I can’t do any more of this ‘tables’ stuff, but I am asked about the issue so much…

Look, here’s a ‘tables’ square, slightly adjusted:

I’ve removed the 1x and 10x sectors. 1x is trivial, **10x** needs special treatment.

If you fully appreciate the **flip rule** you can forget the grey airbrushed section.

The **square numbers** in the blue-green squares are a special beautiful group, well worth studying. Many patterns and much al-jebr live here…

The rest are in 8 columns, from 1 to 8. Add up the numbers from 1 to 8 in your head and it’s 36. [I did 8×9 and halved it).

The orange numbers can be found by **doubling** from single digit numbers. (Conversely by **halving** from the products).

The blue by **treblings** from single digit numbers.

There are 4 spaces left, 5×6, 5×7, 6×7, 6×9.

double 15, the two primes, 5 and 7 make 35, double 21 and double 27.

Study George Cuisenaire’s original product wall chart:

You can see all the doublings. Look carefully.

These products, the numbers in black, form

**MILESTONES in the unknown territory to 100**

By studying them as **numbers**, as we have previously discussed, their **inner structures** will become apparent, thus lessening the awful stress on memory so prevalent in today’s schools.

In addition by briefly studying the **Primes** to 100 it will become apparent to the little yellow belts that many numbers are rich in factors and many are not. They will **generate a ‘feel’ for the rich numbers**, learn their inner structures by familiarity and learn, as an aside, the so called ‘tables’ relevant to that number.

This however takes

**A CHANGE OF PROGRAMMING**

even in the minds of teachers, never mind the administrators

**THIS IS** **PROBLEMATIC…**

because even you and I dear reader

**IMAGINE OURSELVES TO BE FREE**

**huatou: ‘Am I free?’**