Algebra Problems Year 8                                       

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Examples Page Ref  Problem Title Objectives Ref Description Key Words
113 Input Output Express Relationships Describe the rule connecting the dual Inputs to the Output Symbols, Mapping, Table, Relationship, Function
87, 115 Brackets Order of operations, Brackets The difference that the placing of brackets makes!  Brackets, Associative, Commutative
123 Bad Dog! Construct and solve simple equations Cheery the Dog has just swallowed Sweety the Cat - how heavy were they each beforehand?! Like Terms, Solve, Equation
114, 150, 158 The Sum of r 3 Formulae, Proof 13 + 23 + 33 ... from a really simple diagram Formulae, Tn, Predict, Verify 
117 Three Numbers Simplify expressions Find the original numbers, given the sums of the three taken in pairs Simplify, Solve, Equation
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 etc?  Formula, General term
105, 110, 120 Large Perfect Squares Algebraic expressions, Calculations 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
109, 161 Funny Functions Functions, Complex calculations, Analyzing the Calculator functions 'SQRT' and 'INT', looking at associativity etc  Brackets, Associative
123, 127 High But Friendly Simultaneous Equations Linear Equations, Elimination Simultaneous equations in 5 unknowns ... but easy to guess their relative sizes and hence solve (honest!)  Unknown, Expression, Substitute, Solution 
125, 139, 151 How Hot Is That? Linear Equations, Formulae, Graphs, Spreadsheets How good is F =2C+30 at approximating temperature conversions? Substitute, Formulae, Equation
53, 145 Factor Squares Prime Factors, Sequences Does the sequence 6, 12, 24,... contain any square numbers? Prime factor decomposition
149 Parking Meters  Sequences, Spreadsheets A mixture of dollars and quarters make up $29.50 - how many coins of each type, 43 in total? Calculate, Sequence
154, 262 The Knockout Tournament Sequences, Organizing Data How many games are needed in a tournament for 100 teams? How many byes etc?  Predict, Generate, Verify
30, 144 Shelf Tidying Sequences, Justify methods How quickly can you put the Star Trek videos back in order? Sequence, Proof
155 Pick A Shape Generate sequence, Find nth term Pick's Theorem for Areas on a dotty grid Formula, Generate Tn, Proof
149, 161 Toffee Maths Function, Linear sequence A fold-on-itself process that shows up the nature of 'Chaos', using a simple iterative function Flow chart, Transform, Mapping
161, 165, 203 Graphic Convergence Linear Equations, Elimination A mapping for x and y sends points to a convergent 'invariant point' - nice, visual, algebraic exercise  Unknown, Expression, Substitute, Solution 
 173, 81,193 Leg It Ratios, Travel graphs, Similar Triangles Two runners are racing over 100m - how much start (or handicap) is needed to make the race a 'fair' one? Distance, Time, Speed, Ratio
 173, 81,193 Lap Times Ratios, Travel graphs, Similar triangles Two friends are running round a track at different speeds - how often do they pass each other? Distance, Time, Speed, Ratio
175 Die Hard Graphs, Sequencing The old Jugs problem, with a 'graphical' hint  Coordinates, Graph, Sequence