I hope all of you have had a great summer! If you’re just returning to your math drills for the school year, I hope you’ll notice a big change around here at DadsWorksheets! I’ve been busy updating our worksheets starting with switching to PDF files, and I have done a lot of work to give them a more modern look and feel…

I’m especially pleased with the fraction worksheets that I just finished… Not only do the new worksheets look amazing, but the answer keys show work with more clarity, adding a few extra steps to the computations to make some of the problems a little easier to understand. You’ll especially appreciate this when working with the multiplying fractions or dividing fractions worksheets solving those problems can have many steps.

As always, these worksheets show you how to cross-multiply fractions where necessary to get the answer. Cross multiplication is difficult to explain, but having fraction problems that illustrate the steps in the key can be a huge help for kids trying to see where their computations went wrong (or, if you’re an adult, I can tell you from experience they also come in handy more than you might think!)

If you’re starting 3rd, 4th or 5th grade, now’s the time to start learning fraction concepts and these worksheets are a great place to start… I hope you’ll print a few out and let me know what you think in the comments section below!

Reducing Fractions Worksheets
Comparing Fractions Worksheets
Adding Fractions Worksheets
Subtracting Fractions Worksheets
Multiplying Fractions Worksheets
Dividing Fractions Worksheets

And if you find yourself doing (or explaining) lots of fractions problems, be sure to check out my visual fraction calculator…

Fraction Calculator

It’s another great tool for explaining fraction problems and seeing how to solve them!

A hundreds chart? If you’re wondering why, for good gracious, you’d use one of these to teach counting, or even multiplication, you definitely won’t by the end of this post.

If you’re like us, you probably spend time in the car counting over and over again to 100. After having gone down this road (and many many miles of it with four girls now), I’m starting to believe it’s like staying in only one lane of the highway on a road trip to Puerto Williams, Chile (which, for reference is the southern-most city in the world, and I’m not sure you could even get there by car even if the math worked out somehow.)

So what’s wrong with counting, you ask?

When the kids learn to count orally, they’re often just learning a pattern of words, almost like a song. Oral counting is great, as long as there’s a mental model of number sense to back it up.

That’s where these awesome hundreds charts come in.

Printable Hundreds Charts

A hundred chart provides a visual representation of both quantity, and of the relationships between the numbers in the rows and columns of the chart. You’d be amazing how many kiddos can recite the numbers from one to a hundred in order, but when they’re confronted with reading a number off a page have trouble. We struggled here with the difference between 41 and 14 more times than I care to admit.

So print off these hundred charts, then start with some activities that build real number sense. Here’s a list of things to try:

• Play the ‘Guess My Number’ game on the hundreds chart.That simple higher/lower game is great practice for reasoning about which numbers are bigger or smaller, and marking previous guesses on the hundreds chart will give younger kids the support they need. Make it competitive by seeing who can guess a number in the smallest number of turns (for adults who need a little extra edge, read up on binary search algorithms.)
• Roll the chart up into a tube and count around and around and around…Nothing makes it clear that the numbers go in a continuous sequence like rolling a hundreds chart up and counting around the bend.
• Cut the hundreds chart up, then put it back together again.We have an unending fascination with tape here, so this is always a winner. Print out one of the hundreds charts, cut it up randomly then tell the kid to put it back together again with tape. Bonus points if you time them. A good starter is to do this with one of the color hundreds charts which provides some color-cues to help make the assembly go faster, but you should move on to the black and white charts once the concept is clear.
• Color in a hidden picture puzzle on the 100s chart.There are a ton of these online, but obviously the best hidden picture puzzles are right here at DadsWorksheets!
• You can use a hundreds number chart to determine the difference between two numbers.This is a great activity for conceptualizing addition and subtraction. You can use a hundreds chart as a resource when practicing addition facts or subtraction facts as a substitute for finger counting (especially handy when you’re out of fingers.)
• Play race to one hundred on the chart.You’ll need a game piece (or two if you’ve got more than one kiddo on hand) and a die. Start with both players on number 1, and have each player roll the die then move their piece that many numbers forward on the chart. The first one to get to 100 wins. Try having them only roll a number at the end that lands exactly on 100 to win.
• You can do skip counting easily on the hundreds chart. A great activity is to print a hundreds chart and color in odds, evens or multiples of 5. Or, color multiple patterns and see where they overlap, a great start on understanding factors of numbers. Skip counting provides an opportunity to begin understanding the properties of certain sequences of numbers (for example, that adding two to an even number always produces an even number, or that multiples of 5 always end in 5 or 0). Even more so than using a multiplication chart to memorize multiplication facts, skip counting also helps kids build the number sense necessary for multiplication.
• Find prime numbers using the Sieve of EratosthenesOnce you have a student who understands multiplication, division and the idea of prime numbers, you can use a hundreds chart to perform the Sieve of Eratosthenes, which is really simply way to not only introduce primes, but to discover one way that they can be revealed.

