ALEX Lesson Plan

     

Creative Factor Trees

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  This lesson provided by:  
Author:Delia Martinez
System: College/University
School: University of Alabama in Huntsville
  General Lesson Information  
Lesson Plan ID: 33662

Title:

Creative Factor Trees

Overview/Annotation:

Students will explore and review prime and composite numbers. Students will also build a factor tree model by displaying how to write out a prime factorization of a number correctly, how to identify prime and composite numbers, and how to check their results. This hands-on approach allows students to use different mediums and practice their understanding of mathematics. 

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 4
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. [4-OA4]


NAEP Framework
NAEP Statement::
4NPO5b: Identify factors of whole numbers.

NAEP Statement::
4NPO5e: Apply basic properties of operations.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO5b: Recognize, find, or use factors, multiples, or prime factorization.

NAEP Statement::
8NPO5c: Recognize or use prime and composite numbers to solve problems.



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.4- Arrange, match, and/or recognize factor pairs limited to ones, twos, threes, fours, fives, and tens to their products using models or tools.


Local/National Standards:

CCSS.MATH.CONTENT.4.OA.B.4

NCTM Numbers and Operations Grade 4:

  • use factors, multiples, prime factorization, and relatively prime numbers to solve problems

Primary Learning Objective(s):

Students will be able to find the prime factorization of a number as well as identify prime and composite numbers.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

61 to 90 Minutes

Materials and Resources:

  • Teacher: construction paper, popsicle sticks, flash cards, pre-made poster example
  • Students: scissors, markers, poster board, notebook paper, pencil, glue 

        -optional items: crayons, colored pencils, math notebook

Technology Resources Needed:

Teacher laptop with internet, interactive board, projector 

Background/Preparation:

Advance Preparation: The teacher will need to bring in a completed example of the activity (poster), have materials out and ready, have the rubric handout printed out (provided as an attachment), have the math problems worked out ahead of time, and technology charged.

Background Knowledge: Students will need to know their multiplication facts, what a number raised to a power means (3^4 = 3*3*3*3), and what it means to be a prime or composite number. 

  Procedures/Activities: 

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 (attachment) will be provided for this activity

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

Explanation:

  • Class discussion: Have a few students (those that have finished their poster) share their poster with the class.
  • Ask students:
    • What their prime and composite numbers are and how 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) 



Attachments:
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  Assessment  

Assessment Strategies

Evaluation:

Students will be evaluated on their poster using the rubric.

Students can also be given 5 (or more) numbers and find the prime factorization as well as write it out correctly. This can be done in the student’s math notebooks and will need to be turned in so the teacher can check.

(Note: the teacher can choose any composite numbers)

Acceleration:

  • Students can test themselves by playing the “Design a Forest” game that allows them to practice writing out prime factorization factors correctly.

Intervention:

  • ELL: The lesson includes lots of visual demonstrations from games, the explanation of how to write out the factors of a number correctly, and a poster example. Students can also be given additional scaffolding with more visual examples and additional time if needed.

  • Students with disabilities: Students will be given an extended deadline if needed. Students can work with an aide or a peer helper. The poster will also allow students to see their representation as well as use a variety of textures and mediums.

  • Students who struggle academically: Provide additional scaffolding with these students. check to make sure they know how to complete the task starting with smaller examples and moving to higher numerals. Allow enough time for them to practice first and then do the poster.

  • Gifted/advanced: Students who are comfortable working with numbers within 100 will be encouraged to try higher composite numbers to solve the prime factorization. They will also have the option to work as peer helpers for other students who need extra help.


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.