Kiss those Math Headaches GOODBYE!

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Algebra Survival Guide — Second Edition — Fresh Off The Presses!

Algebra Survival Guide — Second Edition
by Josh Rappaport
illustrated by Sally Blakemore

The Algebra Survival Guide — Second Edition is here, but not yet released to the general public. Now’s your chance to order it at a 25% discount through April 10th. Just go to

But first, let me tell you about what’s new … a massive, 62-page chapter on advanced story problems.

It’s no secret that algebra gives students the ‘jitters,’ and word problems give them the ‘shakes.’ As a dastardly duo, the word problems of algebra are just about as nerve-wracking as anything in the teenage years.

The Algebra Survival Guide — Second Edition takes a hard look at algebra’s word problems and offers time-tested advice for cracking them. With a new 62-page chapter devoted to these word problems, the new edition tackles the ultimate math nightmares of the puberty years: problems involving rate, time and distance, work performed, and mixture formulas, among others. Added to the pre-existing 20-page introduction-to-story-problems chapter (in the Algebra Survival Guide — 1st Edition), it’s like having a book within a book.

The Algebra Survival Guide — Second Edition also includes:
  • 12 additional content chapters that explain fundamental and advanced areas of algebra
  • a unique question/answer format so students hear their own questions echoed in the text
  • conversational style written in the voice of a friendly tutor
  • step-by-step instructions
  • practice problems after each new concept
  • chapter tests
  • an expanded glossay and index
  • lively illustrations by award-winning artist Sally Blakemore
Finished Spit Fire
The many cartoons not only provide well-deserved comic relief for math learners, they also offer a visual way to grasp algebra’s challenging abstractions. Example: The above cartoon illustrates a real-world mixture problem by showing different percent concentrations of paint.

With all of these features, the Second Edition Algebra Survival Guide is ideal for homeschoolers, tutors and students striving for algebra excellence.

The Second Edition also aligns with the current Common Core State Standards for Math, so it’s ideal for today’s teachers, as well. Its content chapters tackle the trickiest topics of algebra:

Properties, Sets of Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, and the Coordinate Plane.

So, have some fun learning algebra!

• Updated version of Josh and snake



Here’s the problem —

Al’s Discount Clothing store is trying to entice customers with a

special “20-40” Percent Sale.


Here’s how it works. For all sale items, the Al’s

first takes off 20%. Then the store takes an

additional 40% off the sale price.




a)  How much is the discount, under the terms

of this sale, for a bundle of clothes with retail

value of $250?


b)  How much would the discount be if Al’s had

just run a straight 60% discount sale?


c)  Why do you think that Al’s is running the

sale in this way?


Send replies to:

Make the subject:  POTM


Well, my obsession this summer turns out to be knives.

But don’t get any wrong ideas. When I say knives, I mean knives for whittling and wood carving. That’s the true obsession. But knives themselves are a pretty close second. I am a guy after all.

In getting obsessed with knives, it’s impossible not to get obsessed with that critical aspect of knives: sharpness.

If you’re a guy, you already understand how this could be an obsession. If you’re not — and you don’t get it — just do a Google search for “sharpening knives.” I mean, there’s almost as much stuff on sharpness as there is on, say, wrinkle cream. Well, at least one-tenth as much!

So you’re probably wondering by now why a guy like myself, who’s really into math, would be writing about knives and sharpness. 

The reason has to do with that concept: sharpness. As I’ve been poring over websites about sharpness and then buying and sharpening my own knives for hours on end, to the point where there’s hardly any knife even left, I’ve had some time to think about the sharpness of knives and the sharpness of minds. Those two words rhyme, so take a second look:  knives and minds.

As I’ve been honing and polishing away, I’ve been wondering how much use algebra is for most kids, and I’ve come to the conclusion that for most of us, algebra itself is not really of that much “use.” I mean, c’mon: how many of us — other than engineers — use algebra on a daily basis. Even I don’t! But, what I’ve also realized is that algebra is kind of like a sharpening stone, and our minds are like the knives.

By doing math like algebra, geometry, trig, analytic geometry, and calculus, we are sharpening our minds.

So even though we don’t use these math topics every day, we make our minds sharper and sharper for any occasion when we use numbers.

It might happen when we (when we’re not sharpening our knives) are planning out our garden. We can use math to figure out how much space our rows of carrots will take up when we follow the directions and plant the rows 1.5 inches apart. Or it might happen when we are buying a car and we’re trying to follow the interest and the payment info. 

If we have sharp minds, we can do this stuff with relative ease. We can cut right through it, almost with a joy of power. If we have dull minds, we might just “guess-timate” or leave it up to the car financial guy. Whoa! What a mistake, huh!

So keep on sharpening those minds … and knives. It will pay off, even if you don’t do this very kind of math today or even tomorrow. Numbers are all around. There are all kinds of opportunities to put those sharp minds to good use.

Math + Questions = Life

If your math class is snoozing, try exploring the paradoxes that math touches on. One way is to just listen carefully to student’s questions, and see if there are any “big ideas” hidden in the question. Here’s an example of such an experience.

Recently I was tutoring a girl on the concept of rounding off decimals. This might sound dull, but this girl asked a question that, if you think about it, touches on the concept of infinity.

The student was looking at the number line and noticing how her textbook enlarged one small segment on it to display the problem, which was to round 2.72 to the nearest tenth.

The textbook’s number line took a “magnifier-approach,” blowing up only the section from 2.7 to 2.8, but showing all of the hundredth’s places in between.

The girl took a hard look at that and said, “So couldn’t you also take the space between something like 2.73 and 2.74, and blow that up?”

I asked her to explain. She said that if this smaller space were also ‘blown up’ or expanded, the new number line would display even smaller numbers, like 2.731, 2.732, 2.733, with 2.735 in the middle.

I told her that you could do this.

Then she asked, “Couldn’t you go even further?” Meaning, it turns out, can you then take an ever smaller part of the number line, such as the space from 2.731 and 2.732, and blow up that space?

I said you could.

She said, “Can you just keep doing it forever?”

I said you could.

She paused, then said:  “I just don’t get that idea of ‘forever.'”

That was the moment …

I said it’s a hard idea to understand forever. But it’s an interesting thing to think about. I didn’t mention it to her, but later I realized that this 4th grader was essentially intrigued by the same question that captivated the mathematician/philosopher Blaise Pascal back about 300 years ago. Namely that humans are surrounded by two different infinities:  the infinity of hugeness and the infinity of smallness. For more on Pascal’s words on this amazing matter, see

In any case, following this girl’s thought led her and me into a whole discussion about forever and infinity and the edge of the universe, and the conversation would have literally gone on “forever,” but eventually it was time to stop.

In our daily attempts to teach math we sometimes neglect to mention that math touches on the infinite, as an asymptote approaches a curve, you might say. Taking time, once in a while, to explore the infinite can make your class or tutoring session come very much alive.

And if you’d like to see a book that encourages “edgy” math questions by both students and teachers, check this out:   It’s a book devoted to generating and listening to startling math questions. And it shows how these questions take a jackhammer to old musty classrooms,  letting the light of curisoity and exploration get their day in the sun.