HomeschoolMath.net new design

My main math site, Homeschoolmath.net, has gotten a face-lift... with better NAVIGATION on the left sidebar. Hopefully you'll be able to find your way around better along all the articles, reviews, worksheets, and stuff there.

I especially want to draw attention to the ONLINE RESOURCES section. I used to have this on 9 pages... now I split it into 29 different pages, according to topic.

These pages feature the best online games, quizzes, tutorials, or websites on various math-related topics. Have your pick:

Online math resources menu
	Addition and subtraction Place value Clock Money Measuring	Multiplication Division Math facts practice The four operations Factoring and number theory Geometry
	Fractions Decimals Percent Integers Statistics, Graphs, and Probability	Geometry Algebra Calculus Trigonometry Logic and proof
	Problem solving & math projects For gifted children Math history	Math games and fun websites Sites with interactive math tutorials Math help & online tutoring Review and test prep Online math curricula

I will derive!

Just a fun little song (parody of "I will survive") for all of us who've taken calculus.

Heart of the Matter conference

Heart of the Matter will he hosting an online homeschool conference during July 30 till August 3.

What is a virtual conference all about?

"Each speaker will just log in at her/his scheduled time, with a plugged in microphone, speak about their topic (approximately 30-40 minutes), and then hold a Q/A session with the listeners (approximately 20-30 minutes). All the while the attendees will get to chat amongst themselves in true Instant Message format.

We really want the conference to be less like a "seminar" and more like a bunch of close friends in a chat room. We want everyone to feel comfortable. Some sessions will also be pre-recorded. Just wait till you see what some of your favorite home school personalities have done to educate and entertain you! At the end you will join in to chat with them, ask questions, and they will answer."

Well, yours truly is planning to be a speaker as well...
Anyway, here's a link for more info and you can sign up as well. Place my name (Maria Miller) in the "add special instructions" field, please, so they know I referred you.

Marbles problem to solve

Here's a nice "brain teaser" problem sent to my way... probably a student who wants to know the solution. I'll post it for you all and the solution in a few days.

204 marbles are divided into 3 groups according to colour. Ahmad found that there are twice as many blue marbles as white marbles and there are fewer red marbles than blue marbles. Ben found that the number of marbles in each group are divisible by 4 and 6. Cally found that the number of marbles in each group is less than 100.

How many red marbles are there?

(I do not have a clue where the problem originates, but I DO LIKE it!)

Solution:

Now, we need to find three numbers.

The one hint tells us that one number is double the other, and the third is less than the first (the doubled one). This won't yet get us started.

It is actually the latter hints that provide a starting point.

We learn the numbers are divisible by 4. They're also divisible by 6, which means they're divisible by 2 and 3. But we already knew they're divisible by 2 (since thye were divisible by 4), so the new information in this hint really is that the numbers are divisible by 3.

Divisible by 4 AND divisible by 3 means.... DIVISIBLE by 12!

Also all numbers are less than 100.

This really now restricts our "search space". We're looking at multiples of 12 that are less than 100.

Now, one was double the other. Since the 8th multiple of 12 (96) is the largest we can use, then two of the numbers COULD be the 4th and 8th multiples of 12 (48 and 96). They could also be the 3rd and 6th multiples of 12 (36 and 72).

The first hints will now "lock in" the solution... the sum has to be 204, which is 17 x 12. So, choosing 4 x 12, 8 x 12, and 5 x 12 - or 48, 96, and 60 - as our numbers will work. And, there are therefore 60 red marbles.

Get Math Mammoth Clock for free - CurrClick promotion

UPDATE: The promotion is extended till the 15th of this month so that all can enjoy it (they've had some problems with so much traffic).

I'm sure most of you already know about this... CurrClick is having a mother's day promotion where they have 20 homeschool titles for a free download... and one of them is my Math Mammoth Clock book.

Just click here to download some of them -- or all of them! (You'll have to register if you haven't already.)

My opinion on Saxon math

People sometimes ask me of my opinion of Saxon math.

In a nutshell, I realize that Saxon math works for some children. However, it is not the way I would teach math.

Saxon math presents a concept in a lesson, then has a few exercises about it, and the rest of the lesson is review of previous concepts.

The NEXT lesson usually is not on the same topic as the previous lesson. It jumps around in topics tremendously. One lesson on geometry, next on fractions, next on addition, next on large numbers. It's unbelievably disjointed. It's not the concept presentation nor the exercises in Saxon math -- it is the way the lessons jump around that I dislike.

How can kids get a coherent view of mathematics studying that way?

