Difference Route

This worksheet mixes integer subtraction with a maze challenge. Students begin at START, solve each subtraction problem, and then move only through cells whose answers are even integers. That means students have two jobs at once: first subtract correctly, then decide whether the answer is even. Expressions such as 7 – (-3), -4 – 2, 5 – (-7), 9 – 4, and -6 – 3 give students repeated practice with positive numbers, negative numbers, and double negatives. The maze format adds an extra layer of thinking because the correct subtraction result must also satisfy the “even answer” rule before the student can move forward.

For a parent, the most helpful idea is that subtraction with integers becomes much easier when it is rewritten as adding the opposite. So 7 – (-3) becomes 7 + 3, which equals 10. Since 10 is even, that cell can be used. By contrast, 9 – 4 = 5, and 5 is odd, so that cell cannot be part of the correct route.

Learning Goals

• Subtract Positive and Negative Integers: Students practice several sign combinations.
• Rewrite Subtraction as Addition: Learners use the reliable “add the opposite” strategy.
• Identify Even Results: Students determine whether each answer is divisible by 2.
• Combine Two Skills: Integer subtraction and number classification are practiced together.
• Use Answers to Navigate: Correct calculations guide students through the maze.

Parent-Friendly Teaching Tips

A very simple subtraction routine is:

1. Keep the first number.
2. Change subtraction to addition.
3. Change the second number to its opposite.
4. Solve the new addition problem.
5. Check whether the answer is even.

For example:

5 – (-7)
becomes
5 + 7 = 12

12 is even, so that cell is usable.

Another example:

-4 – 2
becomes
-4 + (-2) = -6

Negative numbers can still be even, so -6 also counts as an even answer.

Why This Worksheet Helps

• Reinforces a Reliable Subtraction Strategy: Students do not need separate rules for every sign combination.
• Combines Concepts: Learners practice integer subtraction and even/odd classification at the same time.
• Encourages Careful Sign Work: A sign mistake may change both the value and the maze route.
• Provides Natural Self-Checking: A dead end gives students a reason to go back and inspect their arithmetic.
• Builds Flexibility: Students see that even numbers can be positive, negative, or zero.

Classroom & Home Use

• Excellent Follow-Up to Integer Subtraction Lessons: The maze gives students a more engaging way to apply the skill.
• Helpful for Parents: The “keep, change, change” routine is easy to remember and explain.
• Good for Centers or Homework: The route provides a clear goal and immediate feedback.
• Useful for Intervention: Students who struggle with subtracting negatives get repeated practice in context.
• Strong for Number Sense: The even-answer rule keeps students thinking about the properties of the result, not just the arithmetic.

This worksheet helps students understand that solving an integer problem is sometimes only the first step. They must also interpret the answer and decide whether it fits a condition. Subtraction, opposites, negative numbers, positive numbers, even numbers, and maze navigation all work together throughout the activity. For parents, the best reminder is: “Rewrite the subtraction first, solve carefully, then ask whether the result is even.” In classroom and homeschool settings, this worksheet gives students a fun and effective way to strengthen integer subtraction while building broader number sense.