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Showing posts from February, 2006

### RightStart Geometry - hands-on middle-school geometry course

I've finally posted the review of RightStart Geometry course on the site.

I think you will want to check it out - this course is excellent, absolutely great!

It teaches geometry with a "hands-on" method, in other words, the course includes A LOT of drawing. And you're using a drawing board, a T-square, and triangle rulers to do your drawing on the worksheets.

It teaches geometry in a way I think geometry should be taught and learned.

You see, many school books sort of reduce geometry to
a) learning vocabulary (what is obtuse angle or parallel lines or vertical angles or diameter etc. etc.)
b) learning how to calculate perimeter, area, and volume...
...but there's not much reasoning.

RightStart Geometry has that reasoning part in it - plus much more, such as proofS of Pythagorean theorem, drawing all sorts of interesting designs and figures, midpoint theorems, tessellations, fractals...

I've tried to do something similar in a small scale in my own geometry ebook, but …

### Answer of the week and algebra

a) Consider the expression 2/x. Can you make 2/x to be any number (any real number), if you just choose the right x?

Answer is NO. You cannot make 2/x to be zero. You CAN make it to be any other real number though.

b) Same for the equation x2 = a. Again the answer is NO. If a is any negative number, then you can't find such x.

Those were kind of little thinking (or maybe just remembering) exercises in algebra.

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This week's question is:

Is algebra a needful subject to study in school?

Get started by reading Mr. Richard Cohen post where he emphatically argues that you shouldn't need algebra to graduate from high school.

He uses interesting arguments to prove his point, such as:
a) he has lived his life without needing (using) algebra (so you don't need it either)
b) algebra doesn't teach reasoning because some math whiz in his algebra class years ago could not remember where Sahara desert was
c) most of math …

### Where did the mental math go?

Recently I saw this kind of problem used as an example; it went something like this:

We're in the grocery store. We're going to buy 6 watermelons, and divide each of them into fourths. How many slices will we get?

I want you to think hard :) ... and find the answer to that question. Also note HOW you found it...

Got it? Now listen how it was solved in this particular mathematics tutorial:

They changed a fourth into its decimal equivalent, 0.25, and proceeded to divide 6 by 0.25 - going thru the motions of multiplying both dividend and divisor by 100 before getting to the long division of 600 ÷ 25, and then finally onto the answer!!!

What happened to mental math?
What happened to solving problems with the most efficient and quickest way?

Well here's a suggestion for an example instead of that one:

You can solve this by…

### Brain power

I've just read an ebook called SMARTKIT from the folks at Ourb.com. They sent me a complimentary copy, and then we had a few emails back and forth, I asked some questions and got answers. They've just recently launched the book.

I have to say it was a very very good and interesting ebook, with very beneficial information.

It contains scientifically proven strategies or things that affect one's memory, concentration, learning, thinking capacity, etc. The author is a neurologist who has studied scientific papers and 'distilled' the information from them into an ebook form - and it was very well done, too, easy reading, well summarized.

Some of the things in the book I already knew about, such as the importance of omega-3 fats, or use of essential oils to help concentration, or about certain eating habits.

Some things in the book were common sense like the chapter about sleep deprivation or stress.

But then there were many more that I wasn't aware of and that are def…

### Math question of the week, week 8

Continuing a little bit on last week's theme. Let's consider two different situations:

a) Consider the expression 2/x. Can you make 2/x to be any number (any real number), if you just choose the right x?

In other words, if we write an equation

2/x = a

and I choose all kinds of different numbers to be a, can you always find the x, no matter what I might choose a to be?

If your algebra is rusty, or this problem feels difficult, try it out with 'easy numbers first': make a to be 2, 1, 4, etc. easy numbers and find x. Then figure out how to find x for more complex situations.

(This is actually a very general problem solving strategy: if the original problem is difficult, first try to solve a related easier problem.)

b) Same for the equation x2 = a.

And lastly, a NOTE to all parents reading this (not to you college professors): please write in the comments section, or email me if you feel this blogpost was over the top of your head, or was way too easy, or not relevant or interest…

Last week I asked that if you multiply 7 by some number, is it possible to make the answer to be no more than 7. And, how would a third or fifth or seventh grader answer the question.

I asked two kids this question. One had studied fractions and decimals, but still only found the easy answers that if you multiply 7 by 1 or 0, then the result is no more than 7. He seemed to be misled by the word 'number' - thinking of only whole numbers.

The other child had studied fractions some but not decimals. He immediately found those two easy ways and was of a definite opinion that there are no other ways to do it.

I hope you realize that there is an infinite number of ways to do this.

Basically we're looking at an expression x*7, or 7x, or 7 multiplied by some number x. So can you make 7x equal something no more than 7? Say, can you make 7x equal 5? Can you make 7x = 2? Can you make 7x = 3/4 ? Can you find a number x so that 7x = -12 ?

