Factors are the numbers that can divide a given number and leave no remainder. To find the factor pairs of a number means to identify all the pairs of numbers that multiply to give that number. This concept is important for students to learn as it forms the basis for more advanced math concepts. Here are some activities that teachers can use to teach students how to find all the factor pairs of a number:

**1. Factor Pair Sort:**

In this activity, students will work in pairs and take turns selecting a number from a pile of cards. They will have to identify all the factor pairs of that number, and write them down on a piece of paper. The first student to find all the factor pairs will win a point. Play continues until all the cards have been used, and the student with the most points wins.

**2. Factor Tree:**

Students can develop a “factor tree” to help them find all the factor pairs of a particular number. Begin with the number at the top of the tree, and draw branches to each factor pair, breaking them down into smaller numbers until all the factors are prime numbers. This method makes it clearer for students to see all the factors and factor pairs of the number.

**3. Multiplication Table:**

Students can use the multiplication table as a reference to identify all the factor pairs of a number. They can identify all the factors of the number and write them down in a column, then match each number with its complementary factor to find all possible factor pairs.

**4. Factor Diagram:**

A factor diagram is another method that can be used to identify all the factor pairs of a number. Draw a rectangle with the number at the top, and divide it into two columns. The factors of the number will be listed in the left column and the complementing factors will be in the right column.

**5. Grouping Method:**

Students can use the linking of factors method to find all the factor pairs of a number. They begin by listing all the factors of the number in pairs. Then divide each pair and list the factors to which they can be further divided. Continue the process until the factor pairs cannot be divided further.

In conclusion, these activities are all effective tools to teach students how to find all the factor pairs of a number. Teachers can use one or a combination of these activities to make math concepts even more exciting and engaging for students. It is essential to help students understand these concepts, as they are the foundation for more advanced mathematics skills.