NCDPI AIG Instructional Resource: Background InformationResource
Title: Abundant, Deficient, Perfect, and Weird Numbers
Subject Area/Grade Level (s): Math/6Time Frame: 45 minute
class
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 Mathematics1. 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): x
Enrichment x Extension Acceleration
Adaptations for AIGs: x Content x Process 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.
Needed Resources/Materials: Abundant, Deficient, Perfect, and
Weird Numbers worksheet
Sources: NA
TEACHER NOTES: NAAnswer key follows the student worksheet
NCDPI AIG Curriculum Resource OutlineSTAGE 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 InstructionAIG ~ IRP Academically and/or
Intellectually Gifted Instructional Resources Project
