Assumption/Supposition Method: When To Use
20 February 2024
BY: matrixmath
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. What is the Assumption/Supposition Method? 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. The assumption method can be a highly efficient method compared to guess and check, especially since it provides targeted and strategic solution attempts via logical reasoning. The assumption method is best employed when your child needs to: Solve a complex math problem with multiple variables or constraints Overcome time constraints Avoid making mistakes via a systematic approach Knowing when to apply the assumption method and adding helpful illustrative guides to visualise the problem at hand can make a difference in successfully solving a seemingly complicated math problem. When to use Assumption/Supposition Method? When these 3 key information are presented in the question: 2 types of items and each has a certain value (e.g. could be 2 types of coins of different values, or 2 different types of animals with different number of legs) Total number of items, without stating how many of each type. Total value of all these items. If these information are present, the question can be solved using Supposition Method instead of Guess and Check method. Applying the Assumption Method When deciding if the assumption method is ideal for solving a question, you should keep these tips in mind. Identify the problem and break it into components to make it easier to understand. Formulate an assumption using logical reasoning. Substitute variables based on your assumption. Apply and solve the assumption. Here is an example of the assumption/supposition method in action: Supposition Method/Assumption Method 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 Supposition Method with Penalty 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 How the Assumption/Supposition Method Can Solve P5 Math Word Problem Sums With the PSLE examination only a month away, there is a palpable tension among students who are apprehensive about the questions they will receive. With time being of the essence, strengthening math foundations is essential to solving problems efficiently and with little difficulty. The assumption (or supposition) method is one of the many problem-solving tools at your child’s disposal, and it