1. Making it count Mathematics and the Heritage

2. Why use mathematics and heritage? The historic environment can offer a context for mathematical problem solving; The historic environment can offer a context for mathematical problem solving; Mathematics can be used as a tool for historical problem solving; Mathematics can be used as a tool for historical problem solving; Both types of problem solving are real problem solving and not just simulations or detached exercises. Both types of problem solving are real problem solving and not just simulations or detached exercises.

3. Mathematics Historic Environment Aids enquiry into Gives a context for enquiry using

4. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13,... (add the last two to get the next)add the last two to get the next The golden section numbers are ±0·61803 39887... and ±1·61803 39887... The Golden Section Or Golden Rectangle

5. Golden Rectangle?

8. How many angles? What sort of Angles? Why?

9. What shapes were used in this place and why were they used? Collecting shapes and explaining them.

10. ShapeWhere?DecorationDefence Taking weight Why use particular shapes?

11. What sorts of symmetry? Rotational or line? Why? Decoration, equal space, equal light, equal weight?

12. What sorts of symmetry? Rotational or line? Why? To take equal weight? Give equal light? To give equal space?

13. What sorts of symmetry? Rotational or line?ShapeWhere?DecorationDefence Taking weight

14. What sorts of symmetry? Rotational or line?

15. What sorts of symmetry? Rotational or line?

16. What repeating patterns can you see here? Can you make a formula for predicting what would be next in the sequence?

17. What was important in the design of this space? Looking for symmetry, number patterns, and proportion.

18. Proportions Suggest a method of gauging the proportions of this building? Why did they use these proportions?

19. Which was the most important room in the Théâtre Royal de la Monnaie - Muntschouwburg? Use the matrix to find the most important room. Choose a room and score each out of 10, with 10 being most of the thing. ROOMHeatLightSpaceFloor covering decorationwalls' decoration FurnitureTotal

20. What maths was used in this room? Squares Line Symmetry Repeating patterns

21. Mathematics, artefacts and chronology How long did it take to make this object? How long did it take to make this object? Could we make the same thing faster or slower in the present? Could we make the same thing faster or slower in the present? Do we know when it was made? Do we know when it was made?

22. Maths, artefacts and symmetry Do the artefacts have repeating patterns of shapes that are symmetrical? Do the artefacts have repeating patterns of shapes that are symmetrical? Are there any artefacts that have patterns that are not symmetrical? Are there any artefacts that have patterns that are not symmetrical?

23. Maths, artefacts and angles Can you find any right angles in the object? Can you find any right angles in the object? Are there any other angles? What sorts are they? Are there any other angles? What sorts are they?

24. Maths, artefacts and symmetry Which artefacts are symmetrical? Why is this? Could it be for taking equal weight on all sides, for decoration, giving equal room on all sides or being able to be held on all sides? Which artefacts are symmetrical? Why is this? Could it be for taking equal weight on all sides, for decoration, giving equal room on all sides or being able to be held on all sides?

25. Maths, shapes and artefacts Give a friend a list of mathematical clues to a mystery object and let them find it. Make collections of artefacts with the same mathematical properties Give a friend a list of mathematical clues to a mystery object and let them find it. Make collections of artefacts with the same mathematical properties

26. Maths and artefacts If the artefact is broken can you suggest what it would have looked like? How have you arrived at your solution? If the artefact is broken can you suggest what it would have looked like? How have you arrived at your solution?

27. Purpose Formats to emphasis this purpose Describing Nominal scales Classifying (sorting into groups) Topic web, Venn diagram, tree diagram, attributes matrix Comparing (showing similarities and differences) Bar-chart, rating, attributes matrix, preference matrix Ordering (arranging in sequence) Time chart, ordered list, network, flow chart Positioning (locating in space) Scale model, map, scale drawing, plan Interrelating (co-ordinating similarities) Table, histogram, scatter graph, graph, algebraic formulae

28. PROBLEM SOLVING WITH HERITAGE