
06145601
j
2013b.00698
Somchaipeng, Tongta
Kruatong, Tussatrin
Panijpan, Bhinyo
Using disks as models for proofs of series.
Math. Teach. (Reston) 106, No. 1, 4650 (2012).
2012
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
I34
U64
mathematical logic
high school students
secondary school mathematics
core curriculum
state standards
series
sums of squares
sums of cubes
manipulative materials
doi:10.5951/mathteacher.106.1.0046
http://www.nctm.org/publications/article.aspx?id=33622
Summary: Exploring and deriving proofs of closedform expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmeticalgebraic or combinatorial in nature, or they may involve mathematical induction. In the activity described in this article, students use balls and disks to prove the general formulas for sums of squares and cubes. (ERIC)