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