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# Divisibility Rules

Do you need extra help for EL students? Try the The Factor Tree Strategy pre-lesson.

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Do you need extra help for EL students? Try the The Factor Tree Strategy pre-lesson.

Students will be able to use divisibility rules to determine factors of whole numbers.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
(5 minutes)
• Write a large number on the board (e.g., 219,438) and ask students, "Is this number divisible by 3?"
• Take a quick poll or ask for students to respond with thumbs up or down.
• Explain: "Today we are going to learn some special rules that will help us recognize divisibility. By the end of our lesson, you will know some shortcuts that will make it easy for you to determine if numbers, even huge numbers like this, are divisible by other numbers like 2, 3, 4...!"
• Leave the number written on the board to revisit at the end of the lesson.
(10 minutes)
• Review the definition of divisible: a number is divisible by another number if you can divide it by that number without a remainder (e.g., 20 is divisible by 5).
• Hand out the Divisibility Rules worksheet and as a class complete the rule chart. Have students volunteer examples to add to the chart.
(15 minutes)
• Write a two-digit number on board and ask: "Is this divisible by 2? 3? 4?" Have students raise hands or show thumbs to respond. Repeat with several numbers.
• Hand out the Divisibility Puzzle worksheet. Read the instructions aloud and have students complete the puzzle with a partner.
• Circulate the room as partners work, providing support as needed, and then review the puzzle as a class.
(10 minutes)
• Direct students' attention to the divisibility challenge on the Divisibility Rules worksheet. Complete the first two boxes as a class.
• Instruct students to finish the challenge independently, using their rules chart as a guide.
• Circulate the room as students work and provide support as needed.
• When students are finished, review the worksheet as a class.

Support:

• Provide students a pre-filled rules chart.
• Provide students a partially completed Divisibility Puzzle.
• Give students extra practice with with simplified worksheets (see optional materials).

Enrichment:

• Have students think of a number that is divisible by all the numbers on the rule chart (2, 3, 4, 5, 6, 9, and 10).
(5 minutes)
• Revisit the number you wrote on the board at the beginning of the lesson. Ask students to look at the number again and ask them, "Is this number divisible by 3?"
• Have students reply with a thumbs up or down, then ask a few students to justify their answers.
• Ask: "What else is this number divisible by? How do you know?"
• Collect finished independent practice worksheet and check for understanding.
• Use observations from guided and independent practice to identify students who will need additional support.
(5 minutes)
• Show the Divisibility Rules Song (see related media).

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