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Students will be able to use divisibility rules to determine factors of whole numbers.
- 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.
- Use a smaller number as the introductory number for students to consider such as 2,364.
- Provide a student-friendly definition of "divisibility" in students' home language (L1) and English (L2) and display it throughout the lesson.
- Have students discuss with a partner whether or not the introductory number is divisible by 3 to activate their prior knowledge.
Explicit Instruction/Teacher modeling(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.
- Provide a word bank of terms needed to complete the Divisibility Rules worksheet.
- Work together with students to create posters with visuals, words, and examples for each divisibility rule.
Guided Practice(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.
- Place students in pairs to discuss the divisibility of the numbers presented in the beginning part of this section.
- Provide students with a partially completed Divisibility Puzzle worksheet.
- Provide student-friendly definitions for relevant terms in L1 and English, such as "sum," "digit," "divisible," and "quotient."
Independent working time(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.
- Allow students to work in partnerships on the Divisibility Challenge.
- Pull aside a few students in a small teacher-led group and guide them through the more complex numbers in this challenge portion of the lesson.
- 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).
- 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).
- 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.
- Display a sentence frame to help students justify their answer: "I know this number is divisible by ____ because ____."
- Allow students to discuss with a partner and use a whiteboard or scratch paper to check for divisibility before showing a thumbs up or down.
Review and closing(5 minutes)
- Show the Divisibility Rules Song (see related media).
- Show the video twice with closed captions and provide definitions for any tricky words.
- Ask students to state one detail they found interesting from the video in their L1 or L2.
- Provide printed copies of the lyrics of the song from the video for students to refer to and take notes on.