Teaching Division

If you work with a child in the fourth, fifth, or sixth grades who's frustrated by division, there is hope. Math doesn't have to be confined to the realm of simple (but boring) memorization. It's always nice if a child can memorize division facts. It's more important for them have some approach they are comfortable with for solving problems.

Introducing the Concept of Division

Often the roadblock to progress in math is a student's failure to learn basic division facts: 28 divided by four is seven, 54 divided by nine is six. You memorize that, right? Well, not necessarily. Memorization is the norm; but if the child has difficulty with the concept of division, memorizing the facts will be difficult (or impossible).

The concept of division can be taught most effectively by manipulating physical items, like blocks. Start with small numbers. Since the immediate goal is to get an idea across (not to test some level of proficiency) problems like 6 ÷ 2 or 12 ÷ 3 are perfectly acceptable starting places - even for fourth and fifth graders. The small, simple numbers help keep attention on the idea of division at the start.

The process works like this:

• Place your blocks in a pile (we'll say there are six for this example) and have the student count the blocks.
• Tell your student you want to divide the blocks in three equal piles.
• Have the student create the three new piles by moving the blocks.
• Have the student count the blocks in the three new individual piles.
• Discuss the conclusion: six blocks divided into three piles means two blocks in each new pile. So six divided by three must be two.

If the process sounds simple, that's because it is. But the activity serves some important purposes with students that are having real difficulty with division. First, it provides a concrete model for a fairly abstract process. And the concrete model can eventually be visualized by most students so that they no longer need actual blocks. Second, it takes division from the normal visual-auditory sort of presentation and makes it a tactile-kinesthetic activity that often better suits the learning styles of many students.

Remember the Steps in Direct Instruction

When you sit down with your student to use the model that's just been described, remember these basic steps in the direct instruction process. First, do it for them while they watch. Second, do it with them by coaching them through the steps. Third, have them do it on their own without any coaching from you.

Keep it Challenging

If it has occurred to you that having fourth or fifth graders working to divide 12 by four isn't very challenging, your concern is well founded. As you teach the model itself, remember that the mathematical challenge is not yet the issue. We want student to understand the process. But once the process has been grasped, you can begin to immediately increase the number of blocks you're using. That will increase the difficulty of the math task.

One of the keys to success with these sorts of block activities is simple. Convince your student that it doesn't matter whether they're rearranging 12 blocks into four piles (12÷ 4) or rearranging 72 blocks into eight piles (72 ÷ 8). If they will follow the steps, they'll get a right answer. As time progresses it is not unreasonable to have a hundred or more blocks out on the table for the child to manipulate.

Making it Real

Almost all math becomes easier to master for any student when they can see a relationship between the math and their own life. Students look at you and ask, "When am I ever going to actually use this?" The question is rhetorical. They think they know the answer already, and they think the answer is never. Who, for example, actually needs to know how to figure the area of a circle? (Then one day they have to figure out how much floor tile to buy for a semi-circular dining room in their house...)

Division can be made "real" for elementary school kids quite easily. A candy bar has 12 segments that can be broken off and you want to share your candy bar with two other friends. So how many segments do each of the three of you get? The fourth grade's fundraiser event needs to sell 320 pizza kits to get enough money for this year's school trip. There are 40 kids in the fourth grade. How many pizza kits much each fourth grader sell? You get the idea...

One Remaining Idea

As a final note, when you first begin teaching division using blocks or other manipulatives it is best to plan your problems well enough to avoid having remainders until after the process is mastered. Once students are fully comfortable with the process, introducing a problem like 13÷ 3 no longer creates unmanageable confusing for the student.

For more on teaching division, see The Partial Quotient Method.

12 Divided by 4 Using Blocks

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