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 problem-and-solution 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 'one-number-at-a-time' 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 '6n-1', 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
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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)(a-b), 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 |