# What's my sum? (lesson)

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Note: for full lesson w/lab questions, open the attached document

Synopsis
Students use paper cutting to understand how an infinite sum can result in a finite number.

Main Standard
MA8.0 Students are familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether certain sequences converge or diverge.

Materials
Scissors
Copies, What’s My Sum?, Part I
Copies, What’s My Sum? Part II

Teacher Directions

Pass out What’s My Sum?, Part I. You may want to model the first cut for the students. Although, in some classes you may find you don’t need to model it for them.

Group Work
Problem #3 – student teams may need help with the fact that this sum is really never ending. They may use ellipsis (…) to show that the sum is infinite.

Discuss problems 1-6, and then depending on when you choose to do this activity, the students may or may not know how to write the notation in number 7.

What’s My Sum?, Part II are also area problems, similar to what they just put together.

You may want to model part (a) for the groups. Cut a piece of square paper into fourths and this time make 3 piles. Then take the fourth sheet and cut that into fourths and distribute the pieces into the 3 piles with one left over, etc.