Thanks very much for the pattern link!
Since you need to increase only 6sts per round on 6 rows (rows 5-10), repeat rows 3 and 4. Increase the number of sc by one each row.
row 5 [3sc, 2sc in the next stitch] 6 times (30sts total)
row 6 [2sc in the next stitch, 4sc] 6 times (36sts)
row 7 [5sc, 2sc in the next stitch] 6 times (42sts)
row 8 [2sc in the next stitch, 6sc] 6 times (48sts)
etc., through row 10
There is an alternative and if one doesn't looks good, you might try this. Since the pattern isn't clear, you might just repeat row 4 increasing the number of single crochet sts between the increases in each row. The idea is to distribute the increases across the row.