My most popular blogposts - 2009

To celebrate the blogging year's end, I compiled a Top 10 list of my most popular blogposts during the year 2009. Some of these were current events, but most are actually timeless and can be helpful anytime, now or future. Maybe you'll find something interesting among these, as well!

There have been 95 blogposts total this year, including this one.

Top 10 Posts at Homeschool Math Blog, year 2009

1. Free algebra worksheets (January 3). This one was by far the most popular. I can see that, seeing as how many people would be looking for free algebra worksheets.

2. The World Math Day (February 8)

3. A conversion chart for measuring units (April 9)

4. A little trick for square roots (mental math) (January 8)

5. Massachusetts teachers' math exam (June 3)

6. Singapore math approach marches on.. to Houghton Mifflin Harcourt (April 29)

7. A word problem Singapore way (May 30)

8. Making the fractions in a proportion (January 29)

9. Learn to recognize coins (August 14)

10. Long division and dyslexia (May 13)

Teaching math to preschoolers - article

Some of you might enjoy this article in New York Times:
Studying Young Minds, and How to Teach Them

It talks about a program called Building Blocks where preschoolers are taught simple math concepts, such as number symbols and counting. Kids that went through the program did much better in kindergarten math than those who did not.

I had not realized that preschoolers are normally not taught much anything about numbers or counting. This program clearly proves how beneficial it is to do so, and how the kids' brains are definitely ready to learn counting at age 4 (and it can happen earlier, as well).

High school math videos - free

Today I wanted to highlight two companies that both offer lots of free high school level math materials in the form of videos. These are real, commercial companies, yet they have chosen to offer the videos online for free. Both have something else they sell, hoping to make some money obviously from that part of the business.

The video content can really be of help for all students, teachers, or parents who need additional help with high school math (algebra, geometry, calculus). And since I'm highlighting these two, if you have a topic you have trouble with (such as polynomials or factoring or inequalities) you can even check out videos for that topic in both places.

1) BrightStorm Math.

They currently have over 2,000 videos available for free - a free registration is required though. Algebra through calculus. What they are selling is test preparation courses.

2) MathTV.com


MathTV.com has over 6,000 free math videos, including some in Spanish. Prealgebra through calculus. What they are selling is their own textbooks, physical and online. However, their online textbooks are available for free for evaluation and class testing through June 2010.

Carnival time

When you get time... perhaps over the holidays, go over to the most recent Math Teachers at Play carnival at Math Mama Writes, and enjoy the variety of blogposts revolving around math.

I especially liked the estimation lesson, and the start of the proof that Pi is irrational. The proof looks familiar so am sure I've seen it in university sometime or another, but of course I don't exactly remember it on my own! Yet, I like being reminded of it, because Pi is a topic in middle school math, and I feel I'm a better teacher if I have at least a mental recognition that I've seen and understood the proof that it's irrational,
even if I cannot exactly present the proof to the students.

And then I also thought these dynamic applets to make nets for pyramids and other solids were neat.

Men and women's IQs

I just read an interesting article today (HT goes to my husband) about men's and women's perceived intelligence.

He's Not as Smart as He Thinks

In a nutshell, men and women are fairly equal overall in terms of IQ, BUT men tend to overestimate their IQ, and women tend to underestimate theirs!

Angles in a parallelogram and a triangle

This is a set of three geometry videos dealing with angles.

First, showing that vertical angles are equal:



Next, finding out about the angles in a parallelogram. I start out with two parallel lines and a transversal (line that intersects them both). We explore the angles formed, which some of them are corresponding angles, some are vertical angles. I draw a new line, and get a parallelogram.



Lastly, here is a short and easy proof about the angles in a triangle.

Using a protractor

I've finally ventured into geometry topics with my latest video:



It shows how to use a protractor to measure angles. I show where the "base line" of the protractor is for three different protractors, and use it to find out the angle measure of different kinds of angles (including a reflex angle).

Math Teachers at Play carnival

Denise has done a good job putting together Math Teachers at Play carnival #20. Lots of stuff to read, head on over!

Ratio word problem solved with block model and algebra

I guess it is time for some more problem solving, since someone sent this question in.

Two numbers are in the ratio of 1:2. If 7 be added to both, their ratio changes to 3:5. What is the greater number?

We can model the two original numbers with blocks. 1 block and 2 blocks makes the ratio to be 1:2.

|-------|

|-------|-------|

Now add the same thing to both (the 7):

          7
|-------|---|

|-------|-------|---|
                 7 

The way I just happened to draw these suggests that I could just split the original block in two, and the problem is solved:

          7
|---|---|---|

|---|---|---|---|---|
                 7 

Here, each little block is 7. The original larger blocks are 14 each.

So the original bigger number, which had two larger blocks, is 28, and the smaller number is 14.

Check:
Their ratio is 28:14 = 2:1. If you add 7 to both, you have 35 and 21, and their ratio is 35:21 = 5:3.


Solving the same problem using algebra

The two numbers in the ratio of 1:2 are x and 2x.

Once 7 is added to both, we have x + 7 and 2x + 7. Their ratio is 3:5, and we can write a proportion using fractions:

x + 7           3
-------   =   ----
2x + 7          5

Cross-multiply to get

5(x + 7) = 3(2x + 7)

5x + 35 = 6x + 21
35 - 21 = x

x = 14

The larger number was 2x or 28. We already checked this earlier.

Mixture problems - algebra 1

I am hoping you can help me. I can not remember how to solve mixture problems and how to set them up. Examples are as follows:

A merchant made a mixture of 150lb. of tea worth $109.50 by mixing tea worth $1.25 a pound with tea worth $.65 a pound. How many pounds of each kind did he use?

Organizing the information in a table or chart is usually very helpful in dealing with mixture problems. Other than that, it helps to study several examples and practice solving them yourself. After a while, it gets easier and patterns begin to emerge.

The first problem has two unknowns. Let x be the amount of more expensive tea, and y the amount of the cheaper tea (in pounds).

In our table, we will look at the amounts of tea (in pounds), price per pound, AND the amount the tea is worth, which is (the amount) times (the price).

amount  |   price per lb  | worth
-------------------------------------
  x    |      $1.25      |  1.25x
-------------------------------------
  y    |      $0.65      |  0.65y
-------------------------------------

Then we add one more row to the table that has to do with the MIXTURE, or the total.

amount  |   price per lb  | worth
-------------------------------------
  x    |      $1.25      |  1.25x
-------------------------------------
  y    |      $0.65      |  0.65y
-------------------------------------
150 lb  |      ??         |  $109.50

Now we get our equations. First of all, x + y = 150. And secondly, 1.25x + 0.65y = 109.50.

