Dear all,

The NRICH website for July is now live at www.nrich.maths.org. This 
month the mathematical theme is Area, a topic which lends itself to 
practical challenges.

The problems begin at the lowest level by looking at what we understand 
by size. Can you order the shapes from smallest to largest in both 
Sizing them Up 
<http://nrich.maths.org/public/viewer.php?obj_id=4962&part=index> and 
Wallpaper 
<http://nrich.maths.org/public/viewer.php?obj_id=4964&part=index> ? How 
did you do it? In Brush Loads 
<http://nrich.maths.org/public/viewer.php?obj_id=4911&part=index> , the 
idea is to find ways of arranging cubes so that you can cover their 
visible faces with the least number of "Brush Loads" of paint and then 
the largest number of "Brush Loads". Perhaps you'll reach some general 
conclusions about your findings.

You'll be applying your knowledge of area to a "real" situation in the 
problem Warmsnug Double Glazing 
<http://nrich.maths.org/public/viewer.php?obj_id=4889&part=index> . Can 
you work out how the company have calculated the price of their windows? 
Which window is incorrectly priced? Or how about investigating the 
number of squares inside rectangles of different sizes. Squares in 
Rectangles 
<http://nrich.maths.org/public/viewer.php?obj_id=4835&part=index> is not 
as straight-forward as it sounds! What size rectangle contains exactly 
100 squares?

The Stage 4 problems continue the idea of shapes, both 2-dimensional and 
3-dimensional. Trapezium Four 
<http://nrich.maths.org/public/viewer.php?obj_id=4960&part=index> 
requires you to compare the areas of the four regions created by the 
diagaonals of a trapezium. Is it possible for two of them to have equal 
areas? How about three of them? All four? For a 3D challenge involving 
an apple, have a look at the aptly named Peeling the Apple or the Cone 
That Lost Its Head 
<http://nrich.maths.org/public/viewer.php?obj_id=4979&part=index> . 
Surely you're intrigued?

At Stage 5, area of course leads into integration and there are three 
problems for you to get stuck into. You might like to start with 
Integral Equation 
<http://nrich.maths.org/public/viewer.php?obj_id=4933&part=index> and 
then go onto Integral Sandwich 
<http://nrich.maths.org/public/viewer.php?obj_id=4934&part=index> which 
involves generalising an equality.

We hope that you will find something that appeals. Don't forget that 
this is just a small sample of the area challenges on the website. You 
could use the Maths Finder on the left-hand menu to pull out some more 
when you've cracked these!

With best wishes from The NRICH Team

-- 
Liz Pumfrey
NRICH Primary Coordinator
University of Cambridge Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WA
01223 764246
www.nrich.maths.org

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