Operations on Sets

Sukanya De, Suman Sarda

The topic chosen for this lesson design is ‘Operations on Sets’ from algebra for the students of class VII. Students already get introduced to algebra in Class VI, where they get some ideas about the concept of a set, and ways of representation of sets. As students start learning algebra, they start knowing and understanding the abstract concepts in mathematics. Sometimes this can be quite challenging for young minds as this is something different from the usual arithmetic they have learnt in the junior classes.

This lesson plan is designed to explain these abstract mathematical concepts in a simple, lucid way by developing a connection with real life situations. The main idea is to help children overcome the phobia of learning complicated concepts and to encourage them to imagine and share their views freely in the class. The teaching aids used are mainly audio-visual aids, such as pictures, videos, photographs – all stitched into a movie made using Windows Movie Maker.

Introduction to the lesson
The teaching-learning process is carried out involving an active participation of the students. The topic is introduced by showing some video clips and picture collages depicting the union and intersection of objects, things joining or merging, overlapping objects, as found in real life. The students are asked to share their views about what comes to their mind when they view such patterns. They would come up with the ideas of ‘Union’ of two or more objects and about objects having a common portion when they overlap or ‘Intersect’. (Figure1)

Figure 1: Picture collage showing intersecting objects in real life
Figure 1: Picture collage showing intersecting objects in real life

The meanings of the words ‘Union’ and ‘Intersection’ as learnt in English language are discussed to help the students relate and express their ideas about the same.

On the basis of these known concepts, the unknown concept of ‘Operation’ on sets is developed. Educational video clips are used to establish the mathematical concepts of ‘Union’ and ‘Intersection’ of two sets. A detailed explanation of the procedure of selecting and writing down the elements of the ‘Union’ and ‘Intersection’ sets is also given using these videos.

An example:

Let the set of people who like soccer be S={a, d, g} and the set of people who like cricket be C={d, g, b, c}, then

the set of people who like soccer or cricket is S Union C written as
S U C = {a, d, g, b, c}

and the set of people who like soccer and cricket is S Intersection C written as S ∩ C = {d, g}

Pictorial representations of sets using venn diagrams are also used to explain these concepts.

Creating motivation by reinforcement of the concepts
Reinforcement activities are carried out where the students are given stationery items of daily use as elements of Universal set and are asked to form different sets and their Union and Intersections respectively.

Also a role play activity can be conducted where the students hold number placards and act as elements of sets themselves. Based on the conditions given by the teacher, they will assemble and form the elements of new sets. (Considering the elements as numbers in this case) (Figure 2)

Figure 2: Role play activity where students act as elements of sets that they form.
Figure 2: Role play activity where students act as elements of sets that they form.

These activities enhance the logical reasoning and kinaesthetic skills of the students, thus making them more active throughout the learning process.

Assessing learning outcome and home assignments
Interactive sessions, puzzles and worksheets, specially designed, catering to different abilities and expertise of different students will help to assess their learning outcome at the end of the session.

Interesting follow up activities can be given to the children as home assignments. One such activity can be where the students conduct a survey and collect information on topics like favourite tv programmes watched by their friends. They can present the data in a venn diagram. The lesson ends with consolidation of the learnt concepts and with a lot of motivation for further learning.

This lesson design has been applied while teaching students of class VII and an overwhelming response has been found from the students. The use of moving images has immensely helped the children where they could think out of the box and understand the abstract mathematical concepts with ease. This helped them to develop a stronger affinity for the subject and an eagerness to learn more.

This lesson plan was prepared for the competition ‘Learning with moving images’ organized by Bichitra Pathshala in collaboration with the Birla Industrial and Technological Museum, Kolkata and has been awarded the best learning design in middle to high school teachers’ category for the year 2016.

The authors are teachers at Mahadevi Birla Shishu Vihar, Kolkata.