1. 1 MANYology MATH a Natural Science about the Natural Fact MANY MATH e CADEMY.net

2. 2 T = llll = = 1 digit M ath : 1.order-counting creates icons 123456789

3. 3 ) ) T = 7 1s = ? 3s = ? 5s ) ) 2 ) 1) = 2.1 3s 1 digit M ath : 2.order-counting creates decimal numbers & units 1 ) 2) = 1.2 5s

4. 4 T = 7 1s = ? 2s 3 ) 1) = 3.1 2s ) ) ) ) ) 1)1)1) = 11.1 2s 1 digit M ath : Overload calls for an extra cup

5. 5 5.8 3s = ? 5.8 3s = 5) 8) = 5 +1 ) 8 -3 ) = 6) 5) 6) 5) = 6 +1 ) 5 -3 ) = 7) 2) 7) 2) = 1 ) 7 -3 ) 2) = 1) 4) 2) 5.8 3s = 6.5 3s = 7.2 3s = 14.2 3s = 21.2 3s 1) 4) 2) = 1 +1 ) 4 -3 ) 2) = 2) 1) 2) 1 digit M ath : Overloads can be removed or created by re-bundling

6. 6 T = ?*b T = ?+b T = (T/b)*b T = (T-b)+b IIIIII = II II II T = (T/b)*b 6 = (6/2)*2 IIIIII = IIII II T = (T-b)+b 6 = (6-2)+2 1 digit M ath : reBundling and reStacking predicted by formulas reBundle Formula reStack Formula -3: take away 3 /3: take away 3s +3: add 3 Nex-to *3: add 3 times On-top

7. 7 4 5s = ? 7s 4 5s = 2.6 7s 4 5s = (4*5)/7 *7 = 2.? *7 4 5s = (4*5 – 2*7) + 2*7 = 6 + 2*7 = 2.6 7s T = (T/b)*b T = (T– b)+b 1 digit M ath : Formulas predict re-counting

8. 8 4£=5$: 7£ = ?$ & 8$ = ?£ T = (T/b)*b, $ = ($/£)*£, £ = (£/$)*$ $ = ($/£)*£ $ = (5/4)*7 = 8.75 £ = (£/$)*$ £ = (4/5)*8 = 6.4 1 digit M ath : Changing units by re-counting 7£ = (7/4)*4£ 7£ = (7/4)*5$ 7£ = 8.75$ 8$ = (8/5)*5$ 8$ = (8/5)*4£ 8$ = 6.4£

9. 9 2.3 *b = ? 23 /b = ? 2.3 *b = 2)3) *b = 2)3)) = 23.0 2.3 *b = 23.0 23 /b = 2.3 1 digit M ath : Adding or removing right-cups moves the decimal point 23 /b = 2.3*b/b = 2.3

10. 10 10 = ? 1 digit M ath : 10 is a cognitive bomb 10 = Bundle = 5 with 5 as the bundle-size 1,2,3,4,10,11,12,13,14,20,21,22,23,24,30… 10 = five, 10 = the follower of four, ten = 20 1,2,3,4,5,6,10,11,12,13,14,15,16,20,21,… 10 = seven, 10 = the follower of six, ten = 13 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,… 10 = ten, 10 = the follower of nine, ten = 10 1,2,3,4,5,6,7,8,9,a,b,10,11,12,13,… 10 = twelve, 10 = the follower of elleven, ten = a

11. 11 2.4 5s + 1.3 5s = ? 2.4 5s = 2) 4) 2.4 5s + 1.3 5s = 4.2 5s 1.3 5s = 1) 3) = 3) 7) = 3 +1 ) 7 -5 ) = 4) 2) 1 digit M ath : Overloads are removed by re-bundling

12. 12 4.2 5s - 1.3 5s = ? 5s 4.2 5s - 1.3 5s = 2.4 5s 4.2 5s = 4) 2) = 4-1) 2+5) = 3) 7) 1.3 5s = 1) 3) = 2) 4) 1 digit M ath : Overloads are created by re-bundling

13. 13 ) ) ) ) = ) ) = ) ) 1.3 4s + 2.4 5s = ? 4s ++++++++ 1.3 4s + 2.4 5s = 5.1 4s 1 digit M ath : Adding On-top means changing units by re-counting 1) 3) 3) 2) = 4) 5) = 5) 1)

14. 14 1.3 4s + 2.4 5s = ? 9s ) ) 2) 3) + 1.3 4s + 2.4 5s = 2.3 9s 1 digit M ath : Adding next-to means integrating

15. 15 ? + 5 = 9 ? * 5 = 9 x+5 = 9 = (9-5)+5 T = x*b (T/b) = x x = 9-5 x*5 = 9 = (9/5)*5 T = x+b T-b = x x = 9/5 1 digit M ath : Reversing Addition on-top creates equations T = (T-b)+b T = (T/b)*b

16. 16 ? 4s + 2 5s = 3 9s p =  T/  x 1 digit M ath : Reversing addition next-to creates differentiation p*4 + 2*5 = 3*9 p*4 = 3*9 – 2*5 p = (3*9 – 2*5)/4 p = 4.1 p*b + T1 = T2 p*b = T2 – T1 p =  T/b p =  T/  x

17. 17 1/2 + 2/3 = 3/5 or 7/6 1 digit M ath : Per-numbers need units to be added Question: 1 of 2 + 2 of 3 = ? Inside School: Outside School: PerNumbers add as Areas: (1/2)*2 + (2/3)*3 = (3/5)*5 1 2 1*3 2*2 7 2 3 2*3 3*2 6 1 2 1+2 3 2 3 2+3 5 + = + = = 1/2 2/3 3/5 = 2 3 5

18. The 4 Ways to Unite 567 = 5*10^2 + 6*10 + 7*1 +: Unite variable unit-numbers *: Unite constant unit-numbers ^: Unite constant per-numbers  : Unite variable per-numbers 18 1 digit M ath : Numbers all have units

19. The Algebra Project Operations unite/split intoVariableConstant Unit-numbers m, s, $, kg T = a + n T – a = n T = a * n T/n = a Per-numbers m/s, $/kg, % T = ∫ a dn dT/dn = a T = a^n logaT = n n√T = a 19 1 digit M ath : Algebra means to reunite in Arabic