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The LEMMA series

Series editor and principal writer: Dr Caroline Yoon (The University of Auckland)

ISBN 978-0-947509-37-8

LEMMA series overview

School mathematics curricula are often criticised as being “a mile wide and an inch deep”. They cover a large range of topics, but only superficially. This can be frustrating for teachers who see mathematics as a joyful, captivating, and aesthetic experience, and wish to empower their students to use mathematical concepts flexibly and productively in contexts within and beyond the mathematics classroom.

The LEMMA series is a collection of booklets that contain sequences of metamathematical activities, which invite students to go beyond memorising and applying rules and skills, to thinking, working, and communicating with intriguing mathematical structures on a higher level.

Topics in the series 

Topics and year levels

Link to the New Zealand Curriculum

Equivalent Proportions (Year 9)
  • Reason with linear proportions (Level 5)
Mixing Ratios (Year 10)
  • Use rates and ratios (Level 5)
Volume and Scale (Year 11)
  • Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae (Level 6: GM6-3)
  • Recognise when shapes are similar and use proportional reasoning to find an unknown length (Level 6: GM6-5) 
Circle Geometry (Year 11)
  • Deduce and apply the angle properties related to circles (Level 6: GM6-4)
Graphical Antiderivatives (Years 12 & 13)
  • Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs (Level 7: M7-9)
  • Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods (Level 8: M8-11)

Each sequence of metamathematical activities follows the same structure: 

  • The sequence begins with a challenging open-ended activity, in which teams of students design a complex mathematical product
  • Follow up activities invite students to critique and manipulate the mathematical structures underlying the initial activity from multiple perspectives
  • Formative assessments tasks encourage students to extend their knowledge to new contexts

Each topic in the series includes:

  • a Teacher Manual with questions, answers and notes on each task.
  • a Student Booklet containing information students require for each task. 
  • a booklet of Answer Sheets for students to write the answers in. (Note that these can also be downloaded for free from the web page of each sequence of tasks - see the links above.)

A sample pack of all five topics in the series is also available for purchase.

Shop for LEMMA 

Development of the LEMMA series

The activities were developed and tested by a team of teachers, researchers, teacher educators, and mathematicians working in industry, with support from the Teaching and Learning Research Initiative and the University of Auckland. The writing of the LEMMA series was made possible through a Beeby Fellowship, jointly administered by the New Zealand National Commission for UNESCO and New Zealand Council for Educational Research.