Operations with the Golden Beads
Division with Remainder
- As for addition
- To help the children understand division
- To teach the term remainder
- 5 years onwards
- This is 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 in charge of the large number
cards. One child is in charge of the small number cards.
The teacher thinks of a division problem that will leave a remainder,
e.g. 457 ÷ 3. The teacher makes the dividend in golden
bead material and the large number cards and puts it on the table mat.
- She tells the children that she is going to divide 457 equally
among three children. She gives a tray to each of the three
children. The children stand in front of her holding their
trays. The teacher divides the hundreds first. She puts a
hundred square on each child's tray. There is 1 hundred
left. This is exchanged for 10 ten bars.
- The ten bars are placed above the tens column on the table mat.
- The teacher says, "There are 10 tens and 5 tens. That makes
15 tens." She divides 15 tens among the children. Each
child gets 5 tens. The teacher divides the units. There are
seven units. Each child gets 2 units and there is one unit
left. The teacher explains that she does not have enough units
for everyone and they must all get the same amount. No one can
have it. The unit must be left. She tells them it is called
the remainder. The teacher puts the small number card 1 beside
- The teacher asks each child in turn to tell her the amount on his
tray. Each has 152. The teacher gives each child
corresponding small number cards.
The teacher takes the small number cards
off one tray. She
puts them above the dividend. She re-caps. "I had 457. I
divided it equally among three children. Each child got 152,
and there was a remainder of 1." She places the remaining golden
bead to the right of the quotient and puts the small number card,"1,"
The teacher can reinforce the terms, dividend,
divisor, quotient and remainder. "We began with
457. This is called our dividend.
We divided this amount among three children. Three is our divisor. Each child got 152
and there was one remaining. This is the answer to our division
problem, and we call it our quotient.
We call our one remaining bead the remainder."
The teacher can point to the cards on the mat and ask the children to
point to the dividend, quotient, and remainder. When she asks for
them to point to the divisor, they point to the three children who
shared the beads. She can then ask the children for the names of
the parts of a division problem. Pointing to the dividend, 457,
she asks the children,"What do we call this? Yes, the
dividend. And this," as she points to the quotient. Yes the
quotient." "And this?" as she points to the remaining bead.
"Yes, the remainder. And what do we call the three of you?
Yes, the divisor."