# The Factor Tree Strategy

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This lesson can be used as a pre-lesson for the Divisibility RulesLesson plan.

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This lesson can be used as a pre-lesson for the Divisibility RulesLesson plan.

Students will be able to use divisibility rules to determine factors of whole numbers.

##### Language

Students will be able to identify prime factors of a whole number using the factor tree strategy.

(3 minutes)
• Write the word "factor" on the board and ask students to discuss what the word means with a nearby partner.
• Invite students to share their discussion and record their responses on the board. Inform students that a FactorIs a number that is multiplied to get another number. For example, in the number sentence 5 x 6 = 30, the numbers 5 and 6 are factors.
• Tell students that today they will a learn a strategy called factor trees to find all the factors of a whole number.
(8 minutes)
• Introduce the remaining vocabulary words to students by displaying the vocabulary cards on the document camera. Read aloud each word and its definition.
• Model to students how you complete a Frayer model for the term Product. Remind students that the word product has other meanings too, but for the purpose of this lesson, the focus is on its mathematical significance.
• Define the term and provide examples, non-examples, an image, and a sentence with the word. Model how to share the completed model with the class, carefully reading aloud each section.
• Place students into A-B partners. Hand out a blank Frayer Model to each student. Assign the A partners the term Prime numberAnd the B partners the term Composite number.
• Instruct students to complete the Frayer model and share it with their partner, explaining all sections of the model.
• Invite a few non-volunteers to share key points of their partner's vocabulary word to check for understanding.
(10 minutes)
• Explain to students that they will first learn how to use the tree factoring method and then they will play a game which involves matching a factor tree to its product and prime factors.
• Reiterate that a Prime numberIs a number that can only be divided by 1 and itself. In other words it cannot be divided, or broken down, further. The only factors of a prime number are 1 and itself.
• Write a list of the prime numbers up to 20 (1, 2, 3, 5, 7, 11, 17, 19) and demonstrate how they cannot be broken down into more factors.
• Inform students that it is helpful to find all the prime factors of a product because they are essentially the building blocks of a product. When you multiply all the prime factors, you will get the number.
• Distribute the Factor Tree worksheet to students and display a teacher copy on the document camera.
• Explain that the strategy is called factor trees because it looks like you are building a tree with branches and leaves.
• Read aloud the teaching box at the top of the worksheet and walk students through the sample problem.
• Model how to make a factor tree for the first problem. Show students that sometimes the factor trees for the same product can look slightly different. Model this with 100 (e.g., start 1 factor tree with 4 x 25, and another with 10 x 10). Demonstrate how you still get the same prime factors (circle the prime factors) no matter which way you break it down. Box the composite numbers and remind students of the definition of composite numbers.
• Place students into effective partnerships and have them work on the remaining three problems collaboratively with their partner. Instruct them to circle the prime numbers and box the composite numbers.
• Display the following sentence frames for students to use as they discuss with their work with their partner:
• "I know that the factors of the number ____Are ____."
• "I know that these are all the prime factors of this number because ____."
• Review the factor trees as a whole class once everyone has completed the exercises. If some pairs solved the problem differently, take some time to compare and contrast the strategies.
(10 minutes)
• Tell students that they will take the knowledge and skills they learned related to factor trees to play a matching game.
• Distribute the premade cards to students; each student should get one card. Explain that some students have a whole number or a product, some have a factor tree, and others have a list of prime factors for said product.
• Explain that this is an activity in which they will have to analyze their card, then communicate or talk to their classmates to find the other two cards that go with their card. Once the three cards have been matched, students will have to justify their thinking.
• Display the following sentence stems and frames prominently so students can refer to them easily throughout the activity:
• "I have a card with..."
• "I need to find cards with ____And ____."
• "These cards match because..."
• Model how to complete the sentences orally while looking at a card and matching them up (e.g., "I have a card with the prime factors 2, 3, and 3. I need to find cards with the factor tree that has 2, 3, and 3 and the product 18. These cards match because when I multiply 2 x 3 x 3, I get the product 18.").
• Instruct students to begin the matching activity by walking around the classroom to find their matches. Remind them to look at the sentence stems/frames to help them talk to their classmates to match the cards. Once students have formed groups of three matched cards, redistribute the cards and repeat the activity. Note: try to give students a chance to work with each type of card.

Beginning

• Allow students to do the matching activity with a partner.
• Translate key terms into students' home language (L1).

• Have students work on matching the cards independently at their desks.
• Ask students to rephrase instructions and paraphrase important learning points throughout the lesson.
(5 minutes)
• Distribute an index card to each student. Write the number 48 on the board.
• Have students find all the prime factors of this number using the factor tree strategy. Tell them to circle the prime factors and box the composite numbers.
• Use the index card as an exit ticket to check for understanding.
(4 minutes)
• Ask students to think-pair-share and consider why it is important to know the prime factors of a product.
• Have them orally complete the sentence stem with their partner: "It is important to know the prime factors of a product because..."
• Call on a few students to share their sentences with the whole class.

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