Science & Numeracy home

Teacher/Tutor - Numeracy

Problem Solving: Reasoning & Decision-Making

Problem solving, reasoning, and decision making are three very interconnected processes that adults engage in continuously. Problem solving is a process that includes seeking to understand the problem, then figuring out what information and math skills are important to use and solve the problem. While problem solving is embedded in mathematics, there are specific skills and strategies that help greatly.

Be sure to look at the different set of resources listed at the Student/Learner webpage for this topic.

Screen shot from siteFamous Problems in the History of Mathematics
As the Math Forum says, "The purpose of this site is to present a small portion of the history of mathematics through an investigation of some of the great problems that have inspired mathematicians throughout the ages." Included are the Bridges of Konigsberg, the Pythagorean Theorum, Famous Paradoxes, the Value of Pi, and Prime Numbers. The latter two problems appear on the learner page of this website; the other problems are not as self-explanatory.

Managing Your Money
A WebQuest is an online activity in which learners use information gathered from pre-selected Internet sites to increase their knowledge and skills. WebQuests are typically designed to make the best use of a learner's time spent online by providing guidance and structure. This WebQuest was designed by the Technology Training Special Collection [add this link] as support material to be used with adult learners within the context of advanced ESL, ABE or GED classes. The Teacher Page of each WebQuest lists the CASAS, SCANS and EFF competencies or skills addressed by the tasks included in the WebQuest and offers strategies for introducing the WebQuest to the class. Each WebQuest includes a vocabulary list and activities to support vocabulary instruction.

Screen shot from siteMath in Daily Life
This website explores the ways in which math is used in daily activities, from playing games (probability), to cooking (ratios), home decorating (geometry), and issues of savings and credit (interest rates). There are useful exercises in calculating compound interest or figuring the better deal in buying or leasing a car. The text print is small and the vocabulary is advanced, but this is a useful site. Teachers can get many good ideas here, and might guide learners to this site directly if the reading level is appropriate.

Screen shot from siteMaths File Game Show
"Even if you don't know who Hypatia is, you're sure to enjoy trying your hand at these animated math games." The Eisenhower National Clearinghouse recommends this website with those words. Divided into four sections--Number, Data Handling, Algebra, and Shape, Space, and Measure--a games wheel offers a variety of interactive math games for students of different ability levels. There are also printable worksheets and information for teachers about the mathematics behind each game. This is a good introduction to British humor, as well.

Screen shot from siteNational Library of Virtual Manipulatives for Interactive Mathematics
This site is still in development, but it includes a wide range of interactive mathematics tutorials, designed to simulate the use of manipulatives in mathematics instruction. The five subjects are Number & Operations; Algebra; Geometry; Measurements; and Data Analysis & Probability. Most of the manipulatives rely on JAVA applets.

Screen shot from siteNational Math Trail
A math trail is a set of problems designed to take a group of learners on an exploration of their communities. The National Math Trail is a website that seeks to expand this to a national network of learner-created math problems and math trails. Many math education standards are exercised with a math trail: problem solving, connections, communication, and number sense. Learners go into their communities and find examples of math problems along a route through that community. Many groups write and illustrate books to present their problems and solutions. This is an excellent way for adult learners to integrate math study with their life roles.

Screen shot from siteOpen-ended Math Problems
This website, from the Franklin Institute, is designed to prepare students for open-ended math problems that lend themselves to more than one way of solving. Each month there are problems in each of these classifications: number theory; measurement; geometry; patterns, algebra, and functions; data, statistics, and probability. There are three levels of difficulty for each category.

The Tower Problem
This project challenges students to construct a "cost-effective" tower that can support a designated load. Students face the same challenges faced by designers and engineers in the real world; specific design parameters as well as material, assembly, and construction cost constraints. This is an activity that can be explored by all levels of students.

To submit ideas and resources for this section, please contact Susan Cowles.