Finding Row with 361 in Odd Number Pattern

1. Given the pattern of the odd numbers below, which row has 361? • 1 • 3 5 • 7 9 11 • 15 17 19 • 21 23 25 27 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | |

2. Given the pattern of the odd numbers below, which row has 361? Multiple approaches to examine the pattern in terms of each row:

3. Given the pattern of the odd numbers below, which row has 361? Multiple approaches to examine the pattern in terms of each row: • The first and the last numbers.

4. Given the pattern of the odd numbers below, which row has 361? Multiple approaches to examine the pattern in terms of each row: • The first and the last numbers. • The middle number.

5. Given the pattern of the odd numbers below, which row has 361? Multiple approaches to examine the pattern in terms of each row: • The first and the last numbers. • The middle number. • The sum of the numbers.

6. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 • 1 • 3 5 • 79 11 • 15 17 19 • 21 23 25 27 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | The first and the last numbers

7. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 1 1 3 5 7 11 13 19 21 29 31 41 43 55 • 1 • 35 • 7911 • 15 1719 • 2123 25 2729 • 3133 35 37 3941 • 45 47 49 51 5355 • : : : • | | | The first and the last numbers

8. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 • 1 • 3 5 • 7 9 11 • 15 17 19 • 21 23 25 27 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | The middle number

9. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 • 1 • 3 5 • 7911 • 15 17 19 • 21 232527 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | The middle number

10. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 • 1 • 3 5 • 7911 • 15 17 19 • 21 232527 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | The middle number

11. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 1 8 27 64 125 216 343 • 1 • 3 5 • 7 9 11 • 15 17 19 • 21 23 25 27 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | The sum of the numbers

12. Given the pattern of the odd numbers below, which row has 361? 1 2 3 4 5 6 7 1 8 27 64 125 216 343 • 1 • 3 5 • 7 9 11 • 15 17 19 • 21 23 25 27 29 • 31 33 35 37 39 41 • 45 47 49 51 53 55 • : : : • | | | 1 4 9 16 25 36 49 ±0 ±1 ±2 ±3 ±4 ±5 ±6 nn3n2± n-1 Average ±Range The sum of the numbers

13. Given the pattern of the odd numbers below, which row has 361? Summary of the pattern Row: 1 2 3 4 5 6 7 1 3 7 13 21 31 43 1st & Last Nos. 1 5 11 19 29 41 55

14. Given the pattern of the odd numbers below, which row has 361? Summary of the pattern Row: 1 2 3 4 5 6 7 Difference 2 4 6 8 10 12 1 3 7 13 21 31 43 1st & Last Nos. 1 5 11 19 29 41 55 Difference 0 2 4 6 8 10 12

15. Row: n 1 2 3 4 5 6 7 Given the pattern of the odd numbers below, which row has 361? Summary of the pattern 1 8 27 64 125 216 343 Sum of the number: n3 Average of the sum:n2 1 4 9 16 25 36 49 ±0 ±1 ±2 ±3 ±4 ±5 ±6 Range about the average ±(n-1)

16. Given the pattern of the odd numbers below, which row has 361? Note: 225 < 361 < 400 152202 162 = 256 192 = 361 172 = 289 182 = 324

17. Given the pattern of the odd numbers below, which row has 361? Note: 225 < 361 < 400 152202 192 = 361 Row: 19

18. The problem is solvable by multiple approaches: 1) Continuing to fill numbers 2) Recognition of a pattern Pattern recognition requires • Identification sequences of numbers • Addition of sequences of numbers • Squaring & cubing of an integer • Average & range of data