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Grade 5: Division, Prime Numbers, Factors, and More

Students in Dr. Rhonda Pickup’s math class showed their understanding of division, divisibility rules, factors, composite numbers, prime numbers, prime factorization, and exponents when they created factor pair and factor tree posters in a classroom activity.
After reviewing the divisibility rules as a class, they practiced breaking down and identifying the factors and prime numbers of 126. They worked individually or with a partner to find a number’s factors and prime factorization.  Students reinforced their knowledge of exponents by writing their prime factorization in exponential form.  Dr. Pickup was able to differentiate the lesson by offering smaller numbers to those who are still getting comfortable with the concept of factors and prime factorization. Those who wanted more challenge could choose a four-digit number.
“We’re going to study fractions soon and being able to identify factors will be important,” Dr. Pickup told students. “I promise you that fractions will be so much easier once you understand factorization.”
Julia Bograd and Sydney Thompson worked together to find the factors and prime factorization of 1,632. “There are a lot of factors,” Julia admitted. They divided the work by odd and even numbers, getting into the 30s by the end of class. They clearly understood that they could only stop finding factor pairs if they hit one of the three rules to stop: If the digit repeats itself (6 x 6), if the factor pair contains consecutive numbers, if the next factor is already listed with the last factor posted. 
Once their work was reviewed and approved, students transferred their work onto colorful sheets of paper that were displayed in the classroom. Before dismissing students for the day, Dr. Pickup reminded students that they are working on finding factors because they will begin to find equivalent fractions and reduce fractions to their simplest form. Recognizing the exponential form from the prime factorization will help solve equations using the order of operations. 
Divisibility Rules: A number can be divisible by … 
1 - all numbers can be divided by one
2 - if the number is an even number
3 - if the sum of the digits is divisible by 3
4 - if the last two digits are divisible by 4
5 - if the last digit is 0 or 5
6 - if the number is divisible by BOTH 2 and 3
7 - divide and find out
8 - divide and find out
9 - if the sum of the digits is divisible by 9
10 - if the last digit is 0

Graland Country Day School

Graland Country Day School is a private school in Denver, Colorado, serving students in preschool, kindergarten, elementary, and middle school. Founded in Denver in 1924, Graland incorporates a rich, experiential learning approach in a traditional classroom setting, emphasizing the development of globally and socially conscious leaders who excel academically.