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…
By special request, variations of the number ordering worksheets with a vertical problem layout have been posted at the link below…
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…
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.
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. Read the rest of this entry »
