Real Number System Reference Sheet

Hand out the Real Number System Reference Sheet first and keep it out during the sorts. Use the classification and comparison sheets for instruction, and save the maze, riddles and mystery picture for review.

A nested diagram of the real number sets with examples, plus the steps that turn 0.454545… into 5/11.

Yes. We made it for 8th Grade number theory, and it works the same at home or at school. At home a student can print it and keep it with their school work. Teachers print a copy per student or one for the whole room, whichever the day needs.

A decimal that ends, like negative 4.25, or repeats, like 0.454545…, is rational. A decimal that goes on forever without a repeating block, like 0.1010010001…, is irrational. Sort Decimals and Fractions as Rational or Irrational asks students to explain this difference.

Yes, sometimes. √2 × √2 = 2, which is rational, but √2 × √3 is irrational. Always, Sometimes or Never With Real Numbers and True or False Statements About Real Numbers test claims like this with examples and counterexamples.

Natural numbers sit inside the whole numbers, whole numbers inside the integers and integers inside the rational numbers. Irrational numbers are the real numbers that are not rational. The card sort and the set diagram sheet place each number in the smallest set it belongs to.

Write both as decimals with enough digits to see which is greater. With π about 3.14159 and 22/7 about 3.142857, 22/7 is greater. Compare Rational and Irrational Numbers practices pairs like this.