Backward Design Model

Teaching Multiples and Factors


Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..

Enduring Understandings

  1. Multiples are the product of a number and an integer.
  2. Factors are the numbers that divide evenly into the number.
  3. Greatest common factor is the largest number that divides into both numbers.
  4. Least common multiple is the smallest multiple two numbers have in common.

Other Learning Outcomes

  • Communicate
  • Collaborate with others
  • CCSS.MATHPRACTICE.MP1 Make sense of problems and persevere in solving them.
  • CCSS.MATHPRACTICE.MP3 Construct viable arguments and critique the reasoning of others.


Instructional Strategies

Teaching Factors and Multiples

  1. Making Arrays of Skittles: Students will work in pairs with a bag of Skittles. They will be given tasks that require them to build arrays with the Skittles. The different arrays will show the factors. They will also look at multiples by following tasks asking them to determine the number of Skittles needed for each person to have a certain number.
  2. Eratosthenes Sieve: Students will follow a set of steps to eliminate multiples of different numbers to recognize trends in hundred chart and understand prime numbers.
  3. Share, Compare, Defend: Students will be given tasks which prompt them to find the GCF and LCM without using that terminology at the beginning of their learning. They will use strategies to solve the problem then compare and defend their answers.
  4. Rally Coach: Students will use the newly acquired strategy of using a factor tree to use the rally coach method of practicing with different problems. They will both act as a coach, listening to and correcting thinking, and as the student, explaining their thought process aloud in words.

Using the Backward Design Model

  1. Learning Outcomes and Enduring Understanding were chosen.
  2. Assessments and evidence of understanding were created.
  3. Teaching strategies were developed.