Download Proposed list of potential topics

Proposed list of potential topics
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Various Sequences, Series
More on fractions, linear Diophantine equations
Congruent triangles, areas, similar triangles, more fractions
Counting, binomial co-efficients, Pascals triangle, sierpenski triangle, polynomials
Areas, Pythagoras, area of a circle
Circle geometry
Polynomials, basic operations (addition, multiplication), quadratic formula, golden ratio
Bases, tie in counting and series, (almost all numbers have a digit 3!)
Proof- induction and contradiction
Geometry- constructions with ruler and compass (and folding?!)
Modular arithmetic
Geometric Transformations
Note that Ciaran highlighted the items in purple as topics he will likely be covering in his own
lesson plans. Also, the majority of these topics should probably be taken in more than one lesson
plan for thoroughness.
Class notes Existing, in work or needed (not an exhaustive list), and others
1. Parity Party – the strength of maths in solving various fun problems
2. Cool counting - uses divisibility (could be reformulated as e.g. “counting by threes”)
Counting problems with two successive tasks – uses products – could be added to cool counting?
3. 1+2+3+... and problems where we try the first few steps
4. Problems using simple linear equations - introduces variables
Systems of two linear equations – could be part of simple linear equations?
5. and 6. Distributivity x2
7 Division with remainder – introduces division as a=bq+r, getting used with variables, case work
8 Superb sums – works with digits, introduces variables, uses distributivity
9 Delightful division – divisibility criteria
10 Intriguing Indices – prepare prime factorisation
11 and 12 Pretty primes x2: Prime factorization, consequences, uniqueness , properties of primes
13-15 Jumping Jiving GCD, LCM x3?
16 Inclusion-exclusion – can potentially use divisibility, LCM.
17 Fun Fractions
Linear Diophantine equations
18 Rational numbers – decimal representation
19 Bases, tie in counting and series, (almost all numbers have a digit 3!)
20 Pristine Proof – Contradiction
21 Pristine Proof – Induction
22 Functions – value at a point, introduce polynomials
23 Congruent triangles
24 Areas – triangle, circles,...
25 Similar triangles
26 Pythagoras, the 30-60-90 triangle
27 Completing the square, system of linear +quadratic equations, golden ratio? x2
30 Polynomials – division with remainder problems?
31 Geometry- constructions with ruler and compass (and folding?!)
32 Modular arithmetic
33 Geometric Transformations