Any of these activities work well with the 100 chart or with the 120s charts available at the link as well… You’ll notice sometimes when kids learn what follows 100, it can be a challenge. That’s why some of the Common Core activities work with 120 instead of 100… It’s just a large enough range to get you well into that third place value, and it also fits nicely into some of those times twelve tables that you’ll undoubtably come across soon as well.

Whether you’re building up number sense or just using these number charts as a way to learn your math facts, I hope these new charts help move your math lessons on down the highway just a bit faster… Do you have some other great hundreds chart games or activities? Leave a comment and let me know!

I give up.

No really, I’ve had it. With HTML that is. We’re coming up on the 9th anniversary of DadsWorksheets.com, and as much as I’ve tried to ride the waves of changing HTML standards, print media style sheets, flexbox and every other solution to wrangling layouts, I’ve finally reached the conclusion that getting consistent printable output from a web page is a bridge too far.

So, dear friends, you’ll notice that over the last week or so I’ve converted all of the worksheets to PDF files. You’ll navigate to them just as you did before, but the worksheet display will be subtly different. Answer keys, where appropriate, are included in the files now. There’s a PDF viewer for each worksheet, and you’ll be able to print directly from the browser using the big “Print” button just as you always have, or alternatively you can download individual worksheet files by clicking the button in the PDF viewer’s controls. If you have trouble printing from the browser (and yes, I’m talking to you Safari), you can always fall back to downloading the worksheet PDF file and printing from Acrobat or another PDF application.

The good news is that this step will allow me much more control over the worksheet layouts. Right now many of the worksheets still look just like they always have, but I’ve completely updated the multiplication worksheets and the multiplication charts.

I think they look amazing, and I hope you do too.

You’ll find the content centered much better and with much nicer font presentation… Many of the problems are laid out for better readability, and I’m able to take full advantage of the page coming out of your printer. You can check them all out at the links below…

Multiplication Worksheets
Multiplication Charts

If you liked what I had on the site before, you’ll love these new worksheets! I’ll be updating the addition, subtraction, division and the other math topics over the coming weeks. Meanwhile, if these new multiplication worksheets or multiplication charts give you any trouble, or if you have any comments on the new layouts, please let me know in the comments below!

Meanwhile, thanks as always for using the site and helping make DadsWorksheets one of the best free math resources on the web!

Are your kids at risk of losing over two months of math skills?

It’s 120 degrees here in Arizona, and we’re blazing through summer vacation even faster than you think… And along the way, every one is trying to avoid summer slide. No, I’m not talking about a fancy bit of seasonal playground equipment. I’m talking about the loss of knowledge that typical students incur over their time away from the classroom.

While many students who are motivated to read over the summer break will actually improve their English skills, students typically lose over two months worth of math learning progress over summer vacation. It can take a corresponding amount of time at the start of the new school year to get back on track. Many of these statistics come from the RAND Corporation, which has studied the effects of summer learning loss, as well how summer learning programmings can reduce or reverse these effects across various demographics. Harvard University has weighed in specifically on math learning loss and this post provides some hints at activities you might consider to help retain math skills over the time away from school.

But obviously, those two months of lost math learning is something we can address right here… One of the most important skills is math fact fluency. There’s a reason we practice math facts so rigorously… They are involved in nearly every math task you perform, and accurate instantaneous recall of math facts is a huge success factor in any other applied math skill your little geniuses will encounter. Keeping fact recall sharp is an easy way to stay ready for back-to-school!

