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 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