Homeschool Math Newsletter, Vol. 3
October 23, 2006

Hello! This is Maria Miller from HomeschoolMath.net. I hope you enjoy this month's math teaching 'package' that I've put together for you.

But before we get to the rest, I want to (finally!) announce the arrival of my newest math ebooks, called Math Mammoth Grade 6-A Worksheets Collection and Math Mammoth Grade 6-B Worksheets Collection (plus full answer keys for both), covering all 6th grade topics.

These collections of worksheets (or workbooks if you'd like) were originally made for and in collaboration with SpiderSmart, Inc. tutoring company.

The worksheets have been created especially for teachers: each problem sheet is one page, concentrating on one topic.

They are not your 'run-of-the-mill' math worksheets. Each sheet in these two workbooks has been "hand-crafted", with varying problems that both emphasize understanding of concepts and practice computation, with variable word problems.

I am selling those two at my new website MathMammoth.com. (I hope that's easy to remember!)

Go pay it a visit; and let me know how you like the mammoth-idea for a "brand"...

... because I will be making more of these worksheet collections for other grades AND I will change over my existing ebooks to be "Math Mammoth" ebooks.

It's a lot of work, so kind of slow, but I hope the results are worthwhile for all you parents and teachers out there. (Next books I'm getting ready are grade 3-A and 3-B workbooks.)

Ok, and now to the other interesting stuff:

In this month's newsletter:

1. Curriculum focal points
2. Study about gender differences in math abilities
3. Division of fractions
4. Websites on math misconceptions

1. Curriculum focal points

Recently National Council of Teachers of Mathematics (NCTM) released a new report Curriculum Focal Points.

For each grade, this report describes THREE focal points for mathematics, and also explains to which other mathematical topics these focal points connect to.

By familiarizing yourself with these few points, you can see the basics of school mathematics unfold before your eyes. Knowing the basic goals is essential for being a good teacher.

On grade 1, the focus is on

• Addition/subtraction: basic basic addition facts and related subtraction facts. Learning to add and subtract two-digit numbers.
• Understanding whole numbers in terms of tens and ones.
• Composing and decomposing geometric shapes.

Measuring and simple bar and picture graphs are presented as applications of these.

Read more about the curriculum focal points here.

2. Study about gender differences in math abilities

This is an interesting study about whether there are differences between men's and women's abilities in math.

The researchers first asked the participants (college students) a question, then they took he Vandenberg Mental Rotation Test, a standard test of visual-spatial ability.

One group was first asked whether they lived in a single-sex or co-ed dorm. That subtly triggers a person to think about their gender. Read on...

3. Division of fractions

This topic is often not understood real well by teachers or students. But we want them to learn, not only the rule, but also the meaning.

These FOUR ideas can help you to explain and understand division of fractions:

1. The rule of "invert and multiply" applies to division in general - not just to division of fractions. It is a general principle. For example:
   
   20 ÷ 4
   
   I can invert and multiply:
   
   20 × 1/4 = 5.
   
   With whole numbers, division can be thought of as making equal parts. When you divide something by 7, you're dividing it into 7 parts, so might as well just take 1/7 part - multiply by 1/7.
   
   You can always change division into multiplication with this principle: 18 ÷ 2.51 = 18 × 1/2.51
    
2. Think of fraction division this way: how many times does the divisor fit into the dividend? You can use this to judge the reasonableness of your answer.
   
   For example consider 1 3/5 ÷ 2/3. Clearly 2/3 can fit into 1 3/5 more than two times.
   
   1 3/5 ÷ 2/3 = 8/5 × 2/3 = 16/15 = 1 1/15 - just a tad over 1 whole.
   CAN YOU SPOT THE ERROR?????
   
   Or, 3/8 ÷ 11/12. Here the divisor is greater than dividend. Well, that means that it won't fit even once into 3/8; it only "fits" into 3/8 about half ways, so the answer should be near half.
   
   And indeed, using the rule, 3/8 ÷ 11/12 = 3/8 × 12/11 = 3/2 × 3/11 = 9/22.
    

Read about the other two ideas.

4. Wesites with math misconceptions

It is very good to know something about the most common misconceptions students might have. The website CountOn.org has 22 examples of them at www.counton.org/resources/misconceptions.

Here are some examples:

#2. Multiplication always increases a number... is that really so?

Well, to small kids it appears to be so - but only if you just try whole numbers. Take 10 for example. If you multiply it by 2, 3, 4, 5, etc., it does get bigger.

But all you have to do is multiply it by a fraction less than 1, or by a negative number, and 10 does not get bigger... 1/2 x 10 is 5. 1/4 x 10 is 2.5. -3 x 10 is -30.

We must remember that repeated addition is not the only meaning or definition for multiplication. That's what it is for whole numbers.

For fractions, 1/3 x 12 is better understood as 1/3 of 12.

Keep reading...

Till next time,
Maria Miller

How did you like this month's newsletter? Is there any topic you'd like to see in the next one? Let me know.