These little equations should look pretty familia…

### The many uses of a hundred chart

One day last week we went to Time4Learning with my daughter again and she did an activity where the cartoon character was making jumps on the number line.

She didn't quite get it when the guy in the activity jumped 10 jumps forward or backwards, so the next day we studied "adding 10 more to a number" with the help of a 100-chart.

I just colored a number on the chart, and then we jumped together 10 jumps forward, on the chart. Then she colored the 'landing' number. After a few of those, she was able to guess where she'd land. We also wrote the corresponding number sentences in her notebook.

Actually I wanted to show the same thing on our abacus, but it's broken right now (needs glued). And, with my 10-bags (I've made those by putting 10 marbles into small bags) - but I couldn't find those since they're put away somewhere so the baby can't get to them. But maybe it was enough for her for the day…

Since I'm supposed to write here on the blog about updates to the HomeschoolMat.net site, here comes:

1) Description of a new advanced Algebra 2 with Trig course for homeschoolers - this comes with a college level algebra textbook, videos, solutions, guides etc. The author Dr. Callahan explains that college level textbooks are more advanced and have better coverage of the material.

2) A link to MathMistakes.info was added to the math help page on the site.

I'd venture to say that this site is good reading for all algebra, trig, and calculus students. When you're reading, you are supposed to find the mistake first, and then with a mouseover see the right solution.

### Math without a computer

I have a dear friend who is not computer oriented (she said herself).

She said one time she went online to find a game to reinforce some math concept for her son but couldn't find anything she liked. Either they were too repetitive, or too difficult to figure out, or something. So she just gave up, and "did things her way".

Which, her way of teaching math is one-one-one teaching, and then she often writes problems for her son in a notebook. Upon seeing how her son solves the problem, she writes the next one. It might be going a little further in the topic, or it might be practicing a different aspect of the topic.

I sincerely admire that! It's like writing a perfectly tailored math curriculum on the spot. (I often write problems for my daughter, too, in her notebook.)
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We have computer games, card games, flashcards, textbooks, workbooks, online lessons, manipulatives - but I think the most essential part of any math curric…

### What's happening at Homeschoolmath.net

Well, all kinds of things!

1) Firstly I have several new advertisers:
NutShellMath offers over 40,000 multimedia explanations (solved textbook problems) for grades 8-11. You hear the teacher's voice and see the handwriting on a whiteboard. Sometimes there's a question for YOU to answer in the lesson.
Might work great if you often find yourself stuck on algebra 1 or 2 or geometry problems, or your student would benefit from direct explanations.Math Goodies Lessons CD offers lessons on about all topics for grades 6-8 plus worksheets, puzzles, and integer football game.TimesTales is an old advertiser, offering a fun mnemonic program to memorize upper multiplication tables. For grade 3 (or later if they didn't get it on third grade :^ ) 2) I have had various folks contact me so I would do a review on their product. I just recently completed Equals Math Jigsaw Puzzles review (it is a great gift to give in case you have birthdays coming up).

Then I will be writing about Time4Lear…

### Problem of the week

There are many websites around that publish "Problem of the Week" and then the answer the following week.

I realize homeschoolers are pretty busy, BUT something like that might be a good idea to do, say, during one month of a year, to get some challenge into your math curriculum.

Obviously challenging math problems are perfect for gifted children / those especially interested in math. And, stretching one's brain with some interesting problems might spark further interest in math for all the rest of them too.

Unfortunatly I cannot recommend any particular, but this site has several lists of websites, arranged by elementary/middle/high school/ advanced : Problem of the Week website lists.

AND, I want to throw in my own "PROBLEM OF THE WEEK" for the homeschooling parents. It's pretty simple but it's connected with teaching math. Answer here next week.

When you multiply a number, say 7 for example, does it always get bigger? In other words, is it possible to …

### Carnival of Homeschooling

Carnival of Homeschooling, week 7 is online at Homeschooling.about.com. My entry is about sharing the math in your life.

### Teaching big numbers

This weekend I was working with one of my ebooks, writing more content for it. I thought I'd share one of the problems I was putting in it.

When you're first studying numbers in the 100,000's and millions, have the child use an encyclopedia or internet to find information such as:
Population in the Northeastern statesland area of the various Midwest statesthe amount of distinct animal species in the 7 continentsnumber of newborn babies annually in European countriessome astronomical distances
...or something similar. You could try tie it in with something you're studying in other school subjects. This way, using real data, it is not just some old made-up math textbook problem.

THEN, the child is to organize the info in ascending or descending order. This lets them practice reading and writing big numbers plus comparing them.

