The Real Number System

The Real Number System is a tricky concept for students. It is very abstract especially irrational numbers and often doesn’t really seem important. To be quite honest, I didn’t fully grasp it until my college level course where our professor demonstrated how to teach it.

Common Core Standards

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

TEK Standards

6.2A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

7.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers

8.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

While students are familiar with the concept of classification, they can struggle when numbers “look” a certain way, but are classified differently. Perusing around Pinterest, I have seen a few great ideas that involve visuals and models to make things more concrete. There are some great ideas!

Classroom Demonstration

The activity below is a great way to introduce the Real Number System. It is engaging, hands-on, and brings a stale math concept to life. This was an idea from a friend of mine, who was happy to share.

Supplies:

– card stock

– 6-8 student volunteers

– yarn, if desired

Set Up:

1. On each piece of card stock list the following:

– name

– hometown

– state

2. Hole punch each piece of cardstock. Tie a piece of string between the two holes to create a necklace.

Story:

Little Johnny is headed to college at __________ and leaving his hometown of Nashville, Tennessee to attend college. When he gets to college, he greets seven other people in the student union.

Procedure:

1. Assign student volunteers a character (a piece of card stock).

2. Have students line up at the front of the room and facilitate the story and discussion.

3. Give students a few minutes to look at the information about the people Johnny meets at college and ask them to silently group the people.

4. Discuss the various groupings.

5. Ask students to think outside the box of classifying them in just two groups (some may have already thought of this).

6. Based on the questioning and discussion, ask students to do the same process with cards of numbers.

Key Concepts

There are multiple ways to classify.
There are more specific ways to classify.
There can be a classification that does not have any representation.

Common Misconceptions

A number written in fraction/decimal form is automatically a rational number.

Anchor Chart

Anchor charts are fabulous ways to showcase the content in a visual manner for students to reference. They can easily be created before the lesson or as you are teaching, depending on the content.

A super simple idea for introducing the number system and how to classify numbers. Want more ideas? Check out my units that cover all the CCSS Number System Standards for