Ohio Resource Center
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Content Supports - Activities and rich problems
Sums of Consecutive Whole Numbers: A Number Series Investigation
Discipline
Mathematics
Grades
8, 9, 10, 11, 12
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Professional Commentary

Students investigate sums of consecutive whole numbers with the aim of answering these questions: Can any whole number greater than 2 be written as a sum of consecutive whole numbers? If not, which can (cannot)? Four related questions are posed, with accompanying hints to be given as needed to prompt the solver toward a productive solution path. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)


Common Core State Standards for Mathematics
Standards for Mathematical Practice
CCSS.Math.Practice.MP2 
Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP8 
Look for and express regularity in repeated reasoning.
High School - Functions
Building Functions
Build a function that models a relationship between two quantities
HSF-BF.A.2 
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Ohio Mathematics Academic Content Standards (2001)
Mathematical Processes Standard
Benchmarks (8–10)
D.
Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.
Benchmarks (11–12)
A.
Construct algorithms for multi-step and non-routine problems.
B.
Construct logical verifications or counter-examples to test conjectures and to justify or refute algorithms and solutions to problems.
D.
Select and use various types of reasoning and methods of proof.
Principles and Standards for School Mathematics
Problem Solving Standard
Build new mathematical knowledge through problem solving
Reasoning and Proof Standard
Recognize reasoning and proof as fundamental aspects of mathematics