Finding Factors and Prime Numbers

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SWBAT find factor pairs for a given number and use them to determine if a number is prime or composite.

Big Idea

Students will compose and decompose numbers using a factor tree.

Warm Up

6 minutes

I review with students the definition of a factor. Students need to know what factors are because as they get older, and have to work more with fractions with like and unlike denominators, factors grow increasingly important.  I also review the definition of product and multiples.

Definitions I use:

Factor-  numbers you can multiply together to get another number.  4 x 5 = 20, 4, and 5 are factors

Product - The answer when two or more numbers are multiplied together.  In the above answer, 20 is the product.

Multiples - A number that is the product of a given number and some other number.  20 is a multiple of 4 since 4 x 5 = 20.


Concept Development

40 minutes

Many students struggle with factoring. Factoring is a necessary step in order to advance into basic addition and subtraction of fractions.  Students must understand the concept that numbers can be broken down into factors. 

I start this lesson by writing several numbers on the board.  I write some prime numbers and some composite numbers, like, 7, 12, 13, 15, 17, 20

I then give students a few minutes to write all the factors they can think of for that number.  After a few minutes, we list the factors together.  I then ask students what they notice about the numbers and factors that are one the board.  Many students are able to see that some of the numbers only have two factors, 1 and its self.  I very dramatically say YES, those are special numbers called prime numbers.  I make sure to tell them that prime numbers are larger than 1. 

We list more numbers that students come up with as prime numbers.  From past experience, students need to hear this new vocabulary and definition many times before it makes sense.  I read it then, I might even say it and use it with my kids during desert or as I'm paying the bill, but I usually don't remember it the next day.  In order for this new knowledge and vocabulary to not end up like a fortune cookie word, I need to use it repeatedly through out the lesson and in the next few days.

Once students have identified prime numbers, I tell them that numbers that have more than one number pair also have a name, composite numbers.  We list some more examples of composite numbers. 

I have a multiplication chart hanging in my classroom and some students started making the connections between multiples and composite and prime numbers. One student commented that if the number was a product listed on the chart, except for 2,3, 5, 7, and 11, it was composite. This led to a great discussion that I was not expecting to have.  I was able to reiterate that yes, those products on the multiplication chart are named by factors other than 1 and the number, so they all were composite numbers.

I then tell students that I have some amazing information for them.  From past experience, fourth graders love rules that you can make about "ALL" numbers.  So, I tell them that all whole numbers, not including 1, are products of prime numbers.  I repeat this several times.

Then I show them a factor tree for 42 with the corresponding equation. 



3 x 2 x 7 = 42

Students think this skill of factoring is fun and engaging. I've tried thinking about why students find this skill so fascinating, and I'm not sure I totally understand why, but I'm glad they do.  I think there is a sense of satisfaction when they complete the tree and see all the prime numbers.  The next step, being able to use the tree to help determine all of a number's factor pairs takes more time. I show the class how to do this, during this lesson, but don't have a lot of time  to explore this in depth.

We also labeled a page in our math notebooks as Divisibility Rules.  In lessons that follow, I will present ways in which students can look for patterns and learn divisibility rules in order to find all the factors of a number in order to master standard 4.OA.4.

Students work with Math Practice Standard 7, make use of structure in this lesson. In order to identify the structure of a mathematical problem, students often need to engage in some form of visual learning or visualization. In early algebra this may mean that students are making a pattern or displaying data in a table to determine where a pattern exists. Structures are used to build place value and number sense. Students use various models in order to understand numbers and how they can be composed and decomposed. Students decomposed numbers into factors and looked or patterns as they determined whether numbers were composite or prime numbers.

Students also use Math Practice Standard 4 in this lesson as they model mathematics with a factor tree. A Factor Tree is a diagram used to break down a number by dividing it by its factors until all the numbers left are prime.

Student Debrief - Wrap Up

10 minutes

Students completed an exit ticket as a formative assessment today.  I asked them to draw a factor tree for 24, and list 4 prime numbers.