I don't know if this is your mom below. Do you know if she had any older siblings? and where they were born - MA, or somewhere else? Do you know her parents names?
Find A Grave Memorial# 126664226 http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=126664226
Name Elaine A Cates
Maiden Name Turtle
Burial 1976 Worcester, Worcester, MA
Birth Date 30 Mar 1940
Death Date 21 Apr 1976
Affiliate Record Identifier 126664226
Cemetery Saint Johns Cemetery
Massachusetts Death Index, 1970-2003," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:VZB4-5LH), Elaine A Cates, 21 Apr 1976; from "Massachusetts Death Index, 1970-2003," database, Ancestry (http://www.ancestry.com : 2005); citing Worcester, Massachusetts, death certificate number 027556, Commonwealth of Massachusetts Department of Health Services, Boston.
I am not related, but found these for you.
1940 United States Federal Census
U.S., Social Security Applications and Claims Index, 1936-2007