The real number system can really confuse students. I will admit, at times, I felt confused too! Let’s check out 4 strategies that will help you teach classifying real numbers, and will help your students master the concept.
Before we jump to that, let’s take a look at the standard and how it progresses through middle school, and then take a look at some STAAR test question examples. I have highlighted some helpful pieces.
Real Number System Test Questions
Strategy #1 – Vocabulary
Vocabulary is crucial when teaching the real number system. Luckily, the content scaffolds by grade level.
- 6th Grade: whole, integer, rational
- 7th Grade: natural, whole, integer, rational
- 8th Grade: natural, whole, integer, rational, irrational
Since the progression of standards is pretty clear, each subsequent year a student must learn one brand new word. Although the vocabulary is important, I think students need to see examples more than they need to memorize the exact definition.
Bright idea! One way to push students’ learning is to ask them to come up with definitions based on observing numbers that have already been classified. Check out the example below.
Some thought provoking questions might be:
- What differences do you see between the numbers inside integers and whole numbers?
- What is different about the fractions classified as whole numbers versus the fractions classified as rational numbers?
Strategy #2 – Visuals
Notice that in each grade level standard, the term “visual representation” is used. In addition, in each test question example, there is a venn diagram of sorts. This means that students will not be expected to classify a number in the real number system without a venn diagram present to guide them, so make sure you are modeling with one, and students are practicing with one.
Students need to be taught how to use the venn diagram. Don’t assume (like me) that it is intuitive. I would start by using a similar venn diagram that is not related to math. You can steal this example if you would like. (Warning: You may be concerned about students’ geography if you use this example.)
You can ask these types of questions:
- If someone is from Texas, can you assume they are also from the United States?
- If someone lives in Oklahoma, where would you place them on the diagram?
If students are struggling to use the venn diagram to understand the relationships between sets of numbers, then try exposing them to the funnel example. Using the number 17: 17 would be dropped into the natural number funnel thus falling through the whole, integer, rational, and real number funnels. The number -17 would be dropped into the integer funnel and thus continue into rational and real numbers. Then you would explain that -17 is an integer, a rational number, and a real number, but you typically call numbers by the funnel that it is dropped in.
Strategy #3 – Simplify Before You Classify
I saw this idea on a Middle School Math Facebook group, and it is so clever and catchy! Teach students to simplify before they classify in the real number system. Fractions like 16/4 are a great example of this. If students are familiar with the definition of rational numbers, they may think, “16/4 must only be a rational number because rational numbers are numbers that can be written as fractions.” That student is technically right, 16/4 is rational, but that is not all. If you teach students to simplify before you classify, a student would simplify this to 4, thus changing its classification.
You see this with square roots too. Many irrational number definitions include the phrase “square roots,” so a student might incorrectly classify the square root of 100 as irrational. Simplify before you classify!
Strategy #4 – Make It Interactive
Since this skill requires very little computation, this is an opportunity to engage students in something hands-on. Here is what I have done:
- Flyswatter Game (ideally after students have shown mastery, so they aren’t just swatting uncontrollably)
- Card sort
- Post-it Notes – have students write down a bunch of different types of numbers on individual Post-it Notes and then swap with a partner. Then they have to categorize the numbers from their partner.
- Grab a 6th grade or 8th grade activity bundle that includes classifying the real number activities.
Classifying numbers in the real number system can be really engaging. It also would provide a math-win for some of my struggling students. How do you make classifying numbers engaging?