Keeping Your Math Skills Sharp Over The Summer
While I certainly understand and support the need for kids to enjoy a summer break from schoolwork, for many children some math work over the summer is helpful; perhaps even needful or essential.
Yet different families' situations, abilities, and resources vary a lot. In this article I go over some common scenarios and suggest ideas on how to either review or relearn math over the summer.
First evaluate
First, you should decide the general amount of math work needed. Ask yourself: how did your child or student do in math in the past year? Will he or she need a lot of review/instruction, or only a little review, or none?
If you don't yet already know what math skills your student is lacking in, assess/evaluate your student's current math skills in detail:
 Math Mammoth assessment tests (for grades 16)
 Math assessment tests from Texas: grades 38 and grades 910 plus exit level
 California Standards Test
 See a longer list of math assessment resources online.
Jump to a scenario:
 Your child did great and does not need review.
 You want to give your child some review so he doesn't forget what he learned.
 You want to prepare your child to the next grade.
 Your child needs intensive work in some or many areas.
 What about math facts?
Different scenarios

Your child did great and does not need review.
Great! Enjoy the summer! Or, you could use the summer to explore some interesting math topics outside the curriculum. Buy or get from library one of the many math readers — story books that have math topics weaved into them (Penrose the Mathematical Cat for example). Maybe surf into one of the interactive and/or fun math websites.
Or, spend time with brain teasers, puzzles or solving interesting problems. These will help develop logical thinking, which will help with math anyway.

You want to give your child some review so he doesn't forget what he learned.
I have authored Math Mammoth Review Workbooks for grades 15. They provide a comprehensive review of a specific grade level of math, and include both topical and spiral review worksheets. They are available as inexpensive downloads ($5.50 apiece) or as printed books ($10.50 apiece).
For students going into middle school, check out A Page A Day  a summer workbook intended for students who are about to begin intermediate math or middle school.
Online math practice programs are also useful. They allow your child to practice unlimited math problems and give you detailed reports. Typically, you pay $1015 per month, which is quite reasonable if you are only doing it for 12 months over the summer.
Additionally, Problem of the week programs can be an excellent solution since they usually involve a little more challenging word problems than what school books typically have. However, some of them don't operate over the summer.
Here is a zerocost solution: Get your student's last year's math book, or go to library to get a few math books for the grade he just finished. They can even be from the 1980s; it won't matter too much. Just get a book that contains review and/or test pages at the end of the each chapter. Then, every once in a while just let your child work through those review pages in the book.

You want to prepare your child to the next grade.
You could get a few math books from the library for the upcoming grade and check what topics are coming up. The ideas above (in point B) are also useful. However, for the most part, it is enough to have mastery of previous year's topics in order to be prepared for the next.

Your child needs intensive work and filling in gaps in many areas.
Depending on your budget, there are many options.
1) Oneonone tutoring programs and summer schools. These take the burden of teaching off your shoulders. Do a Google search on "online math tutoring summer program" to find some. Prices are in hundreds of dollars ($200 or more).
2) There exist MANY online math curricula. Paying the subscription fee for two months for a complete online curricula can be quite worthwhile and allow a lot of learning to happen in that time. Fees for those are $10$50 per month.
3) Teach it yourself. Please read my article how to help a student who is behind for a more complete plan and suggestions.
What materials should you use for an intensive catchup? There exist SO many math books, curricula, videos, and so on... The choices are too numerous to even make a list.
As an inexpensive solution, I want to mention my Math Mammoth Blue Series books. They are TOPICAL books, and are an excellent solution for reviewing a few concepts or concept areas. Math Mammoth Blue Series books are available as both downloads and printed copies. The download prices range from $2 to $7 per book (very affordable!).
The topics covered in Math Mammoth Blue Series books range from 1st grade addition to 7th and 8th grade, such as: place value, addition & subtraction, multiplication, long division, measuring, clock, money, geometry, fractions, decimals, percent, proportions, statistics, probability, problem solving, integers, and more. See a full list of topics with grade level suggestions here.
What about about math facts?
Since this is a question in many parents' minds, I want to touch on it real quickly. What if your child has not mastered his math facts? Here are a few points to consider:
 Don't rely on flash cards alone. They take math facts out of context, and isolated "out of context" facts about anything are always hard to learn for anybody.
 Always show the students FIRST the patterns in the facts and various strategies and tricks to learn them, whether it be addition or multiplication facts. Only later add in random drills. Subtraction and division should be taught as "backwards" addition or multiplication, not as separate sets of facts.
The video below lists several strategies for addition facts (for first and second grade math). I show the pattern of "Sums with 7", which also is used with other sums, then the 9trick, the 8trick, the doubles, doubles plus one more, and how to do random drill using the structure of the addition table.
Video about strategies for learning addition facts
Here is another video about strategies for subtraction facts. I recommend the usage of FACT FAMILIES in order to learn the basic subtraction facts. That way, when children have a subtraction problem, such as 7 − 5 = ____, they will learn to think through addition and fact families: 5 and 2 and 7 form a fact family, OR that 5 + 2 = 7, so 7 − 5 = 2. The video also shows a fun tool for subtraction facts called number rainbows!
Video about strategies for subtraction facts
Next, this video below explains how to use a "structured drill" for multiplication tables:
Structured drill for multiplication tables
Math Mammoth Subtraction 1
A selfteaching worktext for 1st grade that covers subtraction concept, fact families, difference, memorizing basic facts, and lots of word problems.
Download ($5.10). Also available as a printed copy.
Math Mammoth Add & Subtract 2A
A selfteaching worktext for 2nd grade that covers “easy” additions and subtractions within 0100; such as 24 + 5 and 89 − 7, or adding or subtracting whole tens; memorizing the basic addition facts of singledigit numbers, and learning to use them with subtraction.
Download ($3.95). Also available as a printed copy.
Math Mammoth Multiplication 1
A selfteaching worktext for 3rd grade that covers multiplication concept from various angles, word problems, a guide for structural drilling, and a complete study of all 12 multiplication tables.
Download ($5.20). Also available as a printed copy.
Math Mammoth Division 1
A selfteaching worktext for 3rd grade that covers division concept, division & multiplication fact families, word problems, division facts, remainder, zero and one in division, and more.Download ($3.70). Also available as a printed copy.