This gives you a system of two linear equations to solve, using any standard technique. For example, you can solve from the first that y = 150 − x and substitute that into the second.

The solution is: x = 20, y = 130.

Check: we have 20 lbs of tea costing $1.25 per pound, so it is worth $25.
We have 130 lbs of tea costing $0.65 per pound, so it is worth $84.50. Total worth is $109.50. It checks.

---

A pharmacist has 10 oz. of salt and water of which 4 oz. are salt. How may ounces of water must he add so that 5% of the new solution is salt.

This is a very typical (and routine) problem from algebra 1 textbooks. Here, our table will have one row for the original situation, and another for the final situation. We are checking the amounts of salt and water, and then the total amount.

             | salt | water | total
-------------------------------------
1st situation |   4  |   6   |  10
-------------------------------------
2nd situation |   4  |   ?   |  ?
-------------------------------------

The KEY is that there is no salt added, only water. Our unknown is the amount of water added.

             | salt | water | total
---------------------------------------
1st situation |   4  |   6   |  10
---------------------------------------
2nd situation |   4  | 6 + x |  10 + x
---------------------------------------

The equation is gotten from the statement that 5% of the new solution is salt. This means that 5% of the total (which is 10 + x) is salt (which we know to be 4 oz).

0.05(10 + x) = 4.

0.5 + 0.05x = 4
0.05x = 3.5
x = 3.5 / 0.05 = 70.

He needs to add 70 oz of water.

---

In 110 lb. of an alloy of tin and copper, the amount of tin was 5lb. less than 1/3 that of the copper. How may pounds of tin were there?

Again, we organize this into a table:

| tin | copper | total
--------------------------------------
|  t   |   c   |   110
---------------------------------------

We have TWO unknowns: the amount of tin and the amount of copper. Right there we get one equation: t + c = 110. The statement "the amount of tin was 5lb. less than 1/3 that of the copper" allows us to build another equation relating t and c.

t = (1/3)c - 5

Again, a system of equations. Since t is expressed in terms of c in the equation above, I use that to substitute to the first equation:

(1/3)c - 5 + c = 110

(4/3)c = 115

c = 115 * 3 / 4

c = 86.25.

But it asked for t, so t is 110 - 86.25 = 23.75 lb.

I hope these examples were helpful in dealing with "mixture" type problems in algebra.

Fact families on a whiteboard

I just found this picture that I took of the fact families my 4-year old wrote on the whiteboard - totally on her own.



There was a time she loved writing fact families like this every day. Being able to choose different color markers plus it being on the whiteboard seemed to be the main motivating factors, because she didn't want to write them on blank paper... Kids are funny.

Then again, it allows us teachers to use colorful markers as a "motivational tool" : )

Anyway, I was really happy that she had grasped the concept.

Review of Math Apprentice

Math Apprentice is a new free website, meant to show students how math is used in real world. In the game, you are like an apprentice at various companies, applying your math skills to challenges similar to those encountered in the real world and real companies.

Main Street - Click to enlarge

To begin, you click the button on the home page of the site that says "Explore the Math". Then choose your character, and you'll be on the main street (see screenshot above) . Then use arrow keys to move right or left, and click to select a company to visit.

The companies you can visit are:

• Sweet Treat Cafe - baking pies

Sweet Treat Cafe - Click to enlarge

• Wheelworks - constructing bicycles and exploring gear ratios
• Game Pro! - keep track of the distance between superhero and the villain in a computer game, using Pythagorean Theorem
• Spacelogic - study speed of a spacecraft & slope, and then angle & distance commands to get the space rover where it needs go.
• Trigon Studios - Explore the usage of sine and cosine functions to create rhytmic or repeating motion of animated objects.
• Doodles - explore polar curves created with sine and cosine. These can be like stars, flowers, or spirals.
  

Doodles - Click to enlarge

• Builders, Inc. - calculate areas and perimeters of shapes

Builders, Inc. Click to enlarge

• Adventure Rides - study the angle of elevation and height of a roller coaster

While the site is targeted to grades 4-7, many of the mathematical ideas are actually far more advanced than that. In the simulations involving sine and cosine, for example, all you have to do is change the values in the equations using sliders and observe. Also, in some activities there are instructions given how to calculate things.

It says the about page: "Some of the mathematics in Math Apprentice may seem advanced for its targeted age group, grades 4-7. That's ok. It's important for students to interact with math concepts beyond the standards. This is where the joy of math can often be found."

Nevertheless, I feel some activities are definitely best reserved for students who have studied the concept (such as Pythagorean Theorem in Game Pro! company).

In general, I think Math Apprentice has well-made and interesting activities, and kids are sure to enjoy it!

Percentages with mental math

(This is an older post that I have revised plus added a video to it.)
In this article I want to explore some ideas for using MENTAL math in calculating percents or percentages.

I have also made a video about this topic:



And here are the ideas:

1. Find 10% of some example numbers (by dividing by 10).
2. Find 1% of some example numbers (by dividing by 100).
3. Find 20%, 30%, 40% etc. of these numbers.
   FIRST find 10% of the number, then multiply by 2, 3, 4, etc.
   For example, find 20% of 18. Find 40% of $44. Find 80% of 120.
   
   I know you can teach the student to go 0.2 × 18, 0.4 × 0.44, and 0.8 × 120 - however when using mental math, the above method seems to me to be more natural.
4. Find 3%, 4%, 6% etc. of these numbers.
   FIRST find 1% of the number, then multiply.
5. Find 15% of some numbers.
   First find 10%, halve that to find 5%, and add the two results.
6. Find 25% and then 75% of some numbers. 25% of a number is 1/4 of it, so you find it by dividing by 4. For example, 25% of 16 is 4. To find 75%, first find 25% and multiply that by 3.
7. Calculate some simple discounts. If an item is discounted 20%, 15%, 25%, 75% etc., then find the new price.
   
   For example, a book costs $40 and is discounted by 15%. What is the new price?
   First find 15% of $40 (10% of $40 is $4 and 5% of $40 is $2... so 15% of it is $6). Then subtract $40 - $6. So the new price is $34.
   
8. "40% of a number is 56. What is the number?" - types of problems.
   
   You CAN do this mentally: First FIND 10% of the number, and then multiply that result by 10, and you'll get 100% of the number - which is the number itself.
   
   So if 40% is 56, then 10% is 14 (divide by 4). Then, 100% of the number is 140. This result is reasonable, because 40% of this number was 56, so the actual number (140) needs to be more than double that.
9. "34% of a number is 129. What is the number?" (A calculator will help here.)
   
