1. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361?

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. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361? 12345671234567 The first and the last numbers

7. Given the pattern of the odd numbers below, which row has 361? 1 1 3 5 7 11 13 19 21 29 31 41 43 55 The first and the last numbers 12345671234567

8. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361? 12345671234567 The middle number

9. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361? 12345671234567 The middle number

10. Given the pattern of the odd numbers below, which row has 361? The middle number

11. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361? 12345671234567 The sum of the numbers 1 8 27 64 125 216 343

12. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 : : : | | | Given the pattern of the odd numbers below, which row has 361? 12345671234567 The sum of the numbers 1 8 27 64 125 216 343 1 4 9 16 25 36 49 Average ±Range ±0 ±1 ±2 ±3 ±4 ±5 ±6 n n 3 n 2 ± n-1

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 st & Last Nos. 1 3 7 13 21 31 43 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 1 st & Last Nos. 1 3 7 13 21 31 43 1 5 11 19 29 41 55 Difference 2 4 6 8 10 12 Difference 0 2 4 6 8 10 12

15. Given the pattern of the odd numbers below, which row has 361? Summary of the pattern Row: n1 2 3 4 5 6 7 Sum of the number: n 3 1 8 27 64 125 216 343 Average of the sum: n 2 1 4 9 16 25 36 49 Range about the average ±(n-1) ±0 ±1 ±2 ±3 ±4 ±5 ±6

16. Given the pattern of the odd numbers below, which row has 361? Note:225 < 361 < 400 15 2 20 2 16 2 = 256 17 2 = 289 18 2 = 324 19 2 = 361

17. Given the pattern of the odd numbers below, which row has 361? Note:225 < 361 < 400 15 2 20 2 19 2 = 361 Row: 19

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