This worksheet is designed to help middle school students—especially those in Grades 6 to 8—grasp the core skills of multiplying and dividing integers. It uses real-world scenarios, like changes in temperature, elevations, and finances, to illustrate these concepts in ways that feel practical. By connecting math problems to everyday situations, students can see how these skills might be useful beyond the classroom, which often helps boost their confidence in tackling math problems.
Word problems bring math to life by giving students relatable scenarios that go beyond straightforward calculations. For example, instead of just multiplying or dividing numbers, students work through situations they might actually experience, like calculating how deep a diver goes underwater over time. This adds a level of realism that can make learning more engaging and meaningful. Plus, it encourages students to think critically as they set up the problem, figure out which numbers they need, and determine the right operations to solve it.
This worksheet strengthens a few important math and reasoning skills:
Integer Multiplication and Division: Students learn to work confidently with positive and negative integers, getting comfortable with both multiplication and division.
Real-World Application: Problems in familiar contexts help students connect math with their daily lives, making it easier to understand why learning integer operations is important.
Problem-Solving Skills: Each question requires careful reading and decision-making, which helps build critical thinking skills.
Understanding Positive and Negative Values: Integers often represent things like gains or losses. Here, students get used to seeing negative numbers as debts or descents and positives as rises or gains.
Altogether, these skills give students a solid foundation, not just in math but also in logical thinking, which is helpful in many aspects of life.
Yes! Each problem has an answer key with multiple-choice options, making it easy for teachers, parents, and even students working on their own to check answers. The answer keys provide immediate feedback, which can be motivating and helps students learn from their mistakes on the spot. Having clear answer choices also makes it easier for students to double-check their work and understand why a particular solution is correct or incorrect.
Absolutely! Besides the downloadable PDF, there’s an interactive online version available. This allows students to try the problems digitally, giving them instant feedback on whether they got the answer right. Many students find this immediate response helpful for learning and retention. The online option can also be great for those who enjoy interactive activities and gives teachers and parents a way to encourage math practice without paper. Plus, it’s always nice to have a way to keep learning light and flexible.
The worksheet uses real-life examples to show how integers represent different things in the world around us. For instance, if a problem talks about temperature drops over several hours, students will multiply a negative integer to understand the total drop. Another example might involve calculating a debt or a series of payments, which are often represented by negative numbers. This type of problem-solving builds a natural understanding of what positive and negative values mean, helping students relate to math in ways that feel relevant to everyday situations.
Integer operations are surprisingly useful in real life! Someone budgeting their monthly expenses might multiply negative values to get the total spending. Or, a mountain climber might calculate how many feet they descend each day by multiplying a negative number. These types of skills become even more valuable as students get older and need to keep track of finances, monitor distances, or understand scientific changes. By mastering these operations now, students can develop strong math skills they’ll use again and again.
This worksheet brings together all these practical elements to make learning integers more accessible and enjoyable for middle schoolers, showing them that math isn’t just numbers on a page—it’s a tool they can use in the real world!
Time needed: 5 minutes
Step-by-step guide to calculate how deep a scuba diver is after a given time diving at a constant rate.
Identify the given information: The diver goes down 20 feet every minute and has been diving for 7 minutes.
Rate of diving: 20 feet per minute.
Time spent diving: 7 minutes.
Use the formula Depth = Rate of diving × Time to calculate the diver’s depth.
Substitute the known values into the formula: Depth = 20 feet per minute × 7 minutes.
Multiply to find the depth: Depth = 20 × 7 = 140 feet.
Since the diver is going below the surface, the depth after 7 minutes is 140 feet below the surface.
To multiply integers, multiply the absolute values (the numbers without any sign). Then, apply the rule for signs: if both integers have the same sign (both positive or both negative), the result is positive. If the signs are different (one positive, one negative), the result is negative.
For example, 3 × −4 = −12
Dividing integers is similar to multiplication. Divide the absolute values and then apply the sign rule: if both integers have the same sign, the quotient is positive; if they have different signs, the quotient is negative. So, for example, −20 ÷ 5 = −4
When multiplying or dividing integers with different signs (one positive and one negative), the answer is always negative. For example, 6 ×−3 = −18 or −24 ÷ 4 = −6
A common example is: “Multiply -5 and -3, then divide the result by 15.” Start by multiplying −5 × −3 = 15 Then divide by 15: 15 ÷ 15 = 1
This rule exists because multiplying by a negative number reverses the direction on the number line. So, when you multiply a positive number by a negative, it flips the positive value into the negative direction.
Worksheets with problems like “Multiply -4 by 6,” or “Divide -30 by -5,” or questions that mix both operations help you get comfortable with integer rules. Many worksheets also include word problems for real-life context practice.
