Math Elementary

When I first researched homeschooling products and resources, I spent quite some time looking at different math manipulatives. For one thing, there are so many, and for another, I love math. I remember wondering whether these colored rods would really be worth purchasing, as they are on the expensive side. And my math education, as far as I could remember, had been accomplished without a single manipulative.

Then I found Miquon Math, and immediately liked the concept. Miquon uses Cuisenaire rods as their primary manipulative, so with some trepidation, I acquired a starter set.

I needn't have worried. The rods made math so much easier for my very concrete, hands-on son to grasp. That was almost a decade ago, and now my youngest enjoys doing his math with the rods.

The concept behind the rods is simple. Each rod color is a specific length, representing a particular number of units. White rods are "units" 1cm long, reds are twice as long and represent the number 2, and so forth. A starter set comes with several of each rod from 1-10, with more of the smaller rods.

The child then uses the rods in combination to visualize basic math concepts. Perhaps it is obvious that addition can be modeled using such rods, simply by putting them end to end in a "train." However, they can also be used for subtraction, multiplication, and division, and even fractions, areas, and more. Using the Cuisenaire rods, quite young children can understand what multiplication means and can work out simple problems.

We actually own a lot of math manipulatives, including both store-bought and homemade ones, but these are the ones I use the most.

I have long been a fan of the poems for two voices books by Paul Fleischman. This book puts a twist on the idea by covering math topics in poems. It's a really unique and engaging way to memorize a math concept, reciting it as a poem. A poem for two voices is a poem recited by two people where sometimes the same words are said in tandem, sometimes alternately, and sometimes, the speakers speak at the same time saying different things.

Here is a sample of part of a poem from the book: (The first column is the first speaker and the second column, the second - shown smaller than actual size)

Some of the math concepts in the poems are fairly simple ideas that would pertain to a grammar school student, however most of the ideas are for middle schoolers or high schoolers. There were a few math concepts I had never heard of, such as fractals, (the geometry of nature), Fibonacci numbers (adding the last two numbers in a series to give the next number), and Mobius strips (circular strip with a twist in it).

While you don't learn everything you need to know about the math concepts in the poems, you get an introduction to the idea and the basic or interesting facts. For tessellations, the reader learns that not all figures tessellate; for triangles, the reader learns that the angles in the figure must equal 180 degrees. Some of the accompanying illustrations are also instructive. I could not have visualized the Mobius strip without the drawing of it.

This is a fun way to talk about these concepts. Trying to say the poems as a team takes a lot of concentration and brings a lot of laughs along the way. The book would make a great addition to a living math program or be a nice break from a formal textbook program.

Recommended for grades 4-12

Miquon Math is a series of 6 math workbooks designed to be used in 1st through 3rd grade. They are named by color and not by grade level, so that an older child can use them without feeling they are "remedial". The workbooks are designed to be used with Cuisenaire Rods. I have had the books for a couple of years but have only started using them this year as a supplement for my 3rd and 4th graders. I hesitated using them before because they have an unusual format -- the pages don't necessarily have to be done in order, and are grouped by topic rather than in sequential chapters. Multiplication is introduced along with addition in first grade, and advanced concepts such as squared numbers and pre-algebra are introduced through use of concrete manipulatives. However, my 3rd grader now says she "loves this kind of math" and both the children have shown a better grasp of what numbers mean since they have started using the books. We've discovered that when the manipulatives come out and are used to illustrate concepts, the "littlies" want to join in. My 5yo was watching carefully as my 8yo tried to figure out the square of 4, and suddenly announced "It's 16!" He was so proud of himself!
I have ordered the Orange Book (the first one in the series) to start with my almost 6 year old. After completing the Miquon Series, a child can go straight into Saxon Math 54 or 65.

Saxon 2 covers the arithmetic topics of addition and subtraction of one and two digit numbers and simple multiplication and division as well as the related topics of patterns, graphing, time, measurement, money, geometry and estimating. Although it uses manipulatives it is not a "manipulatives-based" program.

Each day's lesson begins with oral exercises called "The Meeting" during which use of a calendar, counting, time, money, and patterns are practiced. The actual lessons follow and are completely scripted in the teachers edition. They are designed for four days of new material and one day of review. Math facts are practiced every day as well, using flash cards provided with the kit and fact sheet drills in the workbook.

The beauty of Saxon is repetition. Concepts are introduced and then reinforced over and over again. In Saxon 2 there are games, art projects and physical activites as part of the lessons which provide a break from strict pencil and paper work. My children had been doing a strictly manipulative based math program previously so I thought they wouldn't like Saxon, but they love it. I believe it is because of the variety of activities.

One drawback to Saxon is the price which is close to $100.00 for the homestudy kit. The kit includes a teacher's manual, workbook, meeting book and cardboard manipulatives and flash cards. It can be found in discount catalogs or used from fellow homeschoolers. It requires a set of manipulatives which can be purchased separately at teacher supply stores or as a kit from the source given by Saxon and various homeschool catalogs.