More Counting

Eva representing 1/27 The first step in learning to count with fractions is learning what you call the result of simple sharing problems like these:
  • If 3 bears share 1 bowl of porridge, then the amount that each bear gets is called one third of a bowl.

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  • If 6 monkeys share 1 banana, each one gets one sixth of a banana.

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  • If 19 children share 1 chocolate bar, each one gets one nineteenth of a chocolate bar.
You may be surprised by how easy it is for children to extend this knowledge. The new sharing problems introduced below will require them to use fractions to count more complex collections - but it isn't hard.
                            Eva representing one twenty-seventh 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.


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.



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.