The programme introduces "design thinking" to students from kindergarten through to the 12th grade via hands-on workshops offered in the classroom.
The national museum – formally referred to as the Cooper Hewitt, Smithsonian Design Museum – launched the programme in 2011 in New York and later added five pilot cities in the US: San Antonio, Washington DC, New Orleans, Minneapolis and Cleveland.
The programme is offered to schools at no cost, and has reached 80,000 students since its inception.
"As the nation's design museum, it is our mission to ensure every student is introduced to the power of design and understands how it can be used to solve everyday problems," said Caroline Baumann, director of the museum.
"We're hopeful that with the public's help we will reach and inspire even more of tomorrow's designers," she added.
The program consists of 45-minute workshops – led by museum educators – in which students use common materials to build a prototype that solves a design problem. The workshop "instills creative confidence and encourages students to approach the world in a visual way," said the museum.
"The program imparts essential 21st-century skills, such as critical thinking, visual literacy, teamwork and problem solving, and can be used to enhance the teaching of any subject matter," the museum added.
If the museum meets its fundraising goal, it plans to host four regional trainings and appoint select educators as regional ambassadors. It will then conduct in-person visits to schools to evaluate the integration of the program.
The museum aims to use a "teachers training teachers" model. "For every 100 educators trained, the program could reach 7,500 students per year," said the museum. "If each of these educators went on to train 10 of their peers, that's 1,000 educators per year and 75,000 students."
ED, a lifestyle brand started by the comedian Ellen DeGeneres, has contributed approximately $100,000 (£64,600) to the Design in the Classroom program.
Founded in 1897, the Cooper Hewitt is the only American museum devoted exclusively to historic and contemporary design. Its permanent collection consists of 210,000 objects from more than 30 centuries.
Last December, the museum completed a significant overhaul of its home inside a mansion on New York's Upper East Side. Recent exhibitions at the museum include David Adjaye Selects, which features 14 pieces chosen by the architect from the institution's trove of Central and West African textiles. It is on view until 14 February 2016.