Circle Segment

Activity One

A number of paper circles can be cut out efficiently in the following way:

Note: You will still need to hold the edges of all your pieces of paper as you cut around your circle shape to stop the bottom pieces slipping out of line.
Folding the circles into quarters is straightforward, but students will have to estimate their folds for thirds and also for fifths, if you wish to extend the activity to include fifths. For example, for fifths:

Thirds can be folded as follows:

Students will be able to find many relationships with their labelled fraction pieces. It is important that these are recorded. Discuss the way fractions are written.

“One-half is written as (1/2). The bottom line (denominator) indicates how many equally sized parts the whole has been divided into. The top number (numerator) gives the number of these parts that is used.”

It is important that fractions with numerators greater than one are discussed.

Three parts are used.
The whole is divided into four equal parts.

The fraction sentences students might find include:
Joining (addition), for example, 1/3 + 1/3 + 1/3 = 1

Differences (subtraction), for example, 1/2 – 1/4 = 1/4
Inequalities, for example, 2/4 < 3/4 (why?)

Multiplication, for example, 2 x 1/4 = 1/2
 

Activity Two

This activity is aimed at developing some readiness for early work with tenths in decimal form. Give the students circles so that they can investigate the problem by cutting out and folding.

The “untidy” fractions, such as the quarters and eighths, could be further investigated using a circle divided into hundredths (see Number, level 3 in Mathematics in the New Zealand Curriculum). Ensure that fractions with numerators greater than one are discussed, for example,
“How would you cut three-fifths of Pieta’s pizza?”

Answers to Activities

Activity One
Answers will vary.
Activity Two
Answers will vary. The teacher will need to check that the fractions are correct.