Teaching rational numbers is very important in middle school. Students are introduced to rational numbers in 6th grade and they are a big part of 7th grade. Middle school students need to recognize these numbers and how they are used to help them be successful in high school mathematics.
What is a Rational Number?
A rational number is a number that can be written as a fraction.
Example: a/b, where a and b are integers and b, is not equal to 0.
This includes decimals that terminate or end and decimals that repeat because they can be written as a fraction. All whole numbers and integers are rational numbers.
Examples: -½ , ¼, 4, -5, 10/5 , 4.5, -3.3333…
To help students understand rational numbers, try the activity below. This activity has students define a rational number by looking at examples and non-examples of rational numbers. Click the image below for an Exploration Activity.
Exploration Activity for Teaching Rational Numbers
Materials: Number Cards
Directions: Give groups/pairs a copy of card one. They are to look at the numbers on the card. Using the examples of rational numbers and numbers that are not rational students are to define a rational number. Provide students something to write their definition on (notebook paper, chart paper, dry erase board, computer). I recommend working in groups or pairs to complete this activity.
Share definitions when groups/pairs are finished. I typically give my students about 5 minutes to come up with a definition. For sharing their definitions students could read them out loud or they could hang them around the room if they wrote it on paper.
When sharing their definitions try to get students to explain why they chose to define rational numbers the way that they did. They should be able to support their definition using the information on the card. Continue sharing definitions until all groups/pairs have had a turn.
If you feel that the students are on the right track with the definition of a rational number, try to come up with the definition as a class.
If your students still need some help with understanding what a rational number is, give them Card Two. Card Two shows numbers that are whole, integer, and rational numbers. Have each group look at the numbers on card one and card two. They should change their definitions for a rational number based on the new information they have received. Next have them share their definitions. Define rational numbers using the information that students shared.
If your students are still having a hard time understanding what a rational number is, try asking some leading questions to get the correct definition.
-Which numbers are whole, integer and rational? What characteristics do they have?
-Which numbers are integer and rational? What characteristics do they have?
-Which numbers are only rational numbers? What characteristics do they have?
Guided Practice Identifying Rational Numbers
Once students understand what rational numbers are they need to practice identifying them. Put the numbers from card three on the board and have students name every set to which the number belongs- whole, integer, rational.
Do the first few problems together and then have them try the other problems in their groups/pairs. Share answers with the class and discuss.
Independent Practice
Students should be able to identify rational numbers on their own. Have students work on the Rational Numbers Practice Sheet. You can use this as classwork or homework assignment to assess their knowledge of rational numbers.
Closure
I hope you will try this activity with your students if you are looking for a way to help them understand what a rational number is. My students enjoy trying to define words using examples and non-examples. Throughout the year I will ask them the names of numbers we are working on to reiterate the concept.
Need help teaching Rational Numbers?
Try this ready-made Rational Number Operations unit! Each of the 12 lessons has an editable PowerPoint, guided notes, activity and practice sheet. You and your students will love it!
We also have a 6th grade unit on Introduction to Integers and Rational Numbers. Click below for more information!
