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A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

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Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

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Holly

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

Flower Power

Stage: 3 and 4 Challenge Level: Challenge Level:1


 
Imagine you are a fabric designer.  This is your brief:

flower design
Create a design for a patterned fabric based on a flower motif.  The motif should show rotational symmetry.  The motif should be repeated across the width and length of the fabric in an interesting way which also shows symmetry.

Start by roughing out a design.  You may wish to use a real flower for inspiration, or you could start from something more abstract provided it can be recognised as a flower.  

When you are happy with your design, use Logo to create a print of the fabric.  If you wish to submit your design, include a screenshot and the Logo program you used to create it, together with a summary of the symmetry shown by the motif and by the overall design.

Ideas to think about:
  • The number of petals of many flowers is given by the Fibonacci sequence.
  • What calculation do you need to do to work out the angle between petals if the flower is to show rotational symmetry?
If you would like help in getting going with Logo, these graded problems will help you.

Windows users can download a free copy of Logo from FMSlogo.

A good free version for Mac users is ACSlogo.

There's a version you can run directly in your browser at http://calormen.com/logo/.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.