In the New Year's Resolution 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 (and even the question!) is not immediately obvious.
  
• reason as they think about and justify their solution, considering all possible variables.
  
• communicate about their thinking by discussing it with classmates, parents, and teachers.
  
• Connect mathematics to a real world situation –weighing oneself, with and without an additional object. This problem also connects the mathematics of number and operations to the mathematics of algebra and measurement.
  
• 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:
Solving a problem, such as the one described in this challenge, falls under the math content standards of Number and Operations and Patterns, Functions, and Algebra. Students must understand how to subtract parts from the whole in order to find the solution. They also must use what they know in order to find out what is unknown. This kind of thinking is algebraic in nature.

About the Challenge:
This problem is actually two problems in one. First, students have to determine the three weights, through the logical use of the subtraction operation. Once this arithmetic task is complete, they then have to use reason to figure out which weight belongs to each child, based on clues in the problem. In order to solve this problem, students must know how to subtract (procedural thinking). This procedural thinking is arithmetic. However, when students also know how to use subtraction effectively to solve problems (operational thinking), they are doing mathematics. Mathematics is a way of thinking about number, space and relationships. Teaching mathematics as thinking requires that teachers set up an environment where reasoning is considered just as important as getting correct answers. As children work on this problem, encourage them to verbalize and defend their thinking and listen to the thinking of others.

About the Focal Points addressed in this challenge:
The National Council of Teachers of Mathematics (NCTM) recently released a document titled Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. These curriculum focal points are the most important mathematical topics for each grade level. They comprise related ideas, concepts, skills, and procedures that form the foundation for understanding and lasting learning. They are the topics that should be considered as the basis for decisions about curriculum development. (For more information about these focal points, visit www.nctm.org/focal points/

The New Year's Resolution challenge addresses the following recently released NCTM focal points:
Grade 1
Number and Operations and Algebra: Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number lines, to model "part-whole," "adding to," "taking away from," and "comparing" situations to develop an understanding of the meanings of addition and subtraction

Number and Operations and Algebra: Children solve both routine and non-routine problems.

Grade 2
Children add and subtract to solve a variety of problems, including applications involving measurement, geometry, and data, as well as non-routine problems

Modifications of the problem for different age and ability groups:
This is a difficult problem, not because of the mathematical thinking involved, but because of the size of the numbers and the number of steps required to solve it. For younger learners, I would suggest modifying the problem by reducing this number size and steps required. For instance:

From there, modify as needed for your children's skill and interest level.

Older learners may wish to use a bathroom scale to create similar challenges for their classmates to solve. (Note to teachers: In this situation, it would be important to be sensitive to some student's reluctance to be weighed or have their weight compared to others. Objects, such as backpacks, could be used instead of using body weight.)

Extensions of the problem:
Algebra / Measurement Connections:
Using actual scales or balances is another way to prepare younger students to think algebraically. Using classroom objects and a scale, you could experiment to find out the answer to questions such as "If 1 object weighs 2 oz, how many will 2 objects weigh? 3 objects? Record the results on a chart, and see if children can discover and describe the pattern. (Young children may generalize what happens by saying "You add 2 each time" or "It doubles every time". Older students may able to generalize this function as n +n or 2n.

A word from Aunt Mathilda about problem solving in the classroom:

Hopefully children will have opportunities to share their different strategies with the group. Teachers should model and encourage good listening behavior when this occurs and encourage the class to comment positively or ask questions about the strategies. However, no one should be allowed to make negative or comparative comments, such as "That's a dumb way!" or "My way is better!" At no time should there be an atmosphere which implies that there is one correct way to solve problems – because, in fact, this is not true. The best way is the one that make sense for the children.

P.S. from Aunty Math:

I would love to see samples of your children's work on this problem and hear any comments you might have. Although I would not be able to return them, I will send a personal thank you to your class and I may mention this work in a later posting on the site. You may send this to me care of:

Aunty Math
Dupage Children's Museum
301 N. Washington St.
Naperville, IL 60540