20 February 2024
Guess and check is a method our children are taught when they are in their early primary years. While it is reliable and guarantees the right answer if a student were to spend enough time on each calculation, a school examination does not provide them with the luxury of going through every single one of them.
Another downside of guess and check is that it involves an element of luck, as well as how strong the logical skills of your child are. If your child happens to get the answer right in their first or second calculation, then they can move on relatively quickly, but if it involves multiple tries to reach the right solution, examinations and timed tasks can turn into a difficult affair.
Continue reading below if you would like to know when and why the assumption/supposition method should be used over guess and check.
The assumption/supposition method, also known as the supposition method, involves strategically assuming values or conditions to simplify a problem. Unlike guess and check, which depend on trial and error, this method relies on logical deductions and problem-solving strategies to ease the solution process.
When these 3 key information are presented in the question:
If these information are present, the question can be solved using Supposition Method instead of Guess and Check method.
Here is an example of the assumption/supposition method in action:
John invited 30 boys and girls to his birthday party. He gave 5 chocolates to each boy and 2 chocolates to each girl. If John gave away 141 chocolates, how many girls did John invite?
Step 1
Assume all are boys (assume the opposite of what the question is asking for. Eg: Qns asking for how many girls so assume opposite = boys)
Total number of chocolates = 30 X 5 = 150
Step 2
Find the difference between the actual and assumed
Extra chocolates = 150 – 141 = 9
Step 3
Find the extra number of chocolates needed for every exchange from 1 boy to 1 girl.
1 exchange = 5 – 2 = 3
Step 4
Find the number of exchanges needed. This will give us the number of girls (when we assume all are boys in step 1, step 4 will give the opposite i.e. girls)
No. of exchanges = 9 ÷ 3 = 3 (no. of girls)
If the question is asking for both girls and boys such as: “How many boys and girls did Yenni invite?”
Step 5
Find the number of boys. Since we know that girls = 3, we can use the total number minus the number of girls
No. of boys = 30 – 3 = 27
In a test, there were a total of 40 questions. For every question answered correctly, a student was awarded 4 points. For each question answered wrongly, 1 point was deducted. If Anna scored 130 points, how many questions did she answer wrongly?
Step 1
Assume all questions answered are correct (Penalty Question, always assume the positive that adds value/earned For e.g.: this question: assume those that are correct to be awarded points).
Total no. of points = 40 X 4 = 160
Step 2
Find the extra number of points that needs to be removed to obtain the actual points.
Extra points = 160 – 130 = 30
Step 3
Find the extra number of pointsdeducted for every exchange from 1 correct question to 1 wrong question.
1 exchange = 4 + 1 = 5
(It is an “addition” for due to the fact that I not only lose the 4 points from removing 1 correct question, I also had to deduct 1 point when I change it to a wrong. As such, I lose 5 points each time I change from a correctly answered question to a wrongly answered question.)
Step 4
Find the number of exchanges needed. This will give us the number of wrong questions (when we assume all questions are correct in step 1, step 4 will give the opposite i.e. wrong questions)
No. of exchanges = 30 ÷ 5 = 6 (wrong questions)
Step 5
Find the number of correct questions. Since we know that wrong questions = 6, we can subtract the number of wrong questions from the total number of questions.
No. of correct questions = 40 – 6 = 34
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Assumption/supposition Method |
Guess and Check |
|
Approach |
Based on making educated guesses and working backwards. |
Relies on systematic trial and error. |
|
Strategy |
Utilises logical deductions and problem-solving strategies. |
Involves trying different values systematically. |
|
Efficiency |
Tends to be more efficient, as guesses are based on logic. |
Can be time-consuming, especially for complex problems. |
|
Precision |
Allows for targeted and strategic solution attempts. |
May involve luck and exhaustive iterations. |
|
Complexity Handling |
Effective for problems with multiple variables or constraints. |
Suitable for simpler problems or situations with few variables. |
|
Time Sensitivity |
Advantageous in timed scenarios or examinations. |
May not be ideal for time-constrained situations. |
When faced with math problems that have multiple variables and require a strategic approach, the assumption/supposition method should be your go-to choice. You break down what seems like a complex problem into manageable steps and avoid being overwhelmed. From there, you are shown a clear pathway to getting closer to the solution with each step taken. This can help students who tend to panic when faced with tough questions, especially when they are racing against the clock.
If you’re working under exam conditions, the supposition method can be a lifesaver. It gives you a structured framework within which can help you stay focused by strategically narrowing down your options based on educated assumptions. This can increase your chances of finding a solution within the allotted time.
The importance of avoiding errors cannot be overstated, especially in complex problem-solving scenarios. When combined with being under exam conditions, every mistake is precious marks lost as the student risks being unable to complete the paper within the time limit. If the situation calls for the minimization of errors, the supposition method directs the student to take a systematic approach guided by logic. This reduces the possibility of overlooking important details or coming to the wrong conclusions.
Complex math problems can be overwhelming, especially if your child has a weak foundation in the subject. By making logical assumptions, the supposition method allows students to focus on specific aspects of the problem one at a time. This simplification process helps students gain a clearer understanding of the problem and makes it easier to identify potential solutions or paths forward.
The assumption/supposition method offers a structured framework for approaching math problems. Instead of feeling overwhelmed by a problem’s complexity, students can follow a step-by-step process that guides them through the problem-solving process. This structure provides clarity and direction, helping students stay focused as they work towards finding a solution.
It is common for students to feel nervous when faced with exams. However, if it heightens at the sight of a math problem they find complicated, their mind may go blank, which can affect their performance. By breaking down the problem into manageable steps through the supposition method, students can build confidence as they make steady progress towards finding a solution.
The assumption/supposition method is about more than finding the right answer. It is about teaching students how to think critically. They’re encouraged to consider different perspectives, weigh evidence, and draw logical conclusions. This not only helps them solve math problems more effectively but also equips them with crucial skills for navigating real-world challenges.
As your child transitions to the upper levels of Primary school, they will be introduced to the assumption/supposition method. While this method is hailed as being much more effective compared to guess and check, it may be difficult to grasp for those who have a weak foundation in math. At Matrix Math, we provide primary math tuition designed to nurture independent learners who are confident in using the assumption/supposition method to solve mathematical problems effectively.
Contact us today to sign your child up for lessons with us and give them the tools they need to excel in math!
