Mathematics is no more computation than typing is literature.

*John Allen Paulos*

Topics below give an idea of general direction I would like to take your child in our exploration of Mathematics. It’s not a quick journey by any means. Our youngest students might just get a taste of some topics on their first year, sometimes in a form of a game or hands-on activity. Returning middle-schoolers, on the other hand, will be challenged to apply the familiar concepts in serious problem solving.

- Cuneiform and Roman numerals (positional vs non-positional numeral systems)
- addition, multiplication and long division puzzles with same digits replaced by same letters
- exploding dots (introduction to positional systems other than decimal)
- operations in other bases, conversion of numbers between bases

- even vs odd numbers, definition and easy recognition
- keeping track of parity in arithmetic operations
- keeping track of parity during a process with alterations (what side of the fence is a grasshopper after 315 jumps)
- recognizing parity in longer arithmetic expressions

- review of divisibility rules by 2, 3, 5, with justification
- skip counting on a circle predicting result
- prime factorization, LCM and GCF

- order of operations, parenthesis
- recognizing order of operations in word problems
- regrouping of long sums for efficiency, introduction to finite series

- review of famous arithmetics problems (heads and legs, birds landing of trees, etc.)
- organizing data into table for certain logic problems
- working backwards problems
- organizing data as a chart (I have twice as much as you:), converting into algebraic expressions
- date, time, calendar and age in word problems (organizing what’s given)
- word problems on fractions

- number line: negative numbers (basement floors, piles and pits in a sandbox)
- number line: what is there between 0 and 1?
- geometry of graph paper

- counting polygons on a given picture
- split a shape into identical parts in all possible ways, construct all possible shapes from parts given
- length, perimeter, when does perimeter stay the same
- direction and angles, properties of angles of polygons
- area of certain polygons, area of a part as a fraction of a whole

- review of nets of a cube, introducing nets of other polyhedra
- building all possible Platonic solids
- observations on numbers of vertices, edges, sides of polyhedra
- connections of a 3d shape and its 2d images
- volume

- graphs: relationships of “phone lines”, “islands and bridges” as graphs, unicursal lines
- elements of topology: labyrinths, verifying if a point belongs to closed shape, 3d topology tricks
- elements of combinatorics: counting paths, permutations
- logic: true and false statements, opposite statement, “knights and liars” problems
- strategy games
- puzzles