Some numbers can be written as a sum of consecutive positive integers, for example:
6 = 1 + 2 + 3
15 = 4 + 5 + 6
= 1 + 2 + 3 + 4 + 5
Exactly which numbers have this property?
When investigating this problem, Joe made the following conjecture: "A number with an odd factor can be written as a consecutive sum and the odd factor will be the same as the number of terms." Agree or disagree with this statement and explain your reasoning.
Consider the following modifications for learners who need additional support, including English learners and students with special needs:
- Discuss what consecutive means by giving an example and non-example
- Discuss what investigating and conjecture mean
- Discuss even and odd numbers
- Remind students of the meaning of factor in this context
- Provide base 10 blocks for students to make the sums manipulatively
Ensure any modification does not reduce the cognitive demand of the task.