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Discover the Basics: Multiplying and Dividing Review by Stacy Kalisz

Jeff Simpson
Mastery Learning Systems
532 North School Street
Ukiah, CA 954582

Discover the Basics: Multiplying and Dividing is a simple text that focuses on the basics: understanding and remembering the multiplication and division facts up to 12. It does not include word problems or cover remainders. (Mastery Learning Systems does have another program that covers those.) Designed for second grade and above, this 128-page text helps children truly understand and remember the math facts. It comes in a sturdy three-ring binder and is plain black and white (no color).

Mastery Learning Systems desires for children to learn math without stress and anxiety. Their goal is for kids to understand concepts, not memorize meaningless facts or formulas. It is suggested that the instructor tell the student what to do instead of explaining the lessons. Students can then figure the concepts and facts for themselves, allowing kids to have their own "A-ha" moment, which seems to make the facts stick so much better. Very clear directions for providing this type of instruction are given in the introductory section.

Discover the Basics: Multiplying and Dividing is a little different from most math programs. Each number family is introduced with a picture rather than a rule or plain math fact. For example, for multiplying by seven, a calendar is shown. Kids can easily see that each week has seven days and that three weeks make 21 days in total and so on. Kids work with this calendar to figure out problems. By associating each number family with a picture, children are able to experience multiplication and division. After this initial experience, questions are asked which help the child process the experience and start understanding the concept.

Kids then practice what they have learned by solving problems. This practice is quite repetitious and helps develop fluency. It isn't long before they are able to instantly recall the facts. Problems are solved with the use of number lines and charts, which makes this a hands-on experience. How to use the number lines and charts is explained in the introduction, which is essential reading since these are not average number lines. (For example: when multiplying by 11, the chart is made up of soccer teams!) Multiplication and division are taught together. This makes sense and has been fairly simple for us to do. In fact, it seems much less painful to teach division right alongside multiplication than to do so separately!

My math-despising nine-year-old told me that she likes this program because "it is easy to do and you learn things fast." She is able to feel successful because the program moves at a slow pace. That doesn't mean it takes a long time to complete. If kids are doing well, they can move through the exercises quickly or skip a few pages. The fact that the program does not leap ahead or cover a concept quickly and then move on is very appealing to me. Facts are not presented in order from one to twelve. Instead, multiplying and dividing by tens is taught first, then elevens, fives, twos, fours, eights, threes, sixes, nines, twelves, and sevens. Reviews and post tests are at the end of the book.

There is very little writing in this program. Children do write answers, but they also speak them. Every exercise is not a long worksheet. Much of the practice is done using the number lines and saying the answers aloud. The ability to instantly remember the facts hinges on the practice pages. These pages consist of math problems (as in 11 x 7) that the students strive to answer in the quickest time possible. They practice these until they can beat the clock. Students are allowed to use the charts and number lines, which enables them to get the right answer every time. As they do this over and over, they build familiarity and come to know the answers without struggling.

The practice pages begin with the real-life concept that was used to demonstrate the math fact when it was first presented. For example, when studying 11s and using the soccer teams chart (which shows twelve soccer teams each made up of eleven people), the first practice pages show: 2 teams = ? players. Then next shows: 22 players = ? teams. This helps kids connect math to real life. Only after these do children move on to problems with math symbols.

We have found this curriculum to be very helpful and easy to use. The only issue we have is that my daughter occasionally tires of the practice pages (but her complaints are much less than with any other program we have used). She is very happy to beat the clock and is also pleased that she is learning multiplication and division so quickly.

I like Discover the Basics: Multiplying and Dividing because it is straightforward and understandable. As a busy homeschooling mom, I also appreciate that I don't have to prepare anything ahead of time, it's all there. This math curriculum is useful for teaching multiplication and division at home or in the classroom. Excellent as an aid for struggling learners, it is also wonderful for those who are just beginning this subject.

I recommend Discover the Basics: Multiplying and Dividing to anyone who desires to teach (or learn) the multiplication and division facts without a lot of fuss. This unique method builds confidence in children and enables them to understand and remember math without stress.

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