Multiplication Tables

 

From time to time the children should be in a group, without any material whatsoever. It is essential that they should understand and know their tables at some stage. Many group lessons must be given, letting them suggest which to say. Invite the child to say the chosen table. A child might say: ‘I know the table of 2’ and so on. At first get them to recite their tables in sequence, in groups or individually. Later ask them out of sequence.

When the child has completed the addition strips, make a table book. Keep charts for children so that you know what tables each child knows by heart.**

NAME      2  3 4  5  6  7 8  9  10   etc.

Ann

John

Exercises with the Bead Bars

Direct Aim

  • Knowledge and deepening of the concept of multiplication.
  • Memorisation of multiplication tables.
  • Exploring sensorially the different aspects of multiplication, such as: Commutative law, multiplication by 10 and 100, and the multiplier and the multiplicand.

Indirect Aim

Preparation for concept of area.

Material

  • Felt cloth.
  • A generous assortment of coloured bead bars.
  • Box of golden tens.

First Exercise

  1. ‘The table of 4’.
  2. Place the bar of 4 horizontally on the mat.
  3. ‘Once 4 is 4, so we put a bar of 4 underneath’.
  4. Take two bars of 4 and place horizontally beside the other bars.
  5. ‘Let’s count and see how many we have: 8.
  6. So we put a bar of 8 underneath’.
  7. Take 3 bars of 4 to count 12.
  8. Place a golden ten and a bar of 2 underneath.
  9. After each sum, stress the multiplication, i.e. two fours are 8, three fours are 12, four fours are 16 and so on.
  10. Continue with the table up to ten fours are 40.
  11. Read over the complete table with the child.
  12. Do other tables at random.
  13. Leave the child to work on his own.
  14. As the tables are being formed, note the geometric shape being formed: a rectangle, gradually becoming a square and then a rectangle again.

This geometrical form of multiplication is very useful:

  • In showing that the multiplier is never a solid body as is the multiplicand. It only indicates how many times a given quantity is to be repeated,
  • That a succession of lines creates a surface (that is why it is called geometrical).

Second Exercise

  1. Write the number (3) on a piece of paper.
  2. Try taking it ten times and see what we get: Lay out ten bars of three, one under the other.
  3. Count them with the child. Result: 30 = 3 tens.
  4. He lays out three golden bars of ten.
  5. 3 taken ten times gives 30 and he writes a zero beside the three.
  6. Repeat with 4, 5 and so on.
  7. The child, left to work on his own, will discover for himself the recurrence of zero every time he multiplies by ten.

Aim: To develop the child’s intellect through his own activity. Here the child discovers for himself that units multiplied by 10 become tens, and that this may be done more quickly by just adding a zero!

**PW If a child of 6 has to leave a Montessori School and he has been using the material, it is not fair to let him continue using the material. He must be taken off as efficiently and quickly as possible. But it is very sad that he cannot finish in a natural way.  The Maths Olympiad for all coutnries often has a Montessori child in the team.