By Michael O'Connor
Geometry and Beyond with Mathomat is a series of lessons for secondary school mathematics which make extensive use of commonly available classroom materials, such as the Mathomat ™ template and dynamic geometry software.
Geometry is one of the oldest areas of mathematics and it runs as a continuous thread throughout the mathematics curriculum. Geometry is present from children's first encounters with shape and remains a part of mathematics learning through to the development of formal proofs.
Geometry and beyond with Mathomat is not a comprehensive text on geometry; it is a collection of activities, using common classroom tools such as MATHOMAT, that guide student development of key concepts that link to the bigger picture.
The five areas in this book are: using units of measurement, shape location and transformation, Pythagoras and trigonometry, and geometric reasoning.
The selected concepts that are used to explore these areas are linked together, if there is a gap in the knowledge or understanding of one concept then the ones that follow will be harder to grasp. However, it is always the role of the teacher to consider what activities the students need to explore.
Activities in this book encourage communal understanding and consensus and always conclude with discussion of key points.
The version 2 Mathomat will be available in June 2018, and is a more powerful product - being the same size as the current Mathomat but with many new functions and features built into its design. These include:
The new large regular octagon, and the resized large regular pentagon combine to form a group of regular polygons with 15mm sides to compliment the very popular existing regular polygons with 10mm sides. Students now have more creative freedom in 2-D designs to suit their project style.
The Mathomat V2 manual is a rich source of creative drawing ideas; for classroom or individual student use.
Sometimes students want to fill the whole page with their drawing. At other times its best to leave space for the remainder of a presentation. The Mathomat V2 offers both creative options.
The solution to a senior school trigonometry problem. Finding the hours of the day at which it is safe to cross the harbour bar of a fishing village by boat
The larger sine curve makes a striking improvement to hand drawn sketches. The integrated unit circle allows students to find angle values as distance travelled around its circumfrence before locating them on the x-axis of the graph of that function.Lesson 11 in Maths with Mathomat in the free resources section of this website provides a comprehensive plan for using Mathomat with the unit circle method of teaching trigonometry.
A new 1:2 scale ruler for detailed drawings, especially useful in engineering drawings
Ask students to redraw this section at a scale of 1:2 using their Mathomat V2 template
The many circles on Mathomat have a revised set of graduations to create interesting fractions such sevenths, and ninths, to challenge students to think flexibly about numbers
A new kite, non isosceles trapezium and concave quadrilateral (arrow head) for drawing
The polygons in the Mathomat V2 template flow in a clockwise direction in hierarchical order according to shape property. Students are encouraged to consider shape property continuously while working with the new V2 template