Creative Factor Trees

Procedure:

• Prior to the game, review key terms such as composite and prime numbers. Also, explain to students that the numbers you multiply to get a result is referred to as factors.

          -For example, in 2*3 =6 the factors would be 2 and 3

(Note: more examples can be included by the teacher if needed)

Engagement:

• Pull up the factor tree game on the interactive board or on the projector. Play the game as a class with volunteers going to the board after you have modeled an example first.

• Example: “Let's look at the number 24. What two numbers multiplied together can give us 24? It can be any two sets that give me 24 such as 2*12, 3*8, 6*4 (explain to students that if you do 1*24 it would lead you back to the same place of still finding factors of 24).” Next type in any two factors (let’s use 6*4 for this example) and ask students, “What factors make 6 and what factors make 4?” At this point, the game will note 6 and 4 as squares because they are composite and can be broken down by additional factors. Explain to students, “Since 6 is composite, it can be broken down by two factors such as 2 and 3 because 2*3=6. 4 can be broken down into the factors 2 and 2 because 2*2 =4.” Then ask “Can the 2’s and the 3 be broken down by anything else except one (1*3=3)? (Students should reply no if they reply yes then ask what other multiplication facts can make these numbers to clear up confusion).” “These numbers are prime because they have no other factors other than one and itself so they will be represented in circles”  

• This game notes prime numbers circled and composite numbers in a square shape. This is helpful so students can differentiate between the two numbers as well as see that prime numbers do not break down.

• After a few examples, make sure to explain how the answer can be checked. The game mentions not only the word “correct” for the answers but displays why the answer is correct with the prime factors of the number written out, for example:

          -Prime factorization of:   20

                                                 /    \

                                              5        4

                                              /          \

                                           2              2

         -This can be checked by multiplying 5*2*2 = 20

(Note: We multiply the prime numbers out which makes the original number)

• Explain to students that when a numeral is repeated it is written as an exponent.                                          -For example, the prime factorization of 20 would be 5* 2^2

• Have students practice a problem from the game (you can choose to do the next problem from the game that comes up or create one of your own) on their own piece of paper. Make sure they show how to check if the answer is correct. 

(Note: Walk around the class and check the work of students as they figure out the answer)

• Go over the problem showing what the factors should be, how to check the problem, and how to write out the problem with an exponent (if it contains more than one repeated numeral). 

• Practice 2-4 more problems. Repeat the process and show how to work out each problem, how to check it, and how to write it out each time.

Exploration:

• Students will be creating a visual representation of a number by showing the factors of each number and writing it correctly on a poster board.

• Students will choose a composite number up to 100. The teacher will show on the projector a list of composite numbers students can choose from.

(Note: Gifted/advanced students can use higher numbers)

• The teacher will note what number the students choose and will make sure all students have different numbers. 

(Note: allow students to think of a different number if students have the same number)

• Encourage students to use higher numbers instead of just one-digit numerals.

• The teacher will show a completed copy of the number 100. Make sure to explain that all composite factors should be represented one way (in the teacher example they are all in pink squares) and prime factors represented in a different way (in the teacher example they are in orange stars).

• The teacher will have popsicle sticks available that students can use for their factor tree model. Students are free to use markers, construction paper, glue, or any materials they need for their poster.

(Note: the teacher will need to have materials ready and out so students can use)

• Students will also be given a flashcard to write their final expression and glue onto their poster.

• A rubric will be provided for this activity

(Note: give students an appropriate deadline for this assignment)

Explanation:

• Class discussion: Have a few students (those who have finished their poster) share their poster with the class.
• Ask students:
  • What their prime and composite numbers are and how do they know this?
  • How to check if their prime factorization is correct.

(Note: Have the rest of the students share their poster after the deadline as the closure to this activity)