# Compare Rational Numbers Sorting Challenge – Grades 7-8

*Do your students need to review and make sense of rational numbers? This low-prep compare rational numbers sort can be used a variety of ways to fit your classroom.*

One of the most challenging topics in middle school math is making sense of rational numbers in all their forms-fractions, decimals, repeating decimals-and knowing how to convert between various forms. Throw in positive and negative signs and things get really crazy! In this simple rational numbers activity, students will use lots of **different math skills and strategies** to **compare rational numbers**.

**What Are Rational Numbers?**

**Rational numbers** is a set of numbers that includes **any number that can be written in fraction form**. Thus, every rational number can also be written as a repeating decimal or a terminating decimal (*meaning it stops, such as 0.5*). Rational numbers also include integers, meaning both positive and negative numbers.

That means rational numbers include **many different forms or sets of numbers**, such as:

- Positive and negative whole numbers
- Positive and negative fractions and mixed numbers
- Positive and negative decimal values, as long as they either repeat or terminate

Although students begin comparing fractions and decimals as early as 4th grade, 7th or 8th grade students look at much more complex rational numbers. More challenging comparisons are what’s included in this sorting challenge.

**Compare Rational Numbers Sorting Activity**

This printable activity includes **12 rational number comparisons**.

This means students are trying to determine **less than, greater than or equal to** with each pair of rational numbers.

Some of the problems **compare two fractions**, some **compare a fraction to a decimal**, and some **compare two decimal values**.

Adding to the challenge, some of the numbers are positive and some are negative.

**Students should use a variety of strategies to compare the quantities, such as:**

*Are both positive or both negative?*If one is positive and one negative, they know right away which is larger, regardless of the number forms*If the numbers are both fractions*, they might rewrite them to have common denominators or use other strategies such as comparing each to a benchmark such as 1/2 or one whole*If the numbers are both decimals*, they should pay attention to place value*If the numbers are in different forms*, they can rewrite one so they are in the same form (such as both decimals) or they can compare the a benchmark, or consider place value*If they’re looking for a visual*, they could put the numbers on a number line

The goal is for students to **find ways to compare the quantities** and then **determine how to correctly complete the comparison** **statement** (<, > or =).

**How to Use the Rational Number Sort:**

This is designed to be a **printable cut and paste activity**, however there are other options as well depending on what will work best for your students.

**Printable Cut and Paste Activity:**

To use as a cut and paste activity, **print the sorting mat** (one per student or one per pair–this works well as a partner activity).

Then **print the page of comparison problems**. There are **two sets per page**, so print enough so you have a complete set for each student or pair of students.

Students then cut out each expression, compare the rational numbers and determine if it goes in the “Less Than,” “Equal To,” or “Greater Than” column on the sorting mat.

Encourage them to * sort all problems first* and then

**let you check it before they glue**the final answer down.

Once students have corrected sorted each comparison statement, they **glue them down and they’re done**!

**Math Center Option:**

If you would prefer to prep this one time and use it again and again, you can **print the sorting mat on colored card stock paper** and **laminate for durability**.

Then** print the comparison statements on another color of card stock paper and laminate**. **Cut out all the comparison statements** to go along with the sorting mat.

Students then work **sort the statements onto the mat**, *but don’t glue them down*.

Then **store the comparison statements in a ziplock bag** along with the sorting mat for another group to use later!

Lastly, one final option is to **print the sorting mat and cards on card stock paper**. **Laminate the sorting mat or place it in a page protector** and **give students a dry erase marker**.

Then students can simply **write the comparison statements onto the sorting mat**, *no cutting or pasting required. *

*(You can also do it this way as an individual review. Just print a page for each student on regular paper and let them write in their comparisons to turn into you). *

When they finish, **be sure they erase their answers** from the mat and store the mat and comparison statements for another day.

I hope this provides a helpful challenge as your students learn to **work with & compare rational numbers**.

*If you enjoy this activity, become a Math Geek Mama+ member and gain access to the entire ad-free library of engaging activities like this one, with hundreds of math games, digital practice, and low-prep review worksheets for grades 5-8!*

**Learn more about Math Geek Mama+ right HERE**.

*If you’re ready to grab it, use the link below to head to my shop to get a free copy!*