The Real Number System


Alright, it's the beginning of the year... so, what topic do you teach first? For me, I always like to begin with the real number system. I understand it isn't the most riveting topic in the world, but I don't know like teaching other concepts without talking about the different classification of numbers, first. So, let's talk about the various resources I have used when discussing the real number system.


I have used three sets of notes when teaching number properties. One set is digital, one set includes carousel notes and the final set uses the 'Real Number System Family' to help teach the concept of the real number system.

The digital notes include a slide with a fill-in-the-blank graphic organizer. Students complete definitions and type in examples. On the second slide, students complete two practice activities, These notes are available, for free, in my TpT store. Click on the image below to download the resource.

The carousel notes are a great way to get students up and moving around the classroom. Each student is given a notes sheet with a blank graphic organizer. They will walk around the room filling in the definitions and examples. I like carousel notes because the students aren't just sitting in their seats ignoring hearing me read the various definitions and examples. Instead, they are the ones responsible for finding the information around the classroom. This resource is also available in my TpT store. Click the image below to check it out.

The third set of notes I have used in class discusses the 'Real Number Family.' Each classification has a character associated with it. Students learn about the various characters and which numbers would fit in with the character. Students fill in the characteristic (definition) for each character and then list examples and non-examples.

Digital Notes

Carousel Notes


I have used several different activities to help reinforce the real number system within my classroom. Some years I use all of the activities and some years I only use a few. It depends on the level of my students and how well they seem to be understanding the concept. Here is a brief description of each activity:

1) Human Number Line - Hand each student a number card and have the entire class organize themselves in order from least to greatest. Discuss which students fit under each classification. Play a quick "stand up/sit down" game where your call out a classification and those students who fit in the classification stand while others sit. You can also take a picture of the students standing in order from least to greatest Use this picture in future class discussions and/or problems of the day/exit slip questions.

2) Word Scramble - This activity can be completed independently, with partners or in groups. Cut out the answer cards and place them around the room. Provide an activity sheet to each individual and/or group. Students will begin by classifying decimals and then move on to classifying a variety of numbers in the real number system. Once students have completed a section, they will need to look for their sum on the answer cards. The answer cards will then provide a work that will go into their mystery question. At the end of the activity, students will form a question and then provide a correct answer.

3) Group Activity - This editable google slide activity includes four different activities. Students will be responsible for completing one activity (this can vary based on group size), while checking the work of one other student. They will sign off on the activity they complete, as well as, the activity they checked. This activity is available, for free, in my TpT store. The link is shown below.

4) Analogy Activity - I like to have students form their own analogy to relate the real number system to the real world. I provide each group of students with a blank graphing organizer. Groups then come up with their own analogy to explain the real number system. For example, you could make natural numbers a city and whole numbers a county. So, students can say, "all people who live in the city, live in the county... but not all people in the county live in the city." This activity provides a little challenge, but it is nice to see students thinking outside of the box.

5) Sum Activity - For this activity, I provide students with a copy of a google slide. One each slide, there is a table of numbers. They begin round 1 by highlighting the cells containing natural numbers. They then have to find the sum of the bold numbers. I walk around and check this sum while they work. Once they are finished, they move on to the next slide which asks them to highlight whole numbers. Students continue until they get to the fifth and final slide which contains irrational numbers.

Group Activity

Practice Sheets

Once students have completed a few activities, I have given practice sheets to help check for student understanding. While I do not have these worksheets listed individually on Teachers Pay Teachers, I do have a bundle of real number system resources and they are included. The bundle titled, 'Everything Under the Sun' has ALL of the materials listed above.

The Real Number Family

The Real Number System Mini-Lesson Plan

The Real Number System - Everything Under the Sun