In collaboration with Nikola Chernev and OpenGeoboard we just made a detailled survey if and how we can use the Open Geoboard in the math classes. Now we proved that you can use the Open Geoboard for almost all compulsory math topics for the 1. to the 9. grade. And of course for many more voluntary and advanced topics. This means that your Geo Board is indeed your great math tool through the whole compulsary education – from the kindergarten till college, from 3 to 16 years. And of course a great games and fun tool for all ages.
Here you can see a list of all mathematics topics from the grades 1. to 9. according to the bulgarian state school system (all covered by the geoboard):
– 1. grade: fundamentals of arithmetics and geometry – digits, numbers, comparing of numbers, counting, addition, subtraction, geometrical figures, square, triangle, line, section, measuring of lengths
– 2. grade: fundamentals of arithmetics and geometry – measuring units, addition and subtraction with bigger numbers, multiplication, division
– 3. grade: fundamentals of arithmetics and geometry – further addition, subtraction, multiplication and division with even bigger numbers, angles, different kinds of triangles
– 4. grade: fundamentals of arithmetics and geometry – addition, subtraction, multiplication and division with all kinds of natural numbers, solution of text problems
– 5. grade: fractions, decimal fractions, addition, subtraction, multiplication and division of fractions, figures triangle, parallelogram, rhomb, trapeze, surfaces of figures, bodies, cube, parallelepiped, cuboid, volumes of bodies, surfaces of bodies, divisibility criteria, percents, diagrammes
– 6. grade: exponents, positive and negative numbers, coordinate system, arithmetic average, circle, surface of a circle, polygon, prism, pyramide, cylinder, cone, proportions, visualisation of data
– 7. grade: beginnings of the algebra, algebraic equations (a geometrical solution with the geoboard is possible), angles between lines, similarity of triangles, constructions problems
– 8. grade: square equations and inequalities, systems of equations and inequalities (a geometrical solution with the geoboard is possible), vectors, middle section, graphics of functions, symmetry, circles and polygons
– 9. grade: rational and irrational equations, Thales theorem, theorem of Pythagoras, right-angled triangle, trigonometry, combinatorics
Here you can also see the topics from the grades 10-12, that are also partly covered by the geoboard. The application of the geoboard is also possible for many of those topics, but needs special investigations.
– 10. grade: further rational and irrational equations (here the geometrical solution with the geoboard is hardly possible), exponents, roots and logarithms (geoboard application is possible, but needs closer investigation), further trigonometry (cosinus and sinus theorem, hardly possible with the geoboard), further vectors (possible, needs closer investigation), surfaces of polygons (possible), probability theory (should be possible, needs greater amount of investigation and creativity)
– 11. grade: arithmetic and geometric series and progressions (not possible?), exponential, logarithmic and trigonometrical equations and inequalities (not possible), stereometry, vector bases and orthogonal projections (possible to some extend, very good for visualising)
– 12. grade: limits of functions (possible to a very limited extend, good for geometrical visualisation), derivatives, continuous functions (hardly possible), local minima and maxima, graphics of functions, complex numbers, statistics (visualisation possible), rotational bodies and conic sections (possible, needs further investigation)
Of course, also most of the waldorf school system topics are covered by the geoboard.