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West, John – Australian Primary Mathematics Classroom, 2018
The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…
Descriptors: Mathematics Instruction, Mathematical Logic, Problem Solving, Fractions
Hohenwarter, Markus – New England Mathematics Journal, 2011
This article discusses two examples of geometric problem solving suitable for middle and high school students. Both problems are related to students' everyday life experience and allow them to discover deep connections between mathematical properties and nature. With the help of dynamic mathematics software, students have the opportunity to…
Descriptors: Geometric Concepts, Geometry, Problem Solving, Middle School Students

Poole, Robert R. – Math Teacher, 1970
Reports a proof of a classical geometry problem. The proposition is - In any triangle there are two equal sides, if the angles opposite these sides have angle bisectors with equal lengths. (RP)
Descriptors: Geometry, Mathematics, Plane Geometry, Problem Solving

Scott, P. R. – Australian Mathematics Teacher, 1978
Investigated here are some of the results which can be obtained using the double-sided straight edge. Seventeen possible constructions are presented with solutions or partial solutions given to most. (MP)
Descriptors: Geometry, Plane Geometry, Problem Sets, Problem Solving

Hiatt, Arthur A. – Mathematics Teacher, 1972
Descriptors: Analytic Geometry, Geometry, Instruction, Mathematics
Steen, Lynn Arthur – Science News, 1979
Describes some unsolved problems in geometry, as well as some recently solved ones. Indicates that each advance generates more problems than it solves, thus ensuring a constant growth in unsolved problems. (GA)
Descriptors: Geometric Concepts, Geometry, Mathematical Models, Mathematics

Levine, Deborah R. – Mathematics Teacher, 1983
The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)
Descriptors: Geometric Concepts, Geometry, Mathematical Enrichment, Plane Geometry

Haigh, Gordon – Mathematics in School, 1982
The material examines areas generated by combinations of: (1) Circles and Triangles; (2) Closely Packed Circles; and (3) Overlapping Circles. The presentation looks at examples of certain areas and at logical ways to generate the necessary algebra to clarify the problems and solve general cases. Ideas for extension are provided. (MP)
Descriptors: Geometric Concepts, Geometry, Instruction, Instructional Materials

Lightfoot, John – Australian Mathematics Teacher, 1978
A program is outlined for the treatment of Tessellations. Major topics are: Introduction; Tessellations; Regular Tessellation; Semi-Regular Tessellations; Nonregular Tessellations; and Miscellaneous Tessellations and Filling Patterns. (MP)
Descriptors: Art Activities, Geometry, Mathematics Education, Patterns in Mathematics