Operations with the Golden Beads
- As for addition
- To understand the concept of multiplication as equal addition
- To learn the vocabulary: multiplication, multiplicand,
multiplier, and product
- (Note: Because multiplication
is the addition of equal quantities, it may be introduced at any time
after children have learned addition. Since these problems do
not include exchanging, the product of any heirarchy must not be
greater than 9, and the largest product possible is 9999.)
- 5 years onwards
- A group exercise for a few children. The material is
arranged as for addition. One child is responsible for the golden
beads material. One child is in charge of the large number
cards. One child oversees the small number cards.
- The teacher thinks of a problem, e.g. 2322 x 3. The teacher
makes 2322, three times in small number cards and puts them on each of
three trays. She gives a tray to each of three children.
the children to read the number on their tray in turn. When they
have done so, she stresses the fact that they each have the same
numeral. "You each have the same numeral. You each have
2322. Will you all go to the bank and collect that amount in
- The children collect 2322 each and come back to the teacher.
- The teacher takes each tray in turn. She takes the
quantities off each tray, saying, "You have brought 2322." She
arranges the quantities on the mat one below the other, and takes the
small number cards and places them under each other at the top of the
mat. The teacher says, indicating the golden beads, "We have 2322
- We will add them together and see how much we have
altogether. She adds the hierarchies. She asks a child to
count the result beginning with the units. After each hierarchy
has been counted, the corresponding amount in large number cards is
placed beside it.
- The teacher superimposes the number cards and places them under
the small ones at the top of the table. She recaps, "We had 2322
three times. We added them together and got 6966." Other
problems can be worked in this way.
- (Note: In multiplication small
equal quantities are added together to make a larger quantity.
Small number cards are used for the quantities and large number cards
for the product to help give this impression.)