Always, Sometimes or Never With Real Numbers

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.

Circle always, sometimes or never for 10 statements about real numbers and give an example for each. The directions on the page read: Circle Always, Sometimes or Never. Then write an example. For Always or Sometimes, show a case where the statement is true. For Never, show a case where it fails. An answer key is included.

Yes, both. We made it for 8th grade number theory, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

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.