No! I actively discouraged my kids (now grown, they excelled academically) from doing their elementary school summer packets (unfortunately, in higher grades, the school required them). Unless your child was struggling with a subject and needs to catch up to the rest of his peers, or you feel the school’s curriculum has gaps that you need to compensate for, summer homework is unnecessary and may be counterproductive. Assuming they mastered the material during the school year, they won’t lose very much. Moreover, the school will review everything when school starts, anyway, and those kids who would probably benefit the most from working over the summer because they didn’t master their lessons are the least likely to do any summer work. After working hard during the year, your kids had to work during their summer “vacation”, so that they can go back to school and review the material they’ve been doing all along.
Please don’t make your kids read. Required reading only makes sense when it serves a purpose. When a child is learning how to read, requiring them to practice makes sense, as practice is necessary to acquire any skill. If a teacher gives a class the assignment of reading the next chapter so the students can discuss it the next day, or tells everyone to read a book of their choice and then write a report on it, that reading has a specific purpose. Making a child read just to be reading is turning an intrinsically enjoyable activity into a dreaded chore. They may read whatever time/material you demand, but if they resent it, they are unlikely to read anymore.
Instead, just help them realize how much fun reading is. Take them to library events and bookstores. Even if they aren’t interested in selecting books, make them wait while you select some books for yourself (and maybe a few fun books for them). Don’t worry about whether they’re reading “literature” or challenging material. Let them read picture books, comic books/graphic novels, magazines, joke books, choose your own adventure, books like Guinness Book of World Records or Ripley’s Believe-It-or-Not, even puzzle books like I Spy or Where’s Waldo. At home, read together (it’s not just for bedtime) maybe while they eat, play, etc., or read to yourself and occasionally share something funny or interesting with them.
Everyone needs a chance to relax and recharge. Growing up, I loved school. Every September, I’d be excited about all the new things I would be learning that year and eager to dive in, but by the Spring, I felt I was hanging on by my fingernails, just dragging myself through the days I was counting down to the next summer vacation. If I hadn’t had those summer breaks from school, I think I would have burned out long before I graduated.
Summer is your golden opportunity to do things with them that the schools can’t. This is your chance to show them how academics can be fun, and let them see things in “real life”, but keep it fun - lessons are for school. Moreover, there’s a lot more to life than academics, but the more they’re exposed to, the more it will help them academically. Take them on field trips to museums, festivals, zoos, forests, beaches, historic sites, performances, etc. Do projects together. Cook together. Learn something new (not necessarily academic) together. Play together. HAVE FUN!