Operations with the Golden Beads
Multiplication 2, with Exchanging
- As for addition
- To understand multiplication
- 5 years onwards
- 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
- 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
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
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
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.