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Why Learning Long Division is so Important

Long Division Calculator

There are many milestones on the road through grade school math, but one in particular marks an especially significant destination. It’s the motherlode of arithmetic, a recipe with so many of the previous numerical ingredients from so many previous grades, a mountain of math skill awaiting its ascent, a task requiring the flexing of a mixed metaphor of mental muscles like no other.

And also, the one thing that strikes terror into a math-phobic 4th grader’s heart like no other.

Long Division.

But does long division really need this huge build up? Is it really that much more difficult than, say, multiple-digit multiplication? Yes and no.

Long division is certainly a test of many different skills, but they are all ones that have been should be largely rote by the time long division is introduced. I believe the main issue that brings tears and seizures when long division pops up is essentially a lack of confidence in basic math facts. Learning the long division algorithm is a little daunting, but it’s a small step if the prerequisites are truly mastered. And to that, let me just say it again… Drill, baby, drill.

That said, why is long division such an important rite of passage?

The four basic steps in long division (partial division, multiplying, subtracting, bringing down) all incorporate concepts ranging from basic operations and place value to simple numerical algorithms. These skills mimic a lot of what later, more abstract, math looks like. I’m staring at you algebra, hiding there around the corner.

Long division is the arithmetic skill that most closely resembles the mechanics of tasks in algebra, trigonometry, calculus and more. It requires doing several basic operations in a particular sequence, thinking about their results, trying intermediate solutions (especially with multiple digit divisors), backtracking and hopefully making sense of the process along the way.

This makes long division not just another skill to learn on the journey… It’s the first step down a completely different road.

Of course I wouldn’t be a good dad if I didn’t offer directions! I’ve had a collection long division worksheets with detailed answer keys on the site for quite some time, and they’re actually some of the top ranked math worksheets on the web.

I’ve also just created a long division calculator, and it’s one of the best teacher resources I’ve built on the site in a long time. Enter a divisor and a dividend, and it will work the problem in front of you, with remainders, in real time, and it provides guides that show where all the numbers come from. Trying to get across where that intermediate product comes from in that jumble below the problem? Watch the calculator run its course, then put your mouse over the digit in the quotient to highlight it and the product. It really is useful and it was a lot of fun to build….

Long Division Calculator

I hope you’ll give it a try yourself and share it with anyone you know that’s learning or teaching long division… It’ll go a long way towards paving that road towards future success in math.

Getting Ready for Multiplication in the New Year


As the end of the year closes in on us like the narrow end of a very pointy trapezoid, it’s easy to let your thoughts slip to holidays, presents and all things calorie laden… But for those of us with younger grade school kids, some might contemplate the beginning of next year when many schools kick off their math fact programs with real enthusiasm.

Now I’m not proposing stuffing stockings with multiplication flash cards, which I’m sure is barely a step above a lump of coal… But a little math prep over the holidays may be just the boost our young Euclid’s need to start the new year off with some extra confidence.

It’s easy to lose track of how difficult memorizing the multiplication facts can be. There are strategies of course, and we all seem to rely on memory tricks for a span of time, like the ones I’ve highlighted in my rules for learning multiplication post.

But if you need an in depth perspective, I found this article really reminded me of some of the mechanics that we went through learning these facts ourselves. We may not want to continuously assess our kids in one of nine different phases of the process (I’d be needing something special in my eggnog if I was a teacher trying to follow this particular program program rigorously with 25 or more kids, for sure), but it does highlight how complicated the learning process really looks under the hood of the sleigh, as it were.

In the end, though, frequent readers know my thoughts… Keep drilling until your student has the facts down hard, cold and fast. Then, stuff them full of cookies, because math is hard work, and nothing says “Good Job!” like something with frosting and sprinkles. Here are some links to some multiplication worksheets to get you started…

Multiplication Worksheets

Fact Family (Mixed Multiplication and Division) Worksheets

Finally, for you clever folks out there looking for a little brain exercise to work off those Hershey’s Kisses that I think were supposed to be kitchen decorations in that little candy dish, but, they taunt me, oh, how they taunt me… Anyway, here’s a quick 12 question quiz for your inner 8th grader to mull…

Are You As Smart as an 8th Grader?

