NCDPI – AIG Instructional Resource: Background Information
Resource Title: Abundant, Deficient, Perfect, and Weird Numbers
Time Frame: 45 minute class
Subject Area/Grade Level (s): Math/6
Common Core/Essential Standard Addressed:
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.4 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.
Common Core Standards for Mathematics
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
5. Use appropriate tools strategically.
6. Attend to precision.
8. Look for and express regularity in repeated reasoning.
Additional Standards Addressed: NA
Brief Description of Lesson/Task/Activity: This lesson is to be used during the unit in which students are working with factors. The standards
require that students work with common multiples and factors. This lesson focuses on proper factors of a number and how they can be used to
classify numbers.
Type of Differentiation for AIGs (include all that apply):
Adaptations for AIGs:
x Content
x Process
x Enrichment
x Extension
Acceleration
Product
Explanation of How Resource is Appropriate for AIGs: This lesson contains content that is not in the Common Core curriculum. It is an extension
lesson of using the factors of a number to classify it deficient, abundant, perfect and in some cases weird. This lesson can be used for students
who have mastered the general curriculum using factors.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Needed Resources/Materials:
•
Abundant, Deficient, Perfect, and Weird Numbers worksheet
Sources: NA
TEACHER NOTES: NA
Answer key follows the student worksheet
NCDPI AIG Curriculum Resource Outline
STAGE ONE: ENGAGE
Students must have mastered the skill of factoring a number. Students must be able to complete the following type of problem without difficulty.
Find all of the factors of 120.
Solution: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Students should be able to employ a problem solving strategy that allows them to find all of the factors. There is a variety of methods students
can use. Allow students to share their solution strategies and discuss the most practical methods for factoring. They may need to be reminded
that factors come in pairs.
STAGE TWO: ELABORATE
Depending on the group, the teacher can review the definitions and examples of a deficient, abundant, and perfect numbers. Some groups may
be able to do this on their own. Students can then complete the assignment individually, in pairs, or in small groups.
STAGE THREE: EVALUATE
Students can be given an exit slip with the following questions:
Are the numbers 110 and 225 abundant, deficient, or perfect? How do you know?
The proper factors of 110 are 1, 2, 5, 10, 11, 22, 55 and the sum of the proper factors is 106. The number 110 is deficient.
The proper factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and the sum of the proper factors is 144. The number 90 is abundant.
TEACHER NOTES: After 70, the next weird number is 836.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project