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Consecutive Sums
A consecutive sum is an adding sequence of consecutive whole numbers.
Examples:
2+3
8+ 9 + 10 + 11 + 12 + 13
7 + 8 + 9 + 10
x + (x+1) + (x+2)
Your Task:
Write the first 35 counting numbers (1 through 35) with as many
consecutive sums as possible.
For example, the number 15 can be written as 7 + 8 or 4 + 5 + 6 or
1 + 2 + 3 + 4 + 5. HINT: Organizing your work will help you to find
patterns.
• Find as many patterns as you find. Are there any numbers that cannot be
written with consecutive sums? Are some numbers easier to find than
others? Write as many generalizations as you can about the patterns you
found.
• Think about WHY your patterns are always true (algebra can be useful
here).
• From the patterns you found, could you find all the consecutive sums
possible for any given number? For example, can you write all the ways
91 or 64 or 200 can be written as consecutive sums?
We will do a project “write-up” for this AFTER Winter Break, so please keep
all of your notes regarding patterns in your binder.
Enjoy your Winter Break…..Happy Holidays!
You final project (which we will do AFTER winter break!) will include:

Title Page. This includes the title (Consecutive Sums), thematic
clipart/decorations, your first and last name, and the due date)

Paragraph 1 – copy the following:
A consecutive sum is an adding sequence of consecutive whole
numbers.
For example:
2+3
8+ 9 + 10 + 11 + 12 + 13
7 + 8 + 9 + 10
x + (x+1) + (x+2)
My task is to write the first 35 counting numbers with as many
consecutive sums as possible, then look for patterns.

Paragraph 2
Describe the patterns you found. Are there any numbers that cannot be
written with consecutive sums? Are some numbers easier to find than
others? Write as many generalizations as you can about the patterns you
found.

Paragraph 3
Discuss how you can find all the consecutive sums possible for any given
number using patterns that you found. For example, can you write all the
ways 91 or 64 or 200 can be written as consecutive sums? Explain
completely.

Attach the Consecutive Sums chart (2 pages) to the back of your report.