Multiplication Worksheets Updated

Learning multiplication is one of the big milestones in learning math. I’ve touched on it before and I imagine this won’t be the last time either. Your school may be using Mad Minutes or Rocket Math or similar timed drills to teach multiplication, but no matter how you approach it, learning multiplication is about worksheets. Lots and lots of multiplication worksheets.

This summer marked the start of teaching my youngest daughter her times tables, and even with the all the earlier worksheets on the site, we managed to identify a few gaps. Here’s a breakdown of the strategy we’ve been using and a link to our new favorite worksheet…

  • Master Dad’s 8 Rules for Learning Multiplication These sheets build the basic skills necessary to figure out the answer to a multiplication fact if it isn’t memorized.
  • Fill in a Multiplication Grid Worksheet at the start of big practice sessions. This can be used as a “cheat sheet” if necessary, but it also helps get some of the facts straight before the pressure of a timed test.
  • Drill with comprehensive worksheets. The current favorite is a new one we just added: 100 Problem Multiplication Worksheet, No x0, x1 or x2. Versions of this worksheet basically has all the easy multiplication problems stripped out, so it’s a great exercise for mastering the facts.
  • When we uncover specific multiplication facts that are giving us problems, we either use the Spaceship Math pages or the Conventional Multiplication Series worksheets to reinforce the problem fact.

Regardless of how you approach it, the site here has a a number of different worksheet series to help you. In addition to the new sheets without 0, 1 and 2 mentioned above, you can find new two minute practice worksheets in the conventional multiplication series at the link here…

Conventional Two Minute Multiplication Worksheets

If you have an idea for worksheets, leave a comment here, or if one of these is working well for you, consider giving a Google “+1” click under the logo above so other multiplication seekers can find success here as well!

Hope your summer vacation has been great!

A Guide to the Division Fact Worksheets

Well, the new school year is officially underway. We touched division last year briefly, but fourth grade here is where we need to get our division facts down cold. Of course, the goal is working up to those long division worksheets but to get there, you really need to establish a solid grounding in the division facts first.

Unfortunately, division isn’t just multiplication in reverse. Oh yeah, we tell them that and it flies for a while, but then one ugly left over spoils the fun. Remainders. You only get so far into division before this remainder thing pops up, so if you arm your kids with only the “reverse the multiplication” strategy, division quickly develops a reputation as the nightmare operator. We relied heavily on the idea that addition and subtraction had “fact families” and you could always reverse them, but that clean relationship just isn’t there for multiplication and division. I mean, what’s the corresponding multiplication fact for 5 / 2 = 2 r 1 ? 2.5 x 2 ? We don’t get closure here until we’ve introduced fractions and decimals… Perhaps division’s reputation as a monster is a bit deserved. Either way, this post describes the various sets of division worksheets on the site to help you introduce division and remainders successfully.

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Over 300 New Number Pattern Worksheets!

Number patterns are a great way to revisit basic addition and subtraction operations in a different format from the usual math drills. They also illustrate some interesting relationships like 15 minute intervals in hours, intervals of 25 in dollars and the ever-useful mechanics of multiples-of-five that seem to show up in every day life.

It seems like number patterns are increasingly appearing on things like AIMS tests and other placement exams. Include a healthy does of number patterns in your regular worksheet diet and pattern problems will be like striped candy. Or, so I keep telling my eldest.

New number pattern worksheets can be found at the link here…

Number Pattern Worksheets

…or under the ‘Worksheets’ menu to the right.

UPDATE! Additional worksheets involving negative numbers, including patterns that cross zero, have been added in their own section…

Negative Number Pattern Worksheets

An Overview of Spaceship Math

Rocket Math Rocket

Welcome to the Rocket Math Spaceship Math home page at  Below you’ll find direct links to the Spaceship Math practice worksheets for all of the basic operations. Also, you’ll find a convenient web-based timer for administering practice tests.

Everything you need to rocket your kid’s math performance straight into orbit is below. If you find these materials useful, be sure to check out the rest of the math related content on the site. Good luck!

