Lesson objective: Understand that all repeating decimals have a fraction equivalent.

Students bring prior knowledge of converting decimals into fractions from 5.NBT.A.3b. This prior knowledge is extended to repeating decimals as students examine multiples of the decimal forms of unit fractions, and compare them to given decimals. A conceptual challenge students may encounter is understanding how to compute multiples of repeating decimals.

The concept is developed through work with reasoning about a claim that all repeating decimals have equivalent fractions, which requires students to find multiples of unit fractions and compare them to a list of repeating fractions to see if any of the given decimals do not have an equivalent fraction.

This work helps students deepen their understanding of number because students come to understand that all repeating decimals are equivalent to some fraction, which means that all rational numbers can be represented as either decimals or fractions.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they use examples to defend their belief that Jack's claim is either true or false.

**Key vocabulary:**

- rational number
- repeating decimal
- unit fraction