📏 Mathematical Instruments
Most of these items would now be called “Manipulatives” or “Concrete Representations” (or ‘Objects to think with’) within Jerome Bruner’s “Concrete Pictorial Abstract” (now ‘Singapore Maths’) thinking. But most Mathematics is Ancient so I prefer to be old-fashioned, inspired by these quotes from one of my favourite mathematicians:
| These works … have a greater aim than mere illustration; I do not introduce colours for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction, and to diffuse permanent knowledge.” (1880) | | “It may be necessary to add that other set squares or triangular rulers may be purchased cheaply at mathematical instrument makers, and employed with advantage, as well as those used and described in this work.” (1865) -Oliver Byrne
🌓 Two-Sided Counters
🧱 Cuisenaire Rods
🔟 Ten-frames & Abacus
💰 Cups & Bags
📦 Blocks & Tile Shapes Activities can include:
- Make a tile sequence. What kinds of numbers can be found on this list? What kinds of numbers cannot? What would the hundredth number be? Is it possible to create a pattern block figure with an odd perimeter?
- Explore angles: Which shapes can surround a point? What is each corner as a portion of \(360°\)? Can you describe the boundary path of the shape as walking instructions (e.g. square = step forward, turn \(90°\) left, repeat)? If you keep adding shapes, how do the total internal angles change?
⛓ Number Paths/Lines/Grids
🍱 Algebra Tiles
- Activities can include: Make a rectangle. Write algebraic expressions for area & perimenter of composite shapes. Demonstrate simple algebra using stories e.g. \((x+1)² = x + x+1 + x²\) i.e. if you start with two adjacent numbers and you want to to make the square of a the bigger number, you add the smaller, the bigger, and the square of the smaller.
📐 Ruler & Compass & Set-Square
🧾 Paper-Folding & Origami
🧮 TI-84 & Ti-Nspire Scientific Calculators