Number Problems Year 7 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 52 Factor This Factors Factor 1000000 into a x b (neither a multiple of 10) Prime factor decomposition 52 Fossils Factors Pretty little investigation of numbers reducing to a 'fossil' upon multiplication of their digits Factor, Multiple 52, 110 Hundred factorial Factors, Powers How many zeros does 100! have on the end ? Factor, Multiple, Verify 56 Double Squares Squares A surprisingly simple trick to writing numbers as the sums of squares - a must-see ! Integer, Square number, Method 60 Egyptian Fractions Fractions Good practice in adding and subtracting to solve a fresh problem Denominator, Numerator, Unit fraction, Multiple, Remainder 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 66 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 80 Ratio Cut Ratio, Proportion A simple transformation makes easy work of a rectangle division. Area, Ratio, Height 82 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 90 Twenty Four Powers and Roots Use three 2s to make 24 etc Calculate, Powers, Roots 86, 90 Pity Four Fours Order of Operations Just the old 'make all the numbers from 1 to 20, using exactly four 4s' problem - with 4! and sqrt4 = 2 as tools... plus all the answers! Arithmetic, Number Facts 96 Nearly Squares Extend mental methods Using the fact that 19 x 21 = 202 - 12 Calculate, Partition 96 Half Squares Extend mental methods Using the fact that 6.52 = 6 x 7 + 0.25 Calculate 100, 206, 260 Mean Square Mental methods A Magic Square, using means Averages 100, 228 Smart Weights Mental methods, Mass The most efficient choice of weights is based on binary, but tertiary is even smarter ! Power, Expression 100, 146 Christmas Partridges Triangle numbers, Mental methods My True Love seems to deal with Triangle numbers... Systematic, Verify, Arithmetic sequence, Tn 100, 230 Britain Rules The Weights? Binary, Mental methods Metric weights aren't quite as efficient as you would hope... Power, Double,  Sequence 110, 35 Millennium Dates Palindromes Checking, Written methods How many Palindromic Dates will there be in the next Millennium ? Systematic, Verify 110, 32 That's A Bit Odd Checking, Reasoning A simple Logic puzzle, requiring an assumption and checking whether that leads to a contradiction or not Verify, Check, Contradiction