| PROCESS STANDARDS* | CONTENT STANDARDS* |
| Problem Solving | Number and Operations |
| Reasoning and Proof | Geometry and Spatial Sense |
| Communication | Measurement |
| Connections | Patterns, Functions and Algebra |
| Representations | Data Analysis, Statistics, Probability |
*According to the N.C.T.M.'s Principles and Standards for School Mathematics document.
In the "Holiday Presents" Challenge, students have opportunities to employ all five process standards. They will problem solve as they search for pertinent information in the challenge, and decide on a strategy for solving a problem where the answer is not immediately obvious. They reason as they choose the appropriate operations and sequence for working through the problem, and again as they justify their solution. They should have opportunities to communicate about their solution by discussing it with classmates, parents, and teachers, as well as by posting their written solution on the message board, and communicating via the message board with other students from around the world solve. They can make connections between math topics, such as estimation, geometry and measurement as they work on the extension activities. Finally, they will have opportunities to create and use representations (drawings, charts, words, equations, manipulatives, etc.) to provide a record of their efforts to understand the mathematics of this challenge and make their understanding available to others.
About the mathematics involved in this challenge:
Problems like this one may seem uncomfortably familiar to those of us who struggled through algebra, because it seems to require solving simultaneous equations containing three unknowns. (We don't know how many presents any of the three children wrapped.) Children can solve this problem, using many different strategies. In fact teachers of older children might decide to assign teams to try to solve it using different strategies: using manipulatives, logic, guess and check, looking for a pattern, making a chart or diagram, drawing a picture, acting it out, or visualizing it. The teams could then present their answer and their strategy to the whole class, and discuss the pros and cons of each strategy.
Modifications and Extensions:
Children love to wrap presents, so teachers and parents can connect this seasonal activity to many different math
concepts. Children can estimate how much ribbon and paper they need to wrap certain presents, or they can estimate how many bows or presents they can wrap using a spool of ribbon or a roll of paper. Children can also practice using metric or standard measurement tools to measure out paper and ribbon. While tying ribbons around packages, the geometric math terms of horizontal, vertical and diagonal can be introduced. Which method of tying ribbon takes the most ribbon? The least ribbon? Older children can use box tops of presents to measure and compare perimeter and area.
Since cookies are an integral part of this problem, children might try their hand at baking several different varieties, practicing mathematics as they halve, double, or triple recipes. Younger children might want to reinforce their understanding of geometric shapes by making square, round, triangular or rectangular cookie shapes. A class graph of favorite holiday cookies is a natural extension of this activity.
Aunty Math problems, copyright 2001, Angela G. Andrews. You may download, print and make copies of "Aunt Mathilda's Math Challenges" for use in your classroom provided that you include the copyright notice shown on that page with all copies.
Copyright 2001 DuPage Children's Museum. All rights reserved.
http://www.DuPageChildrensMuseum.org
