Showing posts from October, 2006

Ejercicios de matemáticas

Recientemente he comenzado la tarea de traducir los generadores de ejercicios de matemáticas en español. Bueno, realmente es un amigo que hace la mayor parte de la traducción.

Ya tenemos algo de presentar: visita y genera ejercicios de matemáticas gratis!

Los demás generadores de problemas siguen pronto...

Some math worksheets now in Spanish

I've had some of my math worksheet generators translated to Spanish, in case you're interested:

Math worksheets in Spanish. It's a new website... : )

Elementary geometry: how much time should you devote to it?

A geometry question from a visitor:

1. How much time should be invested teaching geometry at an elementary level?
2. How much time is actually dedicated towards geometry in a tradicional textbook

Your guidance will be extremely appreciated!
During elementary mathematics, geometry plays more of a sideline role at first. It is intimately tied with measuring topics - and really, the word "geometry" means "measuring the earth", the science to measure the land.

The goal of elementary geometry seems to be that the student be able to find perimeters, areas, and volumes of common two and three dimensional shapes.

I would add to that the goal that the student can understand and form abstract definitions, distinguish between necessary and sufficient conditions for a concept, and understand relationships between different shapes before entering 10th grade. (I've written about that before in the article Why is high school geometry difficult?.

According to the Curriculum Focal Poi…

Word problem question

An interesting math teaching related question again from someone.

Hi Maria,

I have purchased some e-books from you and they are very helpful. My daughter is in 4th grade and I felt that she is weak in understanding the following problems. Would you please suggest which e-book we need to buy from you to help improve her basics.

Problems are as below:

1) Marge spent $4 for a magazine. She spent half of her remaining money on T-shirt. Then she spent $2 on a snack. Marge had $14 remaining. How much money did Marge begin with?

2) Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall, in feet and inches, is each boy?

I have not written an ebook that would concentrate on those kind of problems. I do have some similar ones included in the 6th grade worksheets collection.

However, I wouldn't worry so much about those problems at 4th grade, especially the first one, because it requires quite many steps. She's still young.

You might be interested in Singapore math…

Math Mammoth Grade 6 Worksheets now ready

This is what I've been working on behing the scenes so to speak... and now some of it is finally come to the fruition and is available to the public:

(now comes the sales pitch as was made up by my dear husband)

Meet Mrs. Maria Miller's Most Marvellous & Magnificent Math Mammoth Modified Modern Mathematics Meticulous Multiplication Methodology Major Madness - It's Mmm Mighty Majestic!

Ok, back to normal...
I have been making worksheets for SpiderSmart, Inc. tutoring company and the 6th grade ones are now available as two downloadable ebooks at:

Math Mammoth Grade 6 Worksheets

These aren't your run-of-the-mill worksheets, but more like carefully hand-crafted quality problem sheets, with varying problems that both emphasize understanding of concepts and computation.

The worksheets do NOT have explanations and therefore best suit math teachers or others who can explain the mathematical subject matter to the student(s).

I will later on (next year) be making more worktexts (wi…

Free course materials for college level math

Some of you (if you're a mathematics professor in some college or university) might find this interesting to browse: Massachusetts Institute of Technology offers a LONG list of mathematics undergraduate AND graduate course materials as free downloads...

Some of them have lecture outlines or notes, some have student assignments and tests. I saw even Java applets for calculus with applications, but mostly they seemed to be PDF files.

So here's the link:

Homeschooling Carnival, week 42

I haven't made it to the carnival for a while, but this week I did because Shannon emailed me directly.

The theme of this 42th carnival is "42"! You might recognize that number from the hilarious sci-fi novel "The Hitchhiker’s Guide to the Galaxy". In it, the supercomputer Deep Thought computes the Ultimate Answer to Life, the Universe, and Everything - and spouts out the answer as "42". (Well, then they go to finding out the exact question... if the answer is 42, what is the question?)

Anyways, I enjoyed that book as a teenager. Wikipedia lets us know that the author Douglas Adams just had that there as a joke. (Well, that whole book is just full of jokes, as far as I can remember...)

