Visualising and representing

There are 575 NRICH Mathematical resources connected to Visualising and representing
The Spider and the Fly
problem
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The spider and the fly

Age
14 to 16
Challenge level
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A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Same Length Trains
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Same length trains

Age
5 to 7
Challenge level
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How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Dating made Easier
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Dating made easier

Age
14 to 16
Challenge level
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If a sum invested gains 10% each year how long before it has doubled its value?
Spotting the loophole
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Spotting the loophole

Age
14 to 16
Challenge level
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A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
Reflecting Lines
problem
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Reflecting lines

Age
11 to 14
Challenge level
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Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
Tower of Hanoi
problem
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Tower of hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Areas and Ratios
problem
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Areas and ratios

Age
16 to 18
Challenge level
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Do you have enough information to work out the area of the shaded quadrilateral?
Reach 100
problem
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Reach 100

Age
7 to 11
Challenge level
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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Fitted
problem
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Fitted

Age
7 to 11
Challenge level
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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Perfectly Square
problem
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Perfectly square

Age
14 to 16
Challenge level
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The sums of the squares of three related numbers is also a perfect square - can you explain why?