# Proper and Improper Fractions

## Students` Learning Outcomes

• Differentiate between proper and improper fractions.

### Information for Teachers

• An improper fraction is “top heavy” which means that the numerator is more than the denominator e.g.

• Its value is always more than unit.
• A fraction is proper when it numerator is smaller than denominator, and its value is always less than unit e.g.

• While teaching the lesson, also consult textbook where and when applicable.

### Material / Resources

Writing board, chalk/marker, duster, paper strips, fraction cards, fraction strips, box, coloured chalk

### Introduction

• Show different kinds of diagrams of proper fractions to the class.

• Ask students to tell the fraction of each diagram.
• Show diagram of improper fraction and ask for the difference in both one.

• Tell the students that proper fraction is less than 1 whereas improper fraction is more than 1.
• Write the fraction on the board e.g.

• Ask students how each fraction is different from the other.
• Use proper vocabulary e.g. proper and improper fraction.

### Development

Activity 1

• Show one paper strip to the students.

• Discuss how to share one strip with two students.
• Ask student what fraction each child has; write the fraction on the board.
• Now show three strips and discuss how to share equally among two students.
• Allow the children to try and figure out how this will be done.
• Guide them in dividing all 3 strips in half and each child gets 3 halves.
• Ask how can we write it?
• Ask them to write it mathematically on the board.

• Make student realize that in first situation each student got less than a whole strip but in second case each student gets more than a whole strip.
• Discuss ½ and 3/2 fractions highlight values of numerator and denominator in both cases.
• Draw attention to the fact that in case of ½ the fraction shows a quantity less than 1, the numerator is less than the denominator. Such fractions are called proper fractions.
• Ask “is 3/2 a proper fraction?”
• Draw attention to the fact that 3/2 shows a quantity more than 1 and its numerator is bigger than the denominator. Such fractions are called improper fractions.

Activity 2

• Write different proper and improper fractions on the cards.

• Put them in a box and give this resource to students in groups.
• Ask one group to collect proper fraction cards and other groups of students to collect improper fraction card.
• After cards collection ask each group to paste their collected cards on a chart paper, give a title ‘proper fraction’ and ‘improper fraction’.

• Hang chart papers in front of class and give a presentation about proper and improper fractions.

Activity 3

• Divide class into groups.
• Hang a fraction board (as shown in the figure) on the writing board; provide a coin and colour chalks or marker to the students.

• Call students turn by turn from each group.
• Ask them to flip the coin, if head appears students need to colour a proper fraction with marker. If tall comes they will colour improper fraction.
• If they colour correctly, one point will be given to students otherwise student will lose one mark and turn will go to other group.
• Winner will be appreciated with a gift.

### Sum up / Conclusion

• Conclude the lesson by repeating that in a proper fraction the numerator is less than a denominator is greater than the denominator.
• Ask any two examples of proper and improper fraction.

### Assessment

• Give some fractions to students and ask them to separate proper fractions and improper fraction.
• Ask students to complete the sheet by writing fraction, and also circle improper fractions.