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A Hands-On Lesson Plan on The Divisibility Rule

written by: Keren Perles • edited by: Laurie Patsalides • updated: 9/11/2012

Finding hands-on methods to teach math concepts like divisibility can be difficult. Try using this lesson plan on the divisibility rule to engage even your most math-phobic students.

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    Discovery Learning

    The best way to organize a lesson plan on the divisibility rule is to let students figure out the rules themselves. This is especially helpful for students who have math-related learning disabilities.

    Begin by making a two-column chart on the board, in which the first column has a list of the numbers 2 through 10. Instruct students to copy over the chart and to work in small groups to figure out what divisibility rules work for each number.

    To start them off, help them identify the divisibility rules for 2 and 3. Ask them how they can figure out whether a given number is divisible by 2. They should realize that if the last digit in the number is even, then the number is divisible by 2. To figure out the divisibility rule for 3, they will probably need to have heard of it before. You can explain to them that if the sum of all of the digits in a number is divisible by 3, then the number itself is divisible by 3. This should also help them figure out the divisibility rules for 6 and 9.

    At this point, turn them loose and let them figure out the rest of the divisibility rules on their own. When they discover the rules themselves, they will remember the rules much better. This will also strengthen their math skills in the process.

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    Paired Practice

    Once students know the divisibility rules, they'll need to practice with them in order to become as familiar as possible with them. Write several very long numbers on the board, six or seven digits long, and have students work in pairs to figure out which numbers each of the large numbers is divisible by. They will need to apply each of the divisibility rules in order to accomplish this. When they finish, have one pair come up to the front of the class and explain their answers. Students can self-grade their responses to see which divisibility rules they are still having trouble with.

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    Group Work

    Once students have had plenty of practice with the divisibility rules, it is important to make sure that they understand the logic behind them. To ensure this, challenge students to work in small groups to come up with a number that is divisible by several one-digit numbers. For example, you might have them work to come up with a large number that is divisible by 4, 5, 6, and 7. At first, students might simply multiply all of these numbers together to come up with a very large number. If they do, challenge them to come up with a smaller number that is still divisible by 4, 5, 6, and 7. (The key to this challenge is that 4 and 6 are both divisible by 2, so half of the original response should still be divisible by all four numbers.)

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    If students are able to explain the divisibility of each large number in the Paired Practice, they understand how to use the divisibility rules. If they are able to successfully complete the group work and explain their answers, they understand the concepts behind divisibility. Make sure to circulate around the classroom during the group work portion of the lesson plan on the divisibility rule in order to make sure that each student understands the underlying concepts.

Math Lesson Plans

Math is a lot more than just crunching number, even at the elementary school level. This series contains several different lesson plans that math teachers can use in their classrooms.
  1. That'll Be a Dollar Ninety-Nine: A Rounding Numbers Lesson Plan
  2. A Hands-On Lesson Plan on The Divisibility Rule