Number Problems Year 8  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 36 Millennium Dates Palindromes Checking, Written methods How many Palindromic Dates will there be in this new Millennium ? Systematic, Verify 53 Divide It Divisibility, Factors etc Nice challenge involving tests of divisibility Division, Verify 53 Factor This Factors Factor 1000000 into a x b (neither a multiple of 10) Prime factor decomposition 53, 145 Factor Squares Prime Factors, Sequences Does the sequence 6, 12, 24,... contain any square numbers? Prime factor decomposition 53, 55 Hundred factorial Factors, Powers How many zeros does 100! have on the end ? Factor, Multiple, Verify 55 Fossils Factors Pretty little investigation of numbers reducing to a 'fossil' upon multiplication of their digits Factor, Multiple 57 Double Squares Squares A surprisingly simple trick to writing numbers as the sums of squares - a must-see ! Integer, Square number, Method 57, 67 Non-Calc Square Roots Fractions, Square Roots Newton's cute method to find square roots, and using addition and division of fractions too ! Division, Verify 57, 115 Huge Powers Index Laws, Powers How to compare the relative sizes of numbers as huge as 2800 and 3600 ? Power, Index laws 59, 105 Large Perfect Squares Algebraic expressions, Refine written methods This is based on the idea of squaring a bracket and the first few problems would be a nice 'long' multiplication revision puzzle Partition, Multiply out, Square,  Verify 65 Ordering Fractions Fractions This is a problem concerned with different ways to compare the size of fractions, and looking at alternative approaches, perhaps using approximations, differences or reciprocals. Reciprocal, Equivalent, Estimate 65, 67, 83 That Fraction In Between Fractions Most students have tried the ' add the tops, then add the bottoms ' approach to adding fractions ... so this problem nicely explores the difference that this makes. Equivalent, Estimate, Ascending 65, 83 What Was The Fraction? Fractions, Reciprocals, Checking Working back from a calculator display to the original fraction, using various techniques Reciprocal, Equivalent, Division, Verify 66 Adding Fractions Fractions A series of fractions with horribly large denominators that can be simplified by intelligent grouping ...to give 1! Sum, Factor, Denominator 67 Egyptian Fractions Fractions Good practice in adding and subtracting to solve a fresh problem Denominator, Numerator, Unit fraction, Multiple, Remainder 70, 150 Christmas Partridges Triangle numbers My True Love seems to deal with Triangle numbers... Systematic, Verify, Arithmetic sequence, Tn 67 Spare A Sheep Finding and adding Fractions Old Macdonald tries to share out his 19 sheep with the aid of a neighbour's sheep… Fraction, Denominator 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 Ratio Cut Ratio, Proportion A simple transformation makes easy work of a rectangle division. Area, Ratio, Height 81, 173 Leg It Interpret Graphs Two runners are racing over 100m - how much start (or handicap) is needed to make the race a 'fair' one? Distance, Time, Speed, Ratio 81, 173 Lap Times Interpret Graphs Two friends are running round a track at different speeds - how often do they pass each other? Graphs, Ratio,  Distance, Time 81, 239 What Size Are The Cylinders? Ratio, Volume Two similar cylinders come from a block of material - how big is each? Ratio, Enlargement, Volume, Scale 83 Parking Meters Use of Division, Sequences A mixture of dollars and quarters make up \$29.50 - how many coins of each type, 43 in total? Calculate, Sequence 87, 115 Brackets Order of operations, Brackets The difference that the placing of brackets makes ! Brackets, Associative, Commutative 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 97 Nearly Squares Extend mental methods Using the fact that 19 x 21 = 202 - 12 Calculate, Partition 97 Half Squares Extend mental methods Using the fact that 6.52 = 6 x 7 + 0.25 Calculate 100, 228 Smart Weights Mental methods, Mass The most efficient choice of weights is based on binary, but tertiary is even smarter ! Power, Expression