Series editor and principal writer: Dr Caroline Yoon (The University of Auckland)
ISBN 9780947509378
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) 

Mixing Ratios (Year 10) 

Volume and Scale (Year 11) 

Circle Geometry (Year 11) 

Graphical Antiderivatives (Years 12 & 13) 

Each sequence of metamathematical activities follows the same structure:
 The sequence begins with a challenging openended 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.
Try the for free!
You can download a warmup task and the first task in each of the five LEMMA sequences  select the task suitable for th eyear level you teach from the list below.
Each task has a answer sheet, student booklet and teacher manual to get you started.