Derek Holton and Duncan Symons present the first in a series of three papers that address sequences and their patterns. Their explorations lead to classroom teaching suggestions that involve creative thinking.

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

This paper introduces tools for converting circular-featured-waste into polygonal construction parts and then 3D polyhedra. The tools, including diagrams, 3D printable joiners and mathematical formulae are designed for mathematics-related play, re-use, learning, design and improvisation. Activities for students include making assemblies, gathering…

This article is the third in a series of activities that discusses some interesting relationships with triangles. The first article (EJ1259412) introduced the various circles and centres involved with a triangle, as well as the Euler Line (named after the famous mathematician Leonhard Euler) which passes through four of the five centres. The…

This article is the fourth in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows an activity demonstrating Euler's Theorem, which gives the distance from between the circumcentre and the incentre of a triangle.

This short article continues the exploration of the Common Online Data Analysis Platform (CODAP) and statistics begun in the previous article "Statistical Investigations and CODAP, Part 1: EDA." In Part 2, the author discusses the teaching of statistical inference focusing on activities for the senior secondary years. In particular, the…

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

This article is the second in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to determine the altitudes of a triangle, its area, and the lengths of its circumradius and inradius. [For the first activity in the series, see EJ1259412.]

In this article, the authors present a task that promotes mathematical creativity. The task focuses on defining new geometric concepts, whilst providing students with creative thinking opportunities. They discuss prospective mathematics teachers' experiences while conducting a geometric definition task. Prospective mathematics teachers who…

The short activity presented in this article continues a discussion related to the value of golden ratio explorations in secondary mathematics, and acts as a companion to the earlier paper in this journal (Crawley, 2023). Exploring meaningful ways in which teachers can elicit students' interest and engagement in mathematics is vital, and…

This is the third in a series of articles describing CODAP and where it might be used to address content in the "Australian Curriculum: Mathematics" v9.0 (ACARA, 2022). We've talked before about model-ling and about statistics; this time, we'll talk about exploring probability using CODAP. As before, we have also prepared online pages…

In this article, the authors present variants to the classic problem the Prisoner's Dilemma. They discuss how senior secondary school students can use these variations to explore basic game theory concepts and develop mathematical proficiencies and practices. They also suggest how students can apply these concepts to decision-making processes in…

Two examples of mathematical modelling are explored. Firstly, optimising the distance travelled when jumping from a swing is discussed. The second concerns optimising the distance travelled by monkeys when swinging from branch to branch.

This article presents a series of open-ended tasks exploring the development of algebraic expressions suitable for exploration with Year 7 students. The tasks use a familiar tool, the hundreds chart, to aid the transition between representational tools and abstract ways of working. The tasks outline a developmental progression of patterns and…