Difference between whole numbers, rational numbers and integers

Number families nest inside each other. Whole numbers (0, 1, 2, 3 and so on) sit inside the integers, which add the negatives. The integers sit inside the rational numbers: every number you can write as a fraction of two integers, including decimals that stop or repeat.

That nesting is why 0 is a whole number and an integer at once, and why -100 is rational, an integer and real, but not whole. The question about √7 reaches past Grade 6: irrational numbers are an extension, 8.NS.A.1 in Grade 8.

The sixth grade core is 6.NS.C.6, which treats rational numbers as points on the number line, negatives included.

Read question 1 together and ask, "Can -100 be a whole number?" Most kids say no right away, and that rules out the first two choices.

For -(5/1), let your child argue both sides out loud. "It's a fraction." "It's also -5." Both are true, and the solution page agrees.

A note for you: the solution page marks 55.679 as irrational. It is rational, because the decimal stops: 55.679 is 55,679 over 1,000. Irrational numbers, like √7 in question 2, go on forever without repeating. Ask, "Can you write it as a fraction?" If the answer is yes, it is rational.

Look around the house and you will spot every family. A thermometer reading of -3 degrees is an integer but not a whole number. A price of $2.49 at the store is rational: 249 over 100. Ask your child, "Which family does today's temperature belong to?"

How Much Is a Million? by David M. Schwartz, with its magician Marvelosissimo, makes big whole numbers feel real. After reading, ask whether a million is also an integer and a rational number.

Name what your child did: "You checked every family, not just the first one." This sheet closes the number theory set; the exponents set makes a good review partner.