Each Cornerstone Maths unit of work comprises carefully designed software that is hosted on the London Grid for Learning website and the accompanying student work books, teacher guide and professional development resources (part of this PD Toolkit), which are found on these web pages.
The PD resources are designed for schools that have already engaged with the face-to-face Cornerstone Maths professional development and, having piloted activities on a small scale in some classrooms, are ready to involve more teachers through some school-based PD.
- Linear functions
This unit introduces the topic of linear functions for students in key stage 3 in fourteen investigations that require a total of 12-16 teaching hours, which would normally be spread across the key stage.
It shows how linear functions can be used to model situations, such as motion or money, and solve problems involving a constant rate of change. Informal uses of concepts are introduced to compare rates visually (steeper/faster, for example). It also explores methods for writing equations based on situations, tables and graphs, and the connections between them.
- Geometric similarity
This unit introduces the topic of geometric similarity for students in key stage 3 in twelve investigations that require a total of 8-12 teaching hours, which might be spread across the key stage.
It shows how the variant and invariant properties of different figures can be used to determine geometric similarity. Informal notions of similarity are used within the context of non-similar shapes to highlight the necessary and minimum conditions for similarity. These ideas are extended to provide an introduction to trigonometric ratios from this geometric starting point.
- Algebraic patterns and expressions
This unit introduces the topic of algebraic generalisation for students in key stage 3 in five investigations that require a total of 4-6 teaching hours and is ideally taught early in the key stage.
It supports students to understand and express algebraic generalisations arising from how they visualise the structure of a figural pattern. Students work in a dynamic environment to visualize and generate figural patterns and write algebraic expressions for those patterns. The activities encourage students to identify structures in the patterns to make sense of the letters and numbers in an algebraic expression.
One of the main goals of the unit is to help students develop a solid understanding of variables as representing quantities that vary instead of simply unknowns to be discovered.