# Prime Factorization With Playing Cards

in Our Expert Talks

## An idea by Eric Roy, teacher

### The story took place in a Grade 5 class, while a teacher introduced the concept of factoring a number into its prime factors. Everything was going as planned when he realized that many students had difficulty identifying whether a number was prime or not and they even confused the signs of multiplication and addition when writing the factorization. In response to the dismay of his students, the teacher thought very hard about what he could do to help his students. Back home, he had an idea! See what surprises he had for his students in class!

#### The materials you will need

The model for factoring targets
2 decks of playing cards
The model to create new cards

Or

The model for the playing cards

#### How does it work?

There are two types of cards: the rectangular cards represent composite numbers, while those with their corners cut represent prime numbers.

Step 1
We pick a number (or target) to be factored

Step 2
We identify two factors. We can choose any factors and represent them with the cards. See below, in Example 1 and 2 we have chosen to represent 48 = 4 x 12, while in Example 3, 48 = 6 x 8 is represented.

Step 3
Just below, the rectangular cards are factored, and in each case we carry over the target number (48) to illustrate the equivalence between each step.

Step 4
If there are some rectangular cards remaining, we must factor them into the following line. We also carry over the cards that represent prime numbers. The product of each line should be 48. Here are three examples of prime factorization:

Example 1

Example 2

Example 3

Step 5
We put the similar cards together to find the prime factorization of the selected target number. Note that the three examples above arrive at the following result:

24 x 3 = 48

#### What are the possible interventions in the classroom?

If a student confuses “+” and the “x”
Ask the student to validate that the product of each line corresponds to the targeted number. In this way, the student who confuses the addition and multiplication in this context will be forced to say that it does not work. This will be an opportunity to help them step by step to understand why.

If the student has trouble recognizing a prime number
Gradually, as the student progresses through the factorization, he is exposed to distinction between two groups of cards: “prime number” cards and “composite number” cards. Thus, the use of this material may help recognize a prime number among other whole numbers.

#### Did this activity help your students? Don’t stop there, test them by sending them the activity “Factorization of a number into prime factors” on Netmath.

Strengthen and check your students’ understanding of prime factorization. Assign them this activity on Netmath before or after having accompanied them in class with the material developed by Mr. Eric Roy.

You will find this activity in the 5th grade book.

A big thank you to Mr. Eric Roy, who generously agreed to meet with me to explain how his ingenious creation works. Soon, I will present a small video demo. I invite you to carry out this activity in the classroom and share your experiences on our social networks.

Simon Lavallée,
Netmath Expert