Practice Sheets

(The sheets are at the bottom of this page. But first, a word from the "sponsor":)

Why these sheets? Because in order to do well at math, you must be fluent with your arithmetic skills—that is, being accurate is not enough—you must also be fast. Without fluency, without being able to come up with the correct answers instantly, without knowing them "even without thinking about them", you'll not be able to easily acquire higher level skills. For example, if you're having trouble with factoring, don't waste time doing more factoring problems until you master addition, subtraction, multiplication, and division. (Yes, there are MANY adults who do not know their multiplication tables—or even their addition tables—very well!) Once you master the first skills, you may find that you no longer have any trouble factoring—without even practicing that.

Suppose you want to factor the quadratic equation x² +15x + 56. If you know the addition and multiplication tables well, you will immediately see that 7 + 8 is 15 and 7 x 8 is 56 — and you will know the factors — (x + 7)(x + 8). If you do not know those tables very well, you're going to have a hard time factoring—and neither an expensive calculator nor doing more factoring problems will be able to help you. What may happen is that you'll soon not be doing well in math, then you'll start feeling you're not a "math person", and soon you will hate math. But really, you can be a "math person"— you just need to learn the "language" of mathematics. (After all, imagine going to school in a foreign country where you were not fluent in their language—how could you learn?

In addition, research has shown that there are other benefits to fluency; for example, high fluency leads to better retention (you'll remember better), and better resistance to stress (you should do better on tests).

On the lower-level skills, you should shoot for at least 50 correct answers per minute. Some people can do far more. Unfortunately, some people can only do far less. You can quickly bring these skills up just by practicing a few minutes every day. (See how many you can get correct in a minute—if you do that twice, that's only two minutes per day!) When you get fluent on the first sheets, move up to the next ones. But don't try the next skill until you are fluent in the previous one.

Graphing your results day by day will help you to see how you are progressing. You should graph your correct-per-minute scores and your incorrect-per-minute scores on semi-log paper. If you can't find it, though, use whatever you have. "Precision Teaching" usually includes plotting your results on a semi-log plot sheet of standard form. Then the shapes made by the lines on your graph will tell an experienced Precision Teacher not only how fluent you are becoming, but help diagnose any errors in your learning.

There is a traditional sheet, called the "SCC", for charting your progress. But I like the Giroux-Crow sheets better—they seem more "open" and less confusing to most people starting out. I like the green one the best; it's easier to see the pencil marks on them. (But, of course. you have to use all that color ink!) You may prefer the black-and-white ones. You can print either—or both—from here:

The black-and-white version The green version
And here's more about them, from their designers:
The FAQ

You can also get other types, including Stuart Harder's computerized chart, from Stuart Harder's web site .

If you go to my home page, you will find several links where you can learn more about Precision Teaching -- and get more free resources.

Would a few minutes every day be worth it to make math easier? Well, if you bring your skills up, you will be rewarded with a much easier time in your math courses! (You might even begin to like math—fancy that!) /

As it says on one of my colleague's office door:
MATH IS NOT A SPECTATOR SPORT!
—so like any athlete, practice!

And finally, now we get to the free...

Math Practice Sheets

The following FREE sheets are meant to be used in Precision Teaching "sprints", but will be useful in most arithmetic and mathematics courses as well. People can use them as diagnostic tests to check their abilities. (You may be horrified—even many college freshmen are terrible!) Usually it's best to start at the addition and subtraction sheets for diagnoses, then move up sequentially. However, if there is any question about ability to read and recognize digits, try using the first pages—have them said aloud.

I'm still working on these. They are now updated automatically—they are generated by programs that change the numbers every minute. If you refresh the page and print again a minute later, you'll have a new, original sheet to use.

If you have suggestions, comments, ideas or wants for new sheets, let me know at red@sarna.org.

I want to work on formatting more, but that's hard because each web browser has its own idea of how things (like sheet size) should be. (For browsers, I have Firefox, Google Chrome, Opera, Konqueror, and Lynx. If you have a different browser and things don't work well, let me know what you have and what's happening.) Because of the differences, I have to work to the lowest common denominator. (Math pun intended!)

That's not the way the web is supposed to work—look at this quote from its inventor:

"Anyone who slaps a 'this page is best viewed with Browser X' label on a Web page appears to be
yearning for the bad old days, before the Web, when you had very little chance of reading a document
written on another computer, another word processor, or another network."

—Tim Berners-Lee in Technology Review, July 1996

Let me know what you want added. red@sarna.org