Recursion: Smaller Sibling Pyramids

1 388 Download(s)

Lesson synopsis

humanRecursion, Iteration (Looping), and Concurrency. In the first of two sessions (at most an hour each), students are asked to calculate a simple summation by themselves, based on a procedure they are given. Then, through a guided role-playing procedure, students are asked to do the same problem by pushing a sub-problem off onto a ‘little sibling’. In the second session, they use a divide-and-conquer approach to understand a simple formula for summation. During this session they also talk about the big ideas behind these three problem solving methods.

Age Levels

8 - 13 years


Introduce students to:
how arithmetic sequences solve real world problems
tail-end recursive algorithms for arithmetic series
a divide and conquer approach that leads to a simple formula
informal ideas about time complexity.

Anticipated learner outcomes

Students will be able to describe how to solve an arithmetic sequence summation problem:
by doing it again and again (non-concurrent iteration)
with a smaller sibling (tail-end recursively)
articulate that both methods take the same number of steps, but recursion is less work for the individual
divide and conquer has a surprising outcome – namely a formula that can be calculated in only a few steps.

Optional Writing Activity

This activity introduced the idea of how to efficiently calculate an arithmetic series, such as 1+2+3+4. This could be used to calculate the simple human pyramid where one person is added as support for each layer. Invent your own problem that produces a different arithmetic pattern such as 1,5,9,13,17. Ask someone in your class to solve it by simple addition, by recursion, and to see if they can come up with a formula based on divide and conquer.
Sandra Lerner

It is difficult to imagine a time when computers were not capable of sharing information and resources with great ease. Sandra Lerner pushed the boundaries of network computing as one of the co-founders of Cisco Systems, which introduced one of the first commercially viable routers. The router was born while Sandra was working at Stanford University in the 1980’s after earning her Master’s degree there in Computer Science. To avoid the tedious task of transferring information between computers using floppy disks, she and co-founder of Cisco, Leonard Bosack, created a local area network, or LAN, between their campus offices using a multiprotocol router that Bosack developed. Shortly thereafter the pair started Cisco Systems, and began selling the router which was a success, because it could work with so many different types of computers. After Leaving Cisco in 1990, Lerner started the trendy cosmetics company Urban Decay and became a philanthropist and avid activist for animal rights.

First computer mouse
Douglas Engelbart
Douglas Engelbart

In 1967, Douglas Engelbart applied for a patent for an "X-Y position indicator for a display system," which he and his team developed at the Stanford Research Institute (SRI) in Menlo Park, California. The device, a small, wooden box with two metal wheels, was nicknamed a "mouse" because a cable trailing out of the one end resembled a tail.

In addition to the first computer mouse, Engelbart’s team developed computer interface concepts that led to the GUI interface, and were integral to the development of ARPANET--the precursor to today’s Internet. Engelbart received his bachelor’s degree in electrical engineering from Oregon State University in 1948, followed by an MS in 1953 and a Ph.D. in 1955 both from the University of California, Berkeley.

Liz Gerber - Image credit Lisa Beth Anderson
Liz Gerber
Liz Gerber - Image credit Lisa Beth Anderson

Liz Gerber earned her MS and PhD in Product Design and Management Science and Engineering at Stanford. She specializes in design and human-computer interaction, particularly how social computing supports the innovation process. Her current research investigates crowd-funding as a mechanism for reducing disparities in entrepreneurship.
Gerber's work funded by the US National Science Foundation and the National Collegiate Inventors and Innovators Alliance has appeared in peer-reviewed journals, including Transactions on Computer Human Interactions, Design Studies, and Organization Science.
As an award-winning teacher and researcher, Liz has touched the lives of more than 6,000 students through her teaching at Northwestern's Segal Design Institute and Stanford University's Hasso Plattner's Institute of Design and through her paradigm-shifting creation, Design for America, a national network of students using design to tackle social challenges.

Image credit - Lisa Beth Anderson

CGA palette
Mark Dean

If you have ever used a PC with a color display you have been acquainted with the work of Mark Dean. After achieving a Bachelor’s degree in electrical engineering from the University of Tennessee, Dean began his career at IBM. Dean served as the chief engineer on the team that developed the first IBM PC, for which he currently holds one third of the patents. With colleague Dennis Moeller, he developed the Industry Standard Architecture (ISA) systems bus, which enabled peripheral devices such as printers, keyboards, and modems to be directly connected to computers, making them both affordable and practical. He also developed the Color Graphics Adapter which allowed for color display on the PC. Most recently, Dean spearheaded the team that developed the one-gigahertz processor chip. Dean went on to obtain a MSEE from Florida Atlantic University and a Ph.D. in electrical engineering from Stanford University. He is a member of the National Academy of Engineering, has been inducted into the National Inventors Hall of Fame, and is the first African-American IBM Fellow.

King's Quest
Roberta Williams

Video games immerse users in a world of high tech thrills, stunning visuals, unique challenges, and interactivity. They enable users to become a warrior princess or a gruesome ghoul, create a virtual persona, or even develop worlds that other gamers can play on. But before the games of today became reality, they were the dreams of a few innovative individuals.

Roberta Williams is considered one of the pioneers of gaming as we know it today. During the 80’s and 90’s along with husband Ken Williams through their company On-Line Systems, she developed some of the first graphical adventure games. These included such titles as Mystery House, Wizard and the Princess and the popular King’s Quest series. Williams also helped introduce more girls and women to the world of gaming by bringing games developed from a woman’s perspective to mainstream market.

Image credits