Monthly Archives: April 2016

Stretching math through the summer (part 2)


Whether its warm days spent at the lake, roasting s’mores on a family campout, or long afternoons spent reading in the backyard, summer is a great time for relaxing and decompressing from the rigors of the school year. A break from routine and a chance to get outdoors is good for everyone’s mental health, and children are no exception. For many families, however, summer also causes stress. Aside from issues of childcare and keeping kids occupied during the summer, a three month break from academics can be way too long for some students. All skills are subject to a “use it or lose it” deterioration, but math skills are the most perishable.  A small amount of regular math practice over the summer can mean big gains in the fall, in terms of less review and less frustration.

However, there’s no need to ruin the family vacation with pages of boring worksheets. Parents should be partners in student learning, not taskmasters or adversaries. Math practice at home, particularly in the summer, should be fun and engaging. Last week I covered Art of Problem Solving’s Beast Academy, my favorite program for high-flying elementary students. This week, I’ll talk about two more excellent books: Primary Challenge Math and Real-World Algebra, both by Edward Zaccaro. These books are ideal for students who have a good grasp of basic concepts, and want a little more challenge, but aren’t necessarily ahead.  I recommend Zaccaro’s books for summer math because they are substantive with a focus on problem solving, but they don’t feel like workbooks. With cartoon illustrations and plenty of white space, the pages are inviting rather than intimidating.

Primary Challenge Math is a great starting point for elementary students in grades 1-4. Each chapter covers a particular type of problem with cute headings like “How much does it cost?” (money) or “Oh no! I have to change the recipe” (fractions) and includes 4 different levels of problems from novice to “Einstein.”  This format makes it very adaptable for different ages and abilities. In first grade my son worked to Einstein level in a few chapters, but for topics we hadn’t covered yet in our regular math program like decimals and percent, he only attempted the novice level problems, saving the rest for later.




Real World Algebra is very similar to Primary Challenge Math but is geared towards students in grades 4 and up. It gives younger students a lightweight taste of algebra and older students the chance to build confidence before middle school math. What impresses me the most about Real World Algebra is the focus on using algebra as a language to structure word problems. While there is some focus on procedural steps to problem solving, most of the book is simply about setting up problems correctly by translating the words into equations. As you know, word problems are my favorite because they really build and test the student’s mathematical understanding. Along those lines this book makes algebra seem like an easy way to solve word problems rather than an intimidating conceptual leap.

You can purchase Primary Challenge Math, Real World Algebra, and other books by Edward Zaccaro, from Amazon or other retailers.

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Stretching math through the summer (part 1)


Summer is still a few months away but I know many parents are already looking for ways to build or maintain their child’s math learning over the summer. There are several great options that I’ll be discussing in the coming weeks for every age and ability level, but for math-talented students in grades 3-5 my first recommendation is usually Beast Academy from the Art of Problem Solving (AoPS). 
Although Beast Academy is a full year-long comprehensive math curriculum, it comes in an incredibly fun and cute package, which makes it ideal for summer.

Every grade level has 4 parts (A-D) each consisting of a comic book, which serves as the textbook, and also a corresponding workbook.  The Beast Academy characters in the comic books are fun and talk the student through new concepts, while the workbook problems themselves are very puzzle and game-like. True confession – my son has been through the entire available Beast Academy program and still likes to use the comic books for bathroom reading. They are that engaging!

My only word of warning is that Beast Academy is both challenging and unconventional. Art of Problem Solving made a name for itself with advanced high school and math contest prep materials, and Beast Academy carries their tradition of using a discovery based approach to mathematics and deep problem solving to the elementary level. It is ideal for students who love math and love to figure things out for themselves, but I would not recommend the workbook for a student who already struggles with math, as the problems found in the book can sometimes be intimidating.

When using as a summer supplement expect to get through only one book, unless you’re using it a grade or two behind as review, something that I actually recommend as most fifth graders who have been taught conventionally could still get a lot out of the lower grade Beast Academy books. The depth of this series is incredible – in addition to standard fare like multiplication, fractions, and decimals, Beast Academy covers some topics that are seldom seen in elementary school such as logic and basic combinatorics.   At the same time I also wouldn’t hesitate to try these materials with a very advanced math student who is a grade or two younger (my son started 3A in first grade). The fun presentation and packaging make it ideal for a student who is intellectually ahead but lacking the maturity to jump into more serious math texts.

AoPS has full sample pages of both the guidebooks and workbooks for each level on their website.  Materials can be purchased directly from AoPS or through some discount homeschool catalogs like Rainbow Resource.

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