Misconception Series: Class 4 Fractions, Decimals, Ratios and Percentage: concepts applications


Reading Time: 2 minutes

(1) Why was the question asked in ASSET test?


This question checks the students’ understanding of fractions, and whether they can apply it in real life situations.

(2) What did students answer?


About 31% of students answered A, correctly. And about 55% of the students selected the most common wrong answer, option B.

Possible reason for choosing B:These students are blindly linking “third” in the question to the 3 in the option, and don’t seem to have made any effort to divide the sweets into 3 groups.

Possible reasons for choosing C and D:Very few students selected these options and are most probably making a random guess.

(3) Learnings


Students at this level were expected to use the following strategy:

Step 1:Realize that the 6 sweets will need to be divided into three equal groups 1/3 as of the sweets have to be given away.

Step 2: Make this ‘partition’ of 3 groups as shown in the figure alongside, and appreciate that each equal part here, has two sweets. Hence arrive at 1/3 of 6 sweets is 2.

However students’ response data indicate that

  • Students could not decide how many parts the 6 sweets need to be divided into. If these students were given a set of just 3 sweets instead of 6, as in the given question, many of them may have answered that correctly.
  • Some students may be just counting the numbers in the numerator and denominator and possibly if ‘1’ was one of the options, many students might have chosen it. These suggest that students may have only a superficial understanding of the numbers in a fraction. They may think that 1/3 always refers to a set of 3 identical objects with 1 object to be selected or1 part out of3 is to be shaded, as demonstrated in the figure.

They may not have internalized that a group of objects, with no. of objects as a multiple of 3, can be divided into 1/3. For e.g. 1/3 of a group of 9 objects are 3 objects.

The ‘fractional’ relationship between the part and the whole needs to be internalized by students.

(4) How do we handle this?


Here are some suggestions to help students develop a proper understanding of fractions-

Activity 1:Students have a better intuitive understanding of ‘half’. So take a chocolate bar to class and pose the following questions to them.

  • How many pieces can the bar be divided into?
  • What ‘fraction’ of the whole does each piece represent?Since there are 16 small pieces in this bar, can it be divided into half? If possible then how?
  • Would it be possible to divide the same bar if it is to be shared equally among 4 students?
  • How would they divide the bar for the same?
  • Lead them to the answers through discussion before moving to the next question.

Consolidate the learnings in the end as to how by appropriate partitioning of the same ‘whole’, one can represent different fractions.

Activity 2:Ask the given ASSET question. Ask students to divide 6 sweets into two equal groups and identify the fraction of sweets compared to the total in each group. Now ask them to divide 6 sweets into 3 equal groups, and identify the fraction of sweets in each group. You may ask them to compare number of sweets in each case. Thus get them an intuitive feeling of why 1/2 > 1/3. In this way, the idea of division as equal sharing can also be used to help them learn how different fractions can be represented by choosing the appropriate partitions of the same ‘whole’.

For more information about ASSET, write to us at info@ei-india.com


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Originally published at blog.ei-india.com on June 3, 2015.