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Surd Delights

	Surd Spirals
	Federation Square
	Golden Rectangles

These activities provide delightful ways to enrich the teaching of surds. Explorations with spiral and other geometric patterns, supported by dynamic geometry, are used to link surds with length through Pythagoras’ theorem, emphasise their relative size and to provide attractive contexts for simple and complex surd calculations. The exact value mode of CAS may support students’ work with surds, allowing them to construct patterns and share a world of beautiful mathematics

There are four activites for exploring surds. The 2005 MAV paper by Kaye Stacey and Beth Price titled Surds, Spirals, Dynamic Geometry and CAS provides a detailed description of each activity, practical teaching ideas and possible benefits for student learning of mathematics.

CAS can be used to scaffold students' early learning of symbolic manipulations of surds. The dynamic geometry is used to present the problem situations and to enable measurements to link surds with their numerical approximations.

Activities 1 and 2 - Surd Spirals

These two introductory activities involve students in finding numerical approximations to common surds and simple manipulations with surds.

There are two files for the activities:

SurdSpiralsWorksheet and SurdSpirals.gsp

Both files can be downloaded in this zip file: SurdSpiralsFiles.zip

Activity 3 - Federation Square

This activity involves students in more complicated, but still relatively simple, surd calculations in an interesting real context.

Everything needed for this activity is in the pages of the Geometer's Sketchpad file FedSquare.zip .

Activity 4 - Golden Rectangles

This activity makes use of the Goldern Ratio and requires students to add and subtract surds, and optionally, multiply surds and rationalise surd denominators.

There are three files for the activity:

GoldenRectangleTEACHER

GoldenRectangleWORKSHEET

GoldenRectangleRITEMATHS.gsp

All three files can be downloaded in this zip file: GoldenRectFiles.zip