Students learn to use binary numbers to do basic calculations. This scenario is concentrating in subtraction with binary numbers
| Learning Scenario Identity | |
| Title | JYU25: Basic math with binary numbers using cards: Subtraction |
| Creator | JYU |
| Length | 90 minutes (2×45 minutes) |
| Main idea/description | Students learn to use binary numbers to do basic calculations. This scenario is concentrating in subtraction with binary numbers |
| Target group | 3rd-6th grade |
| Curriculum/learning subjects | Mathematics, Physical Education, ICT |
| Competencies | Students learn to understand how binary numbers work on basic math solutions and how computers work at the basic level. The students learn simple principles of programming languages. |
| Teachers’ wellness competences | TC4: Social e-competency |
| Learning Scenario Framework | |
| Pedagogical method | PI3. Enforcing attention and Awareness |
| Software/materials | For this scenario, students will work in pairs to perform binary subtraction using cards. Seeing each other and working together is key, but clear instructions can make online execution feasible. The task focuses on the principle that subtraction in binary works by adding the complement of a number. Teacher Tools: Use a conferencing tool with breakout rooms for online sessions. The teacher can visit each group to provide guidance. Clear Instructions: Start by explaining binary subtraction as adding the complement of the subtracted number. Use real-life examples, like kilometer counters, to make the concept relatable. Demonstrate subtraction with small numbers, step by step. Engagement and Breaks: To reduce stress, introduce short breaks between tasks for a mindful reset or brief physical activity, keeping energy levels balanced. Gradual Complexity: Begin with simple 3-bit numbers before increasing difficulty with 5-bit numbers. Ensure students are comfortable with the process before moving to more complex calculations. Collaboration and Reflection: Encourage pairs to reflect on their strategies after each task. Use guiding questions such as, “What challenges did you face with the 9th bit carry-over?” and “How did complementing help solve the subtraction?” This structure promotes positive learning, reduces cognitive overload, and ensures an engaging, low-stress experience for students. |
| Evaluation tools | The teacher observes the pairs as they start to work on the assignment. The teacher also follows the discussions after each assignment. |
| Learning Scenario Implementation | |
| Learning activities (description, duration, worksheets) | IntroductionExplain that today, students will practice binary subtraction, which works by adding the complement of a number. Students will use binary cards to represent numbers and perform subtraction step by step. One student will manipulate the cards, while the other gives instructions. The goal is to understand how subtraction in binary is different from decimal subtraction. Computers are made of transistors and they can’t calculate or understand numbers in the very basic level like we do. Computers work with ones and zeros, which can be marked with electrical voltage on or off. No voltage means 0 and voltage on means 1. This is easy enough to understand, but what if we need other numbers or other symbols than just 0’s and 1’s. In binary code we first decide how many bits we want to use. In 8-bit system we use eight numbers every time we want to express even a simple number. For example 1 is 00000001 in 8-bit binary. The first bit from the left is marking plus or minus. If it’s 0 it means it’s a positive integer, if it’s 1, it’s a negative integer. Here comes the interesting part, it has been agreed that negative numbers are compliments of the positive numbers. This means that if every bit in a number is changed, it becomes a negative number. For example 4 is 00000100. If we want to create binary number -4, we change every bit in binary of 4. That means that -4 is 11111011 in binary. This creates a wonderful way to calculate subtractions in binary. For example 5-4 can be thought to be 5 + (-4), which would be 00000101 + 11111011. We learned to do long addition in the last learning scenario, so we can use that or the binary cards. The result will be 9 bit, so we have to move the leftmost digit to the rightmost place. This might be a bit counterintuitive at first, but it will clear out as students advance.  Take note, that there’s a 9th bit in the answer  This means that our number system has gone a full circle. You can think this as a kilometer counter in a car. There is no more room in the meter, so it has to start from the beginning.  This means the 5-4 subtraction is 00000001 or just 1. Exercise 1: Pair Work with Binary Subtraction Pair Up and Choose Roles: In each pair, one student is the card handler, and the other is the instructor. The card handler will move the binary cards according to the instructor’s directions.Start with small 3-bit binary numbers (e.g., 5 – 3), and the instructor guides the handler to calculate the subtraction by converting one number to its complement and then adding it to the other.Step-by-Step Binary Subtraction: The instructor should guide the handler through each step: first, change the subtracted number into its complement (flip all bits).Next, add the two binary numbers using the rules of binary addition.The result will include a 9th bit, which can be moved or discarded, as it represents a carry-over in binary subtraction.Mindfulness Breaks: After completing one calculation, take a brief mindful break—such as deep breathing or stretching—to reset and refocus.Switch Roles: After the break, switch roles so the observer becomes the card handler and performs another binary subtraction with a different set of numbers.Encourage clear communication between the pairs to ensure all steps are followed correctly.DiscussionAfter the first round, bring the class together to reflect: “How was binary subtraction different from what you expected?””What was challenging about complementing the numbers?””Did switching roles help you understand the process better?”Exercise 2: Increasing Complexity with 5-Bit Binary Numbers New Task: Now, work with 5-bit binary numbers. The instructor guides the handler through the same process of complementing and adding.For example, calculate 01001 – 00010, ensuring the proper handling of carries and complements.Introduce Conditional Logic: As students become more comfortable, encourage them to use conditional instructions like “If there’s a carry-over, shift the extra bit.”If Students Finish Early: Let students create their own binary subtraction problems or explore binary subtraction with larger numbers. They can also attempt subtraction without using cards to reinforce understanding.Closing ReflectionOnce all pairs have completed the tasks, hold a final reflection: “What strategies did you use to handle the complementing of numbers?””How does the carry-over work in binary subtraction?””What did you learn from switching roles?”This structure encourages collaboration, clarity, and hands-on learning, while regular mindfulness breaks reduce cognitive overload and maintain a positive, low-stress learning environment. |