String of Beads....

This part of the learning programme is meant for every child who has missed out with The Basics.
However, without a doubt, it is only with the possibility of help from parent,or friend of the family, that the practices described below can succeed...They are meant for a one to one 'teacher' to pupil relationship. There's no doubt too, that the learning sessions can give great joy and satisfaction to both parent and child. Each session can be a revelation to the parent, of what good learning/teaching is about,-- for an active-stirring of the pupil's 'grey matter' can occur during every session. - Now that is a rare happening that can be noticed only when a 'teacher' is very 'close' to a young learner who is making a real effort, mentally, during an activity.

Parents may wonder whether they will be able to cope, with the help that is being asked of them. They needn't worry. The first thing to do should be to read through all the activities below and then to try out one that they fancy, with a friend. Then to try it with their own child and one of her/his friends.
The largest part for a parent to do, will be to select suitable practices; supply the material needed; oversee their child's performances and give encouraging help when needed.
The title 'String of Beads,' covers many complementary practices:

The String of Beads, set out in tens, of different colours will provide a vital learning-to-count exercise: going up one at a time (later,two at a time) to ten, or twenty, or thirty, and then down again each time to zero. However, you, the parent/teacher will soon realise that the most challenging part of this activity, and the part that requires the most mental effort,occurs when a pupil is counting down to zero each time.
If there is time for it at the end of each session with the beads. there should be a repeat practice, with an equal number of 1p coins. This repeat practice will prove to be most benefiiciat to your pupil/child. The parent/teacher should show by example how to count with coins, and especially, after making a pile of ten ones, how to take away 1p at a time, whilst calling out the number of coins that are left each time.

Dotted strips on paper could prove to be a useful substitute for beads.
See Dot Strips1 and Dot Strips 2 in the beanstalks section.

Hand and Finger Displays, which provide clear and sure ways of demonstrating many number values up to ten, especially in terms of 5 and a number.

Dominoes
Matching numbers and learning skills and gamesmanship. (See Dominoes Sheet 1 Sheet 2 and Sheet 3)

Snap Cards A lively traditional game to start with; then there are several games, each with an interesting but different mathematical challenge to enjoy.
See Snap Cards Sheet 1 and Sheet 2.

Working with a bank of 1p coins Help your child/pupil to realise what odd or even means; as well as finding the half of an even number.

Staircase Strips with which to ensure a sound understanding of the properties of every number up to ten.
Easy games with one (1 to 6 dot) dice to start with; then more challenging games with 2 dice.(See Staircase Sheet)

A Loop-over Bead Abacus with ten beads on each of three wires. There should be at least one in every school, for it is an eye-catching piece of apparatus.
In the hands of a teacher with lots of experience with this wonderful learning aid the attention of a large number of pupils can be held, easily.
It is the perfect piece of apparatus to use when working with Natural Numbers.
An alternative to the bead abacus is to use a cardboard calculator, with ten coloured dots marked on each slide. It complements the bead-abacus in the way it can be used to perform the 4 operations of number (
especially in the process of subtraction.

In all of these activities your child will be working with natural numbers- using hand and fingers, or beads on a string, or counters or coins to count up to ten, or twenty or thirty. And that, more or less, would be a safe limit within the reach of most pupils up to 8 years of age.
Whilst thinking about working in natural numbers it is well to realise the quality of the perfect piece of apparatus - the bead abacus, with its three loops of wire, each one carrying ten beads; so easy to move them out of sight to display many different sets of three numbers- to practice the addition of numbers. And many other practices too.
Then, it is excellent for the 10, and11 year olds when illustrating decimal values.

Eventually there will come the readiness to move on to the next learning stage after the 90 addition and subtraction facts. So go to Beanstalks to make a new start in this next mathematical adventure; learning all the multiplication and division facts as well. The truly amazing fact about both practices is that most of the time pupils will be working on their own, and acquiring the enviable achievement of being almost independent of adult help.

