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 essential.

Different families' situations, abilities, and resources vary a lot. In this article I try to go over some common scenarios and suggest ideas and solutions on how to go about either reviewing or relearning math over the summer.

Evaluation and Assessment

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, you need to assess the situation. For evaluating your student's current math skills in detail, you can use for example:

Texas Assessment of Knowledge and Skills (TAKS) - online mathematics tests for student assessment for grades K-11. Multiple choice. Some homeschool math curricula have free placement tests on their websites that you could use for student assessment, for example Math-U-See and Singapore math. Also consider how much you can afford of your money and of your time.

Different Scenarios

A. Your child did great and does not need review. Well great! Enjoy the summer!

You can also 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 type "fractals" into Google and see where you end at!

B. You want to give your child some review so he doesn't forget what he learned.

If you're willing to pay, there exist summer worksheet programs such as Noetic learning (grades 3, 4, and 5 only). Problem of the week programs can be an excellent solution since they usually involve a little more challenging word problems than what your school books typically have.

Here's a zero-cost solution: Get his last year's math book, or go to library to get a few math school books for the grade he just finished. They can be from the 1980s even, 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 (writing in his own notebook of course). Or, you can copy those problems on paper to make a consumable worksheet.

C. You want to prepare your child to the next grade.

Get a few math books from the library for the upcoming grade and check what topics are coming up. For the most part, it is enough to have mastery of previous year's topics in order to be prepared for the next.

D. Your child needs intensive work in some or many areas.

Depending on your budget, there are many options.

1. One-on-one tutoring programs and summer schools. These take the burden of teaching off your shoulders. Many tutoring outfits offer summer programs, and you can do them online, without leaving our home. A skillful tutor is able to determine your child's weaknesses and tailor the instruction accordingly. Do a Google search on "online math tutoring summer program" to find some. Prices are in hundreds of dollars ($200 or more).
2. Some computerized programs also allow this: for example www.mathscore.com adapts the practice according to how much and how quickly the learner can solve the given problems. There exist quite many online curricula also. 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 around $15-$50 per month.
3. Teach it yourself. First you should evaluate your child (unless you already know exactly what he/she knows).

What materials could you use? Math books, complete curricula, the online curricula above, and so on... The choices are too numerous to even make a list.

I do want to mention my Math Mammoth Blue Series books though, since they are an excellent solution for reviewing a few concepts or concept areas. These books are downloadable, thus very affordable - prices range from $2 to $6 per book - and concentrate on a few topics per book. A free solution is to take your child's last year's school book and go through it.

What 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? I list here a few points to consider:

1. 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.
2. Always show the students the patterns in the facts, whether it be addition or multiplication facts. Subtraction and division should be shown as "backwards" addition or multiplication. I've written about that. (Googol Learning's Discovery Multiplication Program emphasizes patterns in addition to math strategies.) Then, do some drills based on those patterns. In other words, when the facts are written in a pattern or order on paper, cover the answers and drill the facts right after the child has "seen" the pattern. The random drill of facts should be reserved for last.
3. Give your child other CONTEXTS to use the math facts in: Use simple card and board games that are free or inexpensive. There are lots of free online activities and music for practicing math facts. Another context to use the math facts in are all the multi-digit operations, such as 183 + 394 or 394 x 28 etc. Look for ways to practice math in their daily activities. Entries from the Crazy 4 Math Contest provide endless ideas for places to find math.
4. Could it be he is a right-brained child (a.k.a. visual-spatial learner)? If your child in general learns things from "whole" to "part" (details), and does not like to learn things in pre-determined sequences, he might be right-brained learner.

It is better to teach these kids the concepts (the whole idea) first, and then go to the details. Keep practicing the math facts on the side, and eventually he should get there. I've read many accounts on how some kids only memorize them well around 10-11 years of age. Definitely don't give up.

In a nutshell, if the math facts aren't "in" yet, don't give up, but continue making your child or student(s) USE the math in various ways.