   You don't need to write an equation. You can just first find 1% of this number, and then find 100% of the number.
   
   If 34% of a number is 129, then 1% of that number is 129/34. Find that, and multiply the result by 100.

Hope you enjoyed these little mental math ideas! They also help students understand the concept of percent where they don't end up relying too much on mechanical calculations or equations.

Cell size and scale

Just a neat link my hubby found this morning...

http://learn.genetics.utah.edu/content/begin/cells/scale/

You can zoom in to see these various things starting from a coffee bean and down to a skin cell, human egg, red blood cell, bacteria, viruses, hemoglobin, glucose and molecules, etc., all the way "down" to a carbon atom.

In measuring scale, you go from millimeters (0.001 or 10^-3m) to micrometers (0.000001 or 10^-6m) to nanometers (0.000000001 or 10^-9m) to picometers (0.000000000001 or 10^-12m).

American Math Challenge

The American Math Challenge is an online math challenge or "competition" where students aged 9-14 from across America can compete in a safe, multiplayer game environment.

This is from the same folks as the World Math Day, if you happen to remember that.

Students will have the task of answering as many correct questions as they can in 60 second mental arithmetic challenges LIVE, against other students. Or, they can also solve questions based on the national curriculum at their own pace.

Why would you take part?

• It's about having fun with math. In fact, there's a good chance your students/children will love it.
  
  
• It's absolutely free. Nothing to lose if you participate. In fact, during the practice week you can find out if your kids like it or not.
  
  
• If your children or students really get into it, they can vastly improve their mental arithmetic and basic facts.
  

Week 1: Nov. 2-8 is Practice week
Week 2: Nov. 9-16 is the actual American Math Challenge

Register at www.americanmathchallenge.com

Wolfram|Alpha homework day

Today October 21st is a Wolfram|Alpha Homework Day. I am not quite sure myself what all this entails, but it is a LIVE interactive event on the web, revolving around what can be done with Wolfram|Alpha search engine.

Here are some highlights (from the website) of what will be happening over there today:

• A special Homework Day Welcome from Stephen Wolfram
• A demonstration by a forward-looking elementary school teacher of lesson plans that use Wolfram|Alpha
• A conversation with the creator of "Shift Happens" about tech trends and their impact on education
• A fun experiment with Wolfram|Alpha's mad scientist Theodore Gray
• Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
• A special live Q&A session tackling the toughest math questions

• A thought-provoking in-depth conversation with an internationally known actor and education advocate
• A live interview with the creator of the Ning social networking group Classroom 2.0
• An insightful dialog with an award-winning physics professor and best-selling author of several popular science books
• A vibrant panel discussion of teaching with technology led by noted journalist Elizabeth Corcoran
• Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
• A special live Q&A session tackling the toughest math questions

• An interview with a renowned theoretical physicist, best-selling author, and frequent PBS contributor
• A special live Q&A session tackling the toughest science questions
• A live concert by Common Loon
• A demonstration of Wolfram|Alpha examples from an innovative college professor
• Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
• A recap of the best highlights of Wolfram|Alpha Homework Day

http://homeworkday.wolframalpha.com/

Math Teachers At Play carnival #17

Math Teachers At Play #17 carnival is posted at Math Recreation. LOTS of stuff there this time!

Here are some of my picks: Circle of fifths and roots of two is of interest if you have studied music. This post explains the difference between equal temperament and Pythagorean tuning, from a mathematical point of view. All about A4 explores this common paper size and its special properties. And Pat's post You Might Be a Mathematician IF... was quite funny.

NAEP math test results are in

The National Assessment of Educational Progress (NAEP) math tests given early in 2009 show that the US fourth graders scored the same as in 2007, and 8th graders gained a little over 2007 tests. This is commonly called "the nation's report card".

I guess it shows things haven't changed since 2007 in the realm of math education; however the test results are better now than when they first started administering the test in 1990's.

If you are interested, NAEP Mathematics 2009 website has charts and much more information.

10/10 and the Metric Week

Photo courtesy of Miss Colleen

Today is 10th of October or 10/10. As we know, the metric system is based on number 10. Thus, the week ending today has been designated as the metric week..

The National Council of Teachers of Mathematics (NCTM) started the National Metric Week tradition in 1976. Please read a little bit more about the history of the Metric Week here.

You could celebrate the Metric Week doing some metric units puzzles and quizzes. Here's a link to postal stamps and cards celebrating the metric system.

NCTM has tons of related resources so I'll mainly point you there.

I grew up using the metric system, and so I've actually had to learn the imperial system while authoring math materials. These days, it seems, I know the U.S. system better than the people around me... But the metric is sure easier, as far as calculations and conversions go, since you just have to remember it goes by 10s.

In fact, to fully operate in this world, it seems it's best to know both.

Converting between metric and U.S. measuring systems

Here are a few helpful guidelines if you find yourself having to switch between one or the other. I have these conversion factors memorized from much of use. Not that everyone else would actually use these all as much as I do, being in the business of authoring math materials, but anyway:

1 quart ≈ 1 liter, but 1 quart is slightly less.
1 liquid ounce ≈ 30 ml. From this, one can figure out that 1 cup ≈ 240 ml and 4 C ≈ 960 ml.

1 inch = 2.54 cm
It's an awkward number but I need to use this conversion factor constantly, when working with images on my computer, which has a resolution of 96 pixels per inch... but I need the image to print out as 5 cm long or whatever.
You could use 1 inch ≈ 2.5 cm.

Another way is to think about those typical student rulers which are 12 inches = 30 cm. So... 4 inches is 10 cm.

Also... 1 inch might very well be the length of your thumb's last bone (the bone that contains the nail). Check! And 1 cm might very well be the width of any of the other fingernails. Check!

1 yard ≈ 1 meter; better yet 1 yard ≈ 90 cm and 1 meter = 100 cm. You see, that student ruler was 12 inches = 1 foot ≈ 30 cm.

1 mile ≈ 1.6 km. Or, 5,000 meters or 5 K is a popular running distance... about 3 miles.

1 pound is about 450 g, but actually it's easier to remember 1 kg = 2.2 lb.

It's fairly easy to multiply by 2.2. I have a metric scale; I might weigh about 55 kg. 55 x 2 = 110 and 55 x 0.2 = 11. So I weigh about 121 lb.

And 1 ounce ≈ 30 g. Just like 1 liquid ounce was about 30 ml.

To convert anything, go to Google and type

25 lb to kg
8 m to inches
22 km to miles
etc.

Math contest for homeschoolers (elementary)

Noetic Learning is holding a math contest for elementary students that homeschoolers can take part in. Here are some details about this contest:

• Registration deadline: October 18,2009 (coming up soon!)
  
