Prime and Composite Numbers – Factoring

Why is factoring so important?

Students enter our math classrooms with a wide range of skills. Many of those skills are essential for success in their current courses. Spending the time in your classroom to teach the essential skills can really pay off. It gives students a chance to show what they know or fill in the gaps. Theses skills also serve as a springboard into a more complex topic.

Something that many of my students have struggled with in the Algebra 1 classroom is factoring. As a result, I usually begin the year with some prime and composite number and prime factorization review. Students complete A LOT of factoring in Algebra 1 so this is definitely an essential skill.

How to introduce students to factoring

Introduce your students to the key terms factor, prime number, composite number, and prime factorization. Then, go through a few examples. Next, build factor fluency for the numbers 1-100.  You can do this by having students start class by completing a prime factorization, inserting some review into homework practice, or by playing a quick game as described below.

Math Game – Prime and Composite Numbers

Use this quick game as a warm-up or review break. Students will get practice identifying prime and composite numbers. They will also develop fluency with factoring numbers 1-100. Work at a beginning or advanced level based on student needs.

Factoring with Beginning Number Cards

The beginning number cards have each number 1-100 identified as a prime or a composite number. The prime factorization is also listed on the card. Use these cards if students are still struggling to identify primes and composites AND/OR they are just beginning to develop fluency with prime factorization.

Factoring with Advanced Number Cards

These cards are just numbers 1-100. Students will need to be able to identify each number as a prime or composite. They will also need to complete the prime factorization of composite number on their own. Use these cards if students are able to successfully identify prime and composite numbers AND/OR they can factor a composite number into the product of prime numbers.

Instructions

This game can be played as a whole class, in small groups, or individually. Students will need a game card — beginning or advanced based on the number card deck they are using. They will draw from the deck until they get a composite number. They will write the prime factorization of the composite number on their game card.

When everyone has their prime factorization written down, the first factor card can be drawn. Students will check their prime factorization to determine whether that factor is in their prime factorization. If the factor is present in their prime factorization, they can write one tally mark in the box. The factor card goes back in the factor card deck and a new factor card is selected.

Students again check to see if they have the factor in their prime factorization, and so on. The same factor may be drawn multiple times and they can get the tally mark each time.

The point of the game is to begin to recognize the factors in each number. The game ends when a student gets 5 tally marks. If time permits, students can draw another number card and play again.

Printing Suggestions

We would suggest printing each set of cards — the Number Cards (Beginning), the Number Cards (Advanced) and the Factor Cards – on different colored card stock so that you can easily identify each set. The game cards can be printed on regular printer paper. You can get the prime and composite number game here for free.

Final thoughts

Fluency with prime factorization will make things like simplifying expressions and factoring binomials much easier. You can help your students get more experience with integers by getting our complete guided notes curriculum for integers here. How do you incorporate review of essential skills into your class routine? Share with us in the comments below.