Decimal Form of a Rational Number

The progression of understanding rational numbers bridges between MATH-7 and MATH-8. (Note: This content is merged in Accelerated MATH-7.) And in the midst of discussing process teaching and concept teaching, we have highlighted the following standards.

7.NS.A.2d
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Hop over to the MATH-7 tab to see the Decimal Form of Rational Numbers post to jump start the conceptual understanding of these standards.

First ensure that students understand the classification of rational and irrational numbers. You could engage students in a sorting activity based on a few provided examples and counterexamples. (If you use all cards in the set, this activity will set the stage for Algebra 1 teachers to discuss the results of rational and irrational number operations.)

Sorting Activity

And then you could spin off of the MATH-7 activity of why some rational numbers terminate and others repeat to continue towards the concept of rewriting a repeating decimal as its equivalent fraction.

Algebraic Discovery

Would it be easier to teach the process for converting a repeating decimal to its equivalent fraction? Which benefits the students today, next month, next year? Process teaching or concept teaching?

Be sure to reflect on other related posts:

CCSS Call for Rigor

Process vs. Concept Teaching