But, the 'meat' of all this is of course the carnival itself... Is homeschooling the ultimate answer to life, the universe, and everything?

My submission was how teaching math in early grades does not have to cost anything.

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. Men in this group did 25 percent to 30 percent better than the women.

In the control group, the students were first asked about how it is to live in Northeastern United States. The results of the visual-spatial test were familiar: men performing 15-20 percent better. (That is the typical result whenever this test is given to men and women.)

BUT the surprise came in the group where students were first subtly made to think about their strengths. They were first asked about why they chose to attend a private liberal arts college.

In this group, there were no significant diff…

Kindergarten math ideas

I recently talked with a friend who was concerned about the cost of math curricula for her soon-5-year-old, doing kindergarten math. Even regarding my ebooks which I've given her free access, she mentioned how even printing costs money and could get costly in the long run.

(And I know some people can print things real cheap, but not everyone. It depends on your printer.)

So I told her, teaching math doesn't have to cost anything in kindergarten or the early grades.

It's not of utmost importance to do worksheet work. You can largely just play games and explore various things. After all, playing is what that age kids do best anyway.

* Playing board games where you roll one die teaches them to recognize the dot patterns on the die.
* Later on, playing board games where you roll two dice can be used for addition practice.
* After learning the dot patterns on a die, use dominoes as "flash cards" for addition. Or better yet, make a simple game out of it: lay them right sid…

Math misconceptions

It's very good to know something about the most common misconceptions students might have.
The website has 22 examples of them at

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.

#3. As 1 x 1 = 1, then 0.1 x 0.1 = 0.1.
This one was new to me. Quite curious. A child might think of 0.1 as some kind of "unit" like 1.

But seriously, 0.1 is one tenth. Taking…

Quite curious music box

This music box shows dots of different colors that move around in a spiraling motion.. as a dot hits a horizontal line, it makes a sound. Well I can't explain it, you have to go see and hear it.

It's not really your "easy listen" music that you'd enjoy for hours but just a fascinating way of combining mathematics and music.

A musical realization of the motion graphics of John Whitney

Addition surprise

With my dd, I've had her study addition and subtraction lately, and fact families, practicing the connection between addition and subtraction.

But she's young. So I know games go over well.

To illustrate the fact families better, I made math "rods" out of cardboard - you know, all different lengths. She really liked them.

But I got quite a surprise at her reaction to my made-on-the-spot Addition Surprise game...

I took three of those rods, so that two of them sum up to the third, and used the two to cover the third. I held them up and said there was a "surprise number" behind.

She saw the numbers on the two rods, added them, and told me the answer. I just said something like, "Ta da ta daa!!!" and uncovered the one on the bottom for her to grab.

She just giggled and giggled, and absolutely loved it.

Such a little thing to us adults - such an impact on a little one.

Amazon actually sells cuisenaire rods, too, so here's a pic if you don't know what … offer

If you're interested, I just got word that is having a Package sale: 3 books and 1 abacus for only US$35.90. This includes shipping and handling charges. sells workbooks to go along with the abacus method of learning basic arithmetic.

The offer will only last till October 31, 2006.

Free scripts to put on your site, plus statistics rant

I got this in the emails today; has worksheets and explanations, but above all, you can DOWNLOAD and freely put on your own website (or just on your home computer) all their games, fraction calculator, charts, and worksheets and stuff.

On a personal note, I've been diligently working on 6th grade worksheets for a tutoring company. But, I'm also going to make a book to sell with the material, and fairly soon too.

So lately I've been just burying myself under statistics and playing with Excel, making charts and graphs and pictures for those worksheets. They're made with Virginia state standards as guidelines, and you know, on 6th grade, the students are supposed to study box-and-whisker plots and stem-and-leaf plots, among the usual stuff such as bar graphs and circle graphs.

My husband didn't even know what those were. I first encountered them during my university studies, as I took statistics as a minor. And I really enjoyed studying it, by the…