Teachers who spend on classroom supplies and Minnesotans attending college are among those who may be able to write off some expenses under two bills quickly moving through the Legislature.

The bills, House File 6 and Senate File 50, would better align the state's tax code to mirror federal law after changes made by Congress and include provisions that could mean tax relief for thousands of Minnesotans.

Lawmakers in both parties are racing to get the legislation to Gov. Mark Dayton's desk for his approval by Jan. 20, when the federal and state tax filing period begins. If the legislation takes longer to be approved, Minnesotans who filed before would have to file amended returns to get the benefit.

The bill is expected to cost $19.9 million in fiscal year 2015 and would add $22.4 million in the next fiscal year, according to estimates by the Minnesota Department of Revenue. The difference in cost from year to year has to do with how federal and state law deals with a provision on expensing and federal bonus depreciation, which covers assets such as cars, office equipment and computers. Federal law allows for more of the deduction to be claimed in one year; Minnesota law requires it be spread over five years.

Dayton said Monday he would sign the legislation, a spokesman said.

"It'd make [Minnesotans] lives easier," said Rep. Greg Davids, R-Preston, the House Tax Committee chairman and chief author of the House bill. "Hopefully we can get this through quickly … we don't have time for hang-ups."

New Revenue Commissioner Cynthia Bauerly also supports the bill. "We've been working closely with tax committee chairs and appreciate them prioritizing this important issue," she said in a statement. "I'm optimistic we will meet the Jan. 20 date to match Minnesota's tax codes to the updated federal provisions. Doing so will make the filing process simpler for millions of Minnesotans."

State Sen. Rod Skoe, DFL-Clearbrook, said the Senate bill has broad bipartisan support, and that members from both bodies are fast-tracking their respective bills. Floor votes could come by the end of the week.

"It's a convenience, and it's a tax savings for some," said Skoe, who leads the Senate Taxes Committee. "It could be thousands of Minnesotans."

Tax-conformity bills come up frequently at the Capitol. Every time Congress updates the tax code, states must decide whether to conform or leave taxpayers to navigate the difference between their state and federal filings.

Among the changes in the offing for Minnesota's tax code:

• Teachers could deduct up to $250 in out-of-pocket classroom expenses. This change would affect as many as 60,000 filers.

• Extending the itemized deduction for mortgage insurance premiums that would affect 60,000 returns.

• A deduction for higher education, between $2,000 and $4,000 — depending on income — that would allow Minnesotans to write off college-related expenses. The income threshold for single filers would be $80,000 and $160,000 for joint filers. An estimated 9,000 filers are expected to qualify.