Mayor Martin Walsh is vowing to tackle housing, education and transportation as the new decade opens, promising more than half a billion in spending in his State of the City address Tuesday night.

“We will lead with our values,” Walsh told a packed house at Symphony Hall. “We will work together across all our differences to tackle our toughest challenges. We will be a city that’s world class because it works for the middle class, and we will leave no one behind.”

The second-term mayor, entering his seventh year in office, announced nearly $500 million over the next five years in new spending toward a range of housing initiatives, most prominently a new city-run voucher program for renters.

“The data shows our strategy is working,” Walsh said. “Rents and home prices are stabilizing, but they’re still too high for too many people. There’s much more work to be done.”

Walsh’s administration is counting on two new revenue sources to pay for all of that spending, which would also go toward public housing, senior housing and income-restricted affordable housing. One is the sale of the city-owned Lafayette Garage downtown that the city expects to put out to bid this year. Walsh wants a longer-term flow of cash to come from a tax of real-estate transfers of more than $2 million, for which the city requires the Legislature’s approval.

Walsh administration officials say they expect that to come expediently, even though Beacon Hill is often reluctant to approve home-rule petitions from municipalities.

Turning to education, Walsh announced a three-year ramp-up to $100 million more in annual funding for Boston Public Schools. This cash, starting around $30 million next year and increasing the following years, will go to initiatives like increasing mental health services, curriculum planning and parent liaisons.

“It will reach every school and it will be carefully targeted, so every dollar makes a difference. We’ll begin with intense support for underperforming schools, so we can become one great district,” Walsh said.

Walsh called the transportation congestion nightmare in Boston “a threat to the future of our economy.” He said police will crack down on unsafe drivers as the cops and Boston Transportation Department further focus on ongoing city efforts to cut down on crashes.

“What I hear in every neighborhood is the need for more enforcement,” Walsh said. “And I agree. The speeding, the texting behind the wheel, blocking lanes and intersections — enough is enough.”

Walsh also announced a new “transportation action committee” for East Boston, which has particularly bad traffic, and reiterated his call for a Boston seat on the MBTA governance board. He said the city would work to further create bike and bus lanes.

Walsh also noted that Boston will host this year’s NAACP convention this summer, an event proponents hope will show how Boston’s improved on its rocky racial history.

“It’s a milestone for our city, marking a new era of progress we have achieved together,” Walsh said.