Eighths, sixths and twelfths

In your book, Maths Mela (Chapter 3), we make a tool to measure turns. Cut a circle out of tracing paper and fold it so that the folds split it into 8 equal parts, like 8 slices of a round cake. Fix a straw at the centre, lying along one fold, and mark that starting point as A. Now turn the straw clockwise (the way clock hands move), one fold at a time.

One fold is a 1/8 turn. A 1/8 turn is half of a quarter turn. Two folds make a 2/8 turn, which is the same as a 1/4 turn, so it makes a right angle. Three folds make a 3/8 turn. Four folds make a 4/8 turn, which is a half turn, so the straw points straight back the other way: a straight angle. Six folds make a 6/8 turn, which is a 3/4 turn. All eight folds make an 8/8 turn: a full turn, and the straw is back at A.

The book also makes a second tool. Fold a circle in half, then fold it again into 3 equal parts. Now it has 6 equal parts, and one part is a 1/6 turn. Fold one 1/6 part in half: half of a 1/6 turn is a 1/12 turn. Three 1/12 turns make a 1/4 turn, and two 1/12 turns make a 1/6 turn.

Turns in the same direction can be added. If an arrow turns clockwise by a 1/4 turn and then by a 1/8 turn more, a 1/4 turn is the same as 2/8, so the arrow has turned 2/8 + 1/8 = 3/8 of a full turn. A 1/2 turn and then a 1/4 turn more, both clockwise, make a 3/4 turn.