Read how professor Hung-Hsi Wu has worded it (emphases and the additional note are mine):

"But I think that what perhaps disturbs me the most about Saxon is to read through it, I myself do not get the feeling that I am reading something that when that the children use it they would even have a remotely correct impression of what mathematics is about. It is extremely good at promoting procedural accuracy {Maria's note: this means teaching procedures such as the correct motions of the long division algorithm, or what to do to find the lowest common denominator, etc.}. And what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. And you would get the feeling that-I think of it as a logical analogy-you can see the skeleton presented with quite a bit of clarity, but you never see any methods, your never see any flesh, nothing-no connective tissue, you only see the bare stuff.

A little bit of this is okay, but when you read through a whole volume of it really I am very, very, uneasy. There are lots of things in it that I admire, but something that is so one-sided-you think once more about yourself and you think about what happens if this thing gets adopted. There might be lots and lots of children using it. And suppose that hundreds of thousands of students are using this book and they go through four years of it. Would you be willing to face the end result? That here are hundreds of thousands of students thinking that mathematics is basically a collection of techniques.

That impression by the way is very easy and is almost obtained-you get it by looking at the topics. There is no rhyme or reason about the sequencing of the topics. For example, the things are really broken up. The report gives the examples. One of the grade levels, grade four or grade five, has exactly two sections on probability (that's right two sections). They belong together and without a doubt there is no increase in sophistication or techniques, and yet I think they are separated by 200 pages. When I do this I want to emphasize that I do not single out one or two examples. I am trying to describe through one or two examples the overall the overriding impression that I have. And when that happens, you get the feel that if my students use this, how could they not get the idea that mathematics is just a collection of techniques? If that is the case, what happens to them when they go on to middle school, and then to high school, and after that, God forbid, you might be facing them in your freshman calculus classes. And that is a frightening thought!

References: http://www.arthurhu.com/2003/11/antisax.txt

http://www.pdkintl.org/kappan/k0111jac.htm

See also reviews of Saxon math left at HomeschoolMath.net. Some people DO like Saxon exactly because of the constant review, but several people also explain their frustration with it. Some math teachers have commented on that page about the total lack of organization of topics.

Teacher appreciation week

I should have posted this earlier but forgot. I even missed one day!

Learning A-Z is having an open house this week; you can access their family of websites for free, one site per day.

The writing site is for today. Vocabulary site is coming up soon, and so is their science site. Lots to explore and download.

Gas price math

Today I just stumbled upon two sources discussing the price of gas in a comparative sense; one was a line graph comparing it to the past, the other was a world-wide comparison.

Both were interesting; and a resourceful teacher can now make all kinds of problems based on the data. First based on the list of gas prices in various countries, for example these come to mind. (And I'm just giving you ideas for a lesson on gasoline lesson; I'm not providing answers but if some of you want to, feel free to comment.)

• Approximately how many-fold is the price of gas in Bosnia-Herzegovina as it is in the USA? In Egypt? In Venezuela?



• If your mileage is 25 miles per gallon, find the price of driving a 120-mile trip in Germany and in the USA.

Looking at the inflation adjusted gas price in 2008 dollars now. Just reading the graph:

• When was the price of gas at its lowest? At its highest? How much was it?



• Find the price of gas (approximately) in 1930, 1960, and 1990 by reading the graph.



• If you overlook the peaks of the late 1930s and early 1980s, describe the general trend in the price of gas from 1918 till about 1999.
  How many dollars did the price change over that period?

Then into percents:

• If you overlook the peaks of the late 1930s and early 1980s, describe the general trend in the price of gas from 1918 till about 1999.
  How many percent was this change?
• What was the price of gas (approximately) when it was at its cheapest in the 1990s?



• How many percent did the price drop from 1981 to that low point of 1990s?



• How many percent has the price risen from the low point of 1990s till now?

And so on! Feel free to change the questions as you see fit and use them with your students.

A simple triangle problem

Someone sent in this very simple question (a student?).

Leg b of the right triangle is twice as long as the base a.
If the area is 36 cm squared, what is the length in of the leg b?

A little bit of algebra helps in this problem.

FIRST strive to make a picture. Need a right triangle, the leg twice as long as the base. Here in my picture things aren't exactly to the scale, but it suffices for illustration purposes:


So we actually know that b = 2a.

The area of a triangle here is base times height over 2, and remember the height is the other leg, and it's twice the base:

area = ba/2 = (2a)(a)/2 , and this is 36 (given).

So we get our equation:

(2a)(a)/2 = 36

a² = 36

a = 6.

The leg b is therefore 12 cm long. check: Legs are 12 and 6, so the area is 12 * 6 / 2 = 36.