In Barney's Broken Finger challenge, students have opportunities to employ all five process standards. They will:

• problem solve as they decide on a strategy for solving a problem where the answer is not immediately obvious.
  
• reason as they think about and justify their solution.
  
• communicate about their thinking by discussing it with classmates, parents, and teachers.
  
• make connections between math and science.
  
• use representations (drawings, charts, words, models, etc.) to provide a record of their efforts to understand the mathematics of this challenge and make their understanding available to others.

About the mathematical content in this challenge:
This challenge falls under the general content standard of Number and Operations and is differentiated for varying levels of mathematical sophistication. Younger learners may need to revert to counting by one all the bones on one hand by touching each joint to solve their easier task. More mature learners may be able to handle a more difficult task by counting in multiples or using repeated addition. The most challenging problem requires some algebraic thinking and additional number sense in order to complete it. In all cases, students must remember the special condition of subtracting the broken finger bone from the subtotal they arrive at.

Extensions of the Challenge:
Statistics and Probability- Data Collection:
A Whole School Data Collection Project – " Broken Bones"
Perhaps as a connection with a study on good health and nutrition or playground safety, the entire school can get involved in this project and post their data in the halls for other students (and visiting parents) to analyze and enjoy.

Primary students might enjoy collecting data in their classrooms about who has and who has not broken a bone?

Other classes might collect the same data but use this data to answer the question "Are more bones broken inside or outside?"

A third class could use the same collected data to answer the question "Do boys more frequently break bones than girls?"

Older students who are studying the skeletal system might use collected to data to figure out what bone is most frequently broken.
Students who are learning about measures of central tendency may want to use a school survey on broken bones and healing time to determine the average time each kind of bone takes to heal in order to see if there is a relationship between the size of the bone and the length of healing time. Such a display might help parents understand how students can use similar raw data to grow understanding and sophistication in how to organize and display data in order to answer important questions and ask new ones.

Math /Science Connections:
As children study the skeletal system, encourage them to pose and answer mathematical questions about the bones in the body, such as:

If there are 206 bones in the human body, how many are not hand bones?

According to some references, the adult has 206 bones, but an infant has 350 bones. These extra bones fuse together as the baby grows. How many more bones does a baby have than an adult?

Measurement:
The smallest bone in the human body is the stirrup bone in the ear which measures about 1/10 of an inch. Find something in the classroom that is about the same length as the stirrup bone.

The longest bone in the human body is the femur or thigh bone, which is about ¼ of your height. How long is your femur? Find something in the classroom that is about as long as your femur.