Authentic Lessons for 21st Century Learning

Getting Real with Rationals

Identifying and Classifying Rational Numbers

K20 Center, Alexandra Parsons, Alex Parsons | Published: July 13th, 2022 by K20 Center


This lesson introduces identifying, classifying, and comparing rational and irrational numbers. Students will label and describe groups of numbers, as well as add new numbers into their appropriate groups. Then, students will predict whether statements are true or not based on their understanding. This lesson is intended for the beginning of a rational numbers unit or as a review. This lesson includes optional modifications for distance learning. Resources for use in Google Classroom are included.

Essential Question(s)

How do classifications help us understand numbers in a deeper way?



Students describe groups of numbers with which they are already familiar.


Students describe groups of numbers with which they are not already familiar. Then, they sort new sets of numbers based on their descriptions.


Students are provided a set of formal definitions to compare against their descriptions of the numbers.


Students determine whether a list of statements about rational numbers are always, sometimes, or never true.


Students reflect on what they feel most and least comfortable with in relation to their knowledge.


  • Getting Real with Rationals slide show

  • Always, Sometimes, or Never True handout (7th- and 8th-grade versions)

  • Descriptions Card Sort handout

  • Numbers Card Sort handout

  • Rational Number Rules handout

  • Muddiest Point Exit Ticket handout (optional)

  • Calculators

  • Writing utensils

  • Projector and computer for sharing the slide show

  • Scissors


Open the slide presentation (attached) and introduce the lesson. Let the students know that class is starting with a review challenge. Group students randomly with up to four or five students per group. No special grouping is required; students may group according to seating chart proximity or any other method you choose.

Display slide four and distribute the first page of the Rational Numbers Rules handout to each group. The goal is for students to look through the number groups, then decide what rule was used to form that group and describe that rule in a way that will help determine if a new number would fit in that group. The students are looking for commonalities in the group of numbers and by finding these commonalities they form a definition of the numbers that will guide whether a potential addition to the group would or would not fit into the number set.