Arranging Numbers in Multiple Ways

Explicit Instruction/Teacher modeling

• 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.

Guided Practice

• 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.

Independent working time

• 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.