Math maze activity for finding the constant of proportionality in ratios and proportions.

- Start at "y = 3x", which has k = 3.
- From there, follow the path labeled k = 3 to the table with x-values 1, 3, 5 and y-values 2, 6, 10. The constant of proportionality is k = 2 (since 2/1=2, 6/3=2, 10/5=2).
- From the k = 2 box, follow the path labeled k = 2 to the graph passing through (2, -4). The constant is k = -2 (since -4/2 = -2).
- From the k = -2 box, follow the path labeled k = -2 to the table with x-values 1, 3, 5 and y-values 7, 21, 35. The constant is k = 7 (since 7/1=7, 21/3=7, 35/5=7).
- From the k = 7 box, follow the path labeled k = 7 to the graph passing through (10, 40). The constant is k = 4 (since 40/10 = 4).
- From the k = 4 box, follow the path labeled k = 4 to the equation y = 0.4x. The constant is k = 0.4.
- From the k = 0.4 box, follow the path labeled k = 0.4 to the table with x-values 9, 15, 21 and y-values 3, 5, 7. The constant is k = 1/3 (since 3/9=1/3, 5/15=1/3, 7/21=1/3).
- From the k = 1/3 box, follow the path labeled k = 1/3 to the graph passing through (2, 0). This point lies on the x-axis; for a proportional relationship, if x=2 then y should be k*2. Since y=0, this implies k=0. However, the path from here is labeled k = 0.5, leading to the next box.
- From the k = 0.5 box (which corresponds to the graph passing through (2, 1), since 1/2 = 0.5), follow the path labeled k = 0.5 to the table with x-values 1, 2, 3 and y-values 3, 6, 9. The constant is k = 3 (since 3/1=3, 6/2=3, 9/3=3).
- From the k = 3 box, follow the path labeled k = 3 to the equation y = -1.2x. The constant is k = -1.2.
- From the k = -1.2 box, follow the path labeled k = -1.2 to the table with y-values 3, 5, 11. The corresponding x-values are not given, but the path leads to a box labeled k = 0.25, which connects to the final box.
- From the k = 0.25 box, follow the path labeled k = 0.25 to the graph passing through (2, 0.5). The constant is k = 0.25 (since 0.5/2 = 0.25).
- From the k = 0.25 box, follow the path labeled k = 0.25 to the equation y = -1.2x. (This appears to be an error in the maze design, as k should be -1.2, not 0.25. Proceeding with the intended path:)
- From the k = -1.2 box, follow the path labeled k = -1.2 to the FINISH box.