The BEST way to keep your kids involved, & not lose any 'brain function' over the summer months, is to keep them busy with both ELA (English Language Arts) & Maths (algebra, geometry, basic math, etc.).
You can take the easy route for Maths by using KhanAcademy.org (free for most of the site - yay!!) for your kids to 'drill' every day in math - whatever is appropriate for their grade. As they get into middle/junior high, & later in high school I would move from standard maths (addition/ subtraction / multiplication / division & fractions) & graduate a bit to simple geometry, then algebras (yep, more than one ;-) & on into trig or calculus - if appropriate.
When it comes to ELA, I always push kids to do a minimum of 2 new words a day (please see my blog on the SAT) with the Barron's SAT (3500 word vocabulary with definitions for all 3500 - awesome!), & a minimum of 2 sentences a day on each word. I normally have them make these up on index cards, then they can use them to 'drill' when they are ready for tests. The Barron's SAT is normally available at Half Price Books store at a good price - there are 6 stores in the greater Houston area, so call one store nearest you & have them check the computer for availability & price of this stellar SAT book.
ELA is a wide range of English related items, so it's a necessity for you to keep up with your student during the summer. One area is vocabulary as we saw in the last paragraph, this helps them build ideas & words in their head. Another area is age/understanding appropriate reading for the summer - for this you can check with your school for "what to read during the summer?" for the next semester. As my momma used to say "keeps 'em busy & off the streets for the summer" ;-) And as I say, you are filling their heads with words & ideas for a new year & for life.
While your child learns new vocab, this supports the reading, but you have to do some homework too. You need to have your child do a short, one paragraph essay/writing about each chapter (people, places, concepts, etc. that are important to that story), & you need to read & discuss with your child a good level of understanding of that story. The one paragraph will help them build good habits for book reports & similar reports later. Verbally pat them on the back when they've done well, point out some areas that maybe they didn't mention in the essay, note new ideas & concepts (like if it's sci-fi, another world, etc.). Be open & creative, find things they like & use them; find things they don't like (new things?) & use them for discussion. Another idea is to take different viewpoints - maybe today's subject is you talking "pro global warming" & they talk "anti global warming" - these are just seed ideas. Talk about it at the dinner table. You are the only one that will invest this much time in your child, they will be thankful for it, even if it does cut into their TV time. Talk about current events & what they think, why they think it...pat them on the back for well reasoned responses even if you disagree with the idea. Give them points for new ideas, changing thought patterns, etc., they will appreciate the kind of praise you give them.
Another area that helps is, after getting the SAT book, you both work on the passage readings, this will promote critical thinking - a crucial area for a child (or anyone) to learn. Critical thinking divides fact from fiction & ensures the child will see things differently, less emotionally, more knowledgeably - it will help promote the ideas that they either do know about a subject, or they don't - but at least they know which it is.
Another item that schools don't teach anymore is research & how to do it. Most people can use the web for info, but I have found that 95% of junior & high schoolers have no clue about "how to look up & research a subject that is in a book or other similar, non-web material". Show them the "how to's" of matching a ToC / Table of Contents to an Index in the back of a book, OR go to the library & get a lesson from them in the "how to's" of proper, book based research.
Other resources - dictionary.com - great info & pulls in multiple dictionaries in many areas - Black's Law, Medical, Thesaurus, etc. Part of the reason that I love dictionary.com is the fact that they have multiple dictionaries available on the page at the same time, there is a tiny speaker symbol next to the word that will 'speak' the word for you/your child for exactly 'how to' say the word correctly, it has sample sentences so student's can see 'how to' use it in a sentence properly - a fantastic reference. worddynamo.com- gives great word matching games, direct to your/your child's email. Very good practice for words & recognizing context usage quickly. KhanAcademy.org - has many subjects, though the main ones are mathematics related. I love it because it has good videos, some really fun ones like the "finger math" - awesome in a nerdy way ;-) Some areas you pay for, but I believe that's all in the higher maths areas; like calculus & more. easybib.com - a site that is a must for your high school or college student, you can plug in all of your info for citations & they will set up your MLA or APA citations (works cited page) for that big paper coming due. They help you be the polished, put together student for those important papers ;-)
Parents...this is a starting point for you to work with your child/children over the summer...& maybe throughout the year, maybe even for life. Education - so much is lost due to lack of reinforcement of school work ethics, keeping up on reading, writing, & arithmetic; the eggheads say that at least 30% of learned info is lost from May through September - that's a huge amount to relearn after the summer!