Developing Algebraic Thinking Murray Britt University of Auckland Faculty of Education Auckland February, 2005

a + b = a + (c + b – c) = (a + c) + (b – c) a – b = (a – c) + (c – b) 39 40 28 1 27 a + b = a + (c + b – c) = (a + c) + (b – c) 39 + 28 = 39 + (1 + 27) = (39 + 1) + 27 7 2 98 100 107 a – b = (a – c) + (c – b) 107 – 98 = (107 – 100) + (100 – 98)

Counting All 4 + 3 = + 1 + 1 + 1 + 1 + 1 + 1 1 2 3 4 5 6 7 4 + 3

Advanced Counting 34 - 6 = 6 5 4 3 2 1 34 28 29 30 31 32 33 34 - 6