If you’ve mastered addition and subtraction, summer can still be a great opportunity to introduce multiplication or division… Regardless of where you’re at, you’ll find all the practice worksheets to keep busy through the summer below!

Addition Fact Practice Worksheets
Subtraction Fact Practice Worksheets
Multiplication Fact Practice Worksheets
Division Fact Practice Worksheets

And of course, I’d be completely skipping the fun part if I didn’t mention again the awesome Math Flash game I just developed. You can choose what type of math facts you want to work on, then the game will work drill you on harder problems at each level. If you miss facts, it repeats them so you get extra practice and with Google Chrome, you can use your voice and a microphone to give those tired fingers a break…

Regardless of how you plan to turn that summer math slide into a climb up the monkey bars, I hope your vacation is filled with lots of fun!

Yes, I’m all about the worksheets. And pencils.

But that doesn’t mean there aren’t times I loosen things up a little bit and amp up the creativity. Because no matter how much fun that old-school math fact practice can be, I know the munchkins need a change of pace. Color, sound, drama… Everything a really good math fact game brings to the table. Along with a really huge twist, an amazing “One More Thing” that I’m going to save for the end of this post.

There many online flash card math games out there, and if you’ve seen the same ones I have, they’re dreadful. Most of them reinforce the idea that you do a few math problems to earn play time, which to me is almost psychologically predisposing kids to think that math is a sort of chore, or even punishment. There had to be a way to make the math practice part of the enjoyment and part of the reward, not the drudgery that gets you to the (lame) prize.

What I came up with is something that I think is the opposite of these attempts at math fact misery. Pick your operation and give it a spin right here, or you can get to it from anywhere on the site using the ‘Math Flash’ entry in the menu on the top of the page…

Math Flash Addition Game
Math Flash Subtraction Game
Math Flash Multiplication Game
Math Flash Division Game

What makes Math Flash different from other online flash card games? For one, the math facts are an integral part of the game… As you solve math problems, you’re building up a supply of color in the machine that will spray over the background. But you have to answer the facts quickly, because the machine leaks quite a bit. The more facts you answer correctly and the faster your answer them, the quicker you get through the level and the more colorful the artwork you’re building up. But importantly, the animation and the interactivity is happening while you answer the problems, and each problem you answer adds to the sense of progress you’re making on the level itself.

The levels in each version of Math Flash (addition, subtraction, multiplication and division) are all tied to the Spaceship Math facts worksheets on this site. The levels start out with easier facts and gradually introduce new facts. You start with a set of the easiest facts for each operation, and subsequent levels add progressively more difficult facts to the mix. So the learning curve is incremental, but still rewarding for kids just beginning their journey of mastering a specific operation’s family of facts.

As I mentioned, you’ll also see that if you’re slow to answer facts or if you get some facts wrong, it’ll take more correct answers to get through a level. This means if you know the easier facts, you’ll move quickly to the next level. If you’re still struggling with certain fact families, you’ll get more practice on the problems you’re slow to answer. If you wind up not answer enough problems correctly on a level, the game will end and you’ll be given a link to the worksheet focusing on the facts you need to practice.

Also, if you miss problems, those will are show up more frequently. The game adapts itself to the specific skills and the specific trouble spots of individual players, getting them to the practice more on the math facts they need the most help with.

When you reach the end, whether you made it all the way through or just started missing too many facts along the way, you’ll have created a unique piece of artwork that will make you feel like Jackson Pollock. You can share this creation on Pinterest or Facebook if you like (and if you would, I’d really appreciate it!)

Oh, and there’s one more thing. If you’re using Chrome on the desktop, and if you have a microphone, Math Flash will make use of the HTML5 Web Speech API to let you give answers to problems using your voice! When I built MathFlash, I wanted to recreate as much of that childhood flash card experience (sans the 70’s print couch) as possible, and this feels like an incredibly natural way to practice math facts. Kids without strong typing or mouse skills will find this is a great way to practice math at their own pace, and it’s really a showcase of what can be done in a web browser today.

You’ll need a reliable internet connection, and for now it only works in Chrome, however the other browsers will hopefully implement this standard soon. If you don’t have Chrome, you can still play by clicking on the correct answers.

