Reasoning Without Arithmetic

A collection of situations in which learners young and not so young can reason mathematically without requiring arithmetic fluency.

Secret Places

Secret Places (homage to Tom O'Brien): 
One of the places at the table has been chosen secretly.
In the applet, if you click on a place it's colour changes to
  • red: meaning that the secret place is either the one clicked OR the place either side of that one
  • blue: meaning that the secret place is not the chosen one, NOR the one either side
In how few clicks can you be guaranteed to locate the secret place?   There is a 2D version inside the zipped folder using surfaces such as a cylinder, möbius band, torus, and Klein bottle
Secret Places.zip
File Size: 3067 kb
File Type: zip
Download File
Qualitative Queuing showing 'facts'  and deduced Queue with one rejected 'fact'. The 'facts' are generated randomly.
Quantitative Queuing showing 'facts', deductions and check with original Queue
Queuing in 2D showing some 'facts'. There is a randomly chosen grid to be deduced. A second version has no pre-determined grid.

Queueing

Designed for primary school use especially, these applets provide sequential information about people in a queue. As each 'fact' is revealed, the user has to decide whether it is consistent with what they know already, or whether it should be rejected as inconsistent.

Quantitative Queuing gives information of the form "A is 3 places ahead of B".

Qualitative Queuing gives 'facts' of the form "A is dead of B" and "A is behind B"; or "A is between B and C"; or both types mixed.

Qualitative 2D Queuing starts with grid and gives 'facts' of the form "A is above (or below) B and to the left of (Right of) B"

The applets stimulate reasoning i trying to persuade others that what a new 'fact' adds to or contradicts 'facts' accumulated so far.
Queuing Reasoning.zipIncludes notes 

Magic Square Reasoning

Reasoning based on the properties of magic squares but without ever referring to a particular magic square