• Contest Date: October 26-30 2009
• Who: any students (grades 2 - 5)
• Location: your home
  
• Fee: $8 per student per contest

My daughter is taking part. We will see how it goes. The purpose of a math contest is definitely NOT to discourage a child or to put additional burden on him. I'm basically checking to see if this contest can be a means of inspiration and motivation for my daughter.

www.noetic-learning.com/mathcontest/homeschool.jsp

Spread of H1N1 (swine) flu and mathematics

I came across an interesting blog post by Murray Borne titled H1N1 and the Logistic Equation. It explains how a logistic function can be used to model the spread of a virus or a disease in a given population.

Now, maybe you don't know what is logistic function or equation. It is shown in the blogpost; it uses the exponential function as a part of it. Basically, it is like an exponential growth function but it is limited after a certain point so that the growth tapers off, and approaches a certain (upper) limit.

Murray shows the graph, and then shows a real-life example about the spread of swine flu in Mexico last spring. It's a great, yet fairly simple, example of how mathematics is used for modeling real-life situations.

You could definitely use it as such an example with your students, even if you don't understand a THING about logistic equations. You see, seeing how math is used is definitely inspiring and motivating to a lot of students - especially when it ties in with some current "hot topic" such as the H1N1 flu.

Understanding basic division

Denise has made a good post on the concept of division, which I heartily recommend. She deals with a study where Finnish researchers gave this problem about division and remainders to high school students and pre-service teachers:

• We know that:
  
  498 ÷ 6 = 83.
  
  How could you use this relationship (without using long-division) to discover the answer to:
  
  491 ÷ 6 = ?
  
  [No calculators allowed!]
  

I really like the question. To solve it, you need to TRULY understand what DIVISION and remainders are all about!

Now, let's think about it. Have you ever seen a pattern in division and remainders, like the one below?

20 ÷ 4 = 5
21 ÷ 4 = 5 R1, or 5 1/4
22 ÷ 4 = 5 R2, or 5 2/4
23 ÷ 4 = 5 R3, or 5 3/4
24 ÷ 4 = 6
25 ÷ 4 = 6 R1, or 6 1/4
26 ÷ 4 = 6 R2, or 6 2/4
27 ÷ 4 = 6 R3, or 6 3/4
28 ÷ 4 = 7
29 ÷ 4 = 7 R1, or 7 1/4
30 ÷ 4 = 7 R2, or 7 2/4
31 ÷ 4 = 7 R3, or 7 3/4

Students need to see and do such patterns when they are first learning basic division.

The pattern shows that every fourth number is evenly divisible by 4, and the ones in between have remainders 1, 2, or 3 in order. If the answer is given as a mixed number, the remainder is the numerator.

Back to 498 ÷ 6 = 83. Since 498 is divisible by 6, so is the number just 6 less than 498, or 492. In fact, 492 ÷ 6 = 82, or in other words, the quotient is one less than 83.

This makes sense when thinking of division as, "How many times does it fit?" If 6 fits into 498 exactly 83 times, then it fits into 492 one less time, or 82 times.

Continuing, also 492 − 6 = 486 is divisible by 6, and this time 486 ÷ 6 = 81.

We can now build the pattern from 486 onward until we have 491 on our list:

486 ÷ 6 = 81
487 ÷ 6 = 81 R1 or 81 1/6
488 ÷ 6 = 81 R2 or 81 2/6
489 ÷ 6 = 81 R3 or 81 3/6
490 ÷ 6 = 81 R4 or 81 4/6
491 ÷ 6 = 81 R5 or 81 5/6
492 ÷ 6 = 82

So, 491 ÷ 6 = 81 R5 or 81 5/6. Problem solved.

Review of Mangahigh games

I got an advance notice of a new games website called Mangahigh.com. It's more than just simple math games, though. These games are designed extremely well, both from mathematical and "enjoyment" perspective. Mangahigh is led by a team of mathematicians, educationalists, and games designers so the games feature commercial-quality gameplay.

I wanted to highlight two of the free games here:

Flower Power
This is the one that I liked most... it's addictive! Grow flowers and harvest them to make money. Practice ordering decimals, fractions, and percentages. The game starts with ordering decimals (daisies), and proceeds into fractions (tulips or roses) and percents. Each time you get a full stem, you need to decide whether to pick the flowers to sell (earn money) or to let them be pollinated and thus get more flowers to grow. Grades 3-8.


Save Our Dumb Planet
Defend Earth from deadly meteorites using missiles. A team of dumb scientists are on hand to suggest possible trajectories. Practice drawing lines, quadratic curves, and some harder curves using their equations. The game has many levels, and you can stay at the easier levels if you so wish. Don't listen to the dumb scientists' talk - they mislead you! Grades 8-11 (algebra).

If I understood right, the games that are there now is just the beginning, and there are more to come.

---

Lastly, Mangahigh also has a powerful game called Prodigi. This is a math learning engine (or a math practice environment) that has thousands of maths problems with worked solutions and hints that adapt to each student's ability and learning speed. You can try Prodigi for free; however, only on a certain "easy" and set level. To enjoy the full possibilities of Prodigi, you need to subscribe.

Carnival time

"Math Teachers at Play" carnival #15 is posted at mathfuture.wikispaces.com/Math+teachers+at+play. Lots of interesting posts, once again. Go check it out!

Strategies for basic addition and subtraction facts

In this video I show several strategies for learning the basic addition and subtraction facts:

• finding all the possible sums for a certain number; e.g. for 6, these would be 0 + 6, 1 + 5, 2 + 4, and 3 + 3;
• writing out all the fact families where the sum is a certain number;
• the 9 "trick"; 9 + 7 is the same as 10 + 6 (9 wants so badly to be 10 so that it "steals" one from 7);
• doubles and the accompanying addition facts;
• number rainbows and how to use them to practice subtraction;
• a structured drill for addition facts.
  

Enjoy!



Strategies for Addition and Subtraction Facts - Video

Unit studies in math - States by the Numbers

There is a book for
each state of the US.

Each book has 38 pages
(80 activities)

Price per book:
$2.99 PDF download

Free Sample (PDF):
North Dakota

---

Bundle of 50 workbooks $19.99
($0.40 per state)

Your order is secure
Shopper help at Kagi

Recently I've had the pleasure of adding to MathMammoth.com a series of workbooks titled States by the Numbers, by Make It Real Learning company.

States by the Numbers is a series of workbooks where the problems in each workbook are based on data from the Census Bureau's 2008 Statistical Abstract of the United States.

