Subtraction - Counting Up vs. Counting Down (Backwards)




Should you subtract by counting up from the small number, or should you subtract by counting backwards from the large number? Before getting into it, let's first acknowledge the difficult landscape faced by children learning how to subtract these days. Observations made in the classroom might suggest children suffer from too many resources. Students confuse several different subtraction methods, and in the end, they come up with the wrong answer. The point is, children benefit from consistency and repetition, no matter which method you choose.

Below you will find a series of subtraction videos that present subtraction in a consistent and simple method. In the method, the student counts backwards from the large number. The amount counted backwards is equal to the subtrahend (the smaller number in subtraction), and it is visualized on the fingers. The key to using these subtraction videos is participation. The videos repeat each problem and have participation cues for the student to practice counting backwards, which will allow children to practice and understand the method.



Subtract Along Videos



 
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Math Subtract 1
 
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Math Subtraction 2
 
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Math Subtraction 3
 
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Math Subtraction 4














Learning the Subtraction Concept

Learning the Subtraction Concept


When trying to explain the theory of subtraction, it is helpful to explain to children that they are starting with an amount, then some amount is "taken away," and you want to know how many are "left." This is the first concept created when you introduce subtraction. For example, you say, "I have 5 apples. 3 were eaten. How many are left?" These problems are usually visualized, and the student doesn't have to worry about counting up or counting backwards. The student usually draws 5, crosses out 3, and counts how many are left. When deciding which method is most similar, which will help make the smoothest transition to harder problems, this method of visualizing does seem to coincide more with the counting backwards method. Since the student is crossing out an amount, or taking away an amount, it is similar to counting backwards an amount to arrive at an answer. +1 Point, Subtraction by Counting Backwards!


Subtracting Without Pictures

Subtracting with Numbers and Without Pictures


When you step it up a notch, and the students are required to do subtraction problems, things can get ugly really fast. Kids don't notice the sign, they draw pictures, they try 3 different methods at once, and they end up with the wrong answer. This is where a consistent approach really helps. If the student tackles the problem the same way every time, he or she will start to get the right answer with practice and repetition. That said, which method should you chose?

Counting up from the subtrahend is easier. An answer can be obtained by counting up, which kids like because they have been doing that in addition when the count up from the addend. +1 Point, Subtraction by Counting Up!

Counting backwards seems to capture the concept better. You are starting at some number, and you are taking away an amount, and you need to know how much is left. +1 Point, Subtraction by Counting Backwards (Down)!


Explaining Subtraction Methods of Counting Up and Down

Explaining the Counting Up and Counting Down Methods


Explaining "why" each method works isn't of paramount importance, but every now and then a curious student will want to know why counting up works. The answer to "why" counting up works deals with the algebraic relationship of addition and subtraction, and is a bit too much for an elementary student. Sure, students stumble onto this answer themselves, and some students use this relationship to solve problems without even thinking about it. That doesn't mean that the explanation is simple. On the other hand, counting backwards presents a much clearer description of what is happening in subtraction. By presenting and explaining subtraction in this way, it is easier to explain to an elementary math student that you are starting with an amount, some amount is taken away, and you want to find how much is left. +1 Subtraction by Counting Backwards (Down)!


Subtracting Large Numbers

Subtracting Large Numbers


When it comes to more difficult subtraction problems, counting backwards is the way to go. Try "56 - 9" when you can't count backwards. Now you have to count up from 9. Yikes! Furthermore, when using the counting backwards technique, the hardest problem you ever encounter is "18 - 9" because you are either subtracting two 1-digit numbers, or you are borrowing 10 at the most. +1 Point, Subtraction by Counting Backwards (Down)!


The Conclusion

The Conclusion


True, counting backwards is more difficult and takes more time (at first). However, in the long run, learning how to count backwards pays off. Furthermore, most kids end up counting backwards by the time they reach middle school anyway!

Counting backwards is something that can be done once a day, from 30 to 0, at the beginning of math class. Kids' number sense will improve, and more difficult subtraction problems become easier. Many people that find this website don't know there is a free 5 part subtraction lesson using subtraction videos. Try the Subtraction Video (easy) and participate by counting out loud and tapping your finders on a table or desk. The videos use the same method for every problem: Starting at the large number and counting backwards (using the fingers). Try the Subtraction Video (medium) or the Subtraction Video (hard) if the beginner subtraction is too easy. You can also try the Counting Backwards Worksheet and Video or the Counting Backwards Subtraction Prep Video for some ideas on how to teach subtraction.






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