Factors are the components of multiplication problems. Students need to understand how to factor numbers, particularly when dealing with fractions. Factorization can be an extremely abstract concept for students. These hands-on activities can help teachers when introducing this complicated concept, making the abstract tangible and bringing the lesson home.

## Factoring “Tree”

On a sheet of brown construction paper, have students draw a tree trunk. On the trunk write the number 24. Below the trunk, have students draw roots with all the possible factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24. Have students complete this activity with other numbers. This is a useful activity for introducing prime factorization by continuing the roots to their prime factors.

## Sieve of Eratosthenes

This activity is effective in introducing prime factorization. Give students a board numbered 1 to 100 and a marker. Have them cross out the even numbers, excluding 2. Have students cross out every third number, excluding 3. Tell students to count by fives and cross out the numbers they count, excluding 5. Finally, have the students cross out every seventh number except for 7. Tell the students that the numbers that are not marked out are prime numbers. All numbers can be factored down or reduced using these numbers.

## Rectangular Arrays

Give students small squares made of paper or colored plastic tiles. Tell the students they are going to build an array to show the number 24. Students should group tiles into rows and columns, such as four rows of six, eight rows of three, and so on. Tell students that the different numbers of rows and columns represent the factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24. Have students represent all the possible arrays for the number 12. Extend the activity by giving students a list of numbers to represent in arrays on graph paper.

## Factor Sticks

Give each student 20 craft sticks and a marker. Have students write the numbers 1 through 20, one number per craft stick. On the back of the sticks, have students write the factors of each number from smallest to largest. Complete numbers 1 through 10 together as a class, and have students write factors for 11 through 20 on their own. Students can take these sticks home and use them to drill the factors for each number.

## Online Games

El Cerrito Wire (see Resources) offers several online games to practice factorization skills: "Factor Feeder," "Giant Rubber Turkeys of Destruction," "The Factor Game," "Factor Bingo," "The Grid Game" and "Factor Tree."