String of Beads
Start the first session with strings of beads - one string for each player if possible. The beads should be about 1cm in diameter. It would be ideal if each 10 of the beads on the string had a different colour. Have 30 beads on each string if possible.
At the start, ask the players to push the beads to one end of the string. Then each player could pass through 3 stages of difficulty.

During this first learning activity your child should be given the first chance to hold a string of beads, to move them one by one whilst reciting the number names to ten. This is not an easy task for all young learners, especially when counting down to zero; but s/he will be getting his/her first comforting experience of working with warm beads. (Hopefully, an experience which s/he will welcome, again and again.) If there is a chance at each learning session, try easy complementary activities:
1) Counting up to ten with a set of ten 1p coins. Scatter them in front of her/him; Ask her/him to bring them together, one at a time to make a pile of ten; then with your help s/he can take one away to leave a pile of nine and this procedure can continue down to zero, removing 1p at a time. Hopefully, in the next practice s/he will need less help and with progress achieve the goal of counting down from ten to zero.
2) Repeat this procedure of counting up to ten and down again to zero by using hand and finger displays. Holding two clenched fists, in front of her/him then raising one finger at a time, starting with the thumb of the left hand whilst counting aloud up to ten. But lowering one finger at a time , starting with the thumb of the right hand (both hands held facing her/him, whilst counting down one at a time, is going to be a little difficult.)

Digits First Red or Blue

A game for your child/pupil and his/her friend.
This game will help young learners to be able to read and to remember the ten digits.
1, 2, 3, 4, 5, 6, 7, 8, 9, T ( The letter T is used for ten as s/he will be working in Natural Numbers.) The reason for marking the numbers red or blue was to add interest to the game. An understanding of odd and even will come later.
If possible provide your child/pupil with a rectangular piece of card 20 x 4cm marked in squares 2 x 2 cm. Use it to make two strips of ten squares. Mark the squares in red or blue as shown on the grid of numbers. It will help a young learner if you underline each number.
Leave one of the strips intact for a pupil to use as a master copy. (For it will help the youngest players to match onto when checking an unknown number.) Then cut the other strip to make ten squares, each square carrying one of the ten digits.



The two players are told to scatter the ten cards face-side-down..
And so the game will be "Reds or Blues" and see who will make the most points. - One point for each card that happens to be in the right colour, when chosen.
In Play
The players take a turn about to pick up 5 cards. Then a dice is thrown - its dots will show a Red or a Blue number. Whatever it is, Red or Blue, that will be the name of the game. Suppose it is 'Blues' and one of the players has turned her 5 cards over to show - 3, 5, 2, 6, T, then she will have scored 3 points, to be marked in tallies.
When the players become proficient, knowing all the digits, then change over to learning the ten number names.

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The next game can be played, at first, with each player finding out more about oddness and eveness. See -

Second Game....Setting out cards which carry digits, on a vertical ladder.
Scatter the cards marked with the ten digits, face-side- down. The two players take a turn about to turn over any one of the cards, leaving each one face-side-up in its own place. But when a player turns up the card marked '1', s/he places it in position as if it were at the bottom of an imaginary ladder....Then the fun begins - s/he has the right to pick up any of the cards which are already face-side-up, S/he might have the luck to see amongst them, cards '2', '3' and '4', so they can be put on the ladder and still have another go when - if her/his luck holds out - s/he turns over card '5' with another possible run up to '8'...."Wow!" But then luck could run out. With just two cards left face-side-down s/he desperately needs card '9', but turns over card 'T' - - - - Would you believe it! Now, after all, the other player has the luck and wins the game along with five points- in tallies. After success with several games, play the same game with number names instead of digits; but remember to underline each number name.
For a similar but much more challenging game 'The Skylark' go to year 11.

