Making Equal Groups Background Information for Teachers, Parents and Caregivers

This page provides information to support educators and families in teaching K-3 students about making equal groups. It is designed to complement the Making Equal Groups topic page on BrainPOP Jr.

There are many approaches to teaching division and we recommend employing different strategies and providing plenty of examples to help children visualize and understand division. Making equal groups and exploring different ways to share helps children understand the basic principles behind dividing. We recommend screening and reviewing BrainPOP Jr.’s Arrays movie to help children understand the relationship between multiplication and division.

Review with your children that when groups are equal, they each have the same number of items. Division can be a difficult for some children to grasp, so it is important to use tangible materials to model real-life division situations. Present your child with 6 counters (pennies, beans, buttons, etc) and pretend they are cookies. Using cookies or another treat is always a good way to get kids engaged. As soon as you tell them that they will be working with cookies, their investment in making sure there are “fair” groups goes up and their math skills suddenly improve. Then ask your child to split them into two fair groups. He or she can dole them out one by one or draw pictures or make a tally chart to divide the counters equally to figure out there will be 2 groups with 3 pennies each. Continue practicing with different numbers of counters and dividing them into different numbers of equal groups.

Then present your child with a story problem to model, such as “There are 12 cookies that must be divided among 4 friends. How many cookies does each friend get?” Provide your child with 12 counters and have him or her divide them into 4 equal groups. Your child can create an array to help divide them into equal groups. An array is a set of items that show equal groups in rows and columns. Your child can make an array to show 4 rows of 3 counters each. This means that each friend, as represented by the rows, get 3 cookies each. Pose different division problems and have your child use arrays to solve them.

Provide another problem for your child that requires him or her to make and count groups. For example, you can pose the following problem: “Moby collects stickers in a sticker album. He has 15 stickers, and 3 stickers can fit on each page. How many pages can he fill?” To solve this problem, your child can model using counters, drawing pictures, or making tallies. He or she can also use a number line and skip count. Have your child start at 0 and skip-count by 3’s to get to 15. Then your child can count the number of times he or she skip-counted to find the answer. Your child can also start at 15 and subtract 3 as many times needed to get to 0: 15 – 3 = 12, 12 – 3 = 9, 9 – 3 = 6, 6 – 3 = 3, 3 – 3 = 0. Then count the number of times he or she subtracted. Have your child practice solving problems using different strategies, and then discuss which strategies work best for which type of problem.

Remind your child that the symbol ÷ means to divide. To write a division sentence, he or she should write the larger number first, as in 18 ÷ 3 = 6. The number you divide into is called the dividend. The number you are using to divide is called the divisor. The answer to a division problem is called the quotient. In the number sentence above, the dividend is 18, the divisor is 3, and the quotient is 6. You can also write the equation using the “little house” where the larger number goes inside the house and the answer is on top. When teaching this method it is important to remind children to line up place value columns in the answer.

Help your child understand the relationship between multiplication and division and realize that they are inverse, or opposite, operations. You can use arrays and a number triangle to help your child see the connection. For example, the equations 3 x 2 = 6 and 2 x 3 = 6 are related to 6 ÷ 2 = 3 and 6 ÷ 3 = 2. Fact families use the same numbers and different operations, so 3, 2, and 6 are in the same fact family.

Division can be a tricky subject for children, but children can grasp concepts more easily by working through different examples and employing different strategies and visualization techniques. We encourage children to use counters and model problems to help them understand basic operations and how they are connected.