Algebra Problems Year 9
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Examples
Page Ref |
Problem
Title |
Objectives
Ref |
Description |
Key Words |
57,
115
|
Huge
Powers |
Index
Laws |
How to compare the relative sizes of numbers as
huge as 2 800 and 3 600 ?
|
Power,
Index laws |
115, 150 |
Paper
Sizes |
Trial +
Improvement, Similarity |
A3, A4 paper etc |
Trial +
Improvement |
115, 151, 159 |
The
Sum of r 3 |
Formulae,
Proof, Index Laws |
13
+ 23 + 33 ... from a really simple diagram |
Formulae,
Tn, Predict, Verify |
59, 105, 110,
121 |
Large Perfect Squares |
Algebraic expressions,
Calculations |
1111� etc -
These are all based on the idea of squaring a bracket |
Partition,
Multiply out, Square, Verify |
120, 240 |
Simpson's Rule and
the Volume of a Sphere |
Using Formulae |
This exercise leads the pupil through applications of
Simpsons rule to the formula for the volume of a
sphere. It is intriguing that all these volumes are given exactly by the rule. |
Cubic
expression, Formulae, Like terms |
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 |
126 |
Simultaneous
Equations |
Equations |
Symmetric, but nasty-looking, Simultaneous
Equations yield beautifully simple answers if an
intelligent approach is taken to their 'adding and
subtracting'. |
Factorize,
Simultaneous Equations |
91, 127, 189 |
The
Magic of Pythagoras |
Forming
and Solving Simultaneous Equations, Elimination |
This Problem is a variation on the Well in the
Courtyard problem... and has a lovely, surprising answer, as all the
unwanted terms 'cancel out' ! |
Simultaneous
Equations |
133,
141, 151, 159 |
Peachy
Pyramids |
Use
ICT to explore non-linear sequences |
Exploring
the beautiful square fruit pyramids that are seen on greengrocers' stalls |
Spreadsheet,
Sequence, Formula, Squares, ICT |
133,
141, 151, 159 |
Plummy
Pyramids |
Use
ICT to explore non-linear sequences |
Exploring
the more-complex rectangular fruit pyramids that are seen on greengrocers'
stalls |
Spreadsheet,
Sequence, Formula, Squares, ICT |
133, 227 |
Overlapping
Squares 1 |
Graphs, Trial +
Improvement |
This problem offers an
element of surprise in that the equation of the locus of possible solutions isn�t the
straight line that pupils may well expect... |
Graphs,
Subject of the formula, Reciprocal |
29, 135, 237 |
Athletics Track |
Equations,
Formulae, Circles, Spreadsheets |
Designing an 'oval' running track, with bend radii,
staggers etc. An algebraic and/or spreadsheet approach. |
Algebraic
expressions, Subject of the formula |
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 |
150, 175 |
Graphical
Convergence |
Functions,
Graphs, Proof |
A
mapping for x and y sends points to a convergent 'invariant point' - nice,
visual, algebraic exercise |
Unknown,
Expression, Substitute, Solution |
155 |
Pick
A Shape |
Generate
sequence, Find nth term |
Pick's
Theorem for Areas on a dotty grid |
Formula,
Generate Tn, Proof |
109, 161 |
Funny
Functions |
Functions,
Complex calculations, |
Analyzing
the Calculator functions 'SQRT' and 'INT', looking at associativity etc |
Brackets,
Associative |
161, 165, 203 |
Graphic
Convergence |
Co-ordinates,
Mappings |
A
pair of mappings for x and y lead to a convergent sequence of points,
which can also be viewed as a combination of transformations - quite
pretty. |
Mapping,
Consecutive, Sequence, Predict, Verify |
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