Please note that Spaceship Math is not the official RocketMath curriculum offered by R&D Instructional Solutions, and as per Dr. Crawford’s request in the discussion below, we’ve renamed the practice worksheets here as ‘Spaceship Math’ to avoid any confusion with the RocketMath commercial product.  Educators interested in using Rocket Math in their classrooms are encouraged to check out for details.

Spaceship Math Strategies

Click Here

Spaceship Math Addition Worksheets

Click Here

Spaceship Math Subtraction Worksheets

Click Here

Spaceship Math Multiplication Worksheets

Click Here

Spaceship Math Division Worksheets

Click Here

Spaceship Math Practice Timer

Click Here

Printable Spaceship Math Progress Check Off Pages

Rocket Math Strategies

Rocket Math Rocket

Many grade schools now using various types of timed tests for basic arithmetic. This web site was originally created to provide practice worksheets for a time testing program used at a local school district. If your child’s school is using a similar program, these worksheets will provide several variations on the single practice sheet that typically comes home for each lesson.

The Rocket Math programs are typically divided into multiple levels usually identified by letter, where each level introduces a small number of basic facts. The problems on each level are built on the The tests are usually given daily, with each test lasting one minute. Practice on the problems is pretty critical to success, especially if your child isn’t one that works well under the pressure of the clock.

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Dad’s Strategy for Learning Multiplication

Rocket Math Rocket

Learning multiplication facts is a challenge because it’s the first math operation where your child needs to contend with relatively large numbers. Two digit addition and subtraction is squarely in the realm of numbers less than 20, which is familiar territory. There’s something concrete about 12 or 15 or similar numbers countable on fingers and toes, but 73 really is a big step out of the pond.

There’s two ways to approach this. One is just brute force memorization. I remember endless flash card drills after school, the timed tests in the classroom and the gradual accumulation of resentment towards anything with that little ‘x’ attached to it. While we love the Rocket Math program the schools use here, it is largely just memorization and could use something to back it up.

The other alternative is to make multiplication something of a game, with systems for some of the numbers. There still an inevitable amount of memorization that goes on, but by getting 90% of the multiplication table down to a few simple rules, the goal is suddenly within everyone’s reach. Split second, memorized results are still going to come, but having some means to reach incremental (albeit slower) success takes the fear and dread out of the process.

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Dad’s Eight Simple Rules for Mastering the Times Tables

Rocket Math Rocket

If you have memorized your addition facts, you can master the entire multiplication table in minutes by learning the eight simple rules below. You only need to memorize the ten facts in Rule #8! Follow the link at the bottom for the full strategy!

Rule #1:

First Number Times Second Number is the Same as Second Number Times First Number

Rule #2:

Any Number Times One is that Number.

Rule #3:

To Multiply by Ten, Attach a Zero.

Rule #4:

To Multiply by Two, Double the Number

Rule #5:

Multiplying by Four is Doubling Twice (Double-Double Rule)

Rule #6:

Multiplying by Five is Just Counting by Five

Rule #7:

The Nine Rule – Tens is Number Minus One, Ones is Nine Minus Tens

Rule #8:

Memorize the Ten Remaining Facts

3 x 3 = 9 Three times three is so fine,
three times three is nine.
3 x 6 = 18 Three times my bird ate six beans, three times six is eighteen.
3 x 7 = 21 Three candies each for seven days, that would be fun, three times seven is twenty-one.
3 x 8 = 24 Three boys on skates fell on the floor, three times eight is twenty-four.
6 x 6 = 36 Six dogs with six sticks, six times six is thirty-six.
6 x 7 = 42 Sticks from heaven, stuck in glue, six times seven is forty-two!
6 x 8 = 48 What do we appreciate? Six times eight is forty-eight!

Flight Six Times Eight! Don’t be late! Leaving at gate forty-eight!

7 x 7 = 49 Seven kids in seven lines, add ’em, up its forty-nine.
7 x 8 = 56 Five – six – seven – eight, Fifty-six is seven times eight.
Seven packs of gum, each with eight sticks. Can you chew fifty-six?
8 x 8 = 64 Eight times eight is sixty-four, close your mouth and shut the door!
Had two eights, dropped them on the floor, picked them up, had sixty-four.

Eight Simple Rules for Mastering Multiplication: The Full Strategy!

Multiplication Worksheets

Worksheet Practice Timer