Students create a factor tree with numbers between 1 and 100.

**Class:** Fourth Grade

**Duration:** One class period, 45 minutes in length

**Materials:**

- blackboard or whiteboard
- paper for students to write on
- If you prefer a more artistic touch, copies with four evergreen tree shapes per page

**Key Vocabulary:** factor, multiple, prime number, multiply, divide

**Objectives:** In this lesson, students will create factor trees.

**Standards Met:** 4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

**Lesson Introduction:** Decide ahead of time whether or not you wish to do this as part of a holiday assignment. If you prefer not to connect this to winter and/or the holiday season, skip Step #3 and references to the holiday season.

**Step-by Step Procedure:**

- Discuss learning target: To identify all of the factors of 24 and other numbers between 1 and 100.
- Review with students the definition of a factor. And why do we need to know the factors of a particular number? As they get older, and have to work more with fractions with like and unlike denominators, factors grow increasingly important.
- Draw a simple evergreen tree shape at the top of the board. Tell students that one of the best ways to learn about factors is by using a tree shape.
- Begin with the number 12 at the top of the tree. Ask students what two numbers can be multiplied together to get the number 12. For example, 3 and 4. Underneath the number 12, write 3 x 4. Reinforce with students that they have now found two factors of the number 12.
- Now let’s examine the number 3. What are the factors of 3? What two numbers can we multiply together to get 3? Students should come up with 3 and 1.
- Show them on the board that if we put down the factors 3 and 1, then we would be continuing this work forever. When we get to a number where the factors are the number itself and 1, we have a prime number and we are done factoring it. Circle the 3 so that you and your students know that they are done.
- Draw their attention back to the number 4. What two numbers are factors of 4? (If students volunteer 4 and 1, remind them that we aren’t using the number and itself. Are there any other factors?)
- Below the number 4, write down 2 x 2.
- Ask students if there are any other factors to consider with the number 2. Students should agree that these two numbers are “factored out”, and should be circled as prime numbers.
- Repeat this with the number 20. If your students seem confident about their factoring abilities, have them come to the board to mark the factors.
- If it is appropriate to refer to Christmas in your classroom, ask student which number they think has more factors - 24 (for Christmas Eve) or 25 (for Christmas Day)? Conduct a factor tree contest with half of the class factoring 24 and the other half factoring 25.

**Homework/Assessment:** Send students home with a tree worksheet or a blank sheet of paper and the following numbers to factor:

- 100
- 99
- 51
- 40
- 36

**Evaluation:** At the end of math class, give your students a quick Exit Slip as an assessment. Have them pull a half sheet of paper out of a notebook or binder and factor the number 16. Collect those at the end of math class and use that to guide your instruction the next day. If most of your class is successful at factoring 16, make a note to yourself to meet with the small group that is struggling. If many students have trouble with this one, try to provide some alternate activities for the students who understand the concept and reteach the lesson to the larger group.