• model factors using tiles and grid paper
• differentiate between prime and composite factor trees
• illustrate prime factorization using factor trees

Chalkboard
Grid paper
Markers
Math journal or paper
Tiles or cut-out paper squares
*White board (Optional) 

Differentiation Strategies

• Varying academic levels: uses mixed-ability groups allow students to learn from one another, small-l and whole-group participation
• Visual learners: incorporates drawings of rectangles and factor trees
• Auditory learners: pairs students to work together and discuss solutions
• Kinesthetic learners: engages students in modeling and drawing rectangles to represent factoring

• Distribute 12 tiles or cut-out paper squares to each student.
• Ask each student to create a rectangle using the tiles or squares.
• Using a felt board with 12 square felt tiles or a white board, create a 12 x 1 rectangle. Ask students to raise their hand if they created a rectangle with these dimensions.
• Repeat this process with a 6 x 2 and a 3 x 4 rectangle.
• Explain to students that the sides of these rectangles represent factors and that 12, 6, 4, 3, 2, and 1 are factors of 12.

• Using grid paper, ask students to draw the rectangle that they create with the tiles.
• Ask them to use the grid paper to draw rectangles with 24 squares, 15 squares, and 11 squares.
• Ask students to share the factors they found for each of these numbers.
• Define composite and prime on the white board, and ask students to copy down these definitions on paper or in their journals.
•  Discuss the difference between the definitions of prime and composite in everyday language and in mathematical language.
• Call on students at random to pick a ping-pong ball or a piece of paper with a number out of a jar.
• Have students raise their hand to indicate whether they think the number is prime or composite.
• Use the white board or chalk board to illustrate how to factor the number to determine whether the number is composite or prime.
• Call on students at random to show on the white board whether the numbers such as 25, 27, and 29 are prime or composite.
• Define composite factor and prime factor on the white board, and ask students to copy down these definitions on paper or in their journals.
• Illustrate the prime factorization of 12 with tiles and using a factor tree.
• Explain to students that prime factors are usually listed from least to greatest.
• If appropriate, mention the use of exponents. 

• Create mixed ability pairs and ask students to use tiles, graph paper, and factor trees to show the prime factorization of three or four numbers.

• Invite students at random to show the factor tree and rectangles that they created to illustrate the prime factorization of each number.
• Ask students to show the prime factorization of two to three additional numbers in their math journal or on paper that they hand-in.

• Ask students to come up with ways to check their answers. If they do not mention them, suggest
• creating an additional factor tree
• multiplying the prime factors