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The city’s Department of Education, Teach for America and several city charter school management companies are angling for federal money designed to encourage cutting-edge educational strategies.

They’re among 145 New York State-based entities that applied for grants under a new federal program known as the Investing in Innovation Fund, or “i3.” Details about the 1,698 applications submitted last month went online yesterday.

Here’s a snapshot of some of the ways local groups are hoping to cash in:

• The city is asking for $40 million to open 150 new small middle and high schools in the next five years.
• The city also asked for $5 million to grow the School of One technology program and $4.5 million to boost the arts in special education schools.
• Other groups angling to open new schools include Eva Moskowitz’s Harlem Success charter network, which is seeking $25 million to open 13 in the next five years, and New Visions for Public Schools, which wants $26 million to create charter schools that serve 10,000 city students.
• The city’s principal training program, the NYC Leadership Academy, wants $30 million to expand into other school districts. Another leadership pipeline, New Leaders, asked for $5 million to improve principal development in New York City.
• The Broader, Bolder Approach is getting back in the game after winding up in second place in the battle of reform agendas between it and Joel Klein’s Education Equality Project. A research center at New York University headed by Pedro Noguera applied for $5 million to push the approach.
• Teach for America, the group that supplies new teachers for needy schools, is aiming to grow its national operation by 80 percent in the next four years. But the group’s i3 application doesn’t say New York City will be a site of growth.

Applicants will find out in July whether they’ve been pre-approved for funding. Pre-approved applicants will have to show that they can secure 20 percent of their project’s cost from private sector sources. Unlike the Race to the Top competition, however, it will be hard to handicap applications ahead of time, because there’s no clear-cut rubric to evaluate i3 proposals.