Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.
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Transcript of Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.
![Page 1: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/1.jpg)
http://nrich.maths.org
eNRICHing Shape & Space
BromleyFebruary 2015
![Page 2: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/2.jpg)
http://nrich.maths.org
Tilted Squares
Can you find a quick and easy method to
work out the areas of tilted squares?
![Page 3: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/3.jpg)
http://nrich.maths.org
Reflecting Squarely
In how many ways can you fit all three pieces
together to make shapes with line
symmetry?
![Page 4: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/4.jpg)
http://nrich.maths.org
Shady Symmetry
How many different symmetrical patterns
can you make?
![Page 5: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/5.jpg)
http://nrich.maths.org
Square It
Can you beat the computer?
![Page 6: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/6.jpg)
http://nrich.maths.org
Opposite vertices
If I give you a line, can you tell me straight away if that line could be:
• the side of a square? • the diagonal of a square?
If such squares CAN be drawn, can you find an efficient method for drawing them?
![Page 7: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/7.jpg)
http://nrich.maths.org
Vector Journeys
If I give you a vector that represents the side of a square, can you find the vectors that complete the square?
If I give you a vector that represents the diagonal of a square, can you find the vectors that complete the square?
![Page 8: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/8.jpg)
http://nrich.maths.org
Isosceles Triangles
Draw some isosceles triangles with an area of 9 cm2 and a vertex at (20, 20).
If all the vertices have whole number coordinates, how many is it possible to draw?
Can you explain how you know that you have found them all?
![Page 9: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/9.jpg)
http://nrich.maths.org
Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
![Page 10: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/10.jpg)
http://nrich.maths.org
Cuboid Challenge
Cut a square from each corner and fold up the flaps.
What volumes are possible for different sizes of cut-out squares?
![Page 11: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/11.jpg)
http://nrich.maths.org
Finding angles in a triangle using a Geoboard environment
Start of a journey: a 9-point circle
![Page 12: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/12.jpg)
http://nrich.maths.org
Kite in a square
What fraction of the total area is shaded?
![Page 13: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/13.jpg)
http://nrich.maths.org
Marbles in a Box
How many winning lines are there?
![Page 14: Http://nrich.maths.org eNRICHing Shape & Space Bromley February 2015.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f2e5503460f94c480c6/html5/thumbnails/14.jpg)
http://nrich.maths.org
Geometry & Measure collection
http://nrich.maths.org/8743