Subtracting by regrouping

Math Lesson Plan: Popsicle Stick Regrouping Fun

If we take one of these tens, so now we're left with 9 tens, and we give it to the ones place, so you give 10 plus 1, you're going to be left with However, effectively teaching "place-value" or any conceptual or logical subject requires more than the mechanical application of a different method, different content, or the introduction of a different kind of "manipulative".

Whereas if you do teach subtractions from 11 through 18, you give them the option of using any or all three methods.

So we're ready to subtract.

Worked example: Subtracting 3-digit numbers (regrouping)

Whenever you have ten white ones, you can exchange them for one blue one; or any time you want to exchange a blue one for ten white ones you can do that.

But one can do other quantities as well; and single digit numbers summing up to and including 18, and single digit subtractions from minuends up to and including 18 that yield single digit answers, are important for children to practice. And what was neat about this is now up here, all of these numbers are larger than the corresponding number in the same place.

There are all kinds of ways to practice using numbers and quantities; if few or none of them are used, children are not likely to learn math very well, regardless of how number words are constructed or pronounced or how numbers are written.

How far can your students go with it. Children do not always need to understand the rationale for the algorithm's steps, because that is sometimes too complicated for them, but they need to understand the purpose and point of the algorithm if they are going to be able to learn to apply it reasonably.

I start out with adding questions, then go to subtraction questions, keeping them simple for a bit, until I see that they understand the concept of regrouping. The first of these, for example is adding 4 blues and 6 whites to 2 blues and 3 whites to end up with 6 blues and 9 whites, 69; the last takes 3 blues and 5 whites away from 5 blues and 6 whites to leave 2 blues and 1 white, The point of repetitive practice is simply to get more adroit at doing something correctly.

But there's nothing here in the tens place. And it may be interesting to students at some later stage when they can absorb it. They think if they do well what the manuals and the college courses and the curriculum guides tell them to do, then they have taught well and have done their job.

It has taken civilization thousands of years, much ingenious creativity, and not a little fortuitous insight to develop many of the concepts and much of the knowledge it has; and children can not be expected to discover or invent for themselves many of those concepts or much of that knowledge without adults teaching them correctly, in person or in books or other media.

They can even be designated in written word form, such as "four thousand three hundred sixty five" -- as when you spell out dollar amounts in word form in writing a check. Place-value involves all three mathematical elements. Teachers ought to have known for some time what researchers have apparently only relatively recently discovered about children's understanding of place-value: So in the ones place, we have an issue.

I believe that there is a better way to teach place-value than it is usually taught, and that children would then have better understanding of it earlier. If the tide comes in for four hours at the rate of 1 foot per hour, at the end of this period, how many rungs will be submerged.

Practice with grouping and counting by groups should, of course, include groupings by ten's, 4 representation of groupings 5 specifics about representations in terms of columns.

Doing this in this way lets you almost see what they are individually thinking and it lets you know who might be having trouble, and where, and what you might need to do to ameliorate that trouble.


To write a ten we need to do something else like make a different size numeral or a different color numeral or a different angled numeral, or something.

The train in the west is traveling 70 mph and the train in the east is traveling 55 mph. Then, of course, subtract the two ten's from the four ten's and end up with Some of these studies interpreted to show that children do not understand place-value, are, I believe, mistaken.

If not, why not.

Subtraction by

Painting your car, bumping out the dents, or re-building the carburetor makes it worth more in some obvious way; parking it further up in your driveway does not. Subtracting single-digit facts is a skill that students generally learn after or while they are learning single-digit addition facts.

It makes sense to say that something can be of more or less value if it is physically changed, not just physically moved. The "new math" instruction, in those cases where it failed, was an attempt to teach math logically in many cases by people who did not understand its logic while not teaching and giving sufficient practice in, many of the representational or algorithmic computational aspects of math.

And, of course, grouping by 10's is a prelude to understanding those aspects of arithmetic based on 10's.

Subtracting mixed numbers with regrouping (unlike denominators)

Do the same for 21…. Mathematicians tend to lock into that method. I am told by teachers that this is not unusual for students who have not had much practice with this kind of subtraction. The point of practice is to become better at avoiding mistakes, not better at recognizing or understanding them each time you make them.

Place toothpicks showing 40 + 3 to begin the question.

Regrouping in Subtraction

Objectives. Learning and practising regrouping; Print examples of regrouping in student math journals. Let's try to subtract fromand I encourage you to pause this video and try it on your own first.

So let's go place by place, and we can realize where we have to do some borrowing or regrouping. Math Playground's step by step math videos cover a range of topics from basic operations and number properties to algebra and geometry.

The Concept and Teaching of Place-Value Richard Garlikov. An analysis of representative literature concerning the widely recognized ineffective learning of "place-value" by American children arguably also demonstrates a widespread lack of understanding of the concept of place-value among elementary school arithmetic teachers and among researchers themselves.

Welcome to The Subtracting 3-Digit Numbers with All Regrouping (A) Math Worksheet from the Subtraction Worksheets Page at This Subtraction Worksheet may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

Sal subtracts 17 4/9 - 12 2/3. - [Voiceover] So we have the expression 17 4/9 minus 12 and 2/3. And I encourage to pause the video and see if you can figure out what this is.

Subtracting by regrouping
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Worked example: Subtracting 3-digit numbers (regrouping) (video) | Khan Academy