It is sort of a hands-on exercise and ties mathematics in with real world: how math is not just for school but is something needful and useful.

You …

### What's for review?

Recently I got a review copy of Equalsmath Jigsaw Puzzles CD. It has jigsaw puzzles that the student completes in the following areas: skip-counting, multiplication, division, factoring, fraction simplification, and adding money (mentally). Well it's all mental math.

Most puzzles are in form of math tables so it reinforces the student's understanding of the underlying structure.

I took it to a friend whose son was supposed to soon do some review (one more time) on fractions - but like he noted, the puzzle sure was a much nicer way to do review than to do problems with pencil and paper.

I think that's a very good idea when it comes to lots of practice or reviewing basic facts or multiplication tables etc.: FIND A GAME FOR IT!

You might already have some math software that you've bought. Or, maybe you know a table game to play. And there of course exist tons of math games online. As you might know, I've compiled a list of them, organized by topics. See for example:
Onlin…

### Where is math in your life?

Math in your life- I'm not talking about schoolwork or teaching now, but everyday situations where you've used math.

I'd like to encourage you to share those 'math' moments with your child. It shows him/her that math is NOT a 'hateful' activity done in school, but something useful and normal!

For example, cooking is an excellent example. Kids will be enthusiastic to do all kinds of measuring while cookies are in the works! (Now I hope you aren't one of those who will rather find another recipe than figure out the half or 3/4 or 1 1/2 of the recipe).

My hubby said he uses math when designing a website layout. He has to figure out what should the table column widths be, if the screen resolution is 600x800, and he wants this wide cell-padding, this wide borders, this wide cell-spacing.

Another example: A few years back I was interested in the essential omega-3 fat alpha-linolenic acid (ALA), and figured out how many ounces of flaxseed would one need to get t…

Addition 1 ebook of mine has undergone a major update. Now the first lessons only use numbers within 0-5 so it is more usable for kids who are just starting with addition concept.

The book still concentrates on the memorization of addition facts, grouped as facts where the sum is 5, or 6, etc. till facts where the sum is 10.

If any old customer happens to be reading this and wants the updated version, let me know.

### Bush urges students study more math and science

The president's "American Competitiveness Initiative" proposes to bolster basic research at government laboratories, improve math and science instruction in public schools and stimulate corporate technological innovations.

Bush talked how students need to study more math and science if they want to be trained for a job that actually exists.

He said, "Take a look at math and science. I'm sure they're saying, you know kind of, 'They're nerd patrol'. It's not. It's the future. The future is engineering and physics and chemistry and math."

This is, of course, very true. More and more jobs in the future require more and more math and science. And if there aren't US workers to do them, the jobs may very well go to China and India.

Read more: Bush pushes proposals to make U.S. workers more competitive

### Scope and sequence chart (grades 1-7)

Since we've been talking about coherent & focused curriculum lately, and someone asked about scope and sequence, I decided to make a chart.

It's just a rough GUIDELINE and it only includes the major topics.

The idea is to show the major focus on each grade and how it changes over the years. And I don't mean that you wouldn't teach a first grader about 1/2. The chart only deals with the major focus
for the topic.

And here you can find more details: Scope and sequence suggestion (grades 1-7)

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### Proof before high school - remember to ask "Why?"

You might think, "Proof? You need it before high school geometry?"

Sure! But, we are talking about a different form of 'proving' here.

What IS proof, first of all? It is something that the person hearing or reading the 'proof' will become CONVINCED that whatever you're proving is, indeed, true.

You will want to convince your youngsters or students that what YOU ARE telling them, is indeed true. That is 'proving', in a general sense. But it doesn't have to be on the same level as later.

For example, when you are showing them how the multi-digit multiplication works and WHY it works (2 &times 371 is the same as 2 × 300 + 2 &times 70 + 2 &times 1), you are proving - or maybe we should say "justifying".

When you take fraction manipulatives and demonstrate why 5 × 2/3 is 3 1/3, you are 'proving' - or demonstrating. (You take 5 times 2/3. You combine the thirds until you get 3 wholes and one third.)

Oftentimes diagrams or p…

### Happy birthday, HomeschoolMath.net!

Happy birthday, my website! It's been 3 years.

I started www.homeschoolmath.net somewhere in the early February in 2003 (don't even remember the exact date).

I've had over 2 million visitors in those 3 years.

Last month was RECORD traffic ever. The site had slightly over 100,000 unique visitors, creating over 550,000 pageviews...

So based on that, I should have another million visitors during this year 2006.

Month Unique vis's Visits Pages Bandwidth
Jan 2006 102845 160015 557613 21.78 GB

Thank you for my visitors! I hope I've been of help. Like I state in the profile, I love math and teaching, and I do love the opportunity to help others teach better.