Bag the Beans

1. Bag the Beans By Jesica Cullen 9/30/09

2. Science Standard 3- The Mathematical World • Indicator 5.5.3- Classify objects in terms of simple figures and solids. • Taken from http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx • Link to activity: http://www.sciencenetlinks.com/lessons.php?DocID=249

3. Definitions • Manipulative- Any of various objects designed to be moved or arranged by hand as a means of developing motor skills or understanding abstractions, especially in mathematics • Misconception- A mistaken thought, idea, or notion; a misunderstanding • Solution- a specific answer to or way of answering a problem • Taken from: www.thefreedictionary.com

4. Background Information • Critical Thinking Skills -is purposeful and reflective judgment about what to believe or what to do in response to observations, experience, verbal or written expressions -it may involve determining the meaning and significance of what is observed or expressed, or determining whether there is adequate justification to accept the conclusion as true -is an active interpretation and evaluation of your observations, communications, information, and argumentation -consideration is given to the evidence, the relevant criteria for making the judgment, and the methods or techniques for forming the judgment -not only is logic involved, but intellectual criteria like clarity, credibility, accuracy, relevance, depth, and significance are needed

5. Bag the Beans • Working with a partner you are going to pack 8 sandwich bags with beans following the directions, or rules, described for each bag, and record your answers in the table that follows • Note: for some bags there is only one possible solution, while for others there are several correct answers Materials Needed: Black beans, Lima beans, Red beans, 8 sandwich bags, and 3 larger Ziploc bags to store the rest of the beans

6. Problem 1 and 2 • This bag contains one fewer Lima bean than Red beans. There are four more Black beans than Lima beans. There are 11 beans in all. • This bag contains 18 beans total. One third of the beans are Red. One half of the remaining beans are Black. How many Lima beans should go in the bag?

7. Problem 3 and 4 3. This bag contains twice as many Black beans as Red beans. There are 8 Lima beans. There are equal numbers of Lima and Black beans. 4. This bag contains a total of 14 beans. There are four more Black beans than Red beans. There are four times as many Black beans as there are Lima beans.

8. Problem 5 and 6 5. This bag contains an equal number of Lima beans and Black beans. There is one less Red bean than there are Black beans. There are no more than 10 Red beans. 6. This bag contains at least 15 beans. There is one more Lima bean than there are Red beans. There is one more Red bean than there are Black beans.

9. Problem 7 and 8 7. This bag contains at least 8 beans. There are three times as many Red beans as Black beans. There is one more Lima bean than Red beans. 8. This bag contains an equal number of Red beans and Lima beans. There are six more Black beans than Red beans. There are no more than 24 beans total.

10. Bag the Beans Table

11. Resources • http://en.wikipedia.org/wiki/Critical_thinking • http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx • http://www.sciencenetlinks.com/lessons.php?DocID=249 • www.thefreedictionary.com • http://www.project2061.org/publications/bsl/online/index.php?chapter=15&txtRef=http%3A%2F%2Fwww%2Esciencenetlinks%2Ecom%2Flessons%2Ephp%3FDocID%3D249&txtURIOld=%2Ftools%2Fbenchol%2Fch15%2Ffindings%2Ehtm

12. Answer Key * There is more than one correct answer.