By Jesica Cullen9/30/09

BAG THE BEANS

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

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

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

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

PROBLEM 1 AND 2

1. 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.

2. 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?

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.

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.

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.

BAG THE BEANS TABLE

Answers to Bag the Beans

1

2

3

4

5

6

7

8

Bag Lima Beans

Red Beans Black Beans

Total

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

ANSWER KEY

Bag Lima Beans

Red Beans Black Beans

Total

1 2 3 6 11

2 6 6 6 18

3 8 4 8 20

4 2 4 8 14

5 11 10 11 32*

6 7 6 5 18*

7 4 3 1 8*

8 6 6 12 24*

* There is more than one correct answer.