These workbooks offer a real-data math adventure across the United States! You can use the workbook for your state along with other resources as a unit study about your own state, or your other favorite states. Meanwhile the students will also learn and practice place values, rounding, estimation, fractions and percentages.

There are 50 workbooks in the series — one for each state. Each workbook includes basic instruction and 80 practice problems. The problems can be used on grades 3-7; probably the best fit is for grades 4-6.

Since the activities teach both mathematics and social studies, many teachers and families enjoy using the workbooks to reinforce mathematics across the curriculum. Although the activities may be effectively used in a formal teaching setting, they are designed specifically for the independent learner.

Please see this page for a list of mathematical objectives in each of the books.

Math Teachers At Play - Sep 4, 2009 edition

Welcome to another edition of "Math Teachers At Play"! It is again a very engaging and interesting assortment of posts, so feel free to stay a while and relax. Thank you for everyone who submitted!

We'll start out in the early years of kindergarten. What happens when a research mathematician goes into a kindergarten class? Something interesting, creative ... and best of all, kids love it. Go check Sequences and Creative Math for Kindergartners.

Next in line, kids in the elementary school (grades 1-4) spend a lot of time with math facts. Consider the fun Joey-Joey math game to help them practice!

We advance to 5th grade. With "Math Buddy" you can explore Fractions as part of life.

"Discrete Ideas" presents The Shortest Path - or mental math multiplication shortcuts for all of us. As a tie-in, I provide a PROOF for one of those shortcuts, which could be used as an exercise in algebra class.

Next, we advance to middle school. Quadrilateral Property Combo Chart shows how the Number Warrior finally untangled the dilemma of explaining the relationships between the quadrilaterals.

Tom from "I Want to Teach Forever" offers us an Erasing Debt Activity with a printable activity sheet. This is based on real-life data (actually offers he's received in the mail), and can get students really engaged in comparing the various options for paying back a debt. For middle school on up.

And lastly, time for miscellaneous math teaching articles.

What is the shape of the Earth? Do you think it's a sphere (a ball)? John Cook from "The Endeavour" answers the question. He also submitted Three algorithms for converting color to grayscale. It actually sounds pretty simple!

Well, now we get off math for a bit. An urban, high school mathematics teacher rambles on about something annoying... but gives us a glimpse to the issues teachers face.
From "Math and Logic Play" we get The Woman, Dog, and Flea riddle.
A complex-sounding question has a surprisingly simple answer.

We end the carnival with something fun. Here's something that most of us have probably not tried... using SKITS to teach math! From "I Want to Teach Forever"...

Thanks for reading - I hope you enjoyed something! Here's where you can submit to the next carnival.

Math trick and its proof: square a number ending in 5

I will be hosting the blog carnival Math Teachers at Play next week. (You can send in submissions here.)

One submission I got about various multiplication tricks or shortcuts got me inspired to write a proof of the particular trick.

You could definitely use this in algebra class. First explain the shortcut or trick itself. Then ask students to prove it, or to explain WHY it works, using algebra.

You could also explain this to younger students as an additional "neat trick" and let them explore and play with it.

THE "TRICK"

If a number ends in 5, then its square can be calculated using this "trick" (I like to call it a shortcut because there's nothing magic about it):

Let's say we have 75 × 75 => Go 7 × 8 = 56. Then tag 25 (or 5 × 5) into that. You get 5625.

Let's say we have 35 × 35 => Go 3 × 4 = 12. Then tag 25 into that. You get 1225.

Let's say we have 115 × 115 => Go 11 × 12 = 132. Then tag 25 into that. You get 13,225.

Let's say we have 245 × 245 => Go 24 × 25 = 600. Then tag 25 into that. You get 60,025.

So, you simply take the digit or digits in front of the 5 and consider those as a number in itself. Multiply that by the next number. Then "tag" 25 to the answer you got in the previous step.

Photo by Lazy butterfly

PROOF

Any whole number that ends in five is of the form A + 5, and A is a multiple of 10. Since A is a multiple of 10, we can write A = 10b, where b is now some whole number. So, our number is of the form 10b + 5. Now, let's square it.

(10b + 5)(10b + 5) and we use the distributive property to multiply this out.

(10b + 5)(10b + 5) = 100b² + 50b + 50b + 25 = 100b² + 100b + 25

Now, notice those 100b's there. We can gather that as a common factor for the first two terms:

= 100 b (b + 1) + 25

This is now essentially in the form that the trick is using.

The trick says to take b, or the number formed by the digits in front of the 5. That corresponds exactly with our b! (For example, in number 645, b is 64. Our number 645 is 10b + 5, or 640 + 5.)

So we take b, multiply it by (b + 1) which is the next number, and also by 100, and lastly add 25.

Now, b × (b+1) is the part of the trick where you multiply the digits in front of the 5 by the next number. To "tag" 25 to those digits means you add 25 only after having multiplied the number by 100 so that it would end in "00". Once it ends in "00" you can add 25 (or any two-digit number) and it is the same as "tagging" 25 to the digits without the "00".

I hope this is clear enough.

By the way, I do not feel all students must learn this shortcut for finding the square of numbers ending in 5. It is a nice addition to one's mathematical knowledge, but not any necessity. However, it is useful as an algebra problem, and of course has been used as such over the course of centuries, I'm sure.

A math review or reference book for adults & students

I just stumbled upon the book Math on Call: A Mathematics Handbook:

Based on the reviews and from the "Look Inside" feature at Amazon it looks like a GREAT math reference book. I've been on the lookout for something like this, because I get emails from adults who want to review or refresh their basic math before going to college or some other course they're taking. So now I have something to refer them to.

The table of contents includes these chapters:

NUMERATION

• The Base Ten System
• Rational Numbers
• Irrational Numbers

NUMBER THEORY

• Factors and Multiples
• Powers and Roots

COMPUTATION

• Addition
• Subtraction
• Multiplication
• Division

ALGEBRA

• Algebraic Notation
• Properties
• Relations and Functions
• Equations
• Inequalities

GRAPHS AND STATISTICS

• Gathering Data
• Organizing and Summarizing Data with Statistics
• Displaying Data in Tables and Graphs
• Interpreting Data

GEOMETRY

• Elements of Geometric Figures
• Angles
• Plane Figures
• Solid Figures

RATIO, PROPORTION, AND PERCENT

• Ratio
• Proportion
• Percent

PROBABILITY AND ODDS

• Permutations and Combinations
• Probability
• Odds

ALMANAC

• Prefixes
• Suffixes
• Problem Solving
• Study Tips
• Using a Computer for Math
• Geometric Constructions
• Test-Taking Skills
• Handy Tables
• The Metric System
• The Customary System
• General Measurement
• Fraction/Decimal Equivalents
• Multiplication Table
• Square and Cube Roots
• Right-Triangle Ratios
• Prime Numbers Less Than 500
• Mathematical Symbols
• Number Patterns
• Number Systems

YELLOW PAGES

• Glossary of Mathematical Formulas
• Glossary of Mathematical Terms

INDEX

A total of 608 pages. I can hardly believe how good reviews it has!

