Dividing Decimals Using Estimation (Coursework Sample)

Dividing Decimals Using Estimation
Going by the words of Sadi A (2007), decimals to students are the biggest challenge of all number concepts. It follows that division of decimals using estimation is a very important skill for elementary school students looking to horn their math skills. Notably, the strategy used in division and multiplication of whole numbers still applies for decimals problems. It is upon the teacher to advice the student to have an estimate of the quotient before actually attempting the problem.
The topic on division of decimals using estimation comes after the class about developing strategies for fraction computation, developing concepts of decimals and percents, and interpretations of dividing fractions. All these are strategies that require mental input and adding this estimation strategy is very beneficial for math conceptual development of students.
In dividing decimals, understanding the concept is very critical for both teacher and student. That is why decimal squares and other concrete materials come in handy in a decimal division lesson. It is very fulfilling to note how easy it is to make a connection between a math problem and day-to-day life. This should form the basis for a concrete understanding of decimal division concepts in students.
This essay revisits the topic of dividing decimals using estimation by solving a mathematical task of that nature. By accomplishing this task, the challenges that students encounter solving a division of decimals problem will be identified.
Part I: Teacher’s challenge
The following is the solution of the task:
Activity 17. 13: Provide a quotient correct to five digits without the decimal point, such as 146÷7=20857. The task is to use only this quotient information and apply estimation strategy to give a precise answer. The solution for each of the figures is given below:
146÷0.7=208.57
1.46÷7=0.20857
14.6÷0.7=20.857
1460÷70=20.857
To get these answers, I used the rounding technique of estimation that helps get and idea of the answer. It is very unlikely to get a wrong estimation by using this technique. Other techniques applicable in this case include front-end estimation, and compensation. Front-end estimation is the approach where changing all other numbers to zero apart from the first digit. Compensation is characterized by adjustment to make the estimate as close as possible to the true answer.
Part II: Student Challenge
Division of decimals is a very interesting topic as it is largely connected to multiplication. In fact, students are encouraged to think more of multiplication when they are dealing with a division estimate problem. The importance of this strategy comes to focus when you consider how the students estimate the following problems.
In most of the questions, the students did not have any problem with division. However, question 4 presented some problem. For example, Student A erroneously added a zero in front of 8 in the number 200857, without knowing this altered the nature of the number completely. This mistake is a clear indication that the students do not have the conceptual understanding of dividing decimals using estimation. One of the misconceptions seen in children is that putting 0s at the front of whole numbers does not matter (Irwin). If this misconception is allowed to continue, the student might think that like in whole numbers, 0.2 is the same as 0.02.
The demonstration here is that the students might have problems determining decimal quotients, using estimation. The insight from this is that it might be necessary to introduce a new strategy for the students to complement estimation.
Encouragingly, the students demonstrate a great deal of understanding of the method used to divide the decimals. However, this should not be confused for complete mastery of the technique. Research shows that it is possible for students to grasp the method without getting the concepts. This is evident in student C’s solution to question 4 where there is confusion while reverting to division of whole numbers.
The rounding off method I used for this task is different from the student’s strategy. Students rely on the method alone without emphasis on concepts and meaning of division of decimals.
Conclusion