
Plan

Similarly 1 and 5. The series can be extended to higher numbers as required
Instructions for making
Using the tray part of the matchbox, print figures on the inside of the bottom as shown. Cut out counters and keep them in another matchbox.

Quantity
Two sets for each class.
Use
Children place the required number of counters in each box. When to be used
When children are relating the written numbers to groups.

Self-Correcting Matching Boards

Materials required
(i) Cardboard or thin wood, paint or white paper and ink, paste.
(ii) Scissors, knife or razor-blade if using cardboard; saw if using wood. Pen or paint-brush.
Plan

2.
Instructions for making
The cards or pieces of wood are cut as shown. If no paint is available, then white paper can be pasted on the cards or boards. On the top section dots or squares are painted or printed, and on the bottom section the corresponding figure. The cards are then cut along the dotted lines. Various types of cuts can be used, the important thing being that no two are alike. Numbers up to 20 can be dealt with in this way.
Quantity

At least one set for the first-year class.
Use
Children, by using these, get experience of matching the written figure with the number of dots it represents. The value of this particular type of exercise is that if they have a wrong impression it becomes immediately apparent to them.
When to be used
In the recognition of numbers during the second and third term of the first year, and the first half of the second year.

Materials required

5 Skittles
(i) Wood sticks or 2″ x 2″ timber. (ii) Saw, chisel, ruler.
Plan

–2–
Instructions for making
Straight branches of fairly dry soft wood are most suitable for making skittles. In sawing them, be careful to cut the bottom so that the skittle stands upright. The top of the skittle can be narrowed a little. A coat of paint, or the painting of the skittles to represent people, adds greatly to the attractiveness of the set. Ten skittles make a set and three tennis balls or rubber balls can be used as bowls.
Quantity
One set for a class.
Use
The skittles are set upright and the ball rolled at them. The children count the number of skittles knocked over and the first child to reach the winning number (known before the game) is the winner. The children can work out their score after each round. This can either be done in their books or on the blackboard. The game can be played either as an individual game or a team game.
When to be used These can be used throughout the first three years; in the first year to count the number knocked down, in the second and third years to add up the numbers and subtract these from the winning numbers so that the children can find out how many more they have to knock down.
3 THE NUMERALS
(Elementary analysis of number)
Materials required
1 Measuring Strips
(i) Cardboard, white paper from exercise books, ink, paste. (ii) Knife, razor-blade or scissors, pen.
Plan

Instructions for making
Cut 2″-wide strips of cardboard in lengths decreasing an inch at a time from 12″ to 1″. Either before or after cutting, paste white paper on both sides. When cut and the paste is dry, write in figures, on both sides of one end, the length of each piece. Make a small hole at the other end and thread the strips together in order so that the smallest is on top and the largest at the bottom.
Quantity
Four for each class.

Use
(i) For measuring lengths in inches. (ii) For analysing numbers, e.g.

When to be used
6+2 = 8 and so on.
(i) For measuring lengths throughout first and second years. (ii) For analysis of numbers-second and third term of first year and for revision afterwards.
Materials required
2 Running Numerals
(i) 3 sheets of exercise-book paper, ink. ii) Ruler, pen.
Plan

Instructions for making
Paste sheets of paper together to make a strip at least 24″ long. If the sheets are pasted double thickness, the paper will be stronger. Draw in the bridge and the figures.

One for each class.

Use
(i) To demonstrate the sequence of numbers-e.g. 5 comes after 4, 6 between 5 and 7, etc.
(ii) To find missing numbers-e.g. cover up one number and ask which one is missing.
(iii) To introduce the meaning of first, second, third, etc.
When to be used
For (i) and (ii) above in the second term of the first year when children are just beginning to use textbooks. For (iii) during the latter half of the second year.
Materials required
3 Number Strips
(i) Cardboard, paint, or writing paper and paste, ink. (ii) Knife, razor-blade or scissors, pen or paint-brush.
Plan

Instructions for making
The cardboard is cut into strips and, if no paint is available, white paper is pasted on. The strip is then divided into either five or ten parts and the figures inked in. Cards with the missing numbers should be cut separately.
Quantity
As many as possible. The number of combinations possible when two or three numbers are missing each time is very large. Use
Children place individual cards in the missing spaces and so gain experience of the sequence of numbers.

When to be used – EQUIPPING THE CLASSROOM

When children are gaining experience in number sequence- throughout the second and third term of first year. More advanced strips can be made in the second and third year involving numbers up to 100.
Materials required
4 Figure Jigsaw
(i) Cardboard, white paper, ink, paints or old pictures, paste. (ii) Knife, scissors or razor-blade, ruler, pen, paint-brush.
Plan

Instructions for making

Two rectangular pieces of cardboard each 6″ x 4″ are cut and white paper pasted over them. The cards are then marked as above. In each space in A a number of objects is drawn ; in B the number is written in the corresponding space. Rect- angle B is then cut along the dotted lines. Use as pictures any objects with which children are familiar.
Quantity
At least six with different combinations of shapes and figures.
Use
The picture card is the master card and the children assemble the cut-out pieces using the pictures as a clue to number recognition. If desired it is also possible to keep the figure card in one piece and cut up the picture card.

When to be used
When learning to interpret the meaning of figures after intro- ductory work has begun during the early part of the second term of the first year.
5 Clock Face (First Type)
Materials required
(i) Cardboard, white paper, paste, ink, screw (round-headed), small piece of wood, string, small piece of leather. (ii) Scissors, pen, screwdriver.
Plan

PENCIL
PIN
STRING
LEATHER WASHER
SCREW
CARDBOARD WASHERS
CLOCK FACE
Instructions for making
Using a compass, or pencil and string-as shown in C-draw a circle with a radius of 6″ or 7″ on cardboard, which, if dingy, should have some white paper pasted over it. Write in the numbers. Cut out the hands and if possible colour them to contrast with the white of the clock face. After making the necessary holes push the screw (i) through a cardboard or leather washer, (ii) through the minute hand, (iii) through the second washer, (iv) through the hour hand, (v) through the third washer, (vi) through the clock-face. Screw into a piece of wood on the back (diagram B). If no screw is available, a flat-headed nail will probably suffice. Bore two small holes on the face of the clock as shown in A. Thread string through; this will make a loop with which to hang up the clock.

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