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# NSW Department of Education and Communities

## Teaching Pythagoras

Pythagoras' theorem is an important component of mathematics. Indeed, it has been described as the most fundamental of all geometric theorems and over the years hundreds of proofs of this theorem have been developed. Yet, if you asked most people what they remember of Pythagoras' theorem, very few would have a deep understanding.

Planning a unit of work (pdf - 214KB)
A diagram outlining considerations when planning a unit of work in mathematics.

Pythagoras unit of work summary (pdf - 56KB)
A brief overview of a possible teaching sequence outlining lesson, structure and time frame.

Pythagoras overview (pdf - 239KB)
An overview of a unit of work on Pythagoras (MS4.1) that may be used with students throughout the unit to connect ideas and lessons.

Are we ready for Pythagoras? (pdf - 202KB)
An assessment task where students can show their understanding of length and calculating areas of rectangles as a precursor to Pythagoras' theorem.

An assessment for learning activity that allows students to show what they know at the start of a unit of work.

Pythagoras homework task (pdf - 55KB)
This task follows the practical activities, What's in the bag? and Make a square using four triangles. It aims to answer the quality teaching question for students - Why does this learning matter?

Generalising with symbols (pdf - 350KB)
A card sorting activity where students match cards under the headings Pythagoras' theorem in pictures, Pythagoras' theorem in numbers and Pythagoras' theorem in algebra.

Share today's mathematics lesson (pdf - 78KB)
A general purpose activity, useful for any mathematics lesson, consolidating student deep understanding. Students are asked to describe what they learnt in maths today and share their writing with a family member.

Area calculations - a practical measurement activity (pdf - 26KB)
Result sheet for Make a square using four triangles activity.

Sequencing activity (pdf - 46KB)
Whole class or small group activity on finding the length of an unknown side in a right-angled triangle. Have students compare and contrast the two types of questions.

##### References for this unit

Lovitt, Charles and Doug Clarke The Mathematics Curriculum and Teaching Program MCTP Professional Development Package Activity Bank - Volume 1 Curriculum Corporation, Carlton, Victoria, 1992.

Bennett, Dan Pythagoras Plugged In Proofs and Problems for the Geometer's Sketchpad Key Curriculum Press, Berkeley, California, 1995.

Huang, Rogiin and Frederick K.S. Leung How Pythagoras' Theorem is taught in Czech Republic, Hong Kong and Shanghai: A Case Study ZDM 2002 Vol. 34(6). This case study analysed three video lessons of Year 8 from the TIMSS study 1999.

##### Internet sites

Pythagoras' Theorem

This site offers 43 proofs of Pythagoras' Theorem some with interactive aspects. There are references to other sites for Pythagoras at the end of the home page.