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Arrays, Factors, and Number Theory

Jennifer Talley
6th grade
Rossville Middle School
Walker County Schools


In this task, students will work to find the arrays of numbers 1-20 and how factors and fact families are used to create the arrays, Students will also analyze number theory properties such as prime, composite, even, odd, and square numbers.

Illustrative Task
Create, draw or shade all possible arrays for the numbers 1-20.
  1. Label all of the dimensions of the arrays, which are the factors of each number.
  2. Look for patterns in the arrangements, factors, or drawings.
  3. Describe the patterns or observations that help you “see” the factors, prime numbers, composite numbers and square numbers.
  4. In the numbers 1-20, label the prime, composite, and square numbers.
  5. Describe all the things you notice about the arrays and patterns, but especially discuss what you notice about the number 1.

GPS Addressed
M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.
  1. Apply factors and multiples.

Video Information
Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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