Exploring Multi-Digit Subtraction Methods

Subject: Science
Type: Expository Essay
Pages: 4
Word count: 1099
Topics: Mathematics, Statistics, Teaching Philosophy


The tradition subtraction algorithm has had issues with the educators complaining it is not effective. For multi digit subtraction students develop, discuss, and use efficient and accurate strategies that use place value and other property of operation (Price, 2017). In general, the standard algorithm involves:  breaking down numbers into base-ten units and after that single-digit calculations with those units utilizing the place value to coordinate the place value of the subsequent number and utilizing the one to ten consistencies of the base ten structure to generalize whole numbers to decimals.

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Place value drawing

Solving 323-159 using place value drawing method

Count the remaining shapes: – squares standing for hundreds are 1, line segments representing tens are 6 and circles representing ones are 4 so the answer is 164.  Once the student has mastered the place value drawing method, it is easier for the student to understand the concept of borrowing from the tens and so on.

The adding up to find an unknown addend method

This method is based on counting on and making a ten. The methods involve introducing a new problem that is easier to solve and implement, but the problem should still be interpreted the same as the original problem. For the case of 323-159, it is correct to conclude that when the answer of the solution is added to 159, then the answer should be 323.

Therefore 323-159 is equals to 164

The traditional expanded notation method

The method involves expanding digits in both figures. For example, in 323, the expanded form will be 300, 20 and 3.The solution for 323-159 using the traditional expanded notation method.

Therefore, 323-159=100 hundred, 60 tens,4 ones, which is 164.

The alternating current common method

The method involves subtracting the place values of both digits. In the case of 323-159, 100, which is the place value of 1 in 159 will be subtracted from 300, which is the place value of 3 in 323

The ungroup first where needed method, subtracting first from the right and then from the left

While using the ungroup first where needed method, one can use two methods: – from the right and from the left. From the right is subtracting the ones first and from the left is subtracting from the hundreds. When using from the left method, one subtracts the place values of the smaller digit from the larger digit.

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Comparing the methods

All the methods involve determining the place value of the digits in the numbers and then subtracting accordingly. They are also similar in that to subtract each digit should be subtracted from it respective place value (Tucker, Singleton, & Weaver, 2013). Each method used above executes the borrowed hundreds and one differently. At the end, these methods produce the same results (Loewus, 2017).

For the place value drawings, the student’s possible misconception is carrying the hundreds to the ones, which is wrong. For the adding up to find the addends, the student may place the box at the wrong place while coming up with the new problem. For instance,

159+        = 323 is the correct format of the new problem, however, a student may write it as 159-       =323. For the traditional expanded notation method, the student might add the carried hundreds to the once instead of to the tens. For the alternating current method, the negative signs introduced while borrowing are confusing to some students. The students may miss the negative sign, and hence they will give the wrong answer. For the ungroup first where needed method, the student might wrongly add up the borrowed hundreds to the ones, which is wrong.

Some of these methods are complicated and they require total concentration for the student to use them completely. In this regard, the misconception is the possibility that the students will subtract the ones from the tens, which is wrong. Using math talk can help the student overcome and address the potential misconception above (Dentel, 2017). Since the students explain how he arrived at his answer, the tutor will identify the problem easily and focus on it to help the student address the misconception.

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Pat’s technique

The expanded notation and the Pat’s technique are quite similar, only that in Pat’s technique the digits in the number are shown how they are multiplied by their place values and in the expanded notation they are already multiplied.

Pat’s technique for the number 537Expanded notation for the number 537

How the third grader managed to come up such an effective method is interesting. Pat explains his method with writing, and Pat is quite clear how he came up with this method (Beckmann, 2017). Solving 547-198 using Pat’s method.

Hence, according to Pat’s method, 547-198=400-50-1=349

Verifying the answer using: –

  1. Using place value drawings

By counting the remaining symbols, the answer to 547-198 is 349

  1. Using the ungroup first where needed method, subtracting from left to right

One begins with the digits from the left.

Step 1:




The answer is 349, just like with the earlier methods.

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Student’s misconception

The student does not understand that carrying over ones from the hundreds is wrong (Talwalkar, 2017). The student should understand that the sequence of place value should be followed, that is, from ones we go to tens then hundreds and so on. When carrying over this sequence should be observed.

The place value drawings are the most effective method to use if the student has issue with carrying over. Although some methods do not involve carrying over and they can prove to be alternatives in this case, the place value drawing gives a clear picture of how to carry over (Harris, 2017). In case the digit on the tens is zero, then one has to borrow from the hundreds to the tens, then from the tens to the ones.

The various student misconceptions include not understanding when to implement an algorithm and when not to implement it. Another misconception is not understanding place value and lastly, the student knows about algorithms but not understanding the concept behind them. As a tutor, always engaging the students in math talk is of great importance, since one interacts and begins to know specific misconception and how to help the children deal with them.


Finally, using different teaching methods is of great importance. These methods are equally important despite the setbacks related to some. The students’ ability to understand vary from student to student hence the recommendation to use different strategies. Similarly, the world is evolving, and new strategies have been developing every day.

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  1. Dentel, E. (2017). 11.06.01: Using Place Value to Teach Addition and Subtraction, Let’s Count the Ways. Teachers.yale.edu. Retrieved 9 December 2017, from http://teachers.yale.edu/curriculum/viewer/initiative_11.06.01_u
  2. Harris, A. (2017). Addition & Subtraction. Ictedusrv.cumbria.ac.uk. Retrieved 24 November 2017, from http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit5/A&S.pdf
  3. Loewus, L. (2017). Common-Core Subtraction: Teaching Many Methods. Education Week – Curriculum Matters. Retrieved 9 December 2017, from http://blogs.edweek.org/edweek/curriculum/2014/11/common-core_subtraction_many_m.html
  4. Price, P. (2017). The potential of computer manipulatives for overcoming place value misconceptions. Merga.net.au. Retrieved 24 November 2017, from https://www.merga.net.au/documents/RP_Price_1_1997.pdf
  5. Tucker, B., Singleton, A., & Weaver, T. (2013). Teaching mathematics in diverse classrooms for grades K-4. Boston: Pearson.
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