Operations with the Golden Beads

Multiplication 2, with Exchanging

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MATERIAL:

As for addition

PURPOSE:

To understand multiplication

AGE:

5 years onwards

EXERCISE:

A group exercise for a few children. The material is arranged as for addition.  One child is in charge of the golden bead material.  One child is responsible for the large number cards.  One child is in charge of the small number cards.  There must be at least as many sets of small number cards set out as the multiplier in the problem to be worked.  The teacher thinks of a problem, e.g. 1345 x 3.  (Note:  The problem involves exchanging in at least one heirarchy.  The product may not be greater than 9999.)

 

  1345 multiplicand

x      3 multiplier

  4035 product

 

The teacher tells the children they will be doing multiplication.  She asks the child in charge of the small number cards to put the cards "1345" on each of three trays.  She chooses three children and gives one tray to each of them.  She asks each child in turn to read the numeral on his or her tray.  She stresses the fact that each has the same amount by commenting on the fact.  She asks the three children to collect 1345 each.  They collect the material from the bead table and return to the teacher.

 

The teacher takes each tray in turn.  She takes the bead material off each tray.  She arranges the three quantities, one under the other, on the mat.  She takes the small number cards off each tray and places one under the other at the top of the mat.

The teacher stresses that the quantities are equal.  She says, "Today we are doing multiplication.  We have 1345 three times.  We will add them together."  One child counts the units.  When she has ten, she exchanges them with the banker for a ten bar.  She places the ten bar over the tens on the mat.  She counts the rest of the units.  There are 5, so the large number card "5" is placed beside them.

The child counts the tens.  When she has ten, she exchanges them for a hundred square.  She places the hundred square over the hundreds on the mat.  She counts the rest of the tens.  There are three.  The large number card "30" is placed beside them.  The child counts the hundreds.  There are 10, so she changes them with the child in charge of the bank for a thousand cube.  The thousand cube is placed over the thousands on the mat.  There are no hundreds remaining.  The child counts the thousands.  There are 4, so the large number card "4000" is placed beside them.

The teacher superimposes the large number cards and re-caps.  "We multiplied 1345 times three.  Our multiplicand is 1345.  We multiplied this by 3, our multiplier, represented by our three students.  The product is 4035."  More problems are worked in this way.