I was unclear if Math on Call contained exercises or not, but I'm thinking not, since I didn't see anyone mentioning such in the reviews or the description.

Math Teachers at Play Carnival

There is lots of interesting stuff today at Math Teachers at Play Carnival #14 at Math Mama Writes. Quite a nice assortment - surely something for everyone!

I particularly recommend Three Applications of High, Abstract Math. We teachers can always use other ideas as to how mathematics is useful in real life.

Learn to recognize coins

Image by Stopnlook

In the past few days I decided it's time for my younger girl to start learning how to recognize coins and learn the cent-values of various coins. She's generally been doing kindergarten-1st grade addition and subtraction and I figured she's ready.

First, I got a pile of pennies, a pile of nickels, and a pile of dimes (no quarters at first). We played where I told her to make a certain amount, such as "Make 24 cents." She made it, I checked. Then she told me to make some amount. We just take turns.

It's like a game, and great fun for her! I figure it'll work the same with other kindergarten or 1st grade kids.

Since she did pretty good, I was able to introduce quarters the next day. I showed her that two of them makes 50, and we practiced making 62 or 58 or other such amounts that use 2 quarters.

Then I showed her a quarter and a nickel, and we figured out how much that was. That's always a difficult thing - to combine just one quarter with other coins. I soon asked her to make 30 cents, or 32 - and she was able to use the quarter and nickel combination to make 30 cents.

One important thing I've done is that I have deliberately NOT yet introduced the words "nickel", "dime", and "quarter". She's heard of the penny so much that she was fine with that. I want to scaffold the teaching so that we'll first learn the coin values, and later the customary names.

So, in essence, for now I've been calling them as "5-cent coin", "10-cent coin", and "25-cent coin". Has anyone else done that?

Review of Algebra Unplugged

Algebra Unplugged by Kenn Amdahl and Jim Loats is not a textbook, nor does it have any exercises. Instead, it is filled with verbose, often humorous explanations of algebra 1 concepts for those who would rather hear or read math explained in many words, instead of in a few symbols.

Algebra Unplugged also often explains the reasons behind some peculiar mathematical notations or terminology, and in general, tells the students WHY things are done the way they are done in your "Real Algebra Book".

Note: the cover image doesn't directly have to do with the contents of the book... the book is not about music, nor graffitis. I think it's just conveying the idea that just like musicians might "jam" freely after the practice, with this book you'll get to experience algebra "freely" after the class.

Excerpt:

The Associative Principle

Organizing your singers into sections won't affect how many are in your choir. Grouping them is creating associations. The associate law recognizes the benefits of confining your tenors to one easy-to-patrol area. Fifteen tenors in a corner is no different from fifteen scattered throughout room. It's just safer.

If all you're doing to a series of numbers is adding them, you can add them one at a time, or you can put them in groups, then add the totals of each group.

I certainly enjoyed reading through the book, and feel it can be very helpful for algebra students who feel "lost" and want to understand more thoroughly how to navigate in the maze of rules, symbols, terminology, and unknowns.

Here's another fun little excerpt to get you a "taste":

Why They Make You Factor

Factoring is, on the surface, a foolish waste of time. You will read many books and factor many polynomials before you have a clue why you are doing it. The next sentence in this book will save you two months of confusion.

We factor to take advantage of some neat properties of zero.

In addition and subtraction problems, zero is powerless. You can add or subtract zero to a number for the rest of your life and you won't change the number at all. But zero become an all-powerful super-hero once you move into the domain of multiplication.

When you multiply any number by zero, you get zero. A million times zero equals zero.

When you divide zero by any number, you get zero. Zero divided by a million equals zero.

But you can't multiply any other two numbers together and get zero. And you can't divide any other number by anything and get zero. If the answer to a multiplication problem is zero, one of the numbers you multiplied must also be zero. And, if the answer to a division problem is zero, your original numerator was zero.

That's why we factor.

By all means, click to Amazon and "click to look inside" the book to read some more and see if you like the style. I did - but I never know if others do, or if teenagers do.

The authors have definitely succeeded in keeping the conversation on a lighthearted level. They make light of mathematicians and mathematics and tenors (of course, some might not like that). The book often uses apples, bananas, rats, kangaroos, catbox, jabberwocky, etc. as variables, instead of always resorting to x, y, and z. The authors let Little Weenie Numbers show us the way when things get complicated (these are 1, 2, 3, 4, 5, 6 and other small, easy-to-handle numbers).

The only complaint I have is that the book could have given a bit more attention to graphing with more graphs and actual visual illustrations. The author Kenn Amdah confesses he is not a visual person, so that is why.

Check also for used copies. The book is listed at both Amazon and Barnes & Noble

The same authors have also written Calculus for Cats, a clear and entertaining introduction to the mysteries of calculus. It is written with similar goals in mind. It doesn't contain exercises. For some reason, the analogies to the world of cats didn't quite "jibe" with me as well as the writing in the algebra book. This doesn't mean that that book is not useful; it can be tremendously useful for people who feel intimidated or even dismayed by calculus. It just didn't feel quite as fun to read as the algebra book to me.

This book is also listed at Amazon and Barnes & Noble.

Multiplication Mountain songs CD - a review

It has been proven that music can help children memorize things. There is something about the music or the rhythm or both that changes or improves the way our brain works. I haven't studied this effect in-depth; I'm just familiar with the general idea.

So, using music to memorize math facts—or in this case, multiplication tables—is definitely a sound idea.



Multiplication Mountain is a CD by Hap Palmer, filled with songs for the multiplication tables. For each table, there is one song, but it is presented twice on the CD: once sung completely, and the second time without the answers sung. That way, the child can try to fill in the answers while listening to the song from the second track.

I found the songs to be pleasant and jolly, easy to listen to. The musical style varied somewhat so that one song was more jazzy, another was bluegrass, another a waltz, and so on. But they all were melodic, harmonic, and had a medium beat—easy to sing along. My favorite was the song for the sixes times table.

The songs are presented in a particular order: the easiest tables first. Learning all the tables is compared to climbing a mountain: you start at the bottom with the 2s, 5s, 10s, and 11s. You gradually climb up till you reach 7s as the top of the mountain — and then you reach for the sun (the 12s)!

