<< Chapter < Page
  The game of pig   Page 1 / 1
Chapter >> Page >

Pow: a sticky gum problem

Intent

As with all POWs, students explore a problem outside of class and communicate their thinking in writing. This POW taps students’ developing skill at finding and using patterns from the previous unit, and asks students to count possible outcomes, a strategy used throughout the current unit to find probabilities. This POW also helps students understand what is meant by a generalization. It also provides a constructive opportunity to understand what distinguishes a POW from an ordinary homework assignment: the focus on generalization and exploration.

Mathematics

At the heart of this activity is the counting concept known as the “pigeonhole principle.” Informally, the pigeonhole principle states that if you have more pigeons than pigeonholes, at least one of the holes will contain more than one pigeon. In this activity, the “pigeonholes” are different colors of gum balls. If two children want to buy gum balls of the same color from a machine containing gum balls of three colors, in the worst case , the first three gum balls would be three different colors (they will fill the three pigeonholes). The next gum ball would have to match one of the first three. So, the children would have to buy at most four gum balls to be sure to get two of the same color.

Progression

This POW is introduced at the start of the unit, with presentations about a week later.

Approximate time

10 minutes to pose activity and short periods to check on progress

1 to 3 hours for activity (at home)

20 minutes for presentations

Classroom organization

Groups of 3 or 4 for brief segments, concluding with whole-class presentations

Doing the activity

Students can begin working on this POW on the first day of the unit. The activity begins with several special cases and then asks students to search for a general method, given any number of children and any number of colors, for finding the number of gum balls one must buy to be sure the children all get the same color gum ball. A class discussion of the first special case—in which the answer is given and students are asked to explain why it is correct—might help students get started.

Discussing and debriefing the activity

After a week or so of having students work outside of class, with perhaps a portion of one day devoted to a progress check, have some students present their results.

Focus the discussion on the process of trying different examples, organizing the information, looking for patterns, expressing patterns symbolically, and explaining patterns, rather than on specific formulas. At this early stage, you might expect only some students to arrive at a general formula.

Key questions

In each specific case, what is the smallest number of gum balls the children could purchase and all get the same color? Why?

In each specific case, how many gum ball purchases would guarantee that the children would all get the same color? Why?

For any specific number of children, how does the number of colors available affect the number of gum balls one would need to buy? What patterns can help you to answer this question?

For any number of available colors, how does the number of children affect the number of gum balls one would need to buy? What patterns can help you answer this question?

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, The game of pig. OpenStax CNX. Nov 19, 2007 Download for free at http://cnx.org/content/col10488/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'The game of pig' conversation and receive update notifications?

Ask