How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school's experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically…

This article provides a task that can be used effectively for exploring arrays in middle and upper primary schools, and the notion of prime and composite numbers in particular. As students are engaging in these activities, teachers can encourage them to record their arrays both diagrammatically and as number sentences.

Tangrams are a traditional Chinese puzzle comprising seven pieces that fit together to make a square. The seven pieces include two large right angled isosceles triangles, one medium size right angled isosceles triangle, two small right angled isosceles triangles, a small parallelogram, and a small square. The literature shows tangrams have been…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

Number fact knowledge spans far beyond conventional automatic mastery practices involving rote learning. Having the ability to automatically recall number facts fluently does not mean students will have strong conceptual understanding. This article provides suggestions for how number fact thinking and fluency might be developed in primary…

In this article, the author describes how to help develop students' conceptual understanding of fractions through the tactical card-based game Nearest to One. Nearest to One promotes number-sense based strategies for comparing fractions, such as benchmarking (e.g., Is the fraction greater or less than one-half?) and building to the next whole,…

In this article, the authors explore a number of interesting games as contexts for students learning geometry and enhancing their development of problem solving and reasoning. The games selected were appealing, content-aligned games for approximately four players with simple rules and 10-30 minutes of play time. The games were integrated by…

Co-written by a student and his teacher, this article illustrates how a carefully structured individual education program supported by appropriate software can provide suitable challenges for a gifted Year 3 student. While the focus is on one student's statistical investigation, the story has relevance to the wider primary school environment.

Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…

Having a nice mathematical task is one challenge for a teacher--another is making it come alive for students in the classroom. The pathway to the latter is pedagogy--the range of teaching strategies possessed and activated by the teacher. This article presents a delightful mathematical activity known as Spirolaterals, a geometrical figure formed…

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.

Working within the context of a contest to find the most beautiful tourist attraction in the world, Year 5 students investigate the most symmetric building from a short-list of three iconic buildings. This involves investigating both line and rotational symmetry in order to make an informed decision about the symmetrical nature of each building.

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

Benchmarking is an important strategy for comparing the size of fractions. In addition, knowing whether a given fraction is greater or less than a particular benchmark (e.g., one-half) can support students with accurately locating the fraction on a number line. This article offers a game-based activity that engages students in discussions around…