Equivalent decimals inquiry

The prompt

Mathematical inquiry processes: Compare and contrast; test cases; find rules. Conceptual field of inquiry: Conversion of fractions to decimals; terminating and recurring decimals.

Amanda Kirby, a teacher of mathematics at St Clement Danes School, Hertfordshire (UK), designed the prompt after thinking about how she had previously encouraged students to discover recurring decimals. She investigated the decimal equivalents of ninths using a calculator before moving on to fractions with a denominator of 99. 

Amanda created the prompt for her high attaining year 9 class. At the start of the inquiry, students made observations and asked questions:

The class went on to make and test conjectures about recurring decimals:

September 2018

See also the Fraction and decimal conversion inquiry.

Explore and generalise

The steps (illustrated) were devised by a year 8 class to determine if the equivalent decimal of a fraction terminates or recurs. 

The class had worked out the decimal equivalents of the unit fractions up to a thirtieth. After examining the prime factors of the denominators, the students made generalisations that they shared and refined during a feedback session orchestrated by the teacher.