The Massachusetts Adoption Resource Exchange, led by Sharon resident Lisa Funaro, has received a $100,000 grant from the Cummings Foundation in Woburn to support its work finding adoptive homes for children in foster care. “Oh my goodness, what a difference this kind of support makes,” said Janice Halpern, another Sharon resident who works as director of public relations and fund-raising for the Boston-based adoption group. The children can be hard to place because they are older — generally 6 to 17 years of age — and social workers have already tried to place them with relatives or preapproved adoptive parents, Halpern said. The grant is part of the foundation’s new “$100K for 100” program, in which it selects 100 organizations serving a variety of causes to receive $100,000 each. Many of the grants are paid over a period of two to five years; the adoption exchange’s will be paid over three.