To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problemandsolution Word document.
Examples Page Ref  Problem Title  Objectives Ref  Description  Key Words 
45, 47  Rounding Errors  Rounding  Showing the difference between correct rounding technique and the 'onenumberatatime' approach  Significant figures 
53  Divide It  Divisibility, Factors etc  Nice challenge involving tests of divisibility  Division, Verify 
55, 117, 121  Prime Time  Algebraic expressions, Proof  Can you show that all Primes are of the form '6n+1' or '6n1', no squares divided by 5 give remainder 2 or 3, and so on ?  Generalize 
57, 91, 133  Power Twins  Index Laws, Powers  2 ^{4} = 4 ^{2}  find some more examples !  Exponent, Index, Reciprocal, Trial + Improvement 
57, 63  Factor Fractions  Indices, Powers, Cancelling Fractions  Can you find three different whole numbers a, b and c, which will make the value of a whole number itself?  Index, Factorize, Common Factors 
57, 115  Huge Powers  Index Laws, Powers  How to compare the relative sizes of numbers as huge as 2^{ 800} and 3^{ 600 }?  Power, Index laws 
59, 105  Large Perfect Squares  Algebraic expressions, Refine written methods  This is based on the idea of squaring a bracket and would follow on from practice in for example squaring 13 as (10+3) or 28 as (20+8).  Factorise, Power, Verify, Brackets, Quadratic expansion 
61, 81, 193,215  Pendants  Similarity, Enlargement  'Area Factors' under enlargement give quick answers to this problem  Similar, Enlargement, Scale factor 
65  Ordering Fractions  Fractions  Introducing different ways to compare the size of fractions, using approximations, differences or reciprocals.  Reciprocal, Equivalent 
65, 83  What Was The Fraction?  Fractions, Checking  Working back from a calculator display to the original fraction, using various techniques  Reciprocal 
70  Smart Weights  Powers  The most efficient choice of weights is based on binary, but tertiary is even smarter !  Power, Expression 
77, 111  Percentage Changes  Percentages, Checking  What % increase will compensate for a 5% decrease ?  Reciprocal, Inverse 
77  The Property Market  Percentage changes  I sell two houses for £156000  one at a 20% profit, the other at a 20% loss  am I winning or losing ?  _{Inverse, Profit, Loss} 
79, 81  Astronomically Accurate  Proportion

_{How long is a year exactly (taking into account leap years and that)... and what about a real 'lunar' month?}  _{Proportion, Unitary, Accuracy} 
81, 173,193  Lap Times  Ratios, Travel graphs, Similar triangles  _{Two friends are running round a track at different speeds  how often do they pass each other? }  _{Ratio, Speed, Proportion} 
81, 91, 233  Average Speed  Rates of Change, Ratio + Proportionality  A nice introduction to ratio methods for combining average speeds over 2 sections of a journey  Ratio, Speed, Average 
91, 233  A Walk In The Bush  Fractions, Measurements  An 'average speed' problem that comes out very sweetly  involving some up and down hills  Speed, Average 
91, 127, 189  The Magic of Pythagoras  Pythagoras  This Problem is a variation on the Well in the Courtyard problem... and has a lovely, surprising answer as unwanted terms 'cancel out' !  Pythagoras, Subject of the formula 
91, 97  Sisterly Squares  Multiplication Strategies, (a+b)(ab), Factorizing  25 and 36 are both squares, and 2+1=3, 5+1=6... when's the next pair ?!  Factorize 
91, 101  Pity Four Fours  Use known Number facts 
Just the old 'make all the numbers from 1 to 20, using exactly four 4s' problem  with 4! and Sq Rt (4) = 2 tools... plus all the answers! 
Arithmetic, Number Facts 