More Counting
The first step in learning to count with fractions is
learning what you call the result of
simple sharing problems like these:


Eva representing one twentyseventh
of a candy bar. 
More
Sharing Problems, More
Collections to Count
Here are some examples of sharing problems. They are different
from the introductory sharing problems on the Counting 1 tab  these
problems have
more than one thing
to be shared. Problems
like these can help your children extend their ability to count.
 If 3 bears share 5 bowls of porridge, how much do they each get?
 If 4 monkeys share 9 bananas, how much do they each get?
 If 7 children share 24 chocolate bars, how much
do the each get?
How
to Help
It is always a good idea to have your child represent the
things to
be
shared. Here for example are the 5 bowls of porridge,
represented by 5
rectangles, that the 3 bears will share. (Rectangles are a good
choice for representing the objects to be shared  it is relatively
easy for children to divide rectangles into relatively equal pieces.)





Once they have drawn the
rectangles, most children
will easily solve
this problem in one of two ways.
One
Way: Each bear can FIRST
be given one whole bowl of porridge. THEN the remaining two bowls of
porridge can each be divided into thirds and distributed so that each
bear gets one third of a bowl from each of those two remaining bowls.
Even without any help, many children can name the amount that each bear
gets  each bear
gets one whole bowl
and two thirds of a bowl  or "one and two thirds bowls."^{1}
Papa's Bowl 
Mama's Bowl 
Baby's Bowl 






In this
video Trixie
wants to share 5 mice between 2 cats. She uses the 5
fingers on one of her hands to represent the 5 mice. FIRST she
gives each
cat 2 mice (2 fingers). THEN she gives each cat one half of a
mouse (one half of her thumb). All of this was very easy for her, but
she needed my help in naming the number of mice that each cat got
altogether.
Another
Way: Here is another way that children use to share 5
bowls among 3 bears. They divide EVERY bowl into 3 pieces
and give each bear one third of each of the 5 bowls. So
each bear
gets 5 thirds of a bowl.















For example, here Rose shares 5 candy bars among 3 chickens by cutting each of the 5 candy bars into thirds.
A
Special Case
These problems are a little bit
different. There are more bears than bowls of porridge, and more
monkeys than bananas, and more children than chocolate bars.
 If 3 bears share 2 bowls of porridge, how much do they each get?
 If 4 monkeys share 3 bananas, how much do they each get?
 If 7 children share 6 chocolate bars, how much
do the each get?
What makes these problems special is that there is really only one easy way to solve them. In the case of the 3 bears and 2 bowls of porridge, you must divide each bowl into thirds. In this video, Eva shares 2 candy bars among 27 horses. To do that she divides each candy bar into 27 parts  I cannot think of another easy way to solve this problem.
There
ARE Other Methods  But They Lead to Problems
Sometimes children will try to
solve problems like these using other methods. Trixie tried to
share 2 snakes among 3 people by first distributing one half snake to
each person. Her reasoning wasn't wrong  but she was not
prepared to handle the difficulties that followed. Trixie's
methods and the resulting difficulties are not uncommon. Click here to see how I
handled the situation.