You can listen to samples at www.myspace.com/happalmer (the songs for nines and twos) and at CdFreedom website.

Here's yet another sample of his music from YouTube. It's called Bean Bag Alphabet Rag. It's not from the Multiplication Mountain CD. I just put the link here in case you want to check out the musical and singing style of this artist.
Bean Bag Alphabet Rag by Hap Palmer .

Multiplication Mountain is not the only CD I have that has songs about multiplication tables. I have gotten one other CD in the past, but much disliked that one, because its musical style was rap with quite heavy beats - reminded me of heavy rock. Hap Palmer's music is quite the opposite of that, so I liked it much better (of course, all of us have VERY varying tastes of music).

My older child already knew the multiplication tables when I got the CD, so I could not test how much she would learn with it, and the younger one is not quite ready for that yet. But, in a nutshell, I feel the CD is well done and there is no reason why it wouldn't be effective in helping children to learn the tables.

I would definitely recommend it for anyone interested in trying musical approach to learning the tables and for elementary teachers & tutors in general. Also, if your child has ADD/ADHD or any learning disability, I would suggest that you try music-enhanced learning simply because of the special effect music has on our brain.

Here's a link to Multiplication Mountain CD at Amazon.com.

Disclaimer: I was given this CD for free to review it. I'm not receiving any monetary gain from the company, however.

Math Mammoth Grade 5 Complete Curriculum now available

163 pages
147 lesson pages


218 pages
179 lesson pages

5-A contents and samples
5-B contents and samples

Finally it is ready! I know some folks have been waiting for the 5-B part to get finished, and now it is here!

Math Mammoth Grade 5 complete curriculum consists of two student worktexts (A and B), a separate answer key for each, chapter tests and an end-of-year test, cumulative reviews, and an easy worksheet maker (Internet access required) to make extra practice worksheets when needed.

The two books (worktext part A and part B) for 5th grade deal with

• multi-digit multiplication and long division
• simple equations
• problem solving
• place value with large numbers and the judicious use of calculator
• all operations with decimals
• statistics and graphing
• all fraction operations
• geometry: classifying and drawing triangles & quadrilaterals; calculating the area of rectangles, triangles, parallelograms, and compound figures; surface area and volume of rectangular prisms
• introduction to integers
• introduction to percent

You can purchase the whole curriculum as a download, or as printed copies.

The downloadable curriculum is available at Kagi and at Currclick. The printed copies are made by Lulu (see links on this page, under the cover image).

Free e-books from Sylvan Dell

Sylvan Dell publishing is allowing the public to view for FREE their new line of ebooks.



These ebooks are animal-themed picture storybooks for children with beautiful illustrations and text. They can be used to learn language or science.

The neat thing is, they are bilingual (English/Spanish). You can switch the language while you're reading one page and it'll stay on that page. Plus you can have the book read to you (audio) in either English or Spanish.

Here is the link:
http://www.sylvandellpublishing.com/ebooktrials.php?e=MSBL9J

Click, and then click the button that says "Validate access code".

A Review of Mathletics

I have completed writing a comprehensive review of Mathletics website. It is an online math practice system for K-12 that includes:

• a regular "curriculum" section where you practice various kinds of math problems;
• a Live Mathletics section where you race with math problems against other kids around the world;
  
• Rainforest Maths - a separate website filled with math activities; and
  
• a parent center with yet more resources such as printable workbooks and videos.

Mathletics is a subscription service, but it offers a lot! Please read my review and see screenshots.

Escher's impossible staircase

Most of us have seen the picture of Escher's paradoxical staircases - but today I saw a model of them built of Legos! Go see it - it's just cool!

Carnival

Go check out Math Teachers At Play blog carnival at Math Mama Writes. There are lots of enjoyable posts there - I'm still reading through!

Sticker Math Fun (K-2)

When I was a kid, my mom sometimes bought my brother and me activity books to fill up our summer time. Well, if you're into activity books, here's a Sticker Math Fun by Usborne that I can recommend for summer math learning and practice (grades K-2) (or for later in the school year as well, for that matter).

It has different mathematically-sound activities for addition, subtraction, beginning multiplication, fractions and clock, mostly on about 1st grade level but some for kindergarten and some for 2nd.

It is filled with quite variable and creative activities, and not just dull simple adding and subtracting. The activities include missing addends or subtrahends, number patterns, finding numbers that add up to a certain number, and so on.

It is in full color with kid-friendly imagery.

We bought this book several months ago, and I can say my kindergartner-1st grader has really enjoyed the book! And the third grader has wanted to do several pages as well.

The normal price is $15, but this morning when I checked, you can get copies from Amazon marketplace sellers for less than $5 (with shipping)! Go check it out!

Office furniture giveaway

Here is your chance to win a piece of office furniture in this little giveaway contest:

• First go check www.csnOfficeFurniture.com website and find a piece you'd like to have if you are the lucky winner. It needs to be $135 or less in value.
  
  
• Then, to participate, purchase any of the Math Mammoth or Make It Real Learning products at Kagi store between now and July 9, 2009.
  
  
• In the comments field on the order page, put either the name of the piece of furniture you'd like to win or the URL to its web page. If you leave this comment field blank, I will not know that you wish to participate, so it is crucial!
  

That's it! I will have a random draw for ONE winner within the participants, and put you in contact with csn Office Furniture company. They will pay for the shipping within United States.

Links you might need:

• www.csnOfficeFurniture.com to check what piece of furniture you'd like to win


• Math Mammoth Blue Series information and order page


• Math Mammoth Golden Series and Green Series information and order page


• Math Mammoth Light Blue Series information and order page


• Math Mammoth discounted packages / CDs information and order page


• Make It Real Learning workbooks information and order page.

Math Teachers At Play #10

Welcome to the tenth edition of Math Teachers At Play blog carnival! Here with the heat of the summer, "less is more". We concentrate on teaching issues, but also get to "play" a bit with binary numbers, geometry, integers, and an optical illusion.

TEACHING

What's a math teacher going to do with Wolfram | Alpha ?



In case you haven't heard... Wolfram|Alpha is a new, computational search engine. And if you're a math teacher, you should be aware of it.

Collection of Web Freebies discusses Wolfram|Alpha as your Personal Free Online Math Assistant.

I wrote an introduction to Wolfram|Alpha as well. I feel it can both be a benefit and a drawback to math education - a benefit because it can free us from routine calculations, and a drawback because students still need to learn to do those, but how can you easily enforce that?

