DadsWorksheets.com

Place Value Variants of Written and Expanded Form Worksheets Posted

2009-10-18T03:58:59Z

By special request, variants of the written and expanded form worksheets have been added that express the component parts of numbers using a format like the following…

1,234 = (1,000 x 1) + (100 x 2) + (10 x 3) +4

You can find new worksheets translating both whole numbers and numbers with decimal parts into and out of this format at the links below…

Write Numbers in Expanded Place Value Form

Write Expanded Place Value Form in Standard Form

Vertical Variants of the Number Ordering Worksheets Posted

2009-10-03T22:36:48Z

By special request, variations of the number ordering worksheets with a vertical problem layout have been posted at the link below…

Vertical Number Ordering Worksheets

Word Form, Expanded Form and Standard Form Worksheets Updated

2009-10-01T16:08:44Z

The standard form, expanded form and word form worksheets have been updated. Thesesheets deal with composing and decomposing large numbers into various forms, including the spoken-form of numbers.

Previously, problems on some of these worksheets that included a large gap in the place-value sequence would have been translated incorrectly. An example would be a number like 5,000,123 which has no value in the middle thousands triplet. Problems of this sort were quite scarce since the way the previous sets of worksheets were constructed, there was only a 1-in-1000 chance that a particular number would have an incorrectly formed answer.

In turned out, these were exactly the sort of problems we were having trouble with on a quiz here and when I went searching for problems of that type, I actually had to create a whole new series of worksheets that specifically included more zeroes in the problems. These new worksheets are identified in their descriptions as “with gaps” and you’ll find them mixed into the existing series.

Hope your school years are all progressing well!

You’ll find the new worksheets here…

Numbers in Standard, Expanded and Word Form

Monster Division Worksheets

2009-09-11T00:56:51Z

So, it’s really time to banish the long division monster. We’ve been working on long division all summer, but still there’s some perception that a three digit long division problem is much harder than a four digit problem, and heaven help us if a five or six digit division worksheet gets shuffled into the daily drills.

So, to finally drive a stake through this beast’s heart, we came up with a sort of agreement. I can assign worksheets with division problems as large as I want, as long as there’s no more than one problem per page. Well, throw the switch, a lightning bolt rips through Dad’s dungeon laboratory and the Monster Division Worksheets are alive!

Of course, one problem per-page works out fine because you need that much space to work the problem out, and to make it easier to keep things lined up, the worksheets carry lines down the problem page.

Give these twelve and fourteen digit leviathans a try, and I promise their four digit kin will seem far less intimidating… Like warm, fuzzy, forest creature division.

Click here to see the new Monster Division Worksheets!

A Guide to the Division Fact Worksheets

2009-08-10T03:53:46Z

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.

There are a number of different ways to tackle division. The conventional RocketMath division problems work by progressively introducing a handful of division facts in a series of drills. We started with these worksheets here. The issue though is right at RocketMath Division Level G, division by divisors larger than the dividend is introduced and the answer (quotient) for all of these problems is given as zero (i.e., no wholes and the remainder is ignored.) This sweeps the whole remainder issue under the carpet, but when we circled back for actual division with remainders we struggled to get rid of this concept. I heard “Zero!” so many times when we were working steps in a long division problem here that I wish we’d never seen this treatment introduced. If your school is using either the RocketMath or Mastering Math Facts curriculum, you may find these division drills useful, but you may save yourself some “unlearning” by taking an alternate path.

Another approach is to introduce initially only the division facts that are perfect reversals of multiplication. This does ignore remainders initially, but it also doesn’t introduce a behavior that makes you think you can ignore them either. The SpaceShip Math Division Just Whole Facts series of worksheets does exactly this. In fact, once this series of worksheets has been completed, you could even step into the Long Division without Remainders worksheets to introduce the long division algorithm. We didn’t follow this route here, but the whole divide/multiply/subtract/bring-down process reinforces the relationship between digits in the quotient to each digit in the dividend, and I think that subtraction step might set up a notion of what the remainder thing is all about.

Whether you tackle introduce long division or not, after the core whole division facts are down, it’s time to introduce remainders in their full glory. The best success we had here over the summer was in simply drilling the division with remainder facts, just like any of the other basic operations.

The SpaceShip Math Division Focus on Remainders worksheets introduces division facts with remainders progressively by increasing the divisor as you go up levels. By starting with lower number divisors, the remainder is pretty easily to calculate and the concepts build up before you get to large remainders that aren’t quite as easy to recognize off the top of the head.

Another shorter series introduces remainders in a slightly different way. The Division with Progressive Remainders Worksheets introduce problems where the remainders increase (the whole part of the quotient may be larger, however). This is a similar approach to the SpaceShip math sheets mentioned above, but it does introduce the problems in a slightly different order that may help if the first series of worksheets seems to be a struggle.

The main division worksheet page also has practice worksheets for a variety of other division topics, including focuses on cubes and roots, factors of ten and powers of two. Of course, your real goal should be to get to the long division worksheets reasonably quickly, which will exercise all of those division facts (with and without remainders) probably much more than your little math fiends will care for. Dad’s supply of Pokemon reward packs is definitely dwindling.

Division has been a longer term project here, and I hope the different approaches are valuable to you. Let me know what worked and what didn’t in the comments below. And best of luck for the 2009/2010 school year!