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Newsletter on DIVISION

Partitive Division

Children often do not solve division problems until after the primary grades. However, children can apply their adddition and subtraction strategies to solve division problems before they are taught how to divide in school. There are two major types of division problems that children can handle. Here's one:

Alyssa has 5 bags of cookies with the same number of cookies in each bag. Altogether she has 15 cookies.
Now many cookies are In each bag?

In this division problem, there are 15 cookies partitioned into 5 groups, but the number in each group is not known (15 divided by 5 = ?) This is called Partitive Division because you know the total (15) and the number of parts or groups but not how many are contained in each part.

Measurement Division

Here is a different kind of division problem:

Henry has 15 cookies to be put in some bags. There are 5 cookies in each bag. How many bags will Henry need?

In this type of division problem, there are 15 cookies and the number in each group is known (5), but the number of groups is unknown. This is called Measurement Division because you know the total (15) and the measure of each group (5) not how many groups. So, even though both problems are division problems, children think about them differently. We will focus this week on children's strategies for solving partitive division problems (when children must find how many are in each group).


Direct model. Children who model division problems with the number in each group unknown try to (1) put the same number in each group and (2) use all the counters. So for the problem with Alyssa 5 bags of cookies, a child may put blocks representing the total number of cookies (15) into the number of groups (5) they have been given in the problem, one to each group per round as adults deal cards. The child can then find the answer by counting the number in each group (3). Sometimes children represent the groups with objects, too. For example, they will use pieces of paper or plates, and then place blocks (or other types of counters) on them until the total has been equally distributed.

To illustrate further, consider this problem: there were 20 pieces of candy to be divided equally among four family members. How many candies can each person get?' Your child might use a napkin for each person and sort out twenty toothpicks to represent the candies onto the napkins. Children may not deal out the toothpicks one by one. Instead they may place toothpicks onto the napkins in a more haphazard way, adding and subtracting items until all toothpicks have been used and an equal number of tooth~ picks are on each napkin. Eventually children will begin to see patterns and learn to distribute the counters (toothpicks) equally among the groups (napkins).

Counting Strategies. Children also use counting and adding strategies to solve division problems with an unknown number in each group. Often a trial and error process is used to find a method that ends at the total number they were given. The number of groups tells them how many times they should count and the total number of objects tells them when to stop adding (or counting). For example, in the candy example children may flat count 4, 8, 12, 16 and realize that they do not have enough and then try again with fives: 5, 10, 15, 20.

Using fact. Children will eventually learn their facts. Because the answer in the cookie example is five, this problem may be solved more easily with facts than some other problems since the halves are often learned before other patterns. For example, children may know that 5 X 4=20 and work off their knowledge of this fact.


This week some of the homework problems will have remainders. It's a good idea to have problems with remainders. Children often deal with them in creative and reasonable ways. Ask your child to explain about the numbers that are left over. Instead of 20 candies and 4 family members, try a problem with 21 candies and 4 family members.

Divide Candy

Children divide candy to share with their families