Number Problems Year 9  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 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