 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Solutions for Session 7, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C8 | C9   Problem C1    Problem C2

Here is the completed table:

 Number of dots on side of square Total number of dots (square number) 1 1 2 4 3 9 4 16 5 25 6 36 10 100 13 169   Problem C3 It is neither a linear nor an exponential graph. Its successive outputs do not have the same ratio; therefore, it cannot be an exponential graph. It is certainly not a straight line, because successive outputs do not have the same difference, so it cannot be a linear graph.   Problem C4 The rule is O = n2, where O is the output, the total number of dots, and n is the number of dots on the side of a square. A recursive rule is Dn = Dlast + (2n - 1).   Problem C5    Problem C6

Here is the completed table.

 Number of dots on side of triangle Total number of dots (triangular number) 1 1 2 3 3 6 4 10 5 15 6 21 9 45 19 190   Problem C7 As with Problem C3, the graph does not demonstrate exponential behavior, because successive terms do not have the same ratio. It's not a linear graph, either, because it is certainly not a straight line. Actually, the graphs of the table of square numbers and the table of triangular numbers look pretty similar.   Problem C8 There is more than one answer, but one is O = (n)(n + 1) / 2. The recursive form is easier to find: Dn = Dlast + n, because n new dots are added in the nth triangle.   Problem C9 Both closed-form rules involve multiplying n by itself at some point, and both recursive rules involve adding something linear to n. Compare this to linear functions, which have only a single use of the variable in their closed-form rules, and a constant in the recursive rule.     Session 7: Index | Notes | Solutions | Video

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