Grade 8: Rational and Irrational Numbers – Real Number Race


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Content Standards

8.NS.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.

8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

Standards for Mathematical Practice

MP.1.     Make sense of problems and persevere in solving them.

MP.2.     Reason abstractly and quantitatively.

MP.3.     Construct viable arguments and critique the reasoning of others.

MP.4.     Model with mathematics.

MP.5.     Use appropriate tools strategically.

MP.6.     Attend to precision.


The lesson titled “Rational and Irrational Numbers – Real Number Race” from the NC Department of Public Instruction focuses on the thinking skill of classification and compare/contrast as students place rational and irrational numbers along a number line in order. The task would be appropriate after students know the definition of rational and irrational numbers and how to classify each. The task would continue to reinforce this classification while also having students compare numbers in order to arrange them. The lesson also includes questioning strategies to promote higher-order thinking. Upon completion, students be able to explain the difference between rational and irrational numbers and can place rational and irrational numbers in order along a number line.


  • Connecticut teachers will need to adjust this lesson with support for diverse learners, provide additional content support for struggling learners, and extending the content for above grade level students.
  • The task is presented within a context but not within an application to a real-world context.
  • Due to the nature of this lesson, there is no removal of scaffold supports.
  • There are no formal assessment criteria, such as student work samples and rubrics.


  • The lesson connects to knowledge from 6th and 7th grade instruction on rational numbers.
  • There is explicit teacher instructional support.
  • Possible misconceptions are addressed with ways to redirect students.
  • The lesson includes questions to assess students throughout the entire lesson and provoke higher-order thinking.