making it count mathematics and the heritage. why use mathematics and heritage? the historic...
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Making it countMaking it count
Mathematics and Mathematics and the Heritagethe Heritage
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Why use mathematics Why use mathematics and heritage?and heritage?
The historic environment can offer a The historic environment can offer a context for mathematical problem context for mathematical problem solving;solving;
Mathematics can be used as a tool Mathematics can be used as a tool for historical problem solving;for historical problem solving;
Both types of problem solving are Both types of problem solving are real problem solving and not just real problem solving and not just simulations or detached exercises. simulations or detached exercises.
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Mathematics
Historic Environment
Aids enquiry into
Gives a context for enquiry using
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The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next)
The golden section numbers are ±0·61803 39887... and ±1·61803 39887...
The Golden SectionOr Golden Rectangle
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Golden Rectangle?
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Golden Rectangle?
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Golden Rectangle?
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How many angles?
What sort of Angles?
Why?
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What shapes were used in this place and why were they used? Collecting shapes and explaining them.
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ShapeShape WhereWhere??
DecoratiDecorationon
DefenceDefence Taking Taking weightweight
Why use particular shapes?
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What sorts of symmetry?Rotational or line?
Why? Decoration, equal space, equal light, equal weight?
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What sorts ofsymmetry?Rotational or line?
Why? To take equal weight? Give equal light? To give equal space?
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What sorts ofsymmetry?Rotational or line?
ShapeShape WhereWhere??
DecoratiDecorationon
DefenceDefence Taking Taking weightweight
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What sorts ofsymmetry?Rotational or line?
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What sorts ofsymmetry?Rotational or line?
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What repeating patterns can you see here?Can you make a formula for predicting what would be next in the sequence?
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What was important in the design of this space?Looking for symmetry, number patterns, and proportion.
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Proportions
Suggest a method of gauging the proportions of this building?Why did they use these proportions?
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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.ROOM Heat Light Space Floor
coveringdecoration walls'
decorationFurniture Total
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What maths was used in this room?
Squares
Line Symmetry
Repeating patterns
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Mathematics, artefacts and Mathematics, artefacts and chronologychronology
How long did it take to How long did it take to make this make this object?object?
Could we make the same Could we make the same thing thing faster or slower in the faster or slower in the present?present?
Do we know when it was Do we know when it was made?made?
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Maths, artefacts and Maths, artefacts and symmetrysymmetry
Do the artefacts have Do the artefacts have repeating patterns of shapes repeating patterns of shapes that are symmetrical?that are symmetrical?
Are there any artefacts that Are there any artefacts that have patterns that are not have patterns that are not symmetrical?symmetrical?
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Maths, artefacts and Maths, artefacts and anglesangles
Can you find any Can you find any right angles in the right angles in the object?object?
Are there any other Are there any other angles? What sorts are angles? What sorts are they?they?
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Maths, artefacts and Maths, artefacts and symmetrysymmetry
• Which artefacts are Which artefacts are symmetrical? Why is this? symmetrical? Why is this? Could it be for taking Could it be for taking equal weight on all sides, equal weight on all sides, for decoration, giving for decoration, giving equal room on all sides or equal room on all sides or being able to be held on being able to be held on all sides?all sides?
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Maths, shapes and Maths, shapes and artefactsartefacts
• Give a friend a list of Give a friend a list of mathematical clues to a mathematical clues to a mystery object and let mystery object and let them find it. Make them find it. Make collections of artefacts collections of artefacts with the same with the same mathematical properties mathematical properties
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Maths and artefactsMaths and artefacts
If the artefact is If the artefact is broken can you broken can you suggest what it would suggest what it would have looked like? have looked like? How have you arrived How have you arrived at your solution?at your solution?
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PurposePurpose Formats to Formats to emphasis this emphasis this purposepurpose
Describing Describing Nominal scalesNominal scales
ClassifyingClassifying
(sorting into (sorting into groups)groups)
Topic web, Venn Topic web, Venn diagram, tree diagram, tree diagram, attributes diagram, attributes matrixmatrix
Comparing Comparing (showing (showing similarities and similarities and differences)differences)
Bar-chart, rating, Bar-chart, rating, attributes matrix, attributes matrix, preference matrixpreference matrix
Ordering Ordering (arranging in (arranging in sequence)sequence)
Time chart, ordered Time chart, ordered list, network, flow list, network, flow chartchart
PositioningPositioning
(locating in (locating in space)space)
Scale model, map, Scale model, map, scale drawing, planscale drawing, plan
InterrelatingInterrelating
(co-ordinating (co-ordinating similarities)similarities)
Table, histogram, Table, histogram, scatter graph, graph, scatter graph, graph, algebraic formulaealgebraic formulae
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Historical and archaeological
evidence
Organise and communicate the solution
Chronology, knowledge and understanding,
interpretation
Solve the historical problem
HISTORICAL CONTEXT
Key questions
Historical enquiry
skills
strategic skills
mathematical skills
REAL LIFE CONTEXT
Problem Solving in History
PROBLEM SOLVING WITH HERITAGE