Material
- Bead bars.
- Use of symbols ‘plus’ and ‘equal’.
Direct Aim
- To permit the child to discover sensorially the commutative law of addition, i.e. a+b= b+a.
- It is also a further aid to the memorization of tables.
Age of great interest
5½ to 6½ years.
Presentation
- Write an addition sum in the child’s book.
- Ask him to do it using the bead bars. e.g. 7 + 2 = .
- Now suggest to the child that, for fun, we will put it out as 2+7 = , and see what happens. (Leave the first bead bars on the table).
- He will find he still gets the same answer, which is 9, although the beads are laid out differently.
- Do a couple more sums with him.
- For work on his own there are prepared slips. He may record them if he wishes.
- Also he may be given sums involving tens as well. E.g.
| 15 + 13 = | 13 + 15 = |
| 12 + 13 = | 13 + 12 = |
Letter symbols may be substituted:
a + b = b + a
Today algebra may be introduced very early. As soon as the child knows what the combinations of 10 are, with the Montessori bead stair, then we can substitute a letter for any of the sides or for the answer and the child finds it very easy to answer….’What value is “a”?’ because he knows the equations.
E.g. 5 + 5 = 10 he knows if we substitute ‘a’ for 10 – 5 + 5 = a
The child will immediately know that ‘a’ will = 10 similarly a + 5 = 10, hence a = 5 or 5 + a = 10, hence a = 5
The children enjoy playing with a friend substituting letter cards for any of the terms and getting the friend to say what the value is for the letter. They may use them first with the bead stair and then without concrete material.
This involves giving such words, or terms as:
- As many as,
- Twice as many as,
- An equal amount of,
- Enough,
- More than,
- Fewer than,less than,
- The total.
- e.g. ‘Are there as many … as there are …?’
- ‘Are there fewer or more … as there are …?’etc.
Group Lesson
(Not to be given in a rigid three period lesson).
First Introduction of the terms (use concrete materials, e.g. books, pencils, etc.).
First stage: Ask a child, “Bring me 6 pencils”, and another one “Bring me 4 pencils”. Get them to put them on the table in front of them, and ask them to count them again. Ask who has fewer pencils.
Another child fetches 10 exercise books, and her friend fetches 3.They count them again and find that as Bhas fewer books than A, then A has more books than B.Ask two children to get 3 counters each.They will learn that they have an equal amount of counters.
Second stage: You ask a childe.g. “Has Tessa gotmore or fewer pencils than Sally?”“Has Sally got as many pencils as Tessa?” “Have A and B got an equal amount of books?”
Get a child to fetch 3 trays and 7 rulers. “Are there as many trays as there are rulers?”“Is there an equal number of trays and rulers?”
N.B. At first use similar objects for comparison, later on different objects (such as trays and rulers).
Second Introduction (less concrete. Use pictures and drawings).
Example: Show a picture of a farm. Get the children to count all the animals in it, e.g. “How many cows do you see?'” “How many pigs are there in the field?” etc. Then ask questions using the terminology learnt in the first introduction:“Are there more ducks in the pond than in the field?” etc.
N.B. Correct terminology is very important.You must give the right terminology for everything, so that he will not develop faulty reasoning and incorrect judgements. Correct terminology for communication: Clarity in the concrete is essential as concepts are at the root of thinking. Get the children to ask one another questions. Their language will grow all the time,throughout the course of arithmetic.
Introduce the symbols for (a) greater than >
(b) less than <
(c) equal to =
and let the children make up examples. e.g.: 5 > 4,etc.