As lawmakers map out a series of public hearings to learn more about Gov. Charlie Baker’s $38.1 billion fiscal 2016 budget, they are also busy passing through the Legislature the governor’s proposal to pour $350 million in fresh appropriations into the fiscal 2015 budget. The House approved the supplemental spending bill this week and the Senate plans to take it up next Thursday, after discussing it during a closed caucus this week. The next move on the fiscal 2016 budget is up to the House Ways and Means Committee. That panel’s recommendation serve as the backbone for the budget bill that clears the House each April. According to a schedule released Friday, the next fiscal 2016 budget hearing is March 24 in Greenfield, which will be followed by hearings March 25 in Worcester, March 31 in Methuen, April 1 in Everett, April 7 in Medford, April 9 in Springfield and April 13 in Boston.