# Leprechaun Tricks: Integer Challenges {FREE}

*Looking for a fun St. Patrick’s Day challenge for your middle schoolers? Take a break from your normal routine and help kids make sense of integer operations with this set of integer challenges.*

If you teach middle school or high school, you probably don’t have a lot of wiggle room in your schedule for fun, interesting challenges or holiday celebrations. But older kids like a break from the normal math routine too! So I created this simple **set of integer challenges** to help kids think deeply about **integer operations this St. Patrick’s Day**. This way, you can do something fun and different without derailing all your plans. Plus, your kids can **explore math in a meaningful way** and be challenged to think about what is really going on with integers!

**Leprechaun Tricks Integer Challenges:**

**The goal of this challenge is simple:** find the largest and smallest sum, the largest and smallest difference and the largest and smallest product of a given set of numbers.

What makes this challenging is that the numbers are integers and so the solution will not always be obvious.

For instance, finding the largest difference requires some thought because when you subtract a positive number, your value decreases. But when you subtract a negative number, your value actually increases.

We often tell students **subtracting a negative number means you add**. *But that seems illogical and nonsensical.*

Instead, try to help your kids see why this is true with visuals. If you think about subtraction a couple of different ways, it actually **makes perfect sense that the difference will be bigger**.

For instance, subtraction can be thought of as the difference between two numbers, or how far apart they are on a number line. So if you are finding the difference between 5 and -3 (or solving 5- (-3) = ), draw those two points on a number line and you will see that they are **8 spaces apart**.

Another helpful visual for integer operations is using a +/- chart.

This can be used to model subtraction as “taking away.” So when you subtract a negative, you are taking away negative values, which means you end up with more positives than you had initially.

Read this post and grab the free integers lesson for more info on +/- charts.

**A Springboard for Understanding Integer Operations**

If your students are new to working with integers and operating with integers, this is a great springboard activity! No experience necessary!

To get your kids started, **provide a number line and a calculator** (depending on how much support they need).

Then tell them this is a challenge and you want to see who can **use the knowledge they have** (knowing what sum, difference and product mean) and **the tools you’ve provided** to figure out each “Leprechaun Trick.”

*Then let them get to work!*

Using the space provided, let your kids **write out each sum** (or difference or product) with the given numbers to **make a list of all possible solutions**. Then circle their final answer!

Using **a number line** or even **a calculator** and then making a list of all the solutions will allow them to look for patterns and make observations about integer operations before you begin formal instruction.

Once students have completed the challenge, **discuss each operation** together as a group and see what **patterns they found** or **observations they made**.

Then **give them page 2** of this download to see if they can **find the solutions in a more efficient way** (*using patterns or rules they noticed the first time*).

**Increase the Challenge with Integer Fractions:**

If your students feel confident working with integers, increase the challenge by giving them page 3 of this download: **integer fractions**.

Operations with fractions adds *a whole other wrinkle* to this tricky challenge, and I think your advanced students will be excited to rise to the challenge!

Be sure to discuss together as a group how **fractions will change** (*or not change*) the activity and what the final solutions look like.

I hope this is a fun St. Patrick’s Day challenge for your students! For some added fun, you might want to **share a “Leprechaun treat”** with the student or group who figures out all the “tricks.” Some **chocolate gold coins** maybe? ðŸ˜‰

However you use this, I hope it is a **meaningful and rich resource** as you seek to guide your students to math mastery.

**Ready to get started?** Click the link below to go to my shop and grab this free integer challenge activity!