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Painless Practice and Proof
Litwiller, Bonnie H.; Duncan, David R. – Mathematics Teaching, 1974
An activity which involves the drawing of geometric designs on familiar number arrangements (such as the addition and multiplication tables and the hundred chart) is used to help students discover patterns and at the same time maintain computation skills. (DT)
Descriptors: Instruction, Learning Activities, Mathematics Education, Number Concepts
The Three Coin Problem: Tangents, Areas, and Ratios
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Mathematics Teacher, 1976
A geometric area problem is analyzed and generalized. (DT)
Descriptors: Elementary Secondary Education, Geometric Concepts, Instruction, Learning Activities
A Question of Coincidences.
Peer reviewed Peer reviewed
Duncan, David R.; Litwiller, Bonnie H. – Mathematics Teacher, 1985
Four answers to a probability problem involving a perceived coincidence are discussed. (MNS)
Descriptors: Diagrams, Learning Activities, Mathematics, Mathematics Instruction
Areas of Polygons on Isometric Dot Paper: Pick's Formula Revised.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Arithmetic Teacher, 1983
The use of square and isometric dot paper to develop area ideas is described. Specific activities relate to the application of Pick's formula. (MNS)
Descriptors: Elementary Education, Elementary School Mathematics, Geometric Concepts, Learning Activities
Calculations You Would Never Make Without a Minicalculator
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Mathematics Teacher, 1977
Ten problems involving large calculations are described for classroom use with a calculator. (JT)
Descriptors: Calculators, Computation, Instruction, Learning Activities
The Case of the Missing Digit
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Arithmetic Teacher, 1974
Descriptors: Elementary School Mathematics, Games, Instruction, Learning Activities
Mathematics of Mortality
Peer reviewed Peer reviewed
Duncan, David R.; Litwiller, Bonnie H. – School Science and Mathematics, 1976
Tables of life expectancy can provide data for use in a great variety of problems related to probability theory. (SD)
Descriptors: Curriculum, Instruction, Learning Activities, Mathematical Applications
Patterns: Digits, Squares, and Bases
Peer reviewed Peer reviewed
Duncan, David R.; Litwiller, Bonnie H. – Mathematics Teacher, 1976
Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)
Descriptors: Instruction, Learning Activities, Mathematics, Mathematics Education
Dueling Dice: An Example of Non-Transitive Probabilities.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Australian Mathematics Teacher, 1981
Several kinds of special dice are displayed and the various winning probabilities in games that could be played with them are discussed. Patterns for dice construction are provided. (MP)
Descriptors: Discovery Learning, Educational Games, Instructional Materials, Learning Activities
Elevator Probabilities: Chances of Coincidences.
Peer reviewed Peer reviewed
Duncan, David R.; Litwiller, Bonnie H. – Mathematics Teacher, 1991
Presented are two examples of real-life examples that can be used to promote or exemplify concepts of probability and statistics. Details of the calculation of these probabilities are given. (CW)
Descriptors: Computation, Creative Thinking, Learning Activities, Mathematics Education
Pentagonal Patterns in the Addition Table.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Arithmetic Teacher, 1985
Three activities and patterns involving the addition table are described, each involving pentagons. (MNS)
Descriptors: Addition, Drills (Practice), Elementary Education, Elementary School Mathematics
Forming and Adjusting Conjectures: Perimeter and Pattern Blocks.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Mathematics in School, 1997
Describes an activity that utilizes four pattern blocks to help students understand and explain perimeter. Engages students in making and supporting conjectures about a scenario that involves trains composed of various shapes with different perimeters. (DDR)
Descriptors: Educational Strategies, Enrichment Activities, Geometry, Learning Activities
Activities: Calculators, Quotients, and Number Patterns.
Peer reviewed Peer reviewed
Duncan, David R.; Litwiller, Bonnie H. – Mathematics Teacher, 1986
This teaching guide contains material, for students in grades 6-9, in which a calculator is used in exploring and developing generalizations about quotient patterns generated from various polygons drawn on a hundred square. Includes suggested procedures and four ready-to-duplicate student worksheets. (JN)
Descriptors: Calculators, Elementary School Mathematics, Intermediate Grades, Junior High Schools
Diamonds on the Right Justified Multiple Triangle: Difference Patterns.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Australian Mathematics Teacher, 1984
Three activities on the right justified multiple triangle are presented. The activities are designed for use in practicing computational skills and for discovering number patterns. (JN)
Descriptors: Computation, Elementary School Mathematics, Intermediate Grades, Junior High Schools
Combinatorics Connections: Playoff Series and Pascal's Triangle.
Peer reviewed Peer reviewed
Litwiller, Bonnie H.; Duncan, David R. – Mathematics Teacher, 1992
Applies Pascal's Triangle to determine the number of ways in which a given team can win a playoff series of differing lengths. Presents the solutions for one-, three-, five-, seven-, and nine-game series, and extends the solution to the general case for any series. (MDH)
Descriptors: Athletics, Competition, Enrichment Activities, Learning Activities
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