W|A presents a dilemma to math teachers... because it can solve SO MUCH. It can solve just about any routine type calculation in algebra 1 or algebra 2 or calculus courses. So what can a teacher do? Jason, The Number Warrior wonders how we can be Teaching to the Limits of Wolfram Alpha. In essence, should teachers strive to find problems that cannot be solved with Wolfram|Alpha?


What's a math teacher going to do with homework?

Photo courtesy of Vicki's pics

Another, an age-old, dilemma for math teachers. What is the best way to assign, grade, and check homework? Sam Shah conducted an unofficial survey on the matter and presents the Homework Survey Results.

I glanced over the survey results, and found one response that really "struck" me as a "sweet" solution to the homework problem. It is from a 5th grade teacher, and I apologize for taking so much space for it here but I just feel it was really good (and if the person feels I shouldn't quote this, please let me know). Emphasis mine:

"I work hard at the beginning to set up a culture of responsibility for themselves. They are responsible for making sure they understand, for asking questions, for asking for more practice or another example.

When we come into class, we check the answers together. I will solve a problem or two on the board that I have learned over the years is confusing. Other than that, I expect them to ask for clarification if a problem is wrong.

They "grade" their own. If it's wrong, they are expected to take a minute right then to figure out why it was wrong. Usually it's a silly mistake. If not, they bookmark it to ask questions during our next work time.

I don't give any grades. I don't assess it. The final test/quiz is their grade. The homework is just them figuring out how to do the skills. They know they won't be graded on it. They know they won't be penalized for getting it wrong. They know that the whole point of the homework is to figure this math stuff out. If they get it wrong, they know they haven't mastered it and need to get help.

On the opposite side, if a student doesn't do their homework, I don't get too upset. We have a talk about how they hurt themselves, because now they don't have an accurate measure of if they can do it on their own. I can't help them because they didn't get the opportunity to make their mistakes before the test. However, I have a few who don't need to do homework. They still earn A's on the final test. They learned it by being in class and paying attention.

With those who obviously do need the homework practice, but aren't doing it, I problem solve that on a case-by-case basis.

It changes the whole culture of learning and mastery in the classroom. But it is VERY important to set up that culture at the beginning."

Now, I'm not claiming that middle and high school teachers could easily transfer these ideas to their classes... but perhaps they can, at least somewhat. Please discuss homework at Sam Shah's post.

A teacher's problems do not end with homework. Can you believe that TEACHING as a profession is so difficult in today's world that sites exist solely to help new teachers to SURVIVE their first year? That's exactly the word that is used. Teaching Degree.org has compiled a list of 100 Helpful Websites for New Teachers, and the list includes new teacher "survival" sites, teacher video sites, freebies, inspirational sites, and several other categories as well.

Some Math As Well

At Exploring Binary blog we find an EXCELLENT way to explain binary numbers that he found when he taught his mother binary numbers . It's true, once you struggle at explaining a concept to someone who's not a math whiz, you really get to the brass tacks of the matter.

Denise from Let's play math! has some geometry challenges for us, some of which are from ancient Egypt. I solved the puzzle under the title "Can You Explain This?", using fractions (and not avoiding them as it tells you to do). I also pondered number (2) but couldn't find an immediate (easy) way to find an answer. I don't think she ever posted answers to those.

John Cook from The Endeavour blog shows us an optical illusion that is so fooling that I couldn't believe my eyes at first. Quite amazing. He also makes an analogy from the optical illusion to a "mathematical" illusion within his own work.

Dr. Jeff is asking us to fold a humongous piece of xerox paper and see how many folds reach to the top of mount Everest or the sun, among other things. You probably won't believe the answers!

If you're into 5th-7th grade math, please check also my videos about integer subtraction.

---

This is where to send your submission for the next carnival on July 10th at Math Mama Writes. Happy summer, everyone!

Wolfram|Alpha is here

Wolfram|Alpha is a new, computational search engine. If you do a query where the answer has quantitative data, Wolfram|Alpha probably gives it.

For example, try enter your last name. Wolfram|Alpha gives you information about the popularity of that name. For example, "miller" ranks 6th within the US and there are about 1,128,000 people with that surname.

Enter a first name, and it will even give you a graph showing the name's popularity over the years. I just found out that Cindy's popularity peaked in about 1960. No wonder it is a common first name among the mothers who ask me questions about their children's math education.

Enter a town - for example Houston, and see what information comes up.

But, the reason I'm writing this post is because Wolfram|Alpha (or Walpha as some called it) especially excels in mathematical queries.

This has implications to mathematics education, especially in high school and college. This tool is completely free, easy to use, and accessible for everyone with an Internet connection (even with a smart phone). Just imagine if you are a math teacher and you assign homework for your 9th graders, "Find the equation of the line that goes through points (2,5) and (-8, -9)." W|A does it in a split second.

It also solves equations. For example, Solve ln(x)+ ln(x-2)+ ln(15). It even gives you the solution steps - just click on "show steps".

Please see a full list of examples of what Wolfram|Alpha can do in mathematics.

While W|A easily computes a lot for the elementary algebra or calculus student, it doesn't stop there. Look at the examples for elementary mathematics given on the site. It also acts as a fraction and percent calculator. Granted, normal calculators do those as well.

So, what is a teacher to do? Will a lot of the content in high school and college math courses suddenly become obsolete?

Now, Wolfram|Alpha is not what started bringing technological tools into classroom. That trend has been here for a while (think graphic calculators, computers). However, it is an extension of the trend that makes the computational tools more easily accessible and available to nearly all students.

I see Walpha both as a benefit and as a drawback.

- BENEFIT: Teaching can focus more on the concepts and less on tedious calculations, since practically all students will have a tool they can use for computations and graphing (all you need is a computer with an Internet connection or a smart phone). Students could be given more problems of the type that require thinking and problem solving, and less of the mechanical calculation problems.

- DRAWBACK: It is a fact that one cannot adequately learn mathematics without also learning many of these "mechanical tasks", such as how to find the slope of a line when given two points, or how to graph a parabola from its equation. If these skills were totally skipped, students wouldn't be prepared for the next mathematics course where such knowledge is needed. So, teachers cannot skip those topics and need to enforce student learning in such a way that cheating with Wolfram|Alpha cannot happen (putting such problems in the test).

Actually, I'm not so sure if W|A will change the actual teaching so much, because many students have already been having graphic calculators, which do similar things as W|A. I wonder if the biggest change it brings along is a decline in the sales of graphic calculators...

Read also what others have blogged about W|A :

Impact of Wolfram Alpha on Math Ed

Wolfram Alpha is up and running

Wolfram|Alpha and the shrinking future of the graphing calculator

Walpha Wiki discussion