Discover the Basics: Negative Numbers is a stand-alone curriculum that encompasses adding, subtracting, multiplying, and dividing using negative numbers. It is suitable for grade 5 and above. In a sturdy 3-ring binder, this 136 page curriculum provides a thorough introduction and overview, pre-test, lessons, practice pages, post-test, and answer keys. The goals of Discover the Basics are to help children truly understand math concepts and to develop fluency. The author, Jeff Simpson, takes great care to make these goals a reality by providing excellent tips and instructions for the parent/teacher and thoughtfully laid out lessons for the student.

The introduction text is so thorough. Mr. Simpson even explains what many students actually think about negative numbers and why they may become frustrated with certain approaches. This made a lot of sense to me and is something I have not found in other math curriculums (and I've seen a few!).

This lesson text begins by defining negative numbers, teaching children how to read negative numbers, and then developing fluency through easy addition, subtraction, and story problems. Once this is successfully mastered, children proceed to owing, having, spending, and earning. This section involves defining negative numbers as "money owed," adding as "earning", and subtracting as "spending." Comparing integers, matching verbal descriptions with equations, easy story problems, missing addends are some of the tools used here.

The next section treats negative and positive numbers as penalties and rewards. Children learn how to combine several rewards and penalties and also how to use the plus and minus signs together. Next, thermometers are employed to help develop understanding, with positive amounts being above 0 degrees and negative amounts being below 0 degrees. Children get the idea that this math topic actually applies to real life! As you can see, negative numbers is approached from a variety of angles in this text. Multiplying and dividing with positive and negative numbers are covered later. A review of multiplication and division concepts is also included.

In Discover the Basics: Negative Numbers, each topic is presented in an easy-to-understand manner. Children develop fluency through lots of reinforcement and repetition. Fun practice pages, where the child strives to beat the clock, allow kids to practice alone or with a friend or parent. This is not your ordinary workbook with a set of fill-in-the-blank answers; children are instructed to write, read, and/or speak the questions and answers on different occasions. Basic number lines are used as are more creative tools, like ladders and thermometers. Working with number lines adds to the multi-sensory experience and builds confidence as children are able to reconstruct problems and find answers fairly easily. In addition, the number lines eliminate the need for extra manipulatives, making this a stand-alone curriculum.

I find this curriculum to be visually pleasing, even though it is in simple black and white. Words and pictures are laid out clearly. The pictures are not just for decoration; they really add to the explanation and help make sense of the concepts. There are no formal lesson plans in Discover the Basics: Negative Numbers, except the recommendation to complete 20-30 minutes each day, with one rest day every week. It is suggested that you combine new pages with a review of old ones during each 20 to 30-minute time slot (or 15 minutes twice per day). The pace is deliberately slow to allow new ideas to be introduced a little at a time (as explained in the introduction), providing students with plenty of time to fully comprehend each concept before moving on.

I recommend Discover the Basics: Negative Numbers to anyone above the age of ten who desires to learn about negative numbers. It is an excellent resource for homeschool, classroom, or tutoring situations. This is more than just a textbook; it fosters the development of reasoning skills and provides an opportunity for kids to really understand (and remember) math.

Product review by Stacy Kalisz, The Old Schoolhouse® Magazine, LLC, January 2011