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The Mathomat V3B geometry template with single scale protractor

As publishers of the Mathomat geometry template we do our best to work with teachers and their preferred classroom practices. In some cases, such as protractor design, there is variation. Our surveys of teacher opinion tell us that significant numbers of teachers prefer 180-degree protractors while many prefer the full circle 360º kind. That is not surprising given that the Australian Curriculum Mathematics (ACMMG112) calls for students to learn to measure and construct angles using both kinds of protractor.

Some of the teachers we work with have told us that they prefer to teach angle using a protractor with a single degree scale. They feel that this keeps things simple while they introduce ideas such as angle measurement in degrees. For this reason, we have introduced the Mathomat V3b geometry template. This version of Mathomat has a protractor with a single degree scale, running anti-clockwise from the positive direction of the X-axis. With this version of Mathomat, bearings need to be measured by flipping the template over so that the scale can be read in a clockwise direction.


Using protractors in the Mathomat Explorer student manual

The protractor measuring and drawing procedures in the Explorer student manual currently cater for both 180° and 360° protractors with dual degree/bearing scales. In future editions of the Explorer manual, we will include reference to the new V3B single scale type as well.

The aim of the angles section in the Explorer manual is to develop in learners a robust understanding of the underlying concept of angle through real-world exploration. This involves the development of a well-constructed mental model for angle that allows students to confidently estimate angle size and structure in real world situations and in abstract textbook problems. Explorer manual students learn to operate a protractor with confidence. This confident operation of a protractor results in the step-by-step procedures learned early in the angles section of the Explorer manual being collapsed into a single efficient action for routine protractor use. We call this “doing the protractor one-step”, it involves unconscious use of the angle concept. In non-routine situations students can bring their mental model of angle into the foreground and use it for problem solving through angle measurement, confident in the knowledge that they are able to analyse and model all situations requiring angle measurement or construction.


John Lawton

December 2022


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