I hope you’ll give Math Flash a try and make it a part of your summer math fact retention plans!

We spend a lot of time focused on multiplication tables, and getting past the stages of memorizing math facts is an important milestone. By the time we are working with multi-digit problems, we’re starting to deal with algorithms, the series of steps, necessary to solve problems. Fortunately, learning multi-digit addition and multi-digit subtraction, even with regrouping, is usually achieved without too much difficulty.

The steps for multi-digit multiplication require are a bit more demanding… In fact, it has all the fun of multi-digit addition on steriods right along with the twists multiplication brings as well. However, I’ve got a great tool that should take away some of the long multiplication anxiety…

Visual Multiplication Calculator

This calculator will let you multiply two long numbers together, and it shows you the intermediate products as it goes. Put a couple of numbers in there and hover your mouse over the work produced by the calculator… You’ll see what parts from the multiplicand and the multiplier are used to create each step, and it clearly shows how the place values are preserved as we work through the multiplier digits. It’s a great tool for developing an understanding of the conventional steps for multi-digit multiplication.

But, the most important thing is practice! These multi-digit multiplication worksheets work hand-in-hand with the multiplication calculator.

If you need review, be sure to also check out the complete series of multiplication worksheets, multiplication tables, and multiplication charts to really get your multiplication facts polished up!

Well, many thanks to DadsWorksheets.com visitor Tracy for pointing out that I had missed the target by a mile on the latest version of the bullseye math facts worksheets! While the worksheets themselves were fine, the answer keys had the answers repeated in each ring. As if memorizing these math facts weren’t hard enough as it was.

Regardless, if you haven’t had a chance to check these worksheets out, they’re a lot of fun and put a slightly different spin on memorizing your math facts. And they’re easier to grade now too!

Bullseye Addition Facts Worksheets

Bullseye Subtraction Facts Worksheets

Bullseye Multiplication Facts Worksheets

Bullseye Division Facts Worksheets

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 the threat of a missed recess.

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 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 so, 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.

Roman Numerals are one of those skills that seem unimportant until you realize you how often they show up all around you. You’ll see Roman numerals on everyday objects like clocks or buildings, but students progress into the science or law related subjects, you’ll start seeing Roman numerals showing up all over the place. Because of this, learning to read Roman numerals is a skill every student should be exposed to in the primary grades.

I’ve added a bunch of great Roman numeral resources to the site, including this Roman numeral converter and these Roman numeral charts. The Roman numeral charts are a great reference tool and include the rules for Roman numerals, so they could make the basis for a Roman numeral unit in the classroom.

But of course, you’ll need some worksheets for practice and assessment! With that in mind, here’s a collection perfect for your little Centurions to work on!

Roman Numeral Worksheets

Radians or degrees, fractions or decimals… There are a lot of places in math (and definitely in other topics) where you can make a case for representing measurements in different forms.

But Roman numerals versus Arabic numerals, there you’ve got a much more compelling argument for letting the sands of history wear away at this 2,000 year old numbering system whose main claim to fame seems to be keeping track of how many times a certain prominent football game has been played (51, or Roman numeral “LI”, as of this post in case you’re curious.) Go ahead and disagree with me, and I’ll be assigning you some Roman numeral multiplication worksheets… We’ll see who gets the last laugh there!

Still, Roman numerals pop up in a number of odd spots unexpectedly and that makes at least knowing how to read them a necessary skill. You’ll bumble across them on traditional analog clock faces, page numbers for those pesky prefaces in books, that weird outline mode in Microsoft Word, and the “IV” at the end of your buddy’s name when his parents, grandparents and great-grand parents couldn’t think of a new first name besides “George” when the baby came. Any place where somebody wants to lend a certain historical gravitas, there too shall ye find Numeris Romanis.

So, learn them we must, but that doesn’t mean the process can’t be at least a little entertaining! This visual Roman numeral converter will help untangle some of the unusual nature of Roman numerals. It breaks down the more confusing parts of adding and subtracting values associated with Roman numeral digits making it a fantastic learning tool, and kind of fun to just play with…

Roman Numeral Converter

Give it a try and let me know what you think, and for more Roman numeral resources be sure to check out the Roman numeral charts on the site as well!