Algebra 1 uses the real number system to describe answers: knowing whether a solution is an integer, a rational number or irrational tells you what kind of number to expect. Questions ask for the most specific set, for every set a number belongs to, and whether a square root is rational.
Also taught in Pre-Algebra, at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
0 is not a natural number, since the natural numbers start at 1.
It is a whole number, so it is also an integer, rational and real.
The answer is Whole, integer, rational, real.
Where students go wrong
Naming only one set when the question asks for every set. A number like 12 is natural, but it is also whole, an integer, rational and real, because each set sits inside the next.
Also called number sets, real number system, classifying numbers or natural whole and integers.
What you can put on this worksheet
The most specific set
Which is the most specific set that contains −4?→ Integer
Is the square root rational
Is 74 rational or irrational?→ Irrational
Every set it belongs to
Name every set that contains −45.→ Rational, real
Questions about these worksheets
Yes. Every classifying real numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the classifying real numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: the most specific set, is the square root rational and every set it belongs to. Tick as many as you want and set how many of each, or let it spread them evenly.
Calling every root irrational. The root of 25 is 5, a perfectly good natural number; only roots of non-squares are irrational.