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# Arranging Numbers in Multiple Ways

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Students will be able to find all of the factors pairs of whole numbers up to 100 and decide whether a given whole number, within 100, is a multiple of a given one-digit number.

(5 minutes)
• To begin, tell students that this lesson focuses on multiplication.
• Ask students to share what they already know about multiplication. If you have already been studying multiplication, build on that, but if you have not, just let students share what they generally know.
• Explain that today's lesson will involve pairs, which you will introduce in a moment. Ask students to give examples of pairs.
(5 minutes)
• Write the number 14 on the board.
• Ask students if they know what a factor pair is. Explain that a factor pair is two numbers multiplied together to get a product.
• Explain that in today's lesson, students will work together to find factor pairs of whole numbers. Ask students what a whole number is. Remind them that a whole number is a number without fractional or decimal parts.
(15 minutes)
• Tell students that you will practice finding factor pairs together, before trying it in pairs.
• Point out the number 14 on the board. To check for understanding, ask students if 14 is a whole number and how they know.
• Model pulling out 14 cubes.
• Tell students that now we will need to make an array using the cubes. Ask students to define array. Remind them that an array is an arrangement in a particular way.
• Model making a 2 row by 7 column array. Write 2 x 7 on the board. Explain that you made a 2 x 7 array, which means that 2 and 7 are a factor pair of 14.
• Ask students other ways that we could arrange the cubes in a rectangle, to make an array. Make sure to show 7 x 2, 14 x 1, and 1 x 14, recording the factor pairs as they are made.
• Explain that they can use factor pairs to help understand multiples. Ask students if they know what a multiple is. Define multiple as the number found when multiplying one number by another.
• Explain that 14 is a multiple of 1, 2, and 7. Model skip counting by those numbers to reach 14.
• If needed, go through this process again, using 21 as the whole number.
(25 minutes)
• Explain to students that they will now work in pairs to find all of the factor pairs of various whole numbers under 100.
• Pair students up and hand out the How Many Ways Can You Arrange My Number? worksheet.
• Remind students to use cubes if they need to. They may also draw arrays on their papers.
• As students work, check in with pairs to make sure they are finding all of the factor pairs for each number.
• Encourage the use of cubes for students who need visual support.
• Students who finish early can work on the How Many Ways Can You Arrange 100? worksheet.
• Enrichment: Students who finish early can work on the How Many Ways Can You Arrange 100? worksheet. If they are also able to complete this, have them work on finding factor pairs of multiples of 100.
• Support: Students who need extra support can either work with partners or in a small group with teacher guidance. Make sure they use the cubes and understand how to make rectangular arrays.
(5 minutes)
• Take note of student participation in the different parts of the lesson.
• Check the worksheet and index card answers for mastery.
(10 minutes)
• Ten minutes before the end of the lesson, ask students to stop working and have them come together.
• Write the number 36 on the board.
• Hand out an index card to each student.
• Tell students to write: "1. One factor pair of 36 is..." and "2. 36 is a multiple of..."
• Tell students to think back over the lesson and fill in the answers on their index card.
• As this is an assessment of student understanding, students who are unable to give an answer will need more practice.

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