Divide the class into groups of two or three students and give each group an equal number of a random assortment of dominoes.
Write a non-prime number on your blackboard and give the student groups 5 to 10 minutes to find all the factors of that number from among their selection of dominoes. Tell students they can use dominoes where both sides are factors of the number or only one side is a factor.
Check with each student group to make sure they correctly identified all of the factors they could. Write down all of the factors for the number you chose on the blackboard. Prompt students to volunteer to help you fill in the missing factors by raising their hands.
Ask the class what the factors for the particular number have in common. For example, for numbers that end in 0, any smaller number that ends in 5 or 0 will be a factor. Even numbers are all divisible by 2.
Repeat the activity for a few rounds until you feel that students are beginning to get the hang of it, or until the end of class period.
Divide your class into student groups of two and give each pair the same number of a random assortment of dominoes.
Give the student groups 5 to 10 minutes to multiply the two sides of each domino and write down the resulting product. The numbers that multiply together are both factors of the product.
Have the students determine which other numbers on their dominoes are also factors of the products they originally found. Have students list their responses on a sheet of paper.
Choose a student group or have a student group volunteer to describe their results to the class. List their products and factors on the board, and have other students volunteer to fill in any missing factors.
Have students describe the characteristics of a certain product that makes it divisible by a certain number. For example, all whole numbers are divisible by 1. Only even numbers are divisible by 2. Explain to students that if a number is divisible by another number, that second number is also a factor.