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
Which numbers have this property?
Sally made this conjecture: "Powers of 2 cannot be expressed as a consecutive sum."
Agree or disagree 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 a non-example
- Discuss what "conjecture" and "powers of two" mean
- Provide base 10 blocks for students to make the sums manipulatively
Ensure any modification does not reduce the cognitive demand of the task.