For young learners who have shown proficiency when counting up to ten and back to zero without the help of hands and fingers they can take the next step of counting up to twenty and down again.
But this particular learning area is a minefield of difficulties.
It could take weeks or more in order to gain a good standard of proficiency. The practices to be used should be with a string of twenty or thirty beads or 1p coins.
During these practices a performer can have a blind spot saying for example; "....- thirteen, fourteen, fifteen, seventeen; although being able to carry on perfectly up to twenty."
The best way to cure this is to work patiently, causing no anxiety; stopping the performance and asking for counting to start again up from zero. The adult present can help by making hand and finger displays of the units digits from 1 to T, and yet again for the units values in the numbers eleven up to twenty and making encouraging remarks, saying, after ten, "Eleven is ten and one," whilst raising one finger, helpully. Then raising 2 fingers as s/he says "Twelve". Then 3 fingers for 13; 4 for 14; 5 for 15; and 6, for the tricky one,16 - followed by 17,18,19 and 20.

It may be surprising, but it is unknown for a performer to object when being stopped time and time again and being told to start again, up from zero. Gratefully, happy progress always results, but it does take time and perseverance.

When your child can perform well with the beads, moving them whilst calling the numbers without faltering, move on to counting up from zero to thirty and down to zero again.As this is a new challenge, work together for the first time, both you and your child calling the numbers from one to thirty, as s/he moves the beads one at a time. So far so good. But when coming down from thirty move very slowly, to help your child to realise the process.

An early practice: Start with a clenched fist to represent zero and make the five displays of one,two,three,four,five fingers of the left hand.
Then proceed with displays for six,seven,eight,nine,ten using both hands.
When each display is made, ask your child to name the display and its complement, (to 5, or ten.)

It will be noticed, as your child becomes familiar with the finger displays for 6,7,8,9,ten that the performance becomes more speedily performed. It could be that the performer is taking in (mentally) the idea of five, after just a brief glance at the left hand, whilst noting carefully the 1 or 2 or 3 or 4 or 5 fingers in the right hand.
This is a classic example of a pupil showing a higher degree of mathematical expertise and maturity , noting at a glance that the left hand represents five.

Now practise counting up in ones to ten, raising one finger each time; and going down to zero by removing one finger at a time.
Then show counting in twos up to ten and back again to zero.
Please note how easy it is when counting in twos from 'one' up to 'nine' and especially when counting down again to 'one'..
Add to the fun of counting in twos by reciting and performing, with hand and finger displays, the rhyme - 'One two buckle my shoe'. Additional vital practices of counting in twos from zero to ten and counting down again to zero are shown on this illustration.

Dominoes
"Dominoes" is a popular game with young players. See dominoes Sheet 1 and Sheet 2 which you can use to make a set of dominoes if you need them. Usually the dominoes are black rectangles of wood, each rectangle being 40mm long, 30mm wide and 5mm thick. They are marked in two sections with a number of white spots in each half; however 8 halves are left blank.

Play a few short games to help your child/pupil to be familiar with them.
Ask your child/pupil to play with a friend.
There are 28 dominoes in a full set, so partition the full set in half and give one half to each player. Then ask the players to arrange them in two horizontal rows in front of them. Begin with an introductory game.
An adult is needed, to supervise and help during the first few games. S/he will need two (1-6) dot dice.
Your child/pupil and a friend can sit opposite to each other, ready to play.
The adult explains the rules: "When I cast two dice in front of you, one of you will be able to match the dots on the dice with one of your dominoes. When that domino has been found and given to me, then you can take a turn about to add to the domino that is here already. If there are two halves on the dominoes which match, then I can put them together.Hey Presto!-"
Then the next player puts out a domino with the hope of making another matching and so on.
The adult will be making a long snake of dominoes as play proceeds.
The players should soon learn to help the adult by looking, themselves, for one of their own dominoes which can be matched to one on either end of the snake.

The game ends when most of the dominoes are used and matching can go no further. Then each player counts the number of dots on their dominoes.
The one with the least number of dots wins 5 points. Score in Tallies.
After a few games the two players should be able to manage to play on their own - without help.