The district will be receiving a $750,000 grant from the Wallace Foundation, a New York charitable organization that supports expansion of arts and music programs in urban districts nationwide. The grant will help the district develop a strategy for rolling out more arts programs, and it could lead to a larger donation to implement more programs.

The announcement follows a report earlier this year that found that about a quarter of the city’s elementary schools and more than half of its middle schools did not meet a district standard of providing arts or music instruction at least once a week. Over the years, many music and arts programs have fallen victim to budget cutting.

“We are very excited about this investment in Boston public schools,’’ said Carol Johnson, school superintendent, who added that many parents consider a strong arts and music program to be a critical component of a good-quality school.

The district has set a goal of having all elementary and middle school students receive weekly arts instruction by 2012. Helping to fund that goal is a $2.5 million fund-raising campaign launched earlier this year by EdVestors, a Boston-based group devoted to school improvement, which is working with other nonprofits. So far, $1.1 million has been raised.

In addition to that effort, four schools - Hennigan Elementary in Jamaica Plain, Haley Elementary in Roslindale, Everett Elementary in Dorchester, and King K-8 in Dorchester - will each receive $30,000 worth of musical instruments this year from VH1. A total of 36 schools have benefited from that program in recent years.

“Arts programming is such a crucial component to a child’s educational success because they connect all that we are trying to do for our children, both in and out of school, by teaching them to think creatively and to express themselves in a healthy manner,’’ Mayor Thomas M. Menino said in a statement. “The BPS Arts Expansion Initiative is a great